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Reliable high-throughput FPGA interconnect using source-synchronous surfing and wave pipelining Teehan, Paul Leonard 2008

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Reliable high-throughput FPGA interconnect using source-synchronous surfing and wave pipelining by Paul Leonard Teehan B.A.Sc., The University of Waterloo, 2006 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF Master of Applied Science in The Faculty of Graduate Studies (Electrical and Computer Engineering) The University Of British Columbia (Vancouver) October, 2008 c Paul Leonard Teehan 2008  Abstract FPGA clock frequencies are slow enough that only a fraction of the interconnect’s bandwidth is used. By exploiting this bandwidth, the transfer of large amounts of data can be greatly accelerated. Alternatively, it may also be possible to save area on fixed-bandwidth links by using on-chip serial signalling. For datapath-intensive designs which operate on words instead of bits, this can reduce wiring congestion as well. This thesis proposes relatively simple circuit-level modifications to FPGA interconnect to enable high-bandwidth communication. High-level area estimates indicate a potential interconnect area savings of 10 to 60% when serial links are used. Two interconnect pipelining techniques, wave pipelining and surfing, are adapted to FPGAs and compared against each other and against regular FPGA interconnect in terms of throughput, reliability, area, power, and latency. Source-synchronous signalling is used to achieve high data rates with simple receiver design. Statistical models for high-frequency power supply noise are developed and used to estimate the probability of error of wave pipelined and surfing links as a function of link length and operating speed. Surfing is generally found to be more reliable and less sensitive to noise than wave pipelining. Simulation results in a 65nm process demonstrate a throughput of 3Gbps per wire across a 50-stage, 25mm link.  ii  Table of Contents Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  ii  Table of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  iii  List of Tables  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  vii  List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  viii  Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  xi  Dedication  xii  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  1 Introduction  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  1  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  1  1.1  Motivation  1.2  Research Questions  . . . . . . . . . . . . . . . . . . . . . . . . . . .  3  Design targets  . . . . . . . . . . . . . . . . . . . . . . . . . .  3  Overview of this work  . . . . . . . . . . . . . . . . . . . . . . . . . .  3  1.2.1 1.3  2 Background and Related Work 2.1  FPGAs 2.1.1  2.2  . . . . . . . . . . . . . . . . . . . . .  5  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  5  Datapath FPGAs  . . . . . . . . . . . . . . . . . . . . . . . .  6  Pipelined interconnect . . . . . . . . . . . . . . . . . . . . . . . . . .  6  2.2.1  Register pipelining . . . . . . . . . . . . . . . . . . . . . . . .  8  2.2.2  Wave pipelining  . . . . . . . . . . . . . . . . . . . . . . . . .  8  2.2.3  Surfing  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  10 iii  Table of Contents 2.3  Serial signalling schemes . . . . . . . . . . . . . . . . . . . . . . . . .  11  2.3.1  Asynchronous  11  2.3.2  Source-synchronous  2.3.3  Receiver-clocked systems  2.3.4  Data encoding  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  12  . . . . . . . . . . . . . . . . . . . .  12  . . . . . . . . . . . . . . . . . . . . . . . . . .  13  Timing uncertainty . . . . . . . . . . . . . . . . . . . . . . . . . . . .  15  2.4.1  Skew and jitter . . . . . . . . . . . . . . . . . . . . . . . . . .  15  2.4.2  Sources of timing uncertainty . . . . . . . . . . . . . . . . . .  17  2.4.3  Process corners . . . . . . . . . . . . . . . . . . . . . . . . . .  17  2.4.4  Statistical static timing analysis  . . . . . . . . . . . . . . . .  18  2.4.5  Statistical jitter modelling . . . . . . . . . . . . . . . . . . . .  19  2.4.6  Normal distributions . . . . . . . . . . . . . . . . . . . . . . .  19  Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  20  3 Design and Implementation . . . . . . . . . . . . . . . . . . . . . . . .  21  2.4  2.5  3.1  System-level design  . . . . . . . . . . . . . . . . . . . . . . . . . . .  21  3.2  Choice of serial signalling scheme . . . . . . . . . . . . . . . . . . . .  22  3.2.1  Global clock  . . . . . . . . . . . . . . . . . . . . . . . . . . .  23  3.2.2  Asynchronous  . . . . . . . . . . . . . . . . . . . . . . . . . .  24  3.2.3  Source-synchronous signalling . . . . . . . . . . . . . . . . . .  25  High-throughput pipelined circuit design . . . . . . . . . . . . . . . .  26  3.3.1  Rise time as a measure of throughput  . . . . . . . . . . . . .  26  3.3.2  Driving buffer strength  . . . . . . . . . . . . . . . . . . . . .  29  3.3.3  Multiplexor design . . . . . . . . . . . . . . . . . . . . . . . .  30  3.3.4  Wire length sensitivity . . . . . . . . . . . . . . . . . . . . . .  33  3.3.5  Wave-pipelining stage  . . . . . . . . . . . . . . . . . . . . . .  35  3.3.6  Surfing stage . . . . . . . . . . . . . . . . . . . . . . . . . . .  35  3.3  3.4  System-level area estimation  . . . . . . . . . . . . . . . . . . . . . .  36 iv  Table of Contents 3.5  Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  4 Robustness Analysis 4.1  . . . . . . . . . . . . . . . . . . . . . . . . . . . .  42  . . . . . . . . . . . . . . . . . . . . . . . . . .  42  4.1.1  Edge interference . . . . . . . . . . . . . . . . . . . . . . . . .  43  4.1.2  Incorrect sampling . . . . . . . . . . . . . . . . . . . . . . . .  47  4.1.3  Summary of criteria for reliable transmission  . . . . . . . . .  51  Quantifying timing uncertainty . . . . . . . . . . . . . . . . . . . . .  52  4.2.1  Process and temperature  . . . . . . . . . . . . . . . . . . . .  53  4.2.2  Crosstalk . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  53  4.2.3  Supply noise model  . . . . . . . . . . . . . . . . . . . . . . .  56  4.2.4  Supply noise analysis  . . . . . . . . . . . . . . . . . . . . . .  58  4.3  Jitter and skew propagation . . . . . . . . . . . . . . . . . . . . . . .  60  4.4  Reliability estimate  . . . . . . . . . . . . . . . . . . . . . . . . . . .  63  4.5  Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  69  4.2  Reliable transmission  41  5 Simulation and Evaluation  . . . . . . . . . . . . . . . . . . . . . . . .  71  Throughput . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  71  5.1.1  Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . .  71  5.1.2  Results  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  73  5.1.3  Comparison . . . . . . . . . . . . . . . . . . . . . . . . . . . .  73  5.2  Latency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  76  5.3  High-throughput wave pipelining . . . . . . . . . . . . . . . . . . . .  79  5.4  Area . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  80  5.5  Energy  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  81  5.6  Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  83  6 Summary and Conclusion . . . . . . . . . . . . . . . . . . . . . . . . .  85  5.1  6.1  Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  85 v  Table of Contents 6.2  Interpretation of results . . . . . . . . . . . . . . . . . . . . . . . . .  88  6.3  Future work  89  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  6.3.1  Low-power design  6.3.2  Architectural exploration  6.3.3  Noise and reliability modelling  6.3.4  Silicon implementation  6.3.5  Wave-pipelined FIFO implementation  References  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  89 89  . . . . . . . . . . . . . . . . .  90  . . . . . . . . . . . . . . . . . . . . .  90  . . . . . . . . . . . . .  90  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  91  Appendices A Auxiliary Circuit Designs . . . . . . . . . . . . . . . . . . . . . . . . .  99  A.1 Serializer and Deserializer . . . . . . . . . . . . . . . . . . . . . . . .  99  A.2 Edge-to-pulse converter A.3 Delay element  . . . . . . . . . . . . . . . . . . . . . . . . . 101  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102  B Area Calculation Details  . . . . . . . . . . . . . . . . . . . . . . . . . 103  B.1 Area measurement methodology  . . . . . . . . . . . . . . . . . . . . 103  B.2 System-level area calculations . . . . . . . . . . . . . . . . . . . . . . 103 B.3 Block-level area tabulation  . . . . . . . . . . . . . . . . . . . . . . . 106  C Bounded Worst-Case Timing Uncertainty . . . . . . . . . . . . . . . 107  vi  List of Tables 2.1  Probabilities for standard normal distribution . . . . . . . . . . . . .  20  3.1  Approximate area cost of serializers, deserializers, and serial buses  .  38  5.1  Supply voltages used . . . . . . . . . . . . . . . . . . . . . . . . . . .  72  5.2  Area tabulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  81  5.3  Energy per transition measurements (fJ) . . . . . . . . . . . . . . . .  83  5.4  Energy estimates for 8b and 16b transfers . . . . . . . . . . . . . . .  83  B.1 Summary of area savings (min-transistors) . . . . . . . . . . . . . . . 104 B.2 Pre-serialization area . . . . . . . . . . . . . . . . . . . . . . . . . . . 104 B.3 Post-serialization area . . . . . . . . . . . . . . . . . . . . . . . . . . 105 B.4 Area tabulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106  vii  List of Figures 1.1  Regular and serial programmable interconnect . . . . . . . . . . . . .  2  1.2  Increased throughput with pipelined interconnect . . . . . . . . . . .  2  2.1  Architectural drawing of an island-style FPGA . . . . . . . . . . . . .  7  2.2  FPGA switch block detail . . . . . . . . . . . . . . . . . . . . . . . .  8  2.3  Skew definition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  16  2.4  Jitter definition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  17  2.5  Illustration of process corners . . . . . . . . . . . . . . . . . . . . . .  18  3.1  Schematic of input and output connections, with existing parts in bold  22  3.2  High-level schematic showing interaction with user clock . . . . . . .  23  3.3  High-level timing diagram . . . . . . . . . . . . . . . . . . . . . . . .  25  3.4  Basic interconnect stage schematic . . . . . . . . . . . . . . . . . . .  26  3.5  Detail of 4-tile wire . . . . . . . . . . . . . . . . . . . . . . . . . . . .  27  3.6  RC wire model used in simulations . . . . . . . . . . . . . . . . . . .  27  3.7  Illustration of wide, minimum-width, and attenuated pulses . . . . . .  28  3.8  Driving buffer size analysis . . . . . . . . . . . . . . . . . . . . . . . .  31  3.9  Sixteen-input multiplexor schematic . . . . . . . . . . . . . . . . . . .  32  3.10 Rise time of muxes . . . . . . . . . . . . . . . . . . . . . . . . . . . .  32  3.11 Rise time of varying length wires . . . . . . . . . . . . . . . . . . . .  34  3.12 Wave pipeline interconnect stage . . . . . . . . . . . . . . . . . . . .  35  3.13 Surfing interconnect stage . . . . . . . . . . . . . . . . . . . . . . . .  37  viii  List of Figures 3.14 Surfing timing diagram . . . . . . . . . . . . . . . . . . . . . . . . . .  37  3.15 System-level interconnect area estimation . . . . . . . . . . . . . . . .  40  4.1  Waveforms showing pulse propagation through five stages . . . . . . .  44  4.2  Pulse width measurement circuit . . . . . . . . . . . . . . . . . . . .  45  4.3  Pulse transfer behaviour . . . . . . . . . . . . . . . . . . . . . . . . .  46  4.4  Pulse width transfer characteristic simulations . . . . . . . . . . . . .  48  4.5  Skew transfer measurement circuit  . . . . . . . . . . . . . . . . . . .  49  4.6  Skew transfer characteristic simulations . . . . . . . . . . . . . . . . .  50  4.7  Crosstalk simulation setup . . . . . . . . . . . . . . . . . . . . . . . .  55  4.8  Delay variation due to crosstalk . . . . . . . . . . . . . . . . . . . . .  56  4.9  VDD noise waveforms . . . . . . . . . . . . . . . . . . . . . . . . . . .  58  4.10 Experimental setup measuring delay impact of VDD noise . . . . . . .  59  4.11 Delay variation due to variations in DC level (σ = 15mV). . . . . . .  60  4.12 Delay variation due to transient supply noise (µ = 0.95V.) . . . . . .  61  4.13 Experimental setup measuring skew and jitter propagation . . . . . .  62  4.14 Jitter and skew propagation (simulation in bold) . . . . . . . . . . . .  63  4.15 Illustration of arrival time probabilities for consecutive edges . . . . .  64  4.16 Probability of error estimates . . . . . . . . . . . . . . . . . . . . . .  68  5.1  Throughput simulation results . . . . . . . . . . . . . . . . . . . . . .  74  5.2  Waveforms showing data at the end of a 50-stage link . . . . . . . . .  75  5.3  Waveforms showing stage-by-stage propagation  . . . . . . . . . . . .  76  5.4  Throughput comparison for all schemes . . . . . . . . . . . . . . . . .  77  5.5  Latency normalized to a regular wire, VDD µ = 0.95V, σ = 30mV . .  78  5.6  Latency with 400ps FIFOs at 5Gbps . . . . . . . . . . . . . . . . . .  80  A.1 Serializer (with clock generator) and deserializer circuits . . . . . . . 100 A.2 Serializer and deserializer timing diagrams . . . . . . . . . . . . . . . 101 ix  List of Figures A.3 Edge-to-pulse converter circuit . . . . . . . . . . . . . . . . . . . . . . 102 A.4 Delay element . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102 C.1 Comparison of normal and bounded models . . . . . . . . . . . . . . 108  x  Acknowledgements I would first like to thank my supervisors, Dr. Guy Lemieux and Dr. Mark Greenstreet, for their guidance, support, dedication, and patience. Each of them has taught me so much in such a short time. I would like to thank Dr. Jesus Calvino-Fraga for giving me an opportunity to teach; I will fondly recall my time in his superb introductory circuit lab courses. Also, I would like to thank Dr. David Pulfrey for his friendship and guidance. This work would not have been possible without the support of my friends and colleagues in the System on Chip lab at UBC. In particular, thank you to Daryl Van Vorst, Andrew Lam, Cindy Mark, David Grant, Rosemary Francis, Alastair Smith, Scott Chin, Marcel Gort, Darius Chiu, Faizal Karim, Mark Yamashita, and Roberto Rosales. Thank you finally to my parents for their unwavering love and support.  xi  To Shabnam, my favourite person in the world. Your love and encouragement has kept me going. Sorry to be cheesy, but I couldn’t have done it without you. This thesis is for you. <3  xii  Chapter 1 Introduction In field-programmable gate arrays (FPGAs), user-created digital circuits are mapped onto prefabricated programmable logic and interconnect. The overhead required to make this logic and interconnect programmable is significant. Compared to an application-specific integrated circuit (ASIC) implementation which fabricates a custom device, FPGAs face a 3 to 4X latency penalty, a 12X power penalty, and a 20 to 40X area penalty [1]. This thesis explores the design of reliable, high-throughput pipelined serial interconnect. By employing this with datapath interconnects, wordwide links can be replaced with serial links to offer a potentially large reduction in area. This approach may open new serial FPGA architectural styles.  1.1  Motivation  Large designs, especially datapath-oriented designs which route words of data instead of single bits, are often wire-constrained when mapped to FPGAs [2]. Adding more wiring resources to an FPGA is not always possible because programmable interconnect consumes a large amount of area. However, the existing wiring resources are underutilized. FPGA designs tend to run at relatively slow clock speeds, on the order of 100 to 200 MHz. Because a wire can carry at most one bit per clock cycle, the throughput of a wire is fixed by the clock speed at 100 to 200 Mbps. However, FPGA wires are regularly buffered as they travel through the programmable fabric and should be able to support a considerably higher throughput. A properly buffered wire, if pipelined, 1  Chapter 1. Introduction Output switches  Input switches Serializer  Serial programmable interconnect  Regular programmable interconnect Data source  Deserializer  Data sink  Figure 1.1: Regular and serial programmable interconnect Pipelined interconnect  Regular interconnect Stage 1 Stage 2 Stage 3 Stage 4  2  1  2  1  1 One bit at a time  3  2  1  1  4 3  2  1  1  4  3  2  1  2  4 3  4  Multiple bits in flight  Figure 1.2: Increased throughput with pipelined interconnect  requires a minimum of about 11 fanout-of-four (FO4) delays between bits in order to prevent intersymbol interference (ISI) [3]. In a typical 65nm CMOS process with a FO4 delay of about 15ps, this translates to a bit period of about 165ps. A properly buffered wire could therefore support a throughput of about 6Gbps, a value 30 to 60 times higher than its typical utilization. Two key changes are required in order to increase wire bandwidth utilization. First, circuitry to access the high-bandwidth interconnect must be added. For example, Figure 1.1 shows how a 4-bit word can be transmitted serially across one wire. Second, interconnect must be pipelined, as shown in Figure 1.2, so that the throughput does not depend on the latency through the link or an externally imposed clock, but rather on the capacity of the wire itself.  2  Chapter 1. Introduction  1.2  Research Questions  This research is intended to address the following two questions: 1. Is it possible to achieve the theoretical maximum pipelined interconnect throughput of 6Gbps in a 65nm FPGA? 2. How would such a scheme work, and what are the benefits and costs to implementing it? 3. How reliable would this scheme be?  1.2.1  Design targets  Implementing high-throughput pipelined interconnect will require modifications to the FPGA interconnect at the circuit level The proposed scheme should meet the following targets: • throughput of 6Gbps in a 65nm CMOS technology; • significant area savings while keeping power and latency penalties low; • support for long cross-chip links, with turns and fanout; • reliable, despite noise and variation; and • minimal modification to existing programmable FPGA interconnect structure.  1.3  Overview of this work  This work is an application of previously published techniques for interconnect pipelining, namely wave pipelining and surfing, to FPGAs, with a specific focus on reliability. Wave pipelined interconnect in FPGAs has been recently studied [4], but that work  3  Chapter 1. Introduction did not address reliability. Prior work in this area is surveyed in more detail in Chapter 2. The primary contributions are as follows: 1. Two pipelining techniques, wave pipelining and surfing, are adapted to enable high-bandwidth serial communication in FPGA interconnect in Chapter 3. A system-level area estimation shows a potential 10 to 60% reduction in interconnect area if serial communication is adopted. 2. The effects of supply noise and crosstalk noise are simulated in HSPICE in Chapter 4. From this, a statistical model of jitter and skew is developed which is used to estimate the reliability of both wave pipelining and surfing. 3. The throughput, latency, area, and power of wave pipelining and surfing in FPGAs are evaluated using HSPICE simulations and compared against a traditional parallel bus in Chapter 5. Both schemes are able to achieve throughputs of about 3Gbps per serial data wire, though wave pipelining can operate at higher speeds if the link is sufficiently short. Area savings are considerable, but power and latency penalties may be prohibitive. The reliability estimates in Chapter 4 expose noise vulnerability in wave pipelining which is not well-modelled in the literature. The surfing scheme, which is more reliable by design, is demonstrated to be considerably less sensitive to noise.  4  Chapter 2 Background and Related Work This section provides some background and prior work related to FPGA interconnect, including techniques in on-chip pipelining, serial signalling, and timing uncertainty modelling.  2.1  FPGAs  In a typical “island-style” FPGA, logic cells cover the FPGA in a grid with vertical and horizontal routing tracks between them; the logic is like an island surrounded by interconnect. To improve area efficiency, modern FPGAs are heterogeneous and include hard memories, multipliers, and processor cores as well. The interconnect structure is slightly irregular in length to accommodate these blocks. However, for simplicity this irregularity will be ignored. Figure 2.1 shows a schematic drawing of an island-style FPGA. The blocks labelled CLB are Configurable Logic Blocks, which contain a number of programmable logic elements. The C blocks are connection blocks which contain multiplexors to connect CLB inputs and outputs to the adjacent horizontal and vertical routing tracks. The S blocks are switch blocks which contain a multiplexor and a driver. The switch and connection blocks are designed to maximize routing flexibility with minimum area overhead. More detail about their design is in [5]. Wire length is often measured in tiles, where one tile is the width of a CLB and its associated interconnect. A wire of length 1 can connect one CLB to its Manhattan neighbor. Wires of length 2, like the red/bold wires shown near the top 5  Chapter 2. Background and Related Work of Figure 2.1, span two blocks. FPGA designers typically provide wires of a few different lengths, such as length 4 for general purpose connections and length 16 for cross-chip connections. All wires in this thesis are assumed to be length 4, as they are the most abundant in modern FPGAs (about 80%). Figure 2.2 shows a detailed view of how a length 2 wire spans two tiles. The segment begins at the output of a multiplexor and driver at the leftmost switch block. After each tile, a multiplexors allows for early turns. The wire terminates at the input to another multiplexor. In this thesis, the tile length is fixed at 0.125mm, which allows for 200 tiles per row in a 25mm device, roughly in line with modern large FPGAs. The 4-tile wires used in this thesis are thus 0.5mm long in total.  2.1.1  Datapath FPGAs  FPGAs are increasingly used to implement datapath designs, in which logic and interconnect both tend to be largely word-oriented. Studies on the merits of providing datapath-oriented interconnect in the form of parallel buses with shared multiplexors show a modest 10% area savings from sharing multiplexor configuration memories [7, 8] when 50% of the routing resources are datapath-oriented, with a bus width of 4. However, that work did not consider the use of serial buses, and tended to rely on older, smaller benchmark circuits; modern circuits which focus on data computation tend to be larger and use wider words, which may favour a wider bus width.  2.2  Pipelined interconnect  The most straight-forward way to increase interconnect throughput is to break the wire into a number of smaller segments through register insertion. The throughput is equal to the clock speed; if the segments are small, the clock speed can be increased. Pipelining can also be accomplished with wave pipelining, in which the  6  Chapter 2. Background and Related Work  Figure 2.1: Architectural drawing of an island-style FPGA, from [6]  7  Chapter 2. Background and Related Work  Logic Block  Logic Block  MUX  Logic Block  MUX  mux  Early Turn  Interconnect Switch Driver  Programmable Wire  Switch Block  MUX  mux  mux  Switch Block  r ly E a ur n T  Logic Block  Switch Block  FPGA Interconnect  Figure 2.2: FPGA switch block detail, from [6]  temporary storage capability of buffered wire segments allows multiple bits to occupy a buffered wire simultaneously. Surfing, a relatively new technique, adds feedback to wave pipelining to make it more reliable.  2.2.1  Register pipelining  Register pipelining is a standard technique in digital design and is used extensively. Some studies have looked at register pipelining in FPGAs by adding latch banks to the switch blocks [9]. A similar design was proposed in [10]. Register pipelining is not the focus of this thesis for two main reasons. First, register pipelining requires a global clock, which may not be practical at high speeds. Second, the registers have considerable area overhead and timing overhead, and some power overhead, relative to surfing and wave pipelining, which are discussed below.  2.2.2  Wave pipelining  It is possible to pipeline logic or interconnect without using additional registers. Logic gates turn out to act as natural storage elements; so long as the time separation between events is sufficiently large to prevent interference, a string of logic gates can  8  Chapter 2. Background and Related Work carry multiple bits in-flight simultaneously. This technique, known as wave pipelining, was first proposed in 1969 and originally applied to logic circuits [11]. See [12] for a survey of this technique.  In Networks-on-Chip Networks-on-chip are ASICs composed of many logic cores inside a network of global interconnect. These devices require long, high-throughput links between cores. A number of recent papers in this field have noted that NoC interconnect is well-suited to wave pipelining; long wires are always broken into multiple shorter segments with repeaters, so the wire is logically a long chain of inverters [13–15]. Some simulated results predict very high throughput, up to 67 Gbps in [14], but the results are not directly applicable to this thesis since FPGA interconnect design faces different constraints. In particular, the NoC literature usually focuses on fixed, non-programmable links between blocks.  In FPGAs High-throughput FPGAs have been explored to improve FPGA performance relative to ASICs. A number of papers recognized that wave pipelining can be applied to FPGA logic to achieve significant performance improvements and area savings [16– 20]. Recently, wave pipelining has been applied to FPGA interconnect [4, 21, 22].1 As in this thesis, source-synchronous signalling was used with a clock transmitted alongside the data. A theoretical throughput of 1.4Gbps was derived for a 6.45mm link, or about 13 stages using the terminology of this thesis, though practical experiments achieved only 0.25 Gbps per wire. The study did not consider noise or reliability. In comparison, this thesis demonstrates through simulations a wave-pipelined link of 1  These three publications all discuss the same project.  9  Chapter 2. Background and Related Work similar length achieving a throughput of 3Gbps. One key improvement on prior work is that this thesis assumes the interconnect circuitry in an FPGA can be customized to better support high-throughput communication, and then determines the maximum achievable throughput given that assumption. For example, driver sizes are chosen with throughput as a primary consideration. In [4], drivers sizes are chosen to model an existing FPGA and are therefore not optimized for throughput.2  2.2.3  Surfing  Reliability is a major issue in wave pipelining; timing uncertainty grows monotonically with the length of the link and tends to limit the maximum operating speed [23]. This is addressed in some detail in Chapter 4 of this thesis. Surfing interconnect is a pipelining technique which is designed to attenuate timing uncertainty to allow for more aggressive timing in noisy environments. Surfing requires a timing strobe that is transmitted alongside the data. Simple circuitry at each stage acts as a delaylocked-loop to remove jitter on the timing strobe and as a “soft” latch to remove skew between the data and the clock [24, 25]. Details of the circuit’s operation are provided in Section 3.3.6. The relative simplicity and small size of the surfing circuitry allows for more reliable operation with minimal additional overhead. The robustness of surfing has also been demonstrated in a prototype chip [26]. Surfing was originally designed for long timing chains in ASICs; its application to FPGAs in this thesis is novel. 2  T. Mak, private communication, 2008.  10  Chapter 2. Background and Related Work  2.3  Serial signalling schemes  If a high-speed global clock operating at the speed of the interconnect is not available, as would be the case in FPGAs, then some mechanism for transmitting and recovering the data must be devised that does not require a global clock. This problem has been dealt with extensively in the literature on globally asynchronous, locally synchronous (GALS) systems, which was surveyed in [27].  2.3.1  Asynchronous  In an asynchronous system, request-acknowledge handshakes accompany each transmission, so an unbounded amount of timing uncertainty can be tolerated. A tutorial survey of asynchronous design techniques is provided in [28]. To implement asynchronous signalling in a serial channel, two additional control wires are usually required to carry request and acknowledge signals. There are a number of schemes which reduce this to one wire by driving the wire from both ends [29–31], but they require bidirectional wires which are typically not found in FPGAs.  In FPGAs A fully asynchronous FPGA was designed in [32] and achieved very high clock speeds in the 600MHz range in a CMOS 0.18µm process. Similar work has become the basis for a recent startup company, Achronix, which claims signalling rates of 1.5Ghz [33]. Other work has suggested applying a GALS approach to FPGAs, applying asynchronous wrappers to synchronous logic blocks [34]. These two approaches tend to represent an overhaul of existing FPGA architectures and their supporting CAD tools which is more extreme than the modifications proposed in this thesis.  11  Chapter 2. Background and Related Work  2.3.2  Source-synchronous  In source-synchronous communication, a timing signal that is synchronous to the data is transmitted alongside the data. The receiver extracts the timing signal and uses it to clock the data. Source-synchronous communication is also known as clock forwarding and is a standard technique in digital communications. The major advantage of source synchronous communication is very high-performance links. Unlike asynchronous communication, no handshake is required. Timing uncertainty must be small enough such that the clock and data can be reliably recovered at the receiver. The technique is relatively robust with respect to process variation and noise; with proper design, the clock and data will experience the same variation along the link, allowing the data to be sampled reliably. In ASICs, a number of wavepipelined schemes rely on source-synchronous clocking [14, 35]. High-throughput source-synchronous pipelining was explored in [36]. The technique was also applied to FPGAs in the recent wave pipelining study previously mentioned [4].  2.3.3  Receiver-clocked systems  Transmitting a timing reference along with the clock incurs significant overhead. If a timing reference is instead regenerated at the receiver, the data can be sent alone on one wire without any additional control signals. There are two types of schemes that implement clocking at a receiver. The first uses a pausible clock which is triggered by incoming data, while the second uses fixed delay elements in a shift register to shift in bits as they arrive. In pausible-clocked systems, both the transmitter and receiver have locally generated clocks, usually implemented with gated ring oscillators [37]. Due to process variation, the receiver clocks may operate at slightly different speeds than transmitter clocks, even if the speed should nominally be the same; some synchronization mechanism is therefore required. A network-on-chip design using ring oscillators at the 12  Chapter 2. Background and Related Work transmitter and receiver was able to achieve a 1Gbps throughput in a 0.18µm CMOS process [38]. In the second scheme, the data is transmitted as a serial burst, and the receiver captures bits at fixed intervals following reception of a pilot bit. The receiver is then essentially a shift-register which relies on fixed delay elements to determine when each incoming bit should be sampled [39, 40]. The design is structurally different from pausible clock designs but relies on a similar principle: delay circuits at the receiver are designed to match the period of incoming data. All schemes that rely on a timing source generated independently at the receiver are vulnerable to process variation; transistors at the receiver which control the sampling period could operate at a different speed than the transistors at the transmitter which control the data period. The use of current-starved delay elements can protect against delay variation due to supply voltage fluctuations [39], but process variation remains a critical limiting factor [40] which is likely to get worse in future processes. Therefore, receiver-clocked systems are not considered for this work.  2.3.4  Data encoding  Depending on which of the above signalling techniques is chosen, there may be the opportunity to encode the data in a more energy-efficient way than simply transmitting it straight over the wire. There is an advantage to regular clock and data transmission in that it allows one clock wire to control a bundle of data wires. However, multiple wires allow for alternate encoding techniques that can simplify transmission or reduce the number of transitions required.  Two-wire pulsing The presence of data is normally signalled by an edge on a timing line, but it could also be signalled by a pulse. A simple scheme introduced in [41] sends a zero by 13  Chapter 2. Background and Related Work pulsing one wire, or sends a one by pulsing the other wire. It also uses arbiterlike logic to avoid skew between wires. Pulse-mode asynchronous signalling was also discussed in [42]. Pulses as atomic units allow for simple reliable transmission, since pulse repeaters naturally restore pulse widths and enforce event spacing. However, pulses use twice as much power and require twice the latency compared to edges and are less likely to be competitive, especially since the large multiplexors in FPGAs force pulses to be much wider than they would be in an ASIC.  LEDR encoding In level-encoded 2-phase dual rail (LEDR) encoding, a clock edge is transmitted only if the data hasn’t changed, such that exactly one edge is transmitted per bit [43]. The encoder and decoder are each a single XOR gate. This encoding saves power: without LEDR, the clock wire alone transmits one edge per bit. LEDR can be applied to wave-pipelining, but not surfing, because surfing relies on an unencoded clock signal to control its jitter attenuation circuitry.  SILENT encoding The SILENT scheme [44] is designed to reduce the switching activity of serial data buses. Serialization destroys temporal correlation between successive words; when the same word value is transmitted twice, the bits of a parallel bus do not toggle, and so consume no dynamic power. In SILENT encoding, each data bit in a word is XOR’d with its value from the previous word before being transmitted. During quiet periods when the words do not change, the encoded data is all zeros. The scheme realizes a significant power savings if the average pre-serialization activity is less than 25% or greater than 75%, with highest savings for extremely low or extremely high activities; for activities between 25% and 75% there is a slight power overhead. In an FPGA, it is difficult to know if SILENT should be applied because  14  Chapter 2. Background and Related Work the activity varies according to the user design. The area overhead of the encoder and decoder, which require an XOR gate and a latch for each bit, is significant. The SILENT scheme will thus not be employed in this thesis.  2.4  Timing uncertainty  Timing uncertainty is a major problem for wave pipelining and surfing links and will be considered in detail in Chapter 4. This sections defines the terminology that will be used and provides some background on sources of timing uncertainty and techniques for dealing with it. Timing uncertainty is distinct from systematic variability in that the latter can be modelled and corrected for, but the former is unknown, random, or too costly to model [45]. There are many different forms of timing uncertainty, but they can be broadly classified into two terms: static uncertainty, and dynamic uncertainty. Static uncertainty refers to variations in mean timing due to slowly varying or one-time effects, while dynamic uncertainty refers to short term or cycle-to-cycle variations in timing [46].  2.4.1  Skew and jitter  Timing uncertainty in this thesis will generally be classified as either skew or jitter. Skew is defined as uncertainty in the relative timing between two different signals, while jitter is defined as unwanted variation within a periodic signal. In this thesis, skew will refer specifically to the time difference between a data signal and its corresponding clock edge. The timing diagram in Figure 2.3 shows an example. Skew can be broken into two components: static or mean skew, and dynamic or cycle-to-cycle skew. Static skew usually has a random component due to process variation, and may have a systematic component which is chosen by the  15  Chapter 2. Background and Related Work Arrival time variation Probability density  data  clock Skew Min  Min skew  Mean  Max  Max skew  Figure 2.3: Skew definition  designer; for example, the surfing circuit in this thesis has a systematic skew of about 100ps. The mean skew shown in the figure represents the static skew. The random component is assumed to be zero in this thesis, since the data and timing wires are side by side. Dynamic timing uncertainty means there is cycle-to-cycle uncertainty in skew, which is modelled by a probability distribution with a certain mean and standard deviation. Reliability estimation in Chapter 4 will be specifically concerned with such random variations in skew. While skew is concerned with the difference between two wires, jitter is concerned with consecutive events on the same wire, particularly with periodic signals such as clocks. In such a signal, the period should be stable, which means the time interval between consecutive edges should be constant. Random variation causes uncertainty in the arrival time of each edge. This translates to uncertainty in the separation of consecutive edges. The timing diagram in Figure 2.4 shows the variation in edge separation due to changes in the arrival time. The term “jitter” will normally be used to describe variations away from the mean edge separation; the terms “period” or “bit rate” are used to describe the mean.  16  Chapter 2. Background and Related Work Probability density Arrival time variation  clock Min edge separation Edge separation  Max edge separation Min  Mean  Max  jitter  Figure 2.4: Jitter definition  2.4.2  Sources of timing uncertainty  The main sources of static timing variation are process, voltage, and temperature, often abbreviated as “PVT variation” or simply “PVT”. The main sources of dynamic timing variation are high-frequency supply noise, crosstalk, and residual charge [47]. The impact of dynamic timing uncertainty on the reliable operation of wave-pipelined and surfing links is the major focus of Chapter 4.  2.4.3  Process corners  One way that designers cope with uncertainty is to bound the space of possible operating points and test the design at all of the worst case points. The worst points are often referred to as “process corners” or simply “corners”. The space is multidimensional with one axis for each source of variation being considered. For example, a common test case is mismatch between NMOS speed and PMOS speed. Figure 2.5 shows how the slowest and fastest possible NMOS and PMOS speeds bound the space of possible fabricated chips. The typical point, TT, is in the middle. The designer would normally simulate a design at each of the four corners in the space and the TT point. Corner information is typically encapsulated in the transistor models provided by the foundry. Simulations in this thesis are usually performed at either the TT corner, indicating 17  Chapter 2. Background and Related Work PMOS speed  Space of possible fabricated chips FF SF  Fast TT Typical Slow  FS SS NMOS speed Slow  Typical  Fast  Figure 2.5: Illustration of process corners (adapted from [45])  typical behavior, or the SS corner, indicating the slowest possible transistors. At the TT corner, the temperature is set to 70o C, while at the SS corner, the temperature is set to 125o C. Process corners are useful because they allow designers to test their designs under worst-case operating conditions. However, they can describe only the mean behavior of a chip; they provide no information about intra-die variation, and they cannot be used to guarantee robustness against noise. Moreover, they can produce designs that are too pessimistic to be competitive [45].  2.4.4  Statistical static timing analysis  A recent alternative approach to modelling variation is to treat process uncertainty as a random variable, usually with a normal distribution. In statistical static timing analysis (SSTA), random process and noise effects are translated into random timing uncertainty. The general thrust of the literature is towards solving optimization problems involving large numbers of correlated random variables which affect the timing of all of the paths in the circuit. See [48] for a survey. The impact of random process effects in wave-pipelined domino logic was analyzed using statistical methods in [49]. Variation was found to accumulate and limit the 18  Chapter 2. Background and Related Work maximum frequency as pipeline depth was increased. Similar results are reported in Chapter 4.  2.4.5  Statistical jitter modelling  Short-term timing uncertainty is a well-known problem in off-chip serial signalling; typically, it involves the characterization of the jitter response of a clock and data recovery circuit (CDR). Jitter modelling in off-chip communication has typically used either peak-to-peak or RMS models. However, it has been argued that probabilistic models using cumulative distribution functions to measure error rates are required for high speed (> 1Gbps) links [50]. Gaussian distributions are usually used to model random jitter [51]. Statistical jitter models do not appear to have been applied to on-chip interconnects before; this thesis will demonstrate that they are required for wave pipelined links.  2.4.6  Normal distributions  A good deal of the work in this thesis will assume that random effects are normally distributed. This assumption can be justified by the central limit theorem, which states that the sum of a sufficiently large number of random variables with finite mean and variance tends to be normally distributed. For example, since noise effects tend to be caused by the aggregation of many small random effects, the overall noise will tend to be normal. This is not a perfect assumption; its limitations will be highlighted later when it is applied. Random variables are characterized by their mean µ, and standard deviation, σ (or the variance, σ 2 ). A normally distributed random variable X with mean µ and standard deviation σ is notated as X ∼ N (µ, σ 2 ). Improbable events are often described in terms of the number of standard deviations away from the mean which corresponds to the event’s probability. For example, about 95% of all events occur 19  Chapter 2. Background and Related Work within two standard deviations of the mean, so a 2σ event occurs with about 5% probability. Table 2.1 lists the probabilities of such events up to ten standard deviations from the mean. In the table, P (|X ∼ N (0, 1)| > n) represents the probability that a random variable X which is normally distributed with mean µ = 0 and standard deviation σ = 1 takes a value greater than ±n. Since the standard deviation of X is 1, n is equal to the number of standard deviations away from the mean. Table 2.1: Probabilities for standard normal distribution n P (|X ∼ N (0, 1)| > n) 1 0.32 2 0.046 3 2.7×10−3 4 6.3×10−5 5 5.7×10−7 6 1.9×10−9 7 2.6×10−12 8 1.2×10−15 9 2.3×10−19 10 1.5×10−23  2.5  Summary  This work applies wave pipelining and surfing to datapath FPGA architectures using source-synchronous signalling. It is not the first study of source-synchronous wavepipelined interconnect in FPGAs, but it is the first to consider surfing for the same application, and the first to consider reliability. The reliability analysis models jitter and skew using statistical methods which do not appear to have been previously applied to on-chip links.  20  Chapter 3 Design and Implementation This chapter describes an FPGA with high-bandwidth, bit-serial interconnect at the system and circuit levels. In the circuit-level description, circuit and timing diagrams are presented. The wave-pipelined and surfing interconnect circuits that will be analyzed later in this thesis are introduced here. Finally, a high-level area estimation is performed to predict the advantages of switching from parallel to serial interconnect.  3.1  System-level design  To efficiently support serial interconnect, the traditional FPGA architecture must be altered. Serializer (SER) and deserializer (DES) blocks must be added to each logic, memory, and multiplier block that supports serial communication. Additional switches to connect the SER and DES blocks to the regular block inputs and outputs are required as well. Finally, the wires must be optimized at the circuit level to maximize speed and reliability. Figure 3.1 shows a high-level architectural drawing of an FPGA with the existing parts in bold. The figure includes dedicated clock lines and a clock generator which is necessary to implement a source-synchronous signalling scheme; this particular choice of signalling is addressed in Section 3.2 Figure 3.2 shows a high-level circuit schematic serial interconnect. Note how the user clock controls a serial clock generator at the data source; this serial clock is sent alongside the data and is used at the receiver to clock the deserializer. Circuit diagrams for the serializer and deserializer circuits are provided in Appendix A. The 21  Chapter 3. Design and Implementation CLB / Memory / Multiplier  CLB / Memory / Multiplier  Block outputs  Output switches  Single wires  Serial buses  SER 11 00 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 Clk gen 00 11 00 11 00 11 00 11 00 11 00 11 SER 00 11 User clock 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 11111111111 00000000000 00 11 00 11 00 11 00 11 11111111111 00000000000 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 11111111111 00000000000 00 11 00 11 00 11 00 11 11111111111 00000000000 00 11 00 11 00 11 00 11 Programmable 11111111111 00000000000 00 11 1 0 11111111111 00000000000 Interconnect 00 11 11111111111 00000000000 1 0 11111111111 00000000000 00 11 1 0 11111111111 00000000000 00 11 data clk data  clk  Block inputs  11 00 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 DES 00 11 00 11 00 11 00 11 00 11 00 11 00 11 0 1 00 11 0 1 00 11 00 11 00 11 00 11 11111111111 00000000000 00 11 00 11 00 11 00 11 0 1 00 11 00 11 00 11 00 11 11111111111 00000000000 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 11111111111 00000000000 0 1 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 11111111111 00000000000 0 1 00 11 00 11 00 11 00 11 0 1 0 1 11111111111 00000000000 00 1 00 11 1 11111111111 00000000000 0 1 00 11 0 1 11111111111 00000000000 1 1 0 0 11111111111 00000000000 00 11 1 0 11111111111 00000000000 0 1 00 11 0 1 0 1 0 1 DES  Input switches  Figure 3.1: Schematic of input and output connections, with existing parts in bold  detailed design of the interconnect segments is described in Section 3.3.  3.2  Choice of serial signalling scheme  The serial data needs to operate at a rate much faster than the regular user clock; an FPGA with serial interconnect will therefore require a way of transmitting and recovering serial data that does not rely on the user clock. Possible techniques for doing so were reviewed in Section 2.3; they include using a high-speed global clock, asynchronous signalling, and source-synchronous signalling. Source-synchronous signalling is chosen because it is likely to require less power than a global clock, and because it is easier to integrate into a typical FPGA than asynchronous signalling. This rationale is elaborated below.  22  Chapter 3. Design and Implementation Destination registers  Source registers  DQ  DQ  DQ  DQ  Local logic and routing  Local logic and routing  DQ  DQ  DQ  DQ  Pipelined high−throughput programmable interconnect Serial data SER  DES Serial clock  Serial clock generator  Programmable delay  User clock (global)  Figure 3.2: High-level schematic showing interaction with user clock  3.2.1  Global clock  The most straightforward way of controlling the SER and DES blocks is with a highspeed global clock that is distributed throughout the chip. This scheme needs just one wire to send data using either wave pipelining or register pipelining. Data validity can be established with a pilot bit. To reach the 6Gbps target rates in this thesis, a low-skew double data rate clock in the 3GHz range is required. Designing clock networks at this speed is challenging, but has been done microprocessors. For example, the IBM Power6 can be clocked as high as 5Ghz, and uses less than 100 W for power-sensitive applications [52]. At 22% of the total power consumption, clock switching is a primary component [53]. Clock power is often controlled by disabling or gating the clock when it is not needed, but this is unlikely to save significant power in this situation. The global clock is needed to control serializers, deserializers, and interconnect pipeline latches. 23  Chapter 3. Design and Implementation Serial interconnect circuits that are not needed could be statically disabled using SRAM configuration bits. However, since clock gating is likely to be implemented at the tile level, any tile which contains active interconnect pipeline latches would not be able to disable the global clock. It would thus be difficult to realize appreciable power savings with clock gating. Source-synchronous is more attractive than global clocks from a power perspective; in the former case, the dynamic power is directly proportional to the number of serial bits transmitted, rather than a large fixed cost as in the latter case.  3.2.2  Asynchronous  Asynchronous schemes are attractive because they can tolerate an unbounded amount of timing uncertainty by using request/acknowledge handshakes instead of relying on signals to arrive within a certain time window. However, in FPGAs, links must be programmable, which requires that the req/ack handshake signals travel over a programmable path. Regular FPGA interconnect is not intended to route asynchronous handshakes. In a two-wire handshake, the acknowledgement must be reverse-routed back to the source, which adds some delay and power overhead. Supporting fanout is a bit more complex: after a request at the splitting point, the sender needs to wait for all receivers to acknowledge before sending the next token. One-wire or bidirectional-wire handshake schemes also exist [30] and have been recently adapted for serial signalling in a network-on-chip [54]. In such schemes, the request resets one end of a shared wire and the acknowledge sets the other end of the wire in response. Implementing this on an FPGA requires bidirectional transmission through the interconnect switches. This would negate the strong advantages of directional, single-driver wiring [55]. In general, source-synchronous signalling seems to be more easily adaptable to typical FPGA programmable interconnect than asynchronous signalling. 24  Chapter 3. Design and Implementation  3.2.3  Source-synchronous signalling  In a source-synchronous link, the timing reference is generated at the data source and is transmitted along with the data. A high-level timing diagram showing an 8-bit source-synchronous serial transfer is shown in Figure 3.3, in which the clock is sent on a separate wire, and data is sent on both edges of the clock. User clock Serial clock Serial data  Figure 3.3: High-level timing diagram  Off-chip serial links often use source-synchronous signalling, but rather than use an extra wire for the clock as in the figure, the timing information is typically embedded into the data signal using specialized encodings. The receiver then recovers the clock from the data using a clock-data recovery (CDR) circuit. This technique is not of interest here for three main reasons: 1. It relies on analog signalling techniques which are not compatible with typical FPGA multiplexors. 2. The transmitter and receiver are relatively complex to design and have high overhead in order to handle the various signal integrity issues in off-chip links, but on-chip links are not nearly as challenged by signal integrity. 3. CDR’s typically use phase-locked-loops, which work well for streams, but not bursts, because they take a relatively long time to lock (for example, 60ns in [56]). Sending the clock on a second wire is a much simpler technique. There is extra area overhead for the wire and power overhead for the extra timing transitions, but 25  Chapter 3. Design and Implementation this is largely unavoidable. An advantage of clock forwarding over using a global clock is that with clock forwarding, the power overhead is proportional to the number of bits transferred which allows the designer to trade off the amount of serial communication against power consumption.  3.3  High-throughput pipelined circuit design  This section describes the design of the multiplexor and drivers which are included in each interconnect stage, with throughput as a primary design goal. Figure 3.4 shows the schematic of each interconnect stage. The first driver is assumed to be twice minimum size, while the last driver is variable and will be determined in this section. The middle driver size is chosen so that each driver has equivalent effort [45]. The 0.5mm wire spans four tiles and includes mux taps after each 0.125mm tile as shown in Figure 3.5. In simulations, each 0.125mm wire is modelled with the 4-segment π-model shown in Figure 3.6, which is sufficiently accurate for this application [45]. 0.5mm 4−tile wire in  out 2x  2W  W  16:1 mux  Figure 3.4: Basic interconnect stage schematic  3.3.1  Rise time as a measure of throughput  In a throughput-centric design, the maximum bandwidth of the link is the inverse of the minimum pulse width that can be transmitted. An analytical throughput model is developed in [57] for a wave-pipelined link. Although the model is designed for inverter-repeated links only (to remain accurate, it would have to be modified to  26  Chapter 3. Design and Implementation Possible outputs  Driving buffer 0.125mm  0.125mm  0.125mm  0.125mm  Nominal output 16:1 muxes  0.5mm wire  Possible outputs  Figure 3.5: Detail of 4-tile wire R/4  R/4  R/4  R/4  in  out C/8  C/4  C/4  C/4  C/8  Figure 3.6: RC wire model used in simulations  include the effect of the multiplexors in an FPGA), a detailed analytical model is not necessary for first-order estimates. In the same study, rise time was shown to be a reasonably good approximation of throughput. To illustrate how rise time approximates throughput, consider the three pulses shown in Figure 3.7; assume these are waveforms at the output of a gate in the signal path which has a constant edge rate. A pulse is composed of a rising edge followed immediately by a falling edge (or vice versa); since each edge represents a data symbol, the pulse is formed by two consecutive symbols. The wide pulse saturates at the rail for some length of time; it could be made narrower with no ill effects. The minimumwidth pulse just barely reaches the supply rail; it is the narrowest pulse that can be transmitted through this gate without intersymbol interference. The attenuated pulse does not reach the supply rail because the edges are too close together in time. This pulse will likely be further attenuated by subsequent gates in the signal path  27  Chapter 3. Design and Implementation Voltage  Voltage  90%  90%  50%  50%  10%  10%  Voltage 90% 50%  10% Time  Time  pw trise  (a) Wide  pw trise  (b) Minimum width  Time pw  (c) Attenuated  Figure 3.7: Illustration of wide, minimum-width, and attenuated pulses  and eventually dropped. The rise time, measured from 10% to 90% of the swing, is trise and the pulse width, measured from 50% of the rising edge to 50% of the falling edge, is pw. Considering the minimum-width pulse and looking at only the rising edge, notice that the time from when the signal crosses the 50% threshold to the time when it reaches the rail is equal to pw/2. Because we assume the edge is perfectly linear, then the time from when the signal starts at 0% to when it reaches the 50% threshold is also pw/2. In other words, the 0% to 100% rise time is equivalent to the minimum pulse width. If rise time is measured from 10% to 90%, as in trise , then pw = trise /0.8. Realistic pulses are not perfectly linear, especially as the approach the rails, but this first order approximation is useful in the design process undertaken in subsequent sections. From this observation, it follows that fast edges are required to achieve a high bandwidth link. Hence, all gates must be properly sized relative to the loads they drive. An underpowered gate will produce slow edges which will limit the achievable bit rate. Of course, larger gates require more area and power, so size must be kept as low as possible while still meeting throughput targets.  28  Chapter 3. Design and Implementation  3.3.2  Driving buffer strength  Since the final driver must drive a 0.5mm wire with mux loads as shown in Figure 3.5, a series of simulations were run to determine how large this driver should be, relative to a minimum-sized inverter. Area, delay, energy, and rise time were measured; areaenergy-delay product and area-energy-delay-rise time product were calculated from the measurements. The methodology is briefly described below. • Area: sum of the area of a multiplexor and three inverters, sized as shown in Figure 3.4. Area is measured in minimum-transistor widths according to the methodology described in Appendix B. • Delay: average latency through a stage, including a 16:1 multiplexor, three tapered inverters, and a wire segment. • Energy: measured by integrating the charge drawn from the supply, multiplying by the supply voltage, and dividing by the number of edges. • Rise time: Measured at wire output (at the input of the next multiplexor3 ) from 10%VDD to 90%VDD . Simulations were conducted at the TT corner at room temperature. Results are shown graphically in Figure 3.8. As expected, area and energy grow with buffer size. Delay is optimal at about 35X, and rise time is optimal for very large buffers. Area-energy-delay product is a cost function that might be used for a typical FPGA wire design which does not explicitly require fast edges. The optimal buffer size in this case is about 15X. However, a 15X buffer is undersized relative to the wire load and produces a slow rise time. The area-energy-delay-rise time product suggests that 30X is the optimal size, but the 3  The measurement is taken here rather than at the multiplexor output so as to make the measurement dependant only on the inverter sizing, not the multiplexor design.  29  Chapter 3. Design and Implementation curve is relatively flat in the 25X to 40X region indicating that any size within this region is close to the optimal. To save area and energy, the final driver size will be fixed at 25X for this thesis.  3.3.3  Multiplexor design  Each interconnect segment includes a 16:1 multiplexor. The architecture is a 2-level hybrid design described in [58, 59] and shown in Figure 3.9. While FPGAs sometimes use NMOS-only multiplexors [58], in this case full CMOS transmission gates are required to improve edge rates and signal swing. Adding the PMOS transistor incurs a significant area penalty as twenty PMOS transistors are required in total. The width of these transistors must be kept as small as possible to save area. The output rise time of the multiplexor was measured from 65nm HSPICE simulations using transmission gates of specific sizes. Figure 3.10 shows the results. The x-axis shows the transistor sizes as multiples of a minimum-width NMOS transistor; for example, a 1x2-sized transmission gate contains minimum-width NMOS and twice-minimum width PMOS transistors. Output rise time is plotted; the data points represent measurements at the TT corner with a 1.0V supply, while the error bars show measurements at the SS corner with an 0.8V supply and the FF corner with a 1.2V supply. Both rising and falling edges are shown. There is not much advantage to increasing the width of the transistors. Rise time decreases slightly with wider transistors, but the magnitude of the decrease is minimal and it is clearly not worth the extra area. This result occurs because the decrease in resistance due to wider transmission gates is accompanied by an increase in diffusion capacitance; the added penalty offsets the gains. Not surprisingly, having an undersized PMOS, such as the 1x1 case, causes slow rising edges. In the SS corner, a rising edge has a rise time of 130ps while a falling edge has a rise time of 70ps. In the 1x2 case, where the PMOS is properly sized to be 30  Chapter 3. Design and Implementation  Delay 150  190  145 Avg stage latency (ps)  Area (Min transistor widths)  Area of stage (mux+all drivers) 200  180 170 160 150 140 130  140 135 130 125 120 115  120 10  20 30 40 Final driver size (min−inv widths)  110 10  50  20 30 40 Final driver size (min−inv widths)  (a) Area  −14  x 10  (b) Delay  Energy  Rise time 180  9.5  160  9  140  Rise time (ps)  Avg energy (joules per bit per stage)  10  8.5 8 7.5  120 100 80  7 10  20 30 40 Final driver size (min−inv widths)  60 10  50  20 30 40 Final driver size (min−inv widths)  (c) Energy  −21  x 10  Area−energy−delay  −19  2.5  1.8  1.6  1.4  1.2  1 10  20 30 40 Final driver size (min−inv widths)  (e) Area-Energy-Delay product  50  (d) Rise time  Area−energy−delay−risetime product  Area−energy−delay product  2  50  50  x 10  Area−energy−delay−risetime  2  1.5  1 10  20 30 40 Final driver size (min−inv widths)  50  (f) Area-Energy-Delay-Rise time product  Figure 3.8: Driving buffer size analysis  31  Chapter 3. Design and Implementation in1  in2  in3  in4 out r1F  in5  in6  in7  in8  r1T r2F  in9  in10  in11  in12  r2T r3F  in13  in14  in15  in16  r3T r4F  r4T c1T  c1F  c2T c2F  c3T  c3F  c4T  c4F  Figure 3.9: Sixteen-input multiplexor schematic Rise time at multiplexor output 140 Rising edge Falling edge 120  Rise time(ps)  100  80  60  40  20  1x1 1x2 2x2 2x4 3x6 Transmission gate size (NMOSxPMOS)  Figure 3.10: Rise time of muxes; error bars show process variation  twice as wide as the NMOS, the rising edge takes 110ps while the falling edge takes 90ps. The latter of the two is preferable since it leads to more consistent behavior, which is especially important for propagating timing edges. Thus, the muxes in this design will use 1x2-sized transmission gates. The simulations indicate a rise time of about 110ps in the worst case; since this is the 10% to 90% rise time, the actual minimum pulse width that the mux can  32  Chapter 3. Design and Implementation propagate is about 110ps/0.8≈140ps. This first-order estimate is relatively close to the 11 FO4-delay limit for ISI [3] of 165ps in this process.  3.3.4  Wire length sensitivity  It has been assumed that each interconnect stage includes a 0.5mm wire split into four segments, with multiplexors between each segment. It is useful to determine if the results in this thesis are sensitive to changes in wire length in case the results are applied to an architecture with different tile dimensions. Assume the driving buffer has a resistance of Rg and a diffusion capacitance of Cd ; assume the wire has a resistance of Rw and a capacitance of Cw ; and assume any additional load is Cl . From [60], the delay of a wire is as follows: 1 Delay ∝ Rg (Cd + Cw + Cl ) + Rw ( Cw + Cl ) 2  (3.1)  To improve the bandwidth, we must decrease the delay. Increasing the size of the driver, and thus decreasing Rg , will decrease the first term in equation 3.1, but not the second; the latter term is fixed for a given wire. If the wire is sufficiently short, such that Rw and Cw are small, then increasing the driver size will improve the bandwidth. If the wire is too long, increasing the driver will have little effect. Figure 3.11 shows the rise time at the end of wires of various lengths, under slow, typical, and fast conditions. At the nominal wire length of 0.5mm, the final driver is 25X minimum-sized. The size of the driver is scaled linearly with the wire, such that a 1mm wire has a 50X driver, and so on. The graph suggests that wires of length 1mm or more in this particular technology are too long to maintain fast edge rates. Such wires could be simply split into segments 0.5mm long with a 25X driver at each segment. Wires of 0.5mm or less are not wirelimited; since the driver is scaled linearly with the wire, they all achieve similar  33  Chapter 3. Design and Implementation Rise time of buffered wires 400 350  Rise time (ps)  300 250 200 150 100 SS/0.8V TT/1.0V FF/1.2V  50 0 0  0.5  1 Wire length (mm)  1.5  2  Figure 3.11: Rise time of varying length wires  bandwidth. Wires in this range could thus achieve higher bandwidth by increasing the driver size. It should also be considered that the worst-case multiplexor rise times are about 110ps. There is no benefit to improving wire rise times below this since the overall system bandwidth is constrained by the multiplexor. In fact, since larger drivers carry area and energy penalties, the drivers should be sized as small as possible so long as the wire edge rate is faster than the mux edge rate. The chosen design point of 25X is reasonably close to that point. To support high-rate serial transfers, both wave pipelining and surfing require some further modifications to the interconnect circuits. The wave-pipelined circuit needs two regular wires placed side by side with transistor sizes optimized for fast edge rates; the surfing circuit is somewhat more complex. One stage for each scheme is described below in more detail. Later in this thesis, multi-stage links will be discussed; these consist of a series of identical interconnect stages like the ones in this section cascaded together. The performance of the overall link is determined by the performance of one such stage, so proper design is very important.  34  Chapter 3. Design and Implementation  3.3.5  Wave-pipelining stage  The wave-pipelined link requires that the corresponding data and timing signal be routed side-by-side to eliminate skew. If we assume the wires are reserved for serial interconnect only, then the multiplexors for the data and timing wires may share one set of configuration bits since they follow the same route. Figure 3.12 shows the circuit diagram for a wave-pipelined interconnect stage with one data wire. Additional data wires may be added as needed. Transistors must be carefully sized to maximize throughput. 0.5mm 4−tile wire Data in  Data out 2x  7x  25x 0.5mm 4−tile wire  Clk in  Clk out 2x  7x  25x  16:1 muxes  Figure 3.12: Wave pipeline interconnect stage  Notice that the circuits are open-loop; jitter and skew can accumulate through many cascaded stages. Surfing interconnect, as described in the next section, may be used to attenuate both jitter and skew.  3.3.6  Surfing stage  The circuit structure of surfing [23, 24], shown in Figure 3.13, is similar to wave pipelining, with two key additions: 1. the clock line has a variable strength buffer which is controlled by a delayed version of the clock, and 2. the data line has a variable strength buffer which is controlled by the clock.  35  Chapter 3. Design and Implementation The variable-strength buffers are composed of a weak inverter in parallel with a strong tri-state inverter. The tri-state inverter is off until its control signal arrives. With proper design, the data or clock edge should arrive at the variable-strength buffer slightly ahead of the control signal, so that its transition is weak for some amount of time, then strong as the tri-state inverter turns on. In this case, if the edge arrives too early, a longer period of time passes before the tri-state inverter turns on, which means the edge has been slowed down. Likewise, if the edge arrives late, the tri-state inverter will turn on earlier (or may already be on), so the output transition is stronger and the late edge has been sped up. This means that edges are attracted to their control signals. Figure 3.14 illustrates timing with surfing. By configuring the clock line to be controlled with an echo of itself, and by setting the delay equal to the nominal clock half-cycle period, the surfing buffer implements a simple delay-locked loop [25]. Likewise, by controlling the data line with the clock, the surfing buffer acts similar to a pulsed latch. The clock edges are converted to pulses using a simple edge-to-pulse converter circuit.4 The two surfing buffers can thus remove jitter on the timing line and skew between the data and timing lines. Circuitlevel details of the delay element and edge-to-pulse circuit are given in Appendix A.  3.4  System-level area estimation  To estimate the possible area savings of a serially-interconnected FPGA, two new architectural parameters are required: M , the serial bus width, and Ps , the percentage of original wiring resources which are now replaced with serial buses. For example, in an FPGA with Ps = 0.25, M = 8, and a channel width W =64, there will be 48 regular wires and 2 serial buses carrying 8 bits of data each; a total of 16 wires or 4  Data edges tend to lag a small amount behind timing edges due to the latency of the edge-topulse converter. The timing path must be slower than the data path in strong mode, but faster than the data path in weak mode. This allows the data signal to keep up with the timing signal. Hence, a few extra inverters are added to the timing path.  36  Chapter 3. Design and Implementation  1x  5x  d1  Data in  0.5mm 4−tile wire  d2  Data out  2x  25x  16:1 mux en  en edge to pulse  1x  5x  2x  2x  0.5mm 4−tile wire  surf_out  surf_in  Clk in  Clk out 25x  2x  16:1 mux surf_en  delay  Figure 3.13: Surfing interconnect stage  Timing buffer strength  weak strong  weak strong  weak strong  Surf_in  Surf_en  Surf_out  en en Data buffer strength  weak  strong  weak  strong  weak  d1  d2  Clk out  Data out  Figure 3.14: Surfing timing diagram  37  Chapter 3. Design and Implementation  Serializer Deserializer Single wire Serial bus  Base transistor cost 138 160 152 272  Transistors per bit 54 54 – 131/8  Total for M=8 570 592 – 403  Table 3.1: Approximate area cost of serializers, deserializers, and serial buses  25% of the channel were replaced by serial resources. Approximate area costs for serializers, deserializers, and interconnect is shown in Table 3.1. This data is based on the circuits described earlier and in Appendix A, and on area details shown in Appendix B. Wire area includes multiplexors, buffers, and other logic. Here, each serial bus contains one timing wire and one data wire. The following assumptions will be made when designing an FPGA with serial interconnect: • The target FPGA is island-style with 512 channel wires5 , all of length 4, and input connectivity of fc = 0.2. Each block has 64 inputs6 and 32 outputs. One quarter of the channel wires are available to be driven from each block. • One serial bus of width M can replace M single wires with no impact on routability. • Each block must contain enough M -bit deserializers such that 100% of block inputs can be supplied from serial buses. Likewise, each block must contain enough M -bit serializers such that 100% of block outputs can be sent over serial buses. These assumptions can be used to estimate area for a range of different architectures. While the precise architectural results will depend on proper benchmarking 5  This represents the sum of both horizontal and vertical channels. The block was assumed to be a DSP/multiplier, which needs more SER and DES blocks than a typical CLB. 6  38  Chapter 3. Design and Implementation and evaluation, we can gain insight into sensitivity of results here without benchmarking. Total interconnect area in a block can be measured by tabulating input connection mux area, wire mux and buffer area, and SER/DES overhead area. The target FPGA initially has a total interconnect area, including all input muxes, output muxes, and output buffers, of about 31616 minimum-transistor-widths per block. Roughly half of this comes from the input muxes: each of the 64 inputs is driven by a 77-input mux. The other half comes from the 16:1 muxes and buffers attached to each output wire. By converting a certain percentage of the 512 wires to serial buses, the input mux widths are reduced, and many of the output muxes and buffers can be removed. The three graphs in Figure 3.15 shows how the interconnect area varies with Ps , the percentage of wires that are converted to serial buses, and M , the serial bus width. These graphs demonstrate that large area savings of 10 to 60% might be achieved by converting a large percentage of FPGA interconnect to serial buses. Wider serial buses lead to more savings, as does a higher percentage of serial wires. The SER/DES overhead is roughly constant, because enough circuitry is present to furnish exactly 100% of block inputs and outputs regardless of the bus width and percentage of serial wires. The number of SER/DES units is purposely overestimated here. The area numbers are good enough to suggest that serial interconnect in FPGAs is worth investigating. Demonstrating a net benefit conclusively would require a more detailed system-level design and a full architectural exploration including benchmarking, as well as a detailed circuit-level design and analysis to prove feasibility and reliability, and to provide latency, throughput, area and power numbers. The remainder of this thesis focuses on the latter question.  39  Chapter 3. Design and Implementation  (a) M = 8, percent serial varied  (b) M = 16, percent serial varied  (c) Ps = 0.5, bus width varied  Figure 3.15: System-level interconnect area estimation  40  Chapter 3. Design and Implementation  3.5  Summary  This chapter proposes adding serializer and deserializer circuits to logic, memory, and multiplier blocks to support high-bandwidth serial communication. A system-level area estimation shows that the interconnect area can be reduced by 10% to 60% by converting some percentage of the wiring resources in an FPGA to serial buses. This result is motivational only and should be considered to be a preliminary step before a full architectural investigation, which is outside the scope of this thesis. Source-synchronous serial signalling is shown to be a promising technique where a serial clock generated at the data source and transmitted alongside the data on an adjacent wire. Source synchronous offers several advantages over the alternatives, especially simplicity, easy integration with existing FPGA structures, and relatively low area and power overheads. Wave-pipelining and surfing are the two leading circuit designs under consideration. The wave-pipelining circuit is essentially two ordinary wires side-by-side, one for data and one for the serial clock, with larger transistors to allow for faster edge rates. However, the circuit is open loop which means jitter and skew may accumulate over the length of a long link. In contrast, the surfing circuit includes a delay element in a feedback loop which acts as a delay-locked loop to attenuate jitter and skew. The next chapter assesses the performance of long wave-pipelined and surfing links in the presence of noise, measures their jitter and skew propagation behavior, and estimates their reliability.  41  Chapter 4 Robustness Analysis One of the main concerns in wave-pipelined and surfing designs is robust, reliable transmission. We must guarantee that bits traverse the channel without fault and can be sampled correctly at the receiver. To do so, this chapter develops noise models and a method to estimate the degree of timing uncertainty. Because the noise sources are random, timing uncertainty is treated probabilistically. Circuit simulations are used to predict the minimum pulse width, or, equivalently, the maximum throughput, of both wave pipelining and surfing. The timing uncertainty measurements and circuit simulations together are used to estimate the probability of error as a function of the operating speed.  4.1  Reliable transmission  There are two ways in which a serial link can fail. First, if consecutive edges are too close together in time, they can interfere and reduce the signal swing, violating noise margins and leading to incorrect data being transmitted. Second, the data and clock signals could arrive at the receiver with too much skew, such that incorrect data is sampled.7 Each of these failure modes will be discussed below. 7  Voltage noise at the receiver could also cause incorrect sampling, but this effect is assumed to be minimal.  42  Chapter 4. Robustness Analysis  4.1.1  Edge interference  Edge interference is most readily visualized by considering two consecutive edges as the leading and trailing edges of a pulse. Nominally, the pulse width, measured at the 50% point of the supply voltage, is equal to the nominal bit period, since each edge represents one bit. The rise time of each edge is a function of the relative sizing of each driver with respect to its load (see Section 3.3). Assume a positive pulse, going from logic low to high to low again, is transmitted down a link. If the bit period is sufficiently long such that the edges do not interfere, then the pulse will be transmitted successfully. If, however, the bit period is too small, the trailing edge of the pulse may arrive before the leading edge has fully completed its transition, which means the pulse may not reach the supply rail. If the trailing edge arrives too close to the leading edge, the pulse may not rise above the downstream gate’s threshold voltage, which means the downstream gate will block the pulse from propagating. Figure 4.1 shows the behavior of a five-stage circuit in which a single pulse is applied at the input. Each stage is the wave pipelined circuit shown in Figure 3.12 with one extra inverter inserted to preserve the polarity. The waveforms are from HSPICE simulations at the TT corner. Three different pulse widths are applied: 150ps, 120ps, and 90ps. The first pulse width, 150ps, is wide enough such that the voltage reaches the supply rail; this pulse is propagated with no noticeable attenuation through all five stages. The second pulse width, 120ps, is close to the boundary; at first glance, the pulses appear to be propagated without attenuation, but in fact the fifth pulse is narrower than the first, indicating that the edges are interfering slightly. The third pulse width, 90ps, causes severe interference; the pulse is dropped after three stages. Notice that the 90ps pulse did not fail right away, but it produced a slightly smaller output pulse that, when applied to the second stage, produced an even smaller pulse. This behavior hints at a relationship between input pulse width and output pulse 43  Chapter 4. Robustness Analysis  Figure 4.1: Waveforms showing pulse propagation through five stages  width in which there is a sharp cutoff. More information about this relationship would be helpful in determining the smallest pulse that a multi-stage link can safely propagate.  Pulse width transfer curves The relationship between input pulse width and output pulse width can be measured using the circuit in Figure 4.2. One-half of a wave-pipelined circuit is shown. An ideal  44  Chapter 4. Robustness Analysis pulse of a specific width with a 50ps rise time is generated at the input; after travelling through the first stage, the pulse will have a realistic shape. The pulse width at the input and output of the device under test is measured and used to create the pulse transfer characteristic. Pulse widths are measured from the midpoint of the supply voltage as shown previously in Figure 3.7. For a nominal supply voltage of 1.0V, pulse width is measured from 0.5V to 0.5V. If the supply voltage is set to 0.9V, then pulse width is measured from 0.45V to 0.45V. Note that the pulse width at the input of the device under test will be different from the pulse width of the ideal stimulus; the former is the important measurement. input pulse width  ideal stimulus  output pulse width  ...  ...  ...  ...  ...  ...  Input shaping stage  Device under test  Output load  Figure 4.2: Pulse width measurement circuit  Figure 4.3 is an illustration of the general shape of the resulting curves for wave pipelining and surfing. (Curves of this type have appeared in published literature [41], but they do not yet appear to have been applied to wave pipelining or surfing.) A dashed line is plotted along the diagonal where input pulse width is equal to output pulse width. For sufficiently large pulse widths, the output pulse width should be equal to the input pulse width, meaning the transfer curve is aligned with the diagonal. On the graph, the point at which the transfer curve first touches the diagonal is labelled as an “operating point”, because a pulse with that width will be transmitted unchanged. By contrast, pulses will become narrower in regions where the curve lies below the diagonal, and will become wider in regions where the curve lies above the diagonal. 45  Chapter 4. Robustness Analysis These curves tell us several things about the behavior of a multi-stage link. First, and most obviously, they show a clear cutoff point, where the curve suddenly drops to zero. More importantly, however, they also show changes to a pulse’s width as the pulse travels down the link. For wave pipelining, if an input pulse is narrower than the operating point, then it will be attenuated, such that the next stage sees a narrower pulse. Since the curve is monotonic, the stage after that will see an even narrower pulse, and so on until the pulse is dropped. For surfing, there is a large region in which the curve sits above the diagonal, meaning pulses are restored; if the trailing edge of a pulse arrives too early, it will produce a wider output pulse at its output, and so on until the pulse width returns to the operating point. If there is a perturbation from the operating point, for example due to transient supply noise, then the two schemes will react differently: in wave pipelining, the pulse will become smaller, but in surfing, the pulse will be restored to its nominal width. At a glance, the curve shows how stable the link is with respect to variations in input arrival times, and shows the regions in which timing uncertainty will be attenuated. Output pulse width  Output pulse width in=out operating point  in=out operating point  out2=in3 out1=in2  out1=in2 out2=in3  in3 in2 in1 (dropped)  Input pulse width  (a) Wave-pipelining  in1  in2 in3 Input pulse width  (b) Surfing  Figure 4.3: Pulse transfer behaviour  46  Chapter 4. Robustness Analysis Simulation Results Figure 4.4 shows pulse transfer curves constructed from HSPICE simulation results. These curves are generated for both wave-pipelining and surfing at the SS and TT corners with DC supply voltages ranging from 0.8V to 1.2V, with no transient supply noise. The delay line in the feedback loop in the surfing circuit is set to a nominal delay of 250ps. Two variations of surfing are simulated: one with an ideal delay element (labelled “ideal”), and one with a practical delay element which is vulnerable to noise and variation (labelled “practical”). The curves show a cutoff pulse width varying from 80ps to 160ps, depending on process and supply voltage; notice, however, that the wave pipelining circuit begins to attenuate pulses as wide as about 250ps. Surfing shows a flat region between about 100ps and 250ps in which pulse width is restored. The operating point in the practical surfing circuit turns out to be sensitive to process and voltage, which could affect noise tolerance since different stages in the link could be operating at different points. The nominal margin between the operating and cutoff points is reduced if a fast stage is followed by a slow stage. The operating speed should thus be chosen to match the slowest expected operating point.  4.1.2  Incorrect sampling  The other failure mode is more straightforward, since it occurs in synchronous systems as well. The data must satisfy setup and hold constraints at the receiver. In wave pipelining, the data and clock signals do not interact until they reach the receiver, at which point the clock is used to sample the data. A proper design will delay the data edge so that it arrives at the midpoint between clock edges; it will thus be assumed that a wave pipelined link can tolerate up to half of a bit period of skew. Note that there is no mechanism for removing skew except at the receiver; it will therefore accumulate along the link. 47  Chapter 4. Robustness Analysis  Wave pipelining pulse width transfer characteristic,TT  Wave pipelining pulse width transfer characteristic,SS 500  500 Vdd=0.8 Vdd=0.9 Vdd=1 Vdd=1.1 Vdd=1.2  400 Output pulse width (ps)  Output pulse width (ps)  400  Vdd=0.8 Vdd=0.9 Vdd=1 Vdd=1.1 Vdd=1.2  300  200  300  200  100  100  0 0  100  200 300 Input pulse width (ps)  400  0 0  500  100  (a) Wave pipelining, SS Surfing (ideal) pulse width transfer characteristic,SS  500  Surfing (ideal) pulse width transfer characteristic,TT 500  Vdd=0.8 Vdd=0.9 Vdd=1 Vdd=1.1 Vdd=1.2  Vdd=0.8 Vdd=0.9 Vdd=1 Vdd=1.1 Vdd=1.2  400 Output pulse width (ps)  400 Output pulse width (ps)  400  (b) Wave pipelining, TT  500  300  200  100  300  200  100  0 0  100  200 300 Input pulse width (ps)  400  0 0  500  100  (c) Surfing (ideal), SS Surfing (practical) pulse width transfer characteristic,SS Vdd=0.8 Vdd=0.9 Vdd=1 Vdd=1.1 Vdd=1.2  500  Surfing (practical) pulse width transfer characteristic,TT  400  300  200  100  0 0  400  500  Output pulse width (ps)  400  200 300 Input pulse width (ps)  (d) Surfing (ideal), TT  500  Output pulse width (ps)  200 300 Input pulse width (ps)  Vdd=0.8 Vdd=0.9 Vdd=1 Vdd=1.1 Vdd=1.2  300  200  100  100  200 300 Input pulse width (ps)  400  (e) Surfing (practical), SS  500  0 0  100  200 300 Input pulse width (ps)  400  500  (f) Surfing (practical), TT  Figure 4.4: Pulse width transfer characteristic simulations  48  Chapter 4. Robustness Analysis  matched edges  data  input skew  output skew  ...  ...  ...  ...  ...  ...  ...  ...  ...  ...  ...  ...  Delay elements  timing  Input shaping stage  Device under test  Output load  Figure 4.5: Skew transfer measurement circuit  Surfing is slightly more complex in that each stage contains a surfing buffer on the data line which behaves like a pulsed latch. Timing constraints for the surfing buffer are derived in [26] but they may also be visualized by constructing a skew transfer characteristic, using techniques similar to those used in developing the pulse width transfer characteristic.  Skew transfer characteristic The skew transfer characteristic is found using the circuit in Figure 4.5, which is very similar to the pulse width measurement circuit in the previous section. In this case, ideal delay elements are inserted into the data and clock lines. The delays are varied to introduce a controllable amount of skew at the input to the device under test. The output skew is then measured. The wave pipelining skew transfer characteristic is not interesting; it is simply a diagonal along the input=output line. The surfing characteristic is shown in Figure 4.6. There is no discernible difference between practical and ideal curves this time. Recall that each timing edge produces a data pulse using the edge-to-pulse converter; the data pulse controls the soft latch  49  Chapter 4. Robustness Analysis  Surfing (ideal) skew transfer characteristic,TT  Surfing (ideal) skew transfer characteristic,SS 200  150  Vdd=0.8 Vdd=0.9 Vdd=1 Vdd=1.1 Vdd=1.2  Output timing/data edge separation (ps)  Output timing/data edge separation (ps)  200  100  50  0 0  50 100 150 Input timing/data edge separation(ps)  150  100  50  0 0  200  (a) Surfing (ideal), SS Surfing (practical) skew transfer characteristic,SS  Surfing (practical) skew transfer characteristic,TT  Vdd=0.8 Vdd=0.9 Vdd=1 Vdd=1.1 Vdd=1.2  Output timing/data edge separation (ps)  Output timing/data edge separation (ps)  200  200  100  50  0 0  50 100 150 Input timing/data edge separation(ps)  (b) Surfing (ideal), TT  200  150  Vdd=0.8 Vdd=0.9 Vdd=1 Vdd=1.1 Vdd=1.2  50 100 150 Input timing/data edge separation(ps)  (c) Surfing (practical), SS  200  150  Vdd=0.8 Vdd=0.9 Vdd=1 Vdd=1.1 Vdd=1.2  100  50  0 0  50 100 150 Input timing/data edge separation(ps)  200  (d) Surfing (practical), TT  Figure 4.6: Skew transfer characteristic simulations  on the data line. The operating point is determined by the latency through the edgeto-pulse converter, which is nominally about 80ps but can vary considerably. The operating point is not labelled on the figure; it is the left-most point at which the curve intersects the diagonal, where the slope of the curve is less than 45 degrees. Again, we see the curves exhibiting a flat, stable region in which changes in the input have relatively little effect on the output. Edges that arrive early (to the left of the diagonal) are snapped back to the operating point almost immediately. Edges that arrive late (to the right of the diagonal) show some interesting behavior which is due to the fact that data pulse has a finite width. Normally, a late edge is sped 50  Chapter 4. Robustness Analysis up, because the strong tri-state inverter is on for the entire transition; indeed we see evidence of this occurring in the region where the skew transfer curves are below the diagonal. However, if the edge arrives too late, then the data pulse will complete and the tri-state will turn back off, causing the delay to shoot back up. The skew tolerance of the inverter is thus limited by the pulse width of the edge-to-pulse converter. In this particular circuit, the edge-to-pulse converter is designed to produce a pulse about 80ps wide. In order to ensure that late transitions are sped up, not slowed down, we must require that the output skew is reduced, which means the curve must sit below the diagonal. For early transitions, the curve may sit above the diagonal, but nominally the circuit will operate at the point where the curve intersects the diagonal. We can thus estimate the amount of skew tolerance by measuring the amount of time between the two diagonal intercepts; it appears to vary from about 30ps to 50ps, which means the circuit can tolerate skew of at least one third of the data pulse. If the nominal bit period is significantly larger than twice the nominal data pulse width, then skew tolerance could be increased by widening the data pulse. This would be desirable for bit periods greater than 200ps. The maximum width of the data pulse should be half the nominal bit period for maximum skew tolerance. In that case, each stage would then be able to tolerate skew of up to one-sixth of the bit period (one third of the data pulse).  4.1.3  Summary of criteria for reliable transmission  Two failure modes have been identified: pulse collapse due to edges interfering, and incorrect sampling due to skew. To prevent pulse collapse, pulses must always be greater than about 160ps wide at the far end of the link; to achieve this width, some margin must be built into the operating bit rate in order to prevent accumulated timing uncertainty from altering a nominally safe pulse into an unsafe pulse. To 51  Chapter 4. Robustness Analysis prevent incorrect sampling in a wave-pipelined link, the total skew across the link, measured at the receiver, must be at most one half of the bit period. In a surfing link, the skew measured at each stage must be at most one sixth of the bit period. The reliability of the link can be assessed using these guidelines as timing deadlines.  4.2  Quantifying timing uncertainty  A distinction needs to be made between fast events that impact arrival times from cycle to cycle, static events that set mean arrival times, and those in between. In [47], sources of uncertainty are classified by their relative time constants: electromigration and the hot electron effect cause delays to drift over several years; temperature cause delays to shift in microseconds; and supply noise/cross-coupling/residual charge have delay impacts in the 10 to 100ps range, with estimated 3σ delay impacts of ±17%/10%/5%, respectively. Of the effects listed in [47], only the last three occur in the sub-nanosecond range and will thus have an impact on cycle-to-cycle arrival times. Other effects may be considered to have a constant impact on arrival time. The uncertainty due to these constant effects must be accounted for by adding appropriate timing margin, but it does not threaten the safe transfer and recovery of data as long as data and timing wires are affected in the same way.8 Faster noise sources are therefore the focus of this analysis. With fast noise, consecutive edges on a wire that are nominally a safe distance apart could be pushed too close together, exacerbating ISI. If the noise affects data and timing wires differently, causing skew, the data may be pushed outside of the safe sampling window indicated by the timing signal. Crosstalk and supply noise are the main sources of fast noise, so they will be addressed in detail in this section. 8  Note that mismatch due to random variation will still be briefly addressed in Section 4.4.  52  Chapter 4. Robustness Analysis  4.2.1  Process and temperature  Process, voltage, and temperature (P, V, and T) are the most significant factors affecting mean delay. Supply voltage can have both slowly varying and quickly varying components and is addressed separately in Section 4.2.3. Process and temperature are mainly accounted for by simulating under the slowest conditions (SS corner at 125o C). However, within-die variation should be accounted for as well. The full possible range of transistor variation due to process is about ±30% [61]. Estimates of within-die variation vary but often fix it at about half the full range [62], up to ±15% from the average, such that a variation from SS to TT is possible within one die (or from TT to FF, or somewhere in between). Speed mismatch between data and timing paths causes systematic skew that can make wave pipelining unreliable. As long as the transistors and wires are close together, they should experience negligible process or temperature skew [61]. However, a pessimistic random skew with zero mean and standard deviation σ = 2% of the stage latency will be applied in Section 4.4 to ensure that the results are not overly sensitive to random process effects.  4.2.2  Crosstalk  Crosstalk is a fast noise source contributing to skew and ISI. In fact, the bit-serial interconnect will itself be a large source of crosstalk noise due to the fast edges employed and close proximity of the wires. Here, serial interconnect is simulated with and without shielding to determine the impact of crosstalk and whether shielding is necessary or not. Changing voltages on neighboring wires has the effect of temporarily increasing or decreasing the coupling capacitance between wires. For example, if two adjacent wires both switch in the same direction simultaneously, then the effective capacitance is cut in half (approximately, depending on geometry) via the Miller effect, because 53  Chapter 4. Robustness Analysis the voltage at both ends of the capacitor is changing at the same time [45]. If the wires switch in opposite directions, the capacitance can double. The change in capacitance produces a change in delay. This model is useful for producing worst-case bounds on crosstalk-induced delay variation. Worst-case bounds are appropriate for synchronous systems with fixed timing constraints and deterministic signals with known timing. In an FPGA, the transition times on neighbouring wires is not known ahead of time; indeed, one signal may encounter crosstalk from many different signals on various neighbouring segments as it traverses the FPGA. Moreover, each bit in a serial stream may encounter crosstalk. Applying worst-case bounds at every possible crosstalk point is far too pessimistic and leads to unrealistically conservative designs. Worst-case bounds are further discussed in Appendix C.  Simulation setup The severity of crosstalk depends on the precise relative timing of edges on adjacent wires, but this timing is not known in advance. However, the impact of crosstalk may be reasonably estimated with Monte Carlo simulations by applying random data on adjacent wires at 50ps intervals. This pessimistic rate helps ensure safe design margins. Figure 4.7 shows a crosstalk measurement circuit. The data and clock wires from a wave-pipelined interconnect stage are shown, along with aggressors above and below. Additional input shaping and load stages are added to ensure realistic conditions. Wires in the input shaping stage have no coupling. All signal wires including aggressors are twice minimum width. In the unshielded case, all wires are spaced apart by twice the minimum spacing, while in the shielded case, minimumwidth shields are inserted between each pair of signal wires at the minimum spacing. All wires are assumed to be in one of the middle metal layers. Coupling capacitances  54  Chapter 4. Robustness Analysis Random aggressor  Data in Data source  Data out  Clk in  Clk out  Input shaping stage  Load stage Random aggressor  (a) No shielding Random aggressor  Data in  Data out  Clk in  Clk out  Data source  Load stage  Input shaping stage  Random aggressor  (b) Full shielding  Figure 4.7: Crosstalk simulation setup  are determined from an HSPICE field solver using process data; second-order coupling capacitances (i.e. from one signal wire through a shield to the next signal wire) are included and found to account for about 3% of total capacitance. The data wire carries a 16-bit pattern while the clock wire has an edge corresponding to each bit. The latency through one wave-pipelined stage from the clock input to clock output is measured for each of the sixteen bits, producing sixteen measurement points. This is repeated with the same word pattern and different random aggressor data until about 12,000 measurements are collected.  Results The resulting delay histograms are shown in Figure 4.8. The curves do not show a normal distribution because of deterministic coupling between the wires. Also, a slight mismatch between rising and falling edges leads to double-peaked behavior. Still, we can observe about σ = 12ps of timing uncertainty per stage in the unshielded 55  Chapter 4. Robustness Analysis  0.25  µ=151ps  0.2  σ=12ps  Delay variation due to crosstalk, shielded  Probability density  Probability density  Delay variation due to crosstalk, unshielded  0.15  0.1  0.05  0 100  0.25  µ=162ps  0.2  σ=1.74ps  0.15  0.1  0.05  120  140 160 Stage latency (ps)  180  (a) No shielding  200  0 100  120  140 160 Stage latency (ps)  180  200  (b) Full shielding  Figure 4.8: Delay variation due to crosstalk  case, which is severe, and about σ = 1.7ps in the shielded case, which is manageable. The magnitude of the effect on delay strongly suggests that serial links should be shielded. Timing uncertainty for the shielded case turns out to be much smaller than supply-induced timing uncertainty, so for simplicity the remainder of the analysis in this thesis will assume perfect shielding (i.e, no crosstalk).  4.2.3  Supply noise model  In general, supply noise can be divided into slowly varying or DC components and quickly varying components. There are many ways to model supply noise. A typical industry rule of thumb of a uniform ±10% [45] provides reasonable DC bounds, but this gives no information about the frequency content of the noise. High-frequency voltage spikes will be present as well. Both effects need to be considered. One recent study suggests that decoupling capacitors can remove this high frequency noise, so the supply should be considered a constant DC voltage [63]. Others include slow sinusoids in the 100-500MHz range [46] to model resonance in the LC circuit formed by the power grid and the lead inductance. Another study of ASICs  56  Chapter 4. Robustness Analysis measured power supply noise and found a mixture of deterministic noise caused by the clock signal and its harmonics, random cyclostationary noise caused by switching logic, and random high frequency white noise [64]. In ASIC designs, power supply noise can be accurately estimated because the circuit design and behavior is known. This is not possible in an FPGA since the circuit’s behavior will change depending on the design the FPGA is implementing. Instead, a generic supply noise model is required. Compared to ASICs, FPGAs have slower user clocks, larger interconnect capacitance driven by strong buffers, and more disperse logic. There do not appear to be any studies of the net effect of such power supply noise in FPGAs. Since a DC-only supply noise model is clearly inadequate, supply noise will be modelled in this thesis as the sum of a nominally fixed DC component and a fast transient component; each component will be varied independently. The transient noise is assumed to be a memoryless random process which is normally distributed and changes value every 100ps.9 The mean or DC level, µ, is nominally 1.0V, but since low supply voltages limit performance more than high supply voltages, this analysis focuses on DC voltage levels below the nominal. The standard deviation σ is left as a central parameter. Figure 4.9 shows example power supply waveforms at µ = 0.95V DC and σ = 15mV, 30mV, and 45mV; these supply voltage waveforms will be applied in circuit simulations. All elements within one interconnect stage see the same supply voltage, but each stage has an independently varying supply.10 There is clearly room for improvement in this model; real power supply noise is not memoryless, for example, and it is certainly not normally distributed; at the very least it must be bounded. However, constructing a more sophisticated model is a difficult task without more detailed information about how FPGA power supply noise 9  This rate is chosen because it has a strong impact on cycle-to-cycle delay at the serial interconnect speeds in this thesis. 10 Multiplexor select lines are directly connected to the noisy supply as well; in an actual device they would see this noise filtered by the SRAM configuration bits.  57  Chapter 4. Robustness Analysis  Figure 4.9: VDD noise waveforms  actually behaves. The model presented here will be useful because it makes it easy to isolate the delay impacts of DC and transient noise. In general, DC noise affects mean delay while transient noise affects cycle-to-cycle delay (this is demonstrated in the next section); since cycle-to-cycle timing uncertainty is the main threat to reliable transmission, the model should be pessimistic in this regard. Note that σ = 45mV leads to 3σ variations of ±0.135V , or ±13.5%, which is considerably more pessimistic than typical bounds of ±10%.  4.2.4  Supply noise analysis  Transient noise has a strong impact on cycle-to-cycle delay because the operating speed of a transistor, which is a function of its supply voltage, can change in between cycles. Slowly varying noise should have almost no effect on cycle-to-cycle delay. This section tests these assumptions.  Simulation setup Similar to the crosstalk simulations described earlier in this chapter, a multi-stage link is constructed and the stage latency is measured over several thousand trials. The measurement circuit is shown in Figure 4.10. Each stage has an independent  58  Chapter 4. Robustness Analysis Vdd1 ~ N (µ, σ 2)  din clkin  Data source  Wave pipelined stage  Vdd2 ~ N (µ, σ 2)  d1 clk1  Wave pipelined stage  Vdd3 ~ N (µ, σ 2)  d2 clk2  Wave pipelined stage  dout clkout  Figure 4.10: Experimental setup measuring delay impact of VDD noise  supply voltage, but all supply voltages have the same distribution, with mean or DC value µ and standard deviation σ. To measure the impact of transient noise, the DC value is fixed at 0.95V, and transient noise ranging from σ = 0mV to σ = 60mV is applied. To measure the impact of DC noise, a small fixed amount of transient noise (σ = 15mV ) is applied, and DC voltage is varied from 1.00V to 0.80V. For each configuration of µ and σ being tested, 100 trials are run. In each trial, a set of random supply voltages are generated for each stage. The delay through the middle stage, from clk1 to clk2, is measured sixteen times, once per bit. The number of measurements, 1,600, should be enough to give a reasonable estimate of the mean and standard deviation of the jitter.  Results Figure 4.11 shows the DC noise histograms, while Figure 4.12 shows the transient noise histograms. The histograms are all normalized to their respective means, so that the variation in latency (i.e., the jitter) is measured as a percentage of the mean. The trend lines clearly show that jitter increases steadily with applied transient noise, but is relatively insensitive to changes in DC value. Slow changes in the DC voltage level will thus have relatively little impact on cycle-to-cycle jitter. It is worth noting that the jitter histograms appear to be normally distributed. To some degree, this is likely an artifact of the normally distributed voltage supply  59  µ=151ps  15  σ=2.1%  10 5 0  20  µ=166ps  15  σ=2.4%  10 5 0  0.8 1 1.2 Stage latency (normalized)  25 20  µ=207ps  15  σ=2.9%  10 5 0  0.8 1 1.2 Stage latency (normalized)  (d) µ = 0.85V  25 20  µ=184ps  15  σ=2.6%  10 5 0  0.8 1 1.2 Stage latency (normalized)  (b) µ = 0.95V  Probability density  Probability density  (a) µ = 1.00V  Probability density  20  25  10  25 20  µ=238ps  15  σ=3.1%  10 5 0  0.8 1 1.2 Stage latency (normalized)  (c) µ = 0.90V  0.8 1 1.2 Stage latency (normalized)  (e) µ = 0.80V  Jitter σ (% of latency)  25  Probability density  Probability density  Chapter 4. Robustness Analysis  8 6 4 2 0 0  0.05 0.1 0.15 Mean Vdd drop (V)  0.2  (f) Trend  Figure 4.11: Delay variation due to variations in DC level (σ = 15mV).  noise model. Actual voltage noise cannot have long unbounded tails as a normal distribution would.  4.3  Jitter and skew propagation  Previously, it was claimed that surfing interconnect can attenuate jitter and skew while wave pipelining allows jitter and skew to accumulate. If jitter can be modelled as a normally distributed random variable with standard deviation σ, and jitter between √ stages is independent, then the jitter at stage N in a wave-pipelined link is N · σ. In a surfing link, the jitter should be constant at all stages, so long as the amount of noise applied does not exceed the local margin. A similar analysis applies to skew as well.  60  µ=166ps  15  σ=1.6%  10 5 0  20  µ=166ps  15  σ=2.4%  10 5 0  0.8 1 1.2 Stage latency (normalized)  25 20  µ=166ps  15  σ=5.8%  10 5 0  0.8 1 1.2 Stage latency (normalized)  (d) σ = 45mV  25 20  µ=166ps  15  σ=4%  10 5 0  0.8 1 1.2 Stage latency (normalized)  (b) σ = 15mV  Probability density  Probability density  (a) σ = 5mV  Probability density  20  25  10  25 20  µ=166ps  15  σ=7.8%  10 5 0  0.8 1 1.2 Stage latency (normalized)  (c) σ = 30mV  0.8 1 1.2 Stage latency (normalized)  (e) σ = 60mV  Jitter σ (% of latency)  25  Probability density  Probability density  Chapter 4. Robustness Analysis  8 6 4 2 0 0  20 40 Supply σ (mV)  60  (f) Trend  Figure 4.12: Delay variation due to transient supply noise (µ = 0.95V.)  Simulation setup The simulation setup, shown in Figure 4.13, is similar to the setup in Figure 4.10, except a longer link with 9 stages is simulated. The goal of this simulation is to measure the skew and jitter at the output of each of the first 8 stages to see if it shrinks, grows, or remains constant as the link length is increased. As before, skew is measured from the midpoint of a data transition to the midpoint of its corresponding clock transition. The nominal time separation between two consecutive clock edges is measured to capture the jitter behavior. One hundred trails are run; in each trial, sixteen jitter measurements and nine data skew measurements (the data pattern had only nine edges) are performed at each of the eight stages. The supply has a mean value of 0.95V and a varying transient component; larger transient noise should produce larger jitter and skew.  61  Chapter 4. Robustness Analysis Vdd1 ~ N (µ, σ 2)  Data source  din clkin  Wave pipelined or surfing stage  Vdd2 ~ N (µ, σ 2)  d1 clk1  Wave pipelined or surfing stage  Vdd8 ~ N (µ, σ 2)  d2 clk2  ...  d7 clk7  Wave pipelined or surfing stage  Vdd9 ~ N (µ, σ 2)  d8 clk8  Wave pipelined or surfing stage  dout clkout  Figure 4.13: Experimental setup measuring skew and jitter propagation  Results The jitter and skew measurements produce histograms with a normal distribution at a certain mean and standard deviation (not shown). Mean skew and jitter appears to be constant, but the standard deviation varies both with the amount of noise applied and with the length of the link. Figure 4.14 shows the standard deviation of jitter and skew for wave pipelining and surfing. Simulation data is marked on the graph with a thick line. At very small levels of noise, the curves are jagged because disparities between rising and falling edges are the dominant source of skew and jitter. The √ simulation data is also fit to curves of the form y = A x + B and extrapolated out to 50 stages using a dashed line. In wave pipelining, the jitter and skew both accumulate in long links as expected and clearly follow a square root curve with respect to the number of stages11 . In surfing, both jitter and skew are small and roughly constant for small amounts of noise. The largest amount of supply noise simulated, σ = 60mV , is too high for the surfing stage; the large spike in skew indicates that data bits were dropped. Moreover, there is a slight accumulation of jitter evident for this noise level, another sign that the surfing mechanism is not working properly. The surfing stage simulated in this trial uses a delay loop of about 250ps; a higher amount of noise can be tolerated simply by increasing this delay. 11  Correlation coefficients are all > 0.99 except for wave pipelined jitter at σ = 0mV (0.84), wave pipelined skew at σ = 0mV (0.83) and σ = 15mV (0.97), and surfing skew at σ = 0mV (0.90) and σ = 15mV (0.97).  62  Chapter 4. Robustness Analysis Wave pipelined extrapolated jitter  150  Surfing (ideal) extrapolated jitter 200  Vdd σ=0 Vdd σ=15mV Vdd σ=30mV Vdd σ=45mV Vdd σ=60mV  Consecutive edge separation σ (ps)  Consecutive edge separation σ (ps)  200  100  50  0 0  10  20 30 Number of stages  40  150  100  50  0 0  50  Vdd σ=0 Vdd σ=15mV Vdd σ=30mV Vdd σ=45mV Vdd σ=60mV  (a) Wave pipelining jitter  10  Vdd σ=0 Vdd σ=15mV Vdd σ=30mV Vdd σ=45mV Vdd σ=60mV  100  50  0 0  10  20 30 Number of stages  50  Surfing extrapolated skew 200 Clock−data separation σ (ps)  Clock−data separation σ (ps)  150  40  (b) Surfing (ideal) jitter  Wave pipelined extrapolated skew 200  20 30 Number of stages  40  50  (c) Wave pipelining skew  Vdd σ=0 Vdd σ=15mV Vdd σ=30mV Vdd σ=45mV Vdd σ=60mV  150  100  50  0 0  10  20 30 Number of stages  40  50  (d) Surfing(ideal) skew  Figure 4.14: Jitter and skew propagation (simulation in bold)  4.4  Reliability estimate  The previous results in this chapter can be used to make some estimate of the link’s reliability. By modelling jitter and skew as normal random variables with the standard deviations taken from the data plotted in Figure 4.14, the probability of error can be estimated.  63  Chapter 4. Robustness Analysis Wave pipelined bit arrival distributions, σj=25ps 0.02 Bit 1 Bit 2  0.018 Stage 1  Probability Density  0.016 0.014 0.012 0.01 0.008 0.006  Stage 10  0.004  Stage 30  Stage 50  0.002 0  0  1000 2000 3000 4000 5000 6000 7000 8000 9000 Arrival time (ps)  Figure 4.15: Illustration of arrival time probabilities for consecutive edges  Methodology If the arrival times of two successive bits are normally distributed, there is a finite probability that the later bit will arrive close enough to the earlier bit to cause intersymbol interference. If jitter grows with the number of stages, then this probability will increase. Figure 4.15 illustrates an example where two bits are sent consecutively down a fifty-stage link. Initially, the probability density curves are very sharply peaked, indicating that there is very little uncertainty in arrival time and correspondingly a low probability of ISI. As the bits travel through the link, their arrival times spread out due to accumulating jitter, and the probability of interference increases. By the fiftieth stage, there is significant overlap in the curves, indicating a high probability of failure. Of course, an overlapping state is not physically possible; the second bit cannot arrive earlier than the first. Two edges that arrive very close together should instead be thought of as a pulse with a very narrow width; such a pulse would be attenuated.  64  Chapter 4. Robustness Analysis To guarantee that jitter does not cause such a failure, we need to determine that the probability of two edges arriving below the cutoff pulse width (i.e. 160ps, determined earlier in this chapter) is sufficiently small. A similar argument follows for the skew. To allow for correct sampling at the receiver, the data and clock may be misaligned by at most one-half of the data period in wave pipelining and at most one-sixth of the data period in surfing. The probability of this occurring also depends on the uncertainty in arrival times, which is captured by the standard deviations measured in the previous experiment. If the probability distributions of consecutive edge separation and skew are known, then the probability of error can be found using the cumulative distribution functions. Let P1 be the probability that the consecutive edge separation is greater than 160ps, and let P2 be the probability that the skew is less than one-half of the nominal bit period for wave pipelining, or less than one-sixth of the nominal bit period for surfing. For successful transmission, both conditions must be true; therefore the probability of error is PE = 1 − P1 · P2 . The mean consecutive edge separation is equal to the nominal bit period. If the bit period is 500ps, for example, then there is 340ps of margin until the cutoff point. The probability of error due to jitter is equivalent to the probability of the variation in edge separation being greater than 340ps. In surfing, there is a slight complication because the operating point varies depending on the DC supply voltage; here we will assume a worst case 30% variation. If the nominal rate is 500ps, then the worst-case operating point is 350ps, meaning there is only 190ps of margin until the cutoff point of 160ps. For skew, wave pipelining can tolerate one-half of the nominal bit period. Hence, if the bit period is 500ps, the probability of error due to skew is equal to the probability that the skew is greater than 250ps. For surfing, the mean skew is one-sixth of the nominal bit period; in this case the maximum tolerable skew would be 83ps.  65  Chapter 4. Robustness Analysis Using this methodology, the probability of error can be estimated as a function of the nominal bit period. This will be shown in the results at the end of this section. First, however, skew and jitter distributions need to be quantified.  Skew and jitter distributions For this analysis, a supply noise level of σ =30mV is chosen and the standard deviations for skew and jitter are taken from the data plotted in Figure 4.14. For wave √ pipelining, this results in jitter of σi = 10.6ps · i for stage i, while for surfing it is constant at σ = 10.8ps regardless of the stage number. Similarly, skew has a standard √ deviation of σi = 5.8ps · i for wave pipelining, and σ = 4.6ps for surfing. The skew distribution assumes the latency through the data and clock wires are identical. In reality, there is mismatch due to random process variation. An additional skew term of µ = 0, σ = 2% of the stage latency is applied to account for this. The overall skew standard deviation is the geometric mean of the process skew and the random skew from supply noise. For wave pipelining, the skew at stage i is √ √ σi = (5.8ps ∗ i)2 + (l ∗ 0.02 ∗ i)2 , where l is the average latency of one stage. For surfing, it is again constant, at σ = 4.6ps+0.02 ∗ l. Since the true distributions of skew and jitter are unknown, they are assumed to be normally distributed. Normal distributions, however, are unbounded. This presents a problem as it means that physically impossible events (e.g., a negative supply voltage, negative arrival times) will occur with finite probability. Rather than arbitrarily bounding the Gaussian and perhaps providing a result that is overly optimistic, the probability of these rare events can be de-emphasized by halving the skew and jitter standard deviations. There is no real physical justification for this step; rather, it is undertaken to show what happens to reliability when the underlying noise model is changed. This provides insight of sensitivity to the underlying noise model.  66  Chapter 4. Robustness Analysis Results Probability of error estimates are shown in Figure 4.16. The x axis shows throughput in Gbps, which can easily be transformed into an edge separation period by taking the reciprocal. The y axis shows the probability of error, PE . The curves assuming normally distributed noise are plotted with solid lines and labelled “norm” (meaning “normal”). The modified normal curves which have half the standard deviations of their corresponding normal curves are plotted with dashed lines and labelled “mod-norm”. The graphs show a clear tradeoff between throughput and reliability; to decrease error rate, the circuits must operate at a slower rate. Notice, however, that surfing is much more reliable than wave pipelining in several respects: it is insensitive to changes in link length, less sensitive to changes in the underlying noise model, and has a much smaller range in throughput with respect to changes in error rate assumptions. There is no hard standard as to what constitutes a sufficiently robust probability of error. Some work assumes a safe bit error rate to be 10−12 [50]. However, since there are about 3·107 seconds in a year, and up to 3×109 events per second if the link operates at 3Gbps, then a continuous link has about 1017 events per year. If there are 104 such links inside an FPGA, then there are a total of 1021 events per year. To achieve hundred-year reliable lifetimes, a probability of error of 10−23 or less may be required. Probabilities of error in this range (10−23 ) occur ten standard deviations away from the mean in a normal curve (see Table 2.1). The noise model cannot capture such improbable events; it is highly likely that the jitter and skew are bounded such that the probability of error is zero for sufficiently large deviations from the mean. Alternatively, failure-inducing events like a 10σ transient voltage spike may be possible, but they are likely to be deterministic (for example, if all possible circuits switch at the worst possible time) and thus not well-modelled with a normal distribution. Nev67  Chapter 4. Robustness Analysis 0  10  Estimated probability of error  −5  10  −10  10  Wave−pipe’d (norm) Wave−pipe’d (mod−norm) Surfing (norm) Surfing (mod−norm)  −15  10  −20  10  −25  10  1  2  3 4 Throughput (Gbps)  5  6  (a) 10-stage link 0  10  Estimated probability of error  −5  10  −10  10  Wave−pipe’d (norm) Wave−pipe’d (mod−norm) Surfing (norm) Surfing (mod−norm)  −15  10  −20  10  −25  10  1  2  3 4 Throughput (Gbps)  5  6  (b) 50-stage link  Figure 4.16: Probability of error estimates. Because of uncertainty regarding the noise models, these results should be considered for illustration only.  68  Chapter 4. Robustness Analysis ertheless, the trends shown in Figure 4.16 provide novel insight into the robustness of wave pipelining and surfing with respect to transient supply noise.  4.5  Summary  Sources of timing uncertainty can be classified based on their time-scale. Slow effects such as DC supply variation and temperature affect mean arrival times, but fast effects such as crosstalk and high-frequency supply noise are critical for wave-pipelined and surfing links because they cause cycle-to-cycle variation in skew and jitter which can lead to intersymbol edge interference and incorrect sampling. In unshielded links, crosstalk may add about ±30ps of jitter per stage; applying minimum-width shields reduces the jitter to ±6ps per stage. Shielded wires are important to minimize the impact of crosstalk. Supply noise is modelled as a slow DC component and a fast transient component with a variable standard deviation. Random simulations demonstrate that DC noise affects mean latency but has very little impact on cycle-to-cycle jitter as a percentage of latency; high-frequency supply noise has a very strong effect on cycle-to-cycle jitter. Simulations of wave-pipelined and surfing circuits show that pulses narrower than about 160ps may be dropped. In the range from 160ps to 250ps, pulses in the wave pipelined circuit are attenuated in width; in the surfing circuit, their width is restored. Simulations of an eight-stage link demonstrate that wave pipelined circuits allow jitter and skew to accumulate with the number of stages in a link. In comparison, surfing circuits are able to maintain a constant level of jitter and skew regardless of link length, as long as the transient noise is not too large. Fitting these simulation measurements to square-root curves allows for an estimate of the amount of jitter and skew for a link of arbitrary length. If the jitter and skew are assumed to be normally distributed, then bit error rate can be estimated for a given  69  Chapter 4. Robustness Analysis operating speed. For a fifty-stage link with a probability of error of 10−20 , surfing can operate at about 2.5 to 3.2 Gbps, while wave pipelining can operate around 1 to 2 Gbps. If the link is only ten stages long, surfing operates at the same speed, but wave pipelining can operate at a faster rate, around 2.1 to 3.2 Gbps.  70  Chapter 5 Simulation and Evaluation The longest link simulated in the previous chapter is eight stages long. In this section, links of up to fifty stages are simulated to verify correct operation. The main analysis is a measurement of the maximum throughput of wave pipelining and surfing relative to link length and supply noise. Latency, area, and power are also evaluated. Unless otherwise stated, simulations are conducted at the SS process corner at a temperature of 125o C to provide pessimistic operating conditions.  5.1  Throughput  The purpose of this section is to show the relationship between throughput and the number of stages in the link under a variety of possible noise conditions. Surfing is expected to have a constant throughput-vs-length curve, while wave pipelining’s throughput is expected to degrade as the link length is increased.  5.1.1  Methodology  The simulation setup is identical to Figure 4.13, except that the number of stages in the link is increased. As before, each stage has an independent power supply. The source generates a sixteen-bit data pattern on the data line and generates a clock signal with one edge per data bit. The data pattern is [0 1 0 1 0 0 0 1 0 0 1 1 1 0 1 1], which is chosen because it includes positive and negative pulses, runs of three zeros and ones, and rapid switching at the beginning.  71  Chapter 5. Simulation and Evaluation  Table 5.1: Supply voltages used Mean µ (V) Std dev σ (mV) 3σ range 0.95 15 0.91 – 1.00 0.90 15 0.86 – 0.95 0.85 15 0.81 – 0.90 0.95 15 0.91 – 1.00 0.95 30 0.86 – 1.04 0.95 45 0.82 – 1.09 For simplicity, the simulations do not include SER/DES blocks; data validity is ascertained with waveform measurements. To simulate a DES receiver, the waveforms are inspected as follows: the clock signal is delayed at the output by one half of the bit period. The voltage on the data line is measured at the midpoint of the clock edge. If the measured voltage is greater than half the supply, a 1 is recorded; if the voltage is less than half the supply, a 0 is recorded. A transmission is defined as successful if the recorded 16-bit pattern matches the input pattern. Determining the maximum throughput is essentially a brute force exercise: the circuit is simulated at progressively faster speeds until the transmission is unsuccessful. For small links, the bit period is changed at a resolution of 10ps; for circuits of thirty stages or more, the step size is 50ps to reduce simulation time. The maximum throughput obtained from such a sweep constitutes one trial. Ideally, many trials would be simulated to provide many different possible combinations of random supply noise. In practice, one trial can take more than a day of CPU time, especially if the link is thirty stages or longer. Typically it was only possible to perform about two or three trials for each circuit. Successive trials almost never produced a different result, so even if more simulation time was available, it would be unlikely to significantly affect the results. Six different supply voltage noise scenarios are tested; they are listed in Table 5.1. The intent is to separately vary both transient noise and DC supply noise to determine the impact of each on performance. 72  Chapter 5. Simulation and Evaluation  5.1.2  Results  Figure 5.1 shows the results for wave pipelining and surfing. The curves are coarse because of the large step size and limited simulation time. According to the simulation results, wave pipelining achieves throughputs exceeding 5Gbps for short links (ten stages or less), but throughput degrades with link length due to accumulation of skew and jitter; for a 50-stage link, the throughput ranges from 2 to 4 Gbps. Surfing is slower, around 3Gbps, but does not degrade with link length and is insensitive to high-frequency supply noise. Notice, however, that surfing is vulnerable to changes in DC supply noise; this is because changes in the DC supply affect the delay through the feedback loop, which in turn alters surfing’s operating point. Waveforms showing the clock and data signals recovered at the end of a fifty-stage link are shown in Figure 5.2. Figure 5.3 has snapshots of the clock at various points through the link. Note how pulses are evenly spaced in surfing, but some unevenness is evident in wave pipelining. These results demonstrate successful operation, but they show higher throughputs than the reliability analysis in the previous chapter. This makes sense because of the small number of trials. In general, the results can be taken to be a demonstration of correct operation which is robust for a limited number of noise scenarios. If millions of trials could be performed, then the curves in Figure 5.1 should shift lower. To get an accurate assessment of reliability, a large number of simulations and an accurate noise model are required. Without a good noise model, it may be more realistic to fabricate a test chip with controllable on-chip noise sources.  5.1.3  Comparison  In Figure 5.4, throughput results from the medium noise level of µ = 0.95V, σ = 30mV are compared. The throughput of a 16-bit parallel bus, wave pipelining, and 73  Chapter 5. Simulation and Evaluation Wave pipelined speed vs transient noise 9  Vdd σ=15mV Vdd σ=30mV Vdd σ=45mV  8  6 5 4 3  7 6 5 4 3  2  2  1  1  0 0  10  20 30 Number of stages  40  0 0  50  (a) Wave pipelining – Transient noise  6 5 4 3  7 6 5 4 3 2  1  1 10  20 30 Number of stages  40  50  50  Vdd µ=0.95 Vdd µ=0.90V Vdd µ=0.85V  8  2  0 0  40  Surfing (practical) speed vs DC noise  Max speed (Gbps)  Max speed (Gbps)  7  20 30 Number of stages  9  Vdd σ=15mV Vdd σ=30mV Vdd σ=45mV  8  10  (b) Wave pipelining – DC noise  Surfing (practical) speed vs transient noise 9  Vdd µ=0.95 Vdd µ=0.90V Vdd µ=0.85V  8 Max speed (Gbps)  7 Max speed (Gbps)  Wave pipelined speed vs DC noise 9  0 0  (c) Surfing (practical) –Transient noise  10  20 30 Number of stages  40  50  (d) Surfing (practical) – DC noise  Figure 5.1: Throughput simulation results  surfing is plotted. For the parallel bus, throughput is taken to be the inverse of latency multiplied by the number of wires. Note that the surfing and wave pipelining throughput assumes only one serial data wire and one clock wire; the throughput could be doubled by adding a second data wire. Both practical and ideal cases are plotted in all cases to show how much throughput is lost due to noise. For wave pipelining and surfing, the ideal throughput is calculated by simulating the circuits with no noise, while the practical results are the simulation results mentioned above (µ = 0.95V, σ = 30mV ). The absence of noise means margins can be reduced and throughput is higher. For the parallel bus, the 74  Chapter 5. Simulation and Evaluation  Figure 5.2: Waveforms showing data at the end of a 50-stage link  throughput is the reciprocal of the link latency multiplied by the number of wires in the bus. The ideal throughput is derived from the latency under typical conditions (TT), while the practical throughput is taken from simulations at the SS corner. Additional required margin due to noise and bus skew is ignored, so the parallel bus throughput is slightly optimistic. Because surfing is less sensitive to noise than wave pipelining, this graph conclusively demonstrates that surfing offers superior throughput compared to wave pipelining for links longer than about 40 stages. In the 20 to 40 stage range, there is no clear winner, but if more trials are performed, wave pipelining would degrade more. Surfing is thus highly likely to outperform wave pipelining in this range as well. Wave pipelining appears to offer very high throughput for very short links. This is evident in both the ideal and practical curves. In the ideal case, the throughput approaches just under 6Gbps for very long links, but is higher for shorter links. This curve is not flat at 6Gbps because the intersymbol interference that limits throughput 75  Chapter 5. Simulation and Evaluation  Figure 5.3: Waveforms showing stage-by-stage propagation  causes small amounts of attenuation that accumulate after many stages. For short links, faster speeds are achievable. The same is true in the practical case. Therefore, it may be possible to construct a long wave-pipelined link out of several short ones in such a way that skew and jitter do not accumulate. This idea will be explored further later in Section 5.3. Next, link latency will be addressed.  5.2  Latency  Serial communication suffers from a latency penalty compared to parallel communication, simply because serial bits arrive sequentially while parallel bits arrive all at once. If the latency of the link is high and the bit period is small, then the penalty of 76  Chapter 5. Simulation and Evaluation Comparison of schemes  Max reliable throughput (Gbps)  12 Wave pipelining (ideal) Wave pipelining (practical) Surfing (ideal) Surfing(practical) 16−bit bus (ideal) 16−bit bus (practical)  10  8  6  4  2  0 0  10  20 30 Number of stages  40  50  Figure 5.4: Throughput comparison for all schemes  serialization should be reasonably small. The purpose of the analysis in this section is to quantify this latency penalty relative to a parallel link, and also to compare the latency of wave pipelining against surfing.  Methodology The latency of each interconnect stage is measured from simulation. The delay through one wave pipelined stage is about 123ps, while the delay through one surfing stage is about 156ps; the difference is due to the extra logic in the surfing stage. Using the bit periods which correspond to the throughput measurements in Section 5.1.2 for a supply voltage with µ = 0.95V and σ = 30mV, the latency of a link of arbitrary length can be estimated. Surfing has a constant throughput of 3.2Gbps which corresponds to a period of 310ps; wave pipelining’s throughput varies from about 7.7  77  Chapter 5. Simulation and Evaluation  Link latency (normalized)  Normalized transit time 10 9 8 7 6 5  Wave pipelining Surfing Regular wire  4 Bit 32  3  Bit 16 2  1 0  Bit 8 Bit 1 10  20 30 Number of stages  40  50  Figure 5.5: Latency normalized to a regular wire, VDD µ = 0.95V, σ = 30mV  Gbps (130ps) down to 2.8 Gbps (360ps) depending on the length of the link. The arrival time of bit i at stage j is simply i · T + j · l, where T is the bit period and l is the latency of one stage. For example, in surfing interconnect operating with a bit period of T = 310ps with a stage latency of l = 156ps, the arrival time of the first four bits at stage 10 is 1.87ns, 2.18ns, 2.49ns, and 2.80ns. In contrast, a wave-pipelined link with T = 200ps and l = 123ps has arrival times of 1.43ns, 1.63ns, 1.83ns, and 2.03ns. For longer links, wave pipelining must operate at a slower bit period, but surfing can maintain the same speed.  Results The arrival time of a bit on a regular FPGA wire is equal to the arrival time of the first bit in a wave-pipelined link. To show the latency penalty of the serial schemes, the estimated arrival time of bits 1, 8, 16, and 32 is calculated relative to the arrival time of the first bit. The results are shown in Figure 5.5; note the log scale on the vertical axis.  78  Chapter 5. Simulation and Evaluation Relative to the first bit, the eighth bit in a serial word has 1.5X to 2X higher latency with surfing. The sixteenth bit has a 1.8X to 4X latency penalty. Longer words have even longer penalties and are probably not practical; instead, two or more data wires should be used. Both serial schemes have higher latency compared to a parallel bus, but wave pipelining tends to be a bit faster than surfing, since its nominal latency is lower. Surfing is able to make up a bit of the difference for very long links and long words because wave pipelining is forced to operate at a slower bit rate, incurring a higher serialization penalty.  5.3  High-throughput wave pipelining  The results in this chapter indicate that wave pipelining is likely able to run at relatively high throughputs for short links (i.e., 10 stages or less). This naturally suggests that higher throughput would be achievable if a long wave pipelined link could be composed of many short links without further accumulation of skew and jitter. To achieve this, a circuit is required which can remove accumulated jitter and skew by realigning the data and timing edges. This could be accomplished by deserializing and then serializing again through spare SER and DES blocks in a CLB, but the latency penalty would be high. Instead, an asynchronous FIFO [28] can be used. In this FIFO, each bit in the serial stream is recovered and retransmitted with the appropriate spacing between edges. This also removes unwanted jitter and skew. Internally, the FIFO needs enough storage to ensure that data is not lost if there is a mismatch between the incoming data rate and the outgoing data rate; ten bits is probably more than enough. Figure 5.6 shows the impact on latency when an asynchronous FIFO is inserted every ten stages. The curves assume the latency through the FIFO is 400ps, which is quite long for an asynchronous FIFO. A staircase pattern is evident due to the  79  Chapter 5. Simulation and Evaluation  Link latency (normalized)  Normalized transit time 10 9 8 7 6 5  Wave pipelining Wave pipelining + FIFOs  4 Bit 32  3 2  1 0  Bit 16 Bit 8 Bit 1 10  20 30 Number of stages  40  50  Figure 5.6: Latency with 400ps FIFOs at 5Gbps  extra latency, but overall latency improves on long links because of the higher bit rates. Designing such a FIFO should be straightforward; its implementation is left for future work.  5.4  Area  In Chapter 3 , a system-level area estimate demonstrated 10% to 60% area savings if parallel interconnect is replaced with serial interconnect. Here, the area required for wave pipelining, surfing, and regular interconnect is compared. These results exclude CLB overhead and savings in switch patterns, so they do not provide a complete picture of total area. However, the area for sending and 8-bit and 16-bit word are shown in Table 5.2. Area is measured in minimum width transistor areas according to the methodology in [65], which is described in detail in Appendix B. Appendix B also contains more detailed tabulations of CLB and serial interconnect area. For wave pipelining and surfing, 16-bit words are assumed to use two serial data 80  Chapter 5. Simulation and Evaluation  Table 5.2: Area tabulation # transistors Transistor area (min. transistor widths) Wave pipelining One data wire 140 262 Two data wires 186 369 Surfing One data wire 207 402 Two data wires 259 532 Regular wire 8 bit bus 592 1216 16 bit bus 1184 2432 wires carrying 8 bits each. Note that configuration bits, and in the case of surfing, delay elements and edge-to-pulse converters, are shared between data wires, so the additional data wires requires only the addition of a multiplexor and set of buffers. A few interesting conclusions are evident from this information: • Surfing requires about 50% more area than wave pipelining. • Compared to an 8-bit parallel bus, a wave-pipelined serial bus uses about 20% of the area, while a surfing serial bus uses about 33% of the area. Also, referring to the tabulations in Appendix B, we can conclude: • The area cost of a serializer and deserializer is roughly equivalent to the area of a single 8-bit parallel bus interconnect stage. • LEDR encoding can be added to a serializer and deserializer for about a 4% area penalty.  5.5  Energy  Serial communication is likely to incur a significant power penalty, for two reasons: 1. Activity increases when a parallel word is serialized, because temporal correlation between successive words is destroyed. 81  Chapter 5. Simulation and Evaluation 2. A 100%-activity clock signal is sent alongside the data. In other words, the number of transitions required to send a serial word is significantly higher than it is for a parallel word. LEDR encoding can be applied to wave-pipelined scheme to reduce the total activity of the clock plus data wire to 100%. Surfing cannot use LEDR encoding.  Methodology Energy is measured in HSPICE by integrating the current drawn from each stage’s power supply. Separate power supplies are applied to both the data and clock lines so that the usage of each can be estimated independently. In wave pipelining they are equal, but in surfing there is additional logic in the clock line which will cause increased power consumption. The total measured energy is divided by the number of transitions to approximate the energy per transition. This is a first-order analysis; as such, only dynamic power is considered, not leakage.  Results Measurements of the dynamic energy per transition are shown in Table 5.3, separated into clock and data lines. Assuming the parallel wires have a nominal activity of 12.5%, Table 5.4 estimates the energy required for an 8-bit and a 16-bit transfer. Serial data wires are all assumed to have an activity of 50%. For wave pipelining, LEDR encoding may be applied so that the combined clock and data activity is 100%. The 16-bit transfers in wave pipelining and surfing are assumed to use one clock wire and two data wires. LEDR encoding is only applied to the first data wire in such cases. The power penalty is large, ranging from 6X to 8X for wave pipelining with LEDR, from 8X to 12X for unencoded wave pipelining, and from 9.4X to 14.7X for surfing. The 100% activity clock is the main reason for the large penalty. 82  Chapter 5. Simulation and Evaluation  Table 5.3: Energy per transition measurements (fJ) Clock line Data line Parallel bus 62 Wave pipelining 62 62 Surfing 82 64 Table 5.4: Energy estimates for 8b and 16b transfers Energy per 8-bit transfer Energy per 16-bit transfer Energy(fJ) Normalized Energy(fJ) Normalized Parallel bus 62 1.0 124 1.0 Wave 744 12.0 992 8.0 Wave/LEDR 496 8.0 744 6.0 Surfing 912 14.7 1168 9.4  5.6  Summary  Simulations of links up to fifty stages confirm that surfing’s maximum throughput is insensitive with respect to link length, but wave pipelining’s throughput degrades as the link length increases. Surfing achieves a throughout of just over 3Gbps; wave pipelining achieves about 5Gbps for ten-stage links and just under 3Gbps for fiftystage links. Because the noise sources are random, and only a limited number of trials can be simulated, extremely rare pessimistic events are excluded. Hence, robust behavior at these rates is not guaranteed, but the simulations do show insight into the relative performance of each link and suggest that surfing is more likely to be robust regardless of the underlying noise model. Wave pipelining tends to have better latency than surfing. Relative to the first bit, the eighth bit in a serial word has 1.5X to 2X higher latency with surfing. The sixteenth bit has 1.8X to 4X higher latency. Longer words have even longer penalties and are probably not practical; instead, two or more data wires should be used. Because wave pipelining works much better for shorter links, very high throughput might be achieved if a long link is broken into several short ones. This could be accomplished by inserting specialized FIFOs into the link every ten stages to resyn-  83  Chapter 5. Simulation and Evaluation chronize clock and data, removing accumulated jitter and skew. The overall latency penalty of such a scheme in shown in Figure 5.6 to be minimal. Full investigation of this technique is left for future work. The area of a surfing interconnect stage is about 50% higher than the area of a wave-pipelined interconnect stage. Compared to an 8-bit parallel bus, a surfing link achieves a 67% savings, while a wave pipelined link achieves an 80% savings. The area cost of a single 8-bit serializer and deserializer circuit is about the same as the area of an 8 bit parallel bus interconnect stage; since each tile contains many such interconnect stages, the overhead to add serializers and deserializers to a tile is thus relatively small. Relative to a parallel bus with 12.5% activity, wave pipelining incurs an 8X to 12X power penalty, while surfing incurs a 9.4X to 13.7X power penalty. The extra power in surfing is due to the extra logic it requires. The wave pipelining penalty can be reduced to 6X to 8X if LEDR encoding is employed. The analysis in this chapter shows that reliable bus communication is possible. Accurate noise models and long simulation times are a problem for predicting reliability and performance of these links. Power overhead is also significant, suggesting future work should focus on this as well.  84  Chapter 6 Summary and Conclusion 6.1  Summary  To take advantage of the relatively high bandwidth of FPGA wires and relatively low clock speed of FPGA designs, high-throughput pipelined interconnect was examined. An example of a serially interconnected FPGA was proposed; high-level area estimation shows a potential reduction in interconnect area of 10% to 60%, depending on certain architectural parameters such as serial word length and the amount of serial wiring resources relative to regular wires. Because the serial interconnect is required to operate at a speed much higher than the slow user clock, alternatives to traditional synchronous or register-pipelined interconnect were explored. The use of a shared high-speed global interconnect clock was considered but ruled out due to power concerns. Asynchronous signalling was discarded because of its incompatibility with FPGA interconnect structures as well as power and latency concerns. Wave pipelining and surfing remain as two promising techniques which allow for interconnect pipelining without a global clock. In these schemes, a source-synchronous clock generated at the source with a ring oscillator is sent on a second wire alongside the data so that the data can be sampled at the receiver. The minimum separation between successive bits was measured to be approximately 160ps for FPGA interconnect in a 65nm technology, which corresponds to a throughput of 6.3Gbps. This represents the cutoff point beyond which pulses are  85  Chapter 6. Summary and Conclusion dropped; it is not a reliable operating point. The throughput is limited by the wide multiplexors in the datapath. This is a significant concern for high-throughput interconnect in FPGAs which does not occur in ASICs. The impact of crosstalk was measured and found to be significant; delay uncertainty due to crosstalk has a standard deviation of about σ =12ps per stage if the wires are not shielded. Adding shields almost completely removes crosstalk; an impact of up to σ = 1.7ps delay uncertainty per stage was observed. The results strongly suggest that high-bandwidth interconnect should be shielded. Wave pipelining and surfing (and similar schemes) are vulnerable to high-frequency supply noise which causes cycle-to-cycle skew and jitter. A reliability model was developed to allow for the independent investigation of the impacts of DC noise and high-frequency noise on delay. DC noise is found to have little impact on skew and jitter, while high frequency noise is found to have a strong impact. Using the reliability model, wave-pipelined interconnect was shown to accumulate √ both skew and jitter stage-by-stage following a n curve with respect to the number of stages, n. Surfing interconnect was demonstrated to attenuate both jitter and skew, making it independent of the number of stages. Using normally-distributed models of jitter and skew, the probability of error of wave pipelining and surfing was estimated as a function of throughput. Surfing is able to achieve a reliable throughput (bit error rate ≈ 10−20 ) of between 2.5 to 3.2 Gbps. Wave pipelining’s reliable throughput is between 1 to 2 Gbps for a fifty stage link and between 2.1 and 3.2 Gbps for a ten stage link. Surfing’s throughput is relatively stable with respect to the desired probability of error. Wave pipelining can operate at much higher throughputs if the reliability requirements are relaxed, but must operate at correspondingly slower throughputs if the requirements are more stringent. In general, surfing is be less sensitive to link length, level of reliability, and the underlying noise model. HSPICE simulations of a fifty-stage link confirm the findings obtained from the  86  Chapter 6. Summary and Conclusion reliability models. HSPICE results suggest higher throughputs than the reliability model predicts are possible, but this may be limited by the number of simulation runs that can be practically performed. Surfing’s throughput is demonstrated to be superior for long links exceeding forty stages, but if reliability is taken into account surfing is likely superior even for twenty-stage links. Both surfing and wave pipelining offer large throughput improvements over a regular wire; for a thirty-stage link, one serial data wire can match the throughput of a sixteen-bit parallel bus while using one-sixth to one-ninth of the area. Serialization of words creates a latency penalty because the bits arrive sequentially instead of all at once. Relative to the first bit, the eighth bit in a serial word has 1.5X to 2X higher latency with surfing. The sixteenth bit has 1.8X to 4X higher latency. The penalty is higher for short links because the amount of time it takes for the bits to arrive sequentially is larger relative to the link latency. Wave pipelining has lower latency than surfing under most circumstances because surfing has extra logic which causes a 33ps penalty per stage. These latency results do not include latency hiding that is sometimes possible by starting early transmission of the first bit before the last bit is ready. Also, the latency of very large bulk data transfers is dominated by the link bandwidth, not the wire latency. The area of a surfing interconnect stage is about 50% higher than the area of a wave-pipelined interconnect stage. Compared to an 8-bit parallel bus, a surfing link achieves an 67% savings, while a wave pipelined link achieves an 80% savings. The area cost of a single 8-bit serializer and deserializer circuit is about the same as the area of an 8 bit parallel bus interconnect stage. LEDR encoding adds a 4% area penalty to the SER/DES circuit. Relative to a parallel bus with 12.5% activity, wave pipelining incurs an 8X to 12X power penalty, while surfing incurs a 9.4X to 13.7X power penalty. The extra power in surfing is due to the extra logic it requires. The wave pipelining penalty  87  Chapter 6. Summary and Conclusion can be reduced to 6X to 8X if LEDR encoding is employed. Note that parallel wires with random bits, such as encrypted data, will have a much higher activity of 50%. This causes a four-fold increase in the parallel bus power, but no change in the serial power.  6.2  Interpretation of results  Given the initial target of 6Gbps, the 2 to 3Gbps throughputs achieved in this work are reasonable and represent a tenfold increase over the typical wire utilization in an existing FPGA. System-level estimates of area savings are modest in most cases, while latency penalties are moderate and power penalties are severe, which suggests that converting existing FPGA interconnect from parallel to serial may not be appropriate for general applications. However, the design is ideal for specialized applications which require very high throughput and low area. There is utility in the methods employed in this thesis, especially given recent academic interest in high-throughput signalling in FPGAs and in networks-on-chip. The analysis herein demonstrates that reliability and noise concerns are a major limiting factor for wave-pipelined designs. Usually, this is not satisfactorily addressed in wave-pipelining research. Noise effects need to be included in analytical models of wave-pipelining, since these have a strong impact on performance. Moreover, designers who wish to implement high-throughput signalling in a programmable network should be cautioned to carefully consider multiplexor design, as this was shown to be a limiting factor in throughput. In addition, the required use of multiplexors in the signal path eliminates as options most of the high-performance analog signalling techniques recently devised for on-chip serial links.  88  Chapter 6. Summary and Conclusion  6.3  Future work  Several areas for future work were identified throughout this thesis. They are listed below.  6.3.1  Low-power design  The large power overhead is going to limit the practical use of source-synchronous serial interconnect. Accordingly, power-reduction techniques, or alternative designs that use less power, are the first priority for future research. It may be possible to reduce the interconnect power through more exotic signalling techniques, such as lowswing signalling, if such techniques can be made compatible with FPGA multiplexors.  6.3.2  Architectural exploration  Several new architectural parameters were proposed and the area impact was estimated for a few possible configurations of bit-serial interconnect. The proposed new architecture raised several questions, including the routability impact of replacing regular wires with serial wires, the number of serializers and deserializers needed per block, the optimal serial word length, and the connectivity between serializers or deserializers and block inputs or outputs. These questions should be answered with a proper architectural exploration including a benchmarking component. Doing so requires the development of serial-capable datapath-oriented CAD tools and benchmark circuits. Serial interconnect may also enable the use of bit-serial FPGA logic structures which may be more tolerant of latency, and offer large area gains.  89  Chapter 6. Summary and Conclusion  6.3.3  Noise and reliability modelling  The noise model used in this thesis is non-physical because it is unbounded. It would be extremely useful to have more information about what supply noise looks like in a real FPGA, especially in an FPGA with high-speed serial interconnect. Such information would enable better models of jitter and skew, and therefore better estimates of reliability and more aggressive performance targets.  6.3.4  Silicon implementation  The work in this thesis has been entirely based on HSPICE simulations in a 65nm CMOS process. Every effort was taken to make the simulations as thorough and as pessimistic as possible, but the results need to be validated with a silicon implementation. The implementation should include programmable delays so that the serial bit rate can be adjusted, and should also include realistic noise sources which can be controlled by the user. Laboratory measurements of bit error rates and power supply noise could then be undertaken to conclusively demonstrate reliability, and also improve noise models.  6.3.5  Wave-pipelined FIFO implementation  Throughput and latency results in Chapter 5 suggest that a long wave-pipelined link could operate at high throughput if asynchronous FIFOs are inserted every ten stages to remove accumulated skew and jitter. The design of such FIFOs should be relatively straightforward; it remains to determine the details of their design, and to verify the predicted gains.  90  References [1] I. Kuon and J. Rose, “Measuring the gap between FPGAs and ASICs,” Proc. ACM/SIGDA Int. Symp. on Field Programmable Gate Arrays, pp. 21–30, 2006. [2] M. Saldana, L. Shannon, J. Yue, S. Bian, J. Craig, and P. 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Stolt, Y. Mittlefehldt, S. Dubey, G. Mittal, M. Lee, J. Friedrich, and E. Fluhr, “ Design and Implementation of the POWER6 Microprocessor,” IEEE Journal of Solid-State Circuits, vol. 43, pp. 21–27, 2008. [53] B. Curran, E. Fluhr, J. Paredes, L. Sigal, J. Friedrich, Y.-H. Chan, and C. Hwang, “Power-constrained high-frequency circuits for the IBM POWER6 microprocessor,” IBM Journal of Research and Development, vol. 51, pp. 715–731, 2007. [54] S. Hollis and S.W. Moore, “RasP: An area-efficient, on-chip network,” Int. Conf. on Computer Design, 2006, pp. 63–69, 2006. [55] G. Lemieux, E. Lee, M. Tom, and A. Yu, “Directional and Single-Driver Wires in FPGA Interconnect,” IEEE Int. Conf. on Field-Programmable Technology, pp. 41–48, 2004. [56] C. Yingmei, W. Zhigong, and Z. Li, “A 5ghz 0.18-µm CMOS technology PLL with a symmetry PFD,” Int. Conf. on Microwave and Millimeter Wave Technology, vol. 2, pp. 562–565, 2008. [57] V. V. Deodhar, “Throughput-centric wave-pipelined interconnect circuits for gigascale integration,” Ph.D. dissertation, School of Electrical and Computer Engineering, Georgia Institute of Technology, Atlanta, GA, USA, 2005. [58] D. Lewis et al., “The Stratix II logic and routing architecture,” Proc. ACM/SIGDA Int. Symp. on Field Programmable Gate Arrays, pp. 14–20, 2005.  97  References [59] E. Lee, G. Lemieux, and S. Mirabbasi, “Interconnect driver design for long wires in field-programmable gate arrays,” IEEE Int. Conf. on Field Programmable Technology, pp. 89–96, 2006. [60] R. Ho, K. W Mai, and M. A Horowitz, “The future of wires,” Proceedings of the IEEE, vol 89, pp. 490–504, 2001. [61] R. R. Dobkin, A. Morgenshtein, A. Kolodny, and R. Ginosar, “Parallel vs. serial on-chip communication,” Proc. Int. Workshop on System Level Interconnect Prediction, pp. 43–50, 2008. [62] P. Sedcole and P. Y. K. Cheung, “Within-die delay variability in 90nm FPGAs and beyond,” IEEE Int. Conf. on Field Programmable Technology, pp. 97–104, 2006. [63] S. Kirolos, Y. Massoud, and Y. Ismail, “Power-supply-variation-aware timing analysis of synchronous systems,” IEEE Int. Symp. on Circuits and Systems, pp. 2418–2421, 2008. [64] E. Alon, V. Stojanovic, and M.A. Horowitz, “Circuits and techniques for highresolution measurement of on-chip power supply noise,” IEEE Journal on SolidState Circuits, vol. 40, pp. 820–828, 2005. [65] V. Betz, J. Rose, and A. Marquardt, Architecture and CAD for Deep-Submicron FPGAs, Springer, 1999.  98  Appendix A Auxiliary Circuit Designs This appendix provides circuit schematics for auxiliary components mentioned in the thesis.  A.1  Serializer and Deserializer  The serializer and deserializer circuits are an important part of the system, but their design is relatively straightforward. The circuits are simply shift registers, except some slight modifications are made to reduce latency penalties. Serial data arriving at the receiver may be shifted out to the parallel deserializer outputs as the bits arrive; it is not necessary to wait for the entire word. Likewise, parallel serializer inputs will be shifted out one at a time, which means the last bits sent in the word have a later deadline. Circuit schematics of serializer and deserializer circuits are provided in Figure A.1 and timing diagrams are provided in Figure A.2. Each is based on a simple shift register design. A serial bus width of M = 4 is shown, but the designs can be trivially altered to support other bus widths. Their operation is briefly described below. The clock generator is a simple pausible ring oscillator which is controlled by an enable signal [27, 37]. Some time after a user clock event, the signal Go must be asserted to indicate that the serial data is ready and the serial transfer should begin. The ring oscillator generates M consecutive clock pulses. The lower bank of flip flops are all initialized low except for the left-most; with each clock tick, the one starting 99  Appendix A. Auxiliary Circuit Designs Go  clk3  D0 D1  Clk_en D2 D3  Data out  delay clk0  0 Ring oscillator  D Q rh  1  D Q  clk1  0  D Q  rl  clk2  0  0  D Q  rl  rl  clk3  D Q  0  Clk out  D Q  rl  rl  reset  Pulse  (a) Serializer with clock generator D0  D1  D Q  D2  D Q  clk0  D3  D Q  clk1  D Q  clk2  clk3  Data in Clk in 0  D Q  1  rh  D Q  0  rl  D Q rl  0  D Q  0  rl  D Q  0  rl  reset Edge to pulse  (b) Deserializer  Figure A.1: Serializer (with clock generator) and deserializer circuits  at the output of the left-most flip flop will shift down the bank. Each of the parallel input bits is connected to the data line through an M -bit multiplexor which is controlled by clk0, clk1, clk2, and clk3. With each clock pulse, one input bit is cut off and the next one is attached. At the same time, a clock edge is transmitted through the channel. The purpose of this design as opposed to a simple parallel-load shift register is to allow for the possibility that the earlier data bits might be ready before the later bits. If this is the case, the transmission can begin early instead of waiting for the  100  Appendix A. Auxiliary Circuit Designs Go  Clk_en  Data in  B0  B1  B2  B3  Pulse  Clk in clk0  Pulse clk1  clk0 clk2  clk1 clk3  Data out  B0  B1  B2  B3  clk2  clk3  Clk out  D0  B0  D0  D1  B1  D1  D2  B2  D3  B3  B0  B1  D2  B2  D3  B3  Input data setup time deadlines  (a) Serializer  (b) Deserializer  Figure A.2: Serializer and deserializer timing diagrams  last bit. This should remove some of the serializer latency penalty. The deserializer operates in a very similar manner. Because both edges of the clock accompany data tokens, an edge-to-pulse circuit is used to clock the shift register. Nominally, data and clock edges arrive at the same time; the latency through the edge-to-pulse converter and through the flip flops provides sampling margin. If more margin is required, then the receiver can be easily adjusted so that clock edges arrive at the midpoint of the data tokens. Similar to the serializer, the deserializer emits the first bit as soon as it is ready, allowing downstream logic to begin early computation.  A.2  Edge-to-pulse converter  The edge-to-pulse converter circuit, shown in Figure A.3, is a self-resetting XOR gate. The delay through the three inverters determines how long the pull-down network is  101  Appendix A. Auxiliary Circuit Designs on; the delay through the self-reset loop determines the width of the output pulse. A keeper is attached so that the internal node remains high during quiet periods when no edges arrive. Self−reset loop 1x  Keeper  1x  4x  0.5x 4x outT  1x  1x in  4x  4x 1x  1x  1x  2x  4x  4x outF  1x 4x  Figure A.3: Edge-to-pulse converter circuit  A.3  Delay element  The delay element used in the surfing circuit is shown in Figure A.4. It is a simple inverter chain with 3fF load capacitances attached to increase the delays. The delay can be altered by either changing the number of stages in the chain, or changing the load capacitances. Note that the delay element must support fast rise times or else it will limit throughput. The capacitance therefore cannot be increased too much or else the rise time will be too slow. in  1x  1x  1x  1x  1x  3fF  3fF  3fF  3fF  3fF  1x  out  Figure A.4: Delay element  102  Appendix B Area Calculation Details B.1  Area measurement methodology  Area is measured in minimum width transistor areas according to the methodology in [65] in which the equivalent area of a transistor t is found as follows, where m is a minimum-width transistor:  Area(t) = 0.5 +  DriveStrength(t) 2 · DriveStrength(m)  (B.1)  Since drive strength is a linear function of transistor width, we can express the area of a transistor in terms of its width. Assume a minimum-width transistor has width W = 1. If the width W of transistor t is expressed in units of minimumtransistor-widths, then the area is simply:  Area(t) = 0.5 +  W 2  (B.2)  This model was developed by examining the layout rules of TSMC 0.35µm and LSI Logic 0.4µm processes, but it is unlikely to have changed significantly with newer processes and thus should still be suitable for first-order estimates.  B.2  System-level area calculations  In Section 3.4, a system-level area estimation showed potential interconnect area savings of 10 to 60%, depending on the serial bus width, M , and the percentage of 103  Appendix B. Area Calculation Details  Table B.1: Summary of area savings (min-transistors) Pre-serialization area Input muxes 12416 Output muxes/buffers 19200 Total 31616 Post-serialization area Input muxes 7168 Single wire output muxes/buffers 9600 Serial wire output muxes/buffers 3224 SERDES area 7784 Total 27776 Savings 12% Table B.2: Pre-serialization area Parameter description Expression a Total channel width Nc b Wire length in tiles L Input mux connectivity fc,in Number of inputs per block Ni Mux width per input Wmux = Nc ∗ fc,in Mux transistors per input c Tin = 2 ∗ (Wmux ) − 2 + 6 ∗ log2 (Wmux ) Total input mux transistors Ain = Ni ∗ Tin Number of outputs per block No d Channel wires driven per block Nc /L Transistor area per output mux/buffer Ao Total output transistor areae Aout = No ∗ Ao Total interconnect area Atotal = Ain + Aout  Value 512 4 0.15 64 77 194 12416 32 128 150 19200 31616  a  Includes horizontal and vertical. Roughly based on Altera Stratix III device. Ignore shorter and longer wires for simplicity. c Assuming 2 ∗ w − 2 transistors for the mux and 6 transistors per SRAM cell [5]. d Because wires are staggered to make layout tileable, 1/L of all wires will begin at a given point. Assumes wires are only driven at their beginning; other wires pass straight through. e See Table B.4. b  wires carrying serial data, Ps . For example, if a bus width of M = 8 was used, and Ps = 0.25 (one quarter) of the wires were serial, then a 7% area savings resulted. The savings for this particular example are summarized in Table B.1; Tables B.2 and B.3 show how the area was tabulated. Assumptions are stated in the tables using footnotes.  104  Appendix B. Area Calculation Details  Table B.3: Post-serialization area Parameter description Expression Bus width M Percent serial wires (out of 1.0) Ps Percent single wires 1 − Ps Single wires in channel Nc ∗ (1 − Ps ) Serial wires in channel Nc ∗ Ps /M Input mux connectivity fc,in Revised mux width per input Wmux = Nc ∗ (1 − Ps ) ∗ fc,in Revised mux transistors per input Tin = 2 ∗ (Wmux ) − 2 + 6 ∗ log2 (Wmux ) Revised total input mux transistors Ain = Ni ∗ Tin Single channel wires driven per block Nc ∗ (1 − Ps )/L Area per single output mux/buffer Ao,single Total single output area Aout,single = Ao,single ∗ Nnew ∗ (1 − Ps )/L Serial channel wires driven per block Nnew ∗ (Ps )/L Area per serial output mux/buffera Ao,serial = 272 + 131 ∗ M/8 Total serial output area Aout,serial = Ao,serial ∗ Nnew ∗ (Ps )/L b Number of deserializers Ndes = Ni /M c Transistors per deserializer Tdes = 160 + 54 ∗ M d Deserializer mux transistors Ndes ∗ M ∗ 8 Total deserializer area Ades = Ndes ∗ Tdes + Ndes ∗ M ∗ 8 e Number of serializers No /M f Transistors per serializer Tser = 138 + 54 ∗ M Serializer mux transistors Nser ∗ M ∗ 8 Total serializer area Aser = Nser ∗ Tser + Nser ∗ M ∗ 8 Total SERDES area Aser + Ades  Value 8 0.5 0.5 256 32 0.15 39 112 7168 64 150 9600 8 403 3224 8 592 512 5248 4 570 256 2536 7784  a  Assuming surfing interconnect, 272 per clock wire and associated circuitry + 131 per data wire, assuming each data wire carries 8 bits. See also Table B.4. b Assume enough deserializers are present to provide 100% of block outputs serially. c From circuit in AppendixA; also tabulated in Table B.4. d Assume a 2-1 mux (8 transistors) connects each deserializer input to two block outputs. e Enough to furnish 100% of inputs from serial buses. f Includes clock generator.  105  Appendix B. Area Calculation Details  Table B.4: Area tabulation Component # trans. Trans. area CLB (per bit) SER DES Clock gen. Base total LEDR enc/dec SILENT enc/dec CLB (8 bit bus) Base total LEDR enc/dec SILENT enc/dec Total w/ LEDR Total w/ SILENT Wave pipelining 2×MuxBuffer 8×Config bits Total Surfing Delay Edge2Pulse 2×MuxBuffer 8×Config bits Total Regular wire 1×MuxBuffer 8×Config bits Total  B.3  34 + 26/bit 79 + 26/bit 26 139 + 52/bit 24 24/bit  64 + 54/bit 160 + 54/bit 74 298 + 108/bit 42 42/bit  555 30 192 579 747  1162 54 336 1204 1498  92 48 140  214 48 262  12 43 104 48 207  25 68 261 48 402  26 48 74  104 48 152  Block-level area tabulation  A detailed tabulation of the area of each component in CLBs and interconnect stages is provided in Table B.4.  106  Appendix C Bounded Worst-Case Timing Uncertainty In Chapter 4, the use of worst-case bounds on timing uncertainty was claimed to lead to unrealistically conservative designs; this claim was used to justify the development of probabilistic models of timing uncertainty. The implications of using worst-case bounds are described briefly in this appendix. Assume the time separation between consecutive edges is a random variable with a mean µ equal to the nominal bit period, and consider two cases: 1. Normal: The edge separation varies about the mean with σ = 10ps 2. Bounded: The edge separation is constrained within ±3σ = 30ps (these are likely optimistic bounds). √ In the normal case, the edge separation at stage i has a standard deviation of σ i (this was demonstrated in Section 4.3). In the bounded case, the edge separation at stage i is bounded within ±3σ · i. For the bounded case, we require that the nominal period equals the worst-case timing uncertainty plus the minimum pulse width. For the normal case, assume we require that the nominal period be a very pessimistic ten standard deviations away from the cutoff, leading to a probability of error on the order of 10−23 . Figure C.1 shows the estimated minimum bit period of the normal and bounded models. Simulation results from Section 5.1 are provided for comparison12 . 12  The simulation shows much better performance because it experienced a small amount of noise compared to the 10σ prediction.  107  Appendix C. Bounded Worst-Case Timing Uncertainty 1800 1600  Bounded Normal (10σ) Simulation  Minimum bit period (ps)  1400 1200 1000 800 600 400 200 0 0  10  20 30 Link length (stages)  40  50  Figure C.1: Comparison of normal and bounded models  Both normal and bounded models are pessimistic with respect to the simulation, but the normal model is much closer to the observed result. The normal model is already quite pessimistic and could probably be relaxed. For the bounded model, variations of ±30ps were actually observed in simulation, so it is difficult to justify relaxing the bounds; however, the worst case scenario (30ps degradation occurring at all stages) is very unlikely. A probabilistic model is a much more useful way of analyzing multi-stage links.  108  

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