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Design and analysis of supply-noise-insensitive all-digital phase-locked loops Yuan, Chen 2018

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DESIGN AND ANALYSIS OF SUPPLY-NOISE-INSENSITIVE  ALL-DIGITAL PHASE-LOCKED LOOPS Chen Yuan  B. Eng., Xidian University, China, 2012  A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF  MASTER OF APPLIED SCIENCE in THE FACULTY OF GRADUATE AND POSTDOCTORAL STUDIES (Electrical and Computer Engineering)  THE UNIVERSITY OF BRITISH COLUMBIA (Vancouver)  January 2018  © Chen Yuan, 2018 ii  Abstract Phase-locked loops (PLLs) are widely used in communication and digital systems to generate high frequency clocks by multiplying a low-frequency reference clock. Scaling of complementary metal-oxide-semiconductor (CMOS) technology over the last decade has benefitted digital circuits by shrinking their size and reducing their power consumption. On the other hand, it has posed challenges for analog design because of the decreasing power supply voltage and output impedance of transistors. Therefore, an all-digital PLL (ADPLL) becomes increasingly preferable over its conventional analog counterparts in terms of area and design flexibility. PLLs employ an oscillator locked to the phase and frequency of the reference clock. An LC oscillator utilizes an inductor (L) to filter noise, but on-chip inductors require large area and need specific thick metal layers for low loss. Compared to LC oscillators, ring oscillators are more suitable for ADPLL implementation since they occupy smaller area and are compatible to digital CMOS processes without a thick-metal layer option. However, the oscillation frequency of a ring oscillator is determined by the propagation delay of the delay-cells, and thereby very susceptible to power supply noise. In fully-integrated systems, switching of large-scale digital circuits can create large supply ripples and degrade the noise performance of the PLL output. Low dropout (LDO) regulators as well as some cancellation techniques have been adopted in prior-art to mitigate the supply sensitivity of ring-oscillator based ADPLLs. However, these techniques suffer from supply voltage headroom, noise penalty, and design complexity.   In this thesis, a low-complexity supply-noise-insensitive ADPLL is proposed that does not degrade the supply voltage headroom, and operates over a wide range of supply-noise amplitude. Fabricated in a 65nm CMOS process, the ADPLL achieves ~ 45 mV of tunable supply-noise-iii  insensitive range where the frequency pushing is less than 10%, operating at 850 mV supply. With the tuning range from 1 GHz to 1.4 GHz, the ADPLL achieves 16 ps integrated jitter at 1.25 GHz output frequency and consumes 2.73 mW of power. iv  Lay Summary  CMOS process scaling poses challenges for analog design, while benefits digital design. Therefore, an all-digital phase-locked loop with an area-efficient ring oscillator is preferable to implement in a fully-integrated digital system to provide clocking signal. However, ring oscillators are inherently sensitive to supply noise, of which performance can be degraded by supply ripples existing in large-scale digital systems. Therefore, supply-noise sensitivity suppression or cancellation techniques should be adopted in ring-oscillator all-digital phase-locked loops. Existing techniques suffer from supply voltage headroom, noise penalty, and design complexity. In this thesis, a low-complexity supply-noise-insensitive ADPLL is proposed, which maintains supply-noise insensitivity over a wide-range supply-noise magnitude without degradation of supply voltage headroom.    v  Preface This Thesis is an original intellectual product of the author Chen Yuan.  All the work presented henceforth was conducted in the System-on-Chip (SoC) Laboratory at the University of British Columbia, Point Grey campus.  vi  Table of Contents Abstract .......................................................................................................................................... ii Lay Summary ............................................................................................................................... iv Preface .............................................................................................................................................v Table of Contents ......................................................................................................................... vi List of Tables .............................................................................................................................. viii List of Figures ............................................................................................................................... ix List of Abbreviations .................................................................................................................. xii Acknowledgements .................................................................................................................... xiv Chapter 1: Introduction ................................................................................................................1 1.1 Analog Phase-Locked Loop ............................................................................................ 3 1.2 All-Digital Phase-Locked Loop ...................................................................................... 5 1.3 Research Objective ......................................................................................................... 7 1.4 Thesis Outline ................................................................................................................. 7 Chapter 2: Background .................................................................................................................9 2.1 Phase Noise and Jitter ..................................................................................................... 9 2.2 LC and Ring Oscillators................................................................................................ 10 2.3 Supply-Noise Sensitivity of Ring-Based ADPLLs ....................................................... 13 2.4 Prior Art ........................................................................................................................ 16 2.4.1 Supply-Noise Suppression/Regulation ..................................................................... 16 2.4.2 Supply-Noise Cancellation ....................................................................................... 18 Chapter 3: Proposed Supply-Noise-Insensitive DCO ...............................................................21 vii  3.1 Evolution of the Oscillator Core ................................................................................... 21 3.2 Capacitor Bank with Bridging Capacitor ...................................................................... 28 3.3 Digitally Controlled Resistor Bank ............................................................................... 30 Chapter 4: Supply-Noise-Insensitive ADPLL ...........................................................................31 4.1 Bang-Bang Phase Detector ........................................................................................... 31 4.2 Proportional-Integral Based Digital Loop Filter ........................................................... 32 4.3 Multi-Modulus Divider ................................................................................................. 32 Chapter 5: Measurement Results ...............................................................................................34 5.1 Measurement Setup ....................................................................................................... 34 5.2 PCB Design ................................................................................................................... 35 5.3 DCO Measurement ....................................................................................................... 36 Chapter 6: Conclusion .................................................................................................................47 Bibliography .................................................................................................................................48  viii  List of Tables Table 2-1 Comparison of supply-noise mitigating techniques in ring oscillators ........................ 20 Table 5-1 DCO phase noise (PN) with clean VDD ...................................................................... 37 Table 5-2 PN measurements under different supply noise conditions ......................................... 43 Table 5-3 ADPLL performance summary .................................................................................... 45 Table 5-4 Comparison to prior-art ring-based ADPLLs ............................................................... 46  ix  List of Figures Figure 1-1 Block diagram of QUALCOMM snapdragon 835 [1]. ................................................. 1 Figure 1-2 A typical wireline transceiver. ...................................................................................... 2 Figure 1-3 Block diagram of a wireless transceiver. ...................................................................... 3 Figure 1-4 A CP-based analog phase-locked loop. ......................................................................... 4 Figure 1-5 Timing sequence diagram for a locked PLL. ................................................................ 4 Figure 1-6 A conventional all-digital PLL block diagram.............................................................. 5 Figure 1-7 A standard digital design flow. ..................................................................................... 6 Figure 2-1 Output spectrum of a (a) noiseless and (b) noisy oscillator. ......................................... 9 Figure 2-2 An illustration for different jitter definitions. ............................................................. 10 Figure 2-3 (a) A conventional LC-VCO topology. (b) LC-tanks occupy large on-chip area, as shown in this representative die micrograph [20]. ........................................................................ 11 Figure 2-4 (a) Single-ended ring oscillator. (b) Oscillation waveform at each node. .................. 12 Figure 2-5 Intrinsic gate capacitance as a function of (a) gate-source bias, Vgs, and (b) drain-source bias, Vds [22]. ............................................................................................................................... 14 Figure 2-6 Impact of supply noise on ADPLL. ............................................................................ 14 Figure 2-7 Supply sensitivity of 3-stage inverter ring oscillator. ................................................. 15 Figure 2-8 ADPLL supply-noise suppression with LDOs. ........................................................... 16 Figure 2-9 ADPLL supply noise suppression with embedded regulation techniques. ................. 17 Figure 2-10 (a) Ring VCO with current-source based cancellation. (b) Ring ADPLL with supply-noise cancellation and calibration. ................................................................................................ 19 x  Figure 3-1 A 2-stage differential ring oscillator with inverter delay cells and latches: (a) Conventionally-drawn, and (b) redrawn for clarity. ..................................................................... 22 Figure 3-2 Supply sensitivity analysis of differential ring oscillator. ........................................... 22 Figure 3-3 (a) A 2-stage ring oscillator with inverter delay cells and latches loaded by passive resistors, ........................................................................................................................................ 23 Figure 3-4 Simulated frequency pushing versus supply voltage for oscillator ............................. 24 Figure 3-5 (a) Supply insensitive ADPLL with background calibration. ..................................... 25 Figure 3-6 (a) Proposed supply-noise-insensitive oscillator with a resistor-triode load. ............. 27 Figure 3-7 Supply sensitivity curve of the proposed oscillator (a) in comparison to an oscillator with resistor-loaded inverter latch delay cells, and (b) as a function of bias setting .. ............... 27 Figure 3-8   Phase noise of proposed DCO in comparison to the conventional DCO shown in Figure 3-1. ................................................................................................................................................ 28 Figure 3-9 (a) DCO schematic with capacitor bank. (b) Detailed illustration of the capacitor bank........................................................................................................................................................ 29 Figure 3-10 (a) Schematic and (b) AC-response of the DCR used to generate VDD. ............... 30 Figure 4-1 Block diagram of proposed supply-noise-insensitive ADPLL. .................................. 31 Figure 4-2 (a) Block diagram of a BBPD. (b) Timing diagram for BBPD input and output. ...... 32 Figure 4-3 A 5-stage MMD with re-timing DFF. ......................................................................... 33 Figure 5-1 Die micrograph of the proposed supply-noise-insensitive ADPLL. ........................... 34 Figure 5-2 Measurement setup...................................................................................................... 35 Figure 5-3 Designed PCB for prototype measurements. .............................................................. 36 Figure 5-4 Measured phase noise plots at minimum and maximum oscillation frequency. ......... 38 xi  Figure 5-5 Supply sensitivity measurement with varying (a) supply voltage for a specific DCR bit supporting maximum insensitivity range, (b) DCO frequency tuning bits, (c) supply voltage for another DCR bit supporting minimum insensitivity range, (d) DCR bits. ................................... 41 Figure 5-6 Calculated frequency pushing based on measurement results. ................................... 41 Figure 5-7 Impact of supply-noise on closed-loop ADPLL phase noise. ..................................... 42 Figure 5-8 Effect of 50 mVpp sinusoidal supply noise at 10 MHz on measured jitter and spurs: 44 Figure 5-9 (a) Supply noise spurs and (b) period jitter, as a function of the supply noise frequency........................................................................................................................................................ 45  xii  List of Abbreviations ADPLL All-digital phase locked loop BBPD Bang-bang phase detector  CMOS Complementary metal-oxide-semiconductor CP Charge pump DAC Digital to analog converter dB Decibel dBc Decibels relative to the carrier dBm Decibel-milliwatt DCO Digitally-controlled oscillator  DCR Digitally-controlled resistor DFF D flip flop DLF Digital loop filter FPGA Field programmable gate array HDL Hardware description language LF Loop filter MMD Multi-modulus divider PD Phase detector P-I Proportional-integral PJ Period jitter PLL Phase-locked loop xiii  PN Phase noise RX Receiver SerDes Serializer-Deserializer SMA Subminiature version A  SOC System-on-chip SSA Signal source analyzer TDC Time-to-digital converter TIE Time interval error TX Transmitter VCO Voltage-controlled oscillator                     xiv  Acknowledgements First and foremost, I want to express my deepest gratitude to my advisor Prof. Sudip Shekhar. I would not have finished my master studies without his continuous guidance, help and support. His insight into circuits design guided me towards the successful tape-out and measurement. His dedication to research and students always motivates me to overcome the obstacles both in my master study and personal life. His support is endless in every aspect of my graduate study at UBC - from research, to coursework, internship and thesis writing. I feel so fortunate to have worked with him for two and half years.  I would like to acknowledge Prof. Shahriar Mirabbasi and Prof. Mieszko Lis for serving as my thesis committee members. I thank for their time, interests and valuable comments on my thesis and defense. I also want to thank Prof. Shahriar Mirabbasi for instructing Analog Integrated Circuits Design. It is one of the most important courses for my research and his excellent instruction helps me build a solid foundation for my research and further career.  I want to thank Roozbeh Mehrabadi and Dr. Roberto Rosales for their daily technical support in the SOC lab. I would like to thank my colleagues in Sudip’s group and SOC lab. It is their help and company that makes my work and life more pleasant.   I want to deliver my gratitude to all of my friends. I would also like to thank my bestie, Ms. Fan Wu, who shares sorrows and joys in good days and bad days.  Finally, I would like to express my deepest gratitude to my parents and all my family members for loving, caring, supporting and tolerating me for more than twenty years.  1  Chapter 1: Introduction High quality clock signals are necessary in most of the synchronous digital systems, as well as for wireless and wireline communication systems. In digital systems, clock signals are needed to ensure synchronicity between different circuits, and prevent race conditions. In a modern microprocessor, synchronous circuits are clocked using a high frequency signal provided by a clock multiplier or a frequency synthesizer, which generates a variable multiple of a fixed reference frequency from a crystal oscillator. Figure 1-1 shows a block diagram of a Qualcomm Snapdragon 835 mobile platform system-on-chip (SOC), in which different blocks of a smartphone are integrated in one single chip [1]. In an SOC, each of the building block needs one or several clock signals, necessitating several frequency synthesizers.   Figure 1-1 Block diagram of QUALCOMM snapdragon 835 [1]. In high-speed wireline communications, such as data communication between a processor and memory, a precise clock signal is necessary for synchronization and serialization of parallel data at the transmitter (TX) and deserialization of serial data at the receiver (RX). Figure 1-2 shows a block diagram for a typical wireline Serializer-Deserializer (SerDes) transceiver including the channel. 2   Figure 1-2 A typical wireline transceiver. In wireless communication, a TX-RX pair, called a transceiver, is allocated a certain frequency channel to communicate. At the TX, the desired information is modulated on a carrier frequency and transmitted precisely at a specific frequency channel, with minimum leakage to neighboring channels to prevent interference. At the RX, the demodulation frequency is precisely tuned to the same carrier frequency so as to demodulate the desired information from the received signal. Figure 1-3 shows a block diagram for a typical wireless transceiver. The frequency tuning is done using a frequency synthesizer that is able to generate a variable multiple of a fixed reference frequency from a crystal oscillator.  3   Figure 1-3 Block diagram of a wireless transceiver. 1.1 Analog Phase-Locked Loop A phase-locked loop (PLL) is adopted in a frequency synthesizer to provide a high frequency clock signal by multiplying a low frequency clock from a low-noise crystal oscillator. The frequency multiplication must be done in such a way so as to add minimum extra noise, consume low power, and occupy small on-chip area.  Figure 1-4 shows one of the most popular implementation for a PLL – a charge-pump (CP) based analog PLL [2]. It is composed of a phase-frequency detector (PFD), a CP, a loop filter (LF), a voltage controlled oscillator (VCO) and a frequency divider. The PFD detects the phase difference between reference clock signal and divided signal, and generates a pulse with the width proportional to the phase difference. The CP then injects or sinks current from LF by turning on the up or down switch. The LF filters out the ripples in the output current of CP and converts the current to a voltage that controls the oscillator frequency of the VCO. The output of the VCO is 4  the desired signal. Its output is also divided by the frequency divider, so as to align the frequency and phase of reference signal with the frequency and phase of divided signal. The negative feedback in the loop drives the PLL to a “lock”, with the frequency and phase difference between the reference clock and divider output driven to zero. Since the phases of the VCO output and divider output are aligned, VCO output phase is also aligned with that of the reference clock. Hence the name, phase-locked loop. Figure 1-5 shows a timing sequence diagram for a locked PLL (divider ratio = 5).   Figure 1-4 A CP-based analog phase-locked loop.  Figure 1-5 Timing sequence diagram for a locked PLL.  5  1.2 All-Digital Phase-Locked Loop With shrinking feature sizes driven by CMOS process scaling, it is becoming increasingly harder to maintain the performance of analog circuits. CMOS scaling is increasing device mismatches, leakage current, and short channel effects, all of which often necessitate extra area, power consumption and design efforts to overcome. On the contrary, digital circuits benefit from process scaling because of lower power, higher speed and smaller area. Large loop filters in analog PLLs also require large silicon area. Therefore, it is desirable to replace analog circuits with their digital counterparts.   Figure 1-6 A conventional all-digital PLL block diagram. A simplified schematic for an all-digital phase-locked loop (ADPLL) is shown in Figure 1-6. It consists of a time-to-digital converter (TDC), digital loop filter (DLF), digitally controlled oscillator (DCO) and frequency divider. The TDC senses the phase error between the reference clock (Ref) and divider output (Div), and generates the digital output bits proportional to the phase error. The DLF filters the output of the TDC and generates multiple-bits of digital outputs to tune the frequency of the DCO [3]. In addition to the advantage of digital circuits over their analog counterparts due to CMOS process scaling, an ADPLL also has other advantages. The coefficients of DLF can be 6  reconfigured easily, which facilitates dynamic performance optimization. The DFL does not need huge capacitors, which saves a large area. The DLF and even the whole ADPLL can be implemented using standard digital design flow, from high-level hardware description language (HDL), to gate-level connections and automatic place and route (APR) to final physical layout, as shown in Figure 1-7. This facilitates design portability [4].   Figure 1-7 A standard digital design flow. 7  1.3 Research Objective The main objective of this research is to implement a supply-noise-insensitive ADPLL in a standard CMOS process. In large digital systems, ripples resulting from switching of digital circuits perturb the power supply of ADPLLs. TDCs and DCOs are based on delay cells and therefore sensitive to supply noise. This degrades the noise performance of ADPLLs.  Several techniques have been proposed to mitigate the supply noise sensitivity of DCOs and ADPLLs. These include the use of supply noise suppression using low-dropout regulators (LDOs) [5]–[8] and embedded regulation [9]–[12], or supply noise cancellation [13]–[19]. Nevertheless, a digital friendly design for DCOs and ADPLL that is able to reliably operate over large excursions on the power supply without significant overhead in any of the power, performance or area (PPA) metrics is still being actively researched. In this thesis, we present a DCO that uses an inverter-based delay cell with a resistor-triode load and a weak cross-coupled latch cell to cancel the supply noise. Together with a bang-band phase detector (BBPD), the scaling-friendly ADPLL is able to operate reliably over 50 mVpp of power supply excursions with good rejection and minimal overhead to the PPA metrics.   1.4 Thesis Outline The thesis is organized as follows. Chapter 2 provides the background information on this research. The basics of phase noise and jitter are introduced. A comparison between LC oscillator and ring oscillator is presented that reveals the advantages of utilizing the latter in ADPLLs. The supply noise sensitivity of ring oscillators is also analyzed. The limitations of prior-art in noise-insensitive DCO topologies and the associated challenges and tradeoff are briefly described. 8  Chapter 3 elaborates the design of the proposed supply-noise-insensitive DCO. Chapter 4 describes other building blocks in the proposed ADPLL and system-level considerations. Chapter 5 presents the measurement setup and result, followed by conclusions and a brief discussion on future work in chapter 6  9  Chapter 2: Background 2.1 Phase Noise and Jitter The output of an ideal oscillator can be expressed as 𝑥(𝑡) = 𝐴𝑐𝑜𝑠𝜔𝑐𝑡. In the frequency domain, the output is represented by an impulse in the spectrum, as shown in Fig. 2-1(a). However, various noise sources in the oscillator perturb its output, and result in the output expressed as 𝑥(𝑡) = [𝐴 + 𝑎𝑛(𝑡)]𝑐𝑜𝑠[𝜔𝑐𝑡 + ∅𝑛(𝑡)] , where an and ∅𝑛  represent the noise perturbing the output amplitude and phase, respectively. Therefore, the spectrum is broadened by the noise, as shown in Figure 2-1 (b). Often, an oscillator is followed by a limiting buffer which saturates its output amplitude, thereby making its amplitude noise less important.  Phase noise can be quantitated by measuring the power in a unit bandwidth of the spectrum at an offset ∆𝑓 from the carrier (oscillating) frequency, and normalizing the result to the carrier power, i.e., the peak of the spectrum. The phase noise value varies with different frequency offsets, which reflects the purity of the oscillator output in frequency domain.  Figure 2-1 Output spectrum of a (a) noiseless and (b) noisy oscillator. In the time domain, a noiseless clock should have a constant time period and cross the threshold level always at the exact time interval which equals the clock period. However, noise sources perturb the clock signal and result in deviations in the crossings from idea time interval.   The 10  deviation is called jitter, which can be represented in several ways, as shown in Figure 2-2. Period jitter (PJ) is given by the time period of each clock cycle. Cycle-to-cycle jitter measures how much the clock period changes between any two adjacent cycles. Time interval error (TIE) measures how far each edge of the clock varies from its ideal position.    Figure 2-2 An illustration for different jitter definitions.  2.2 LC and Ring Oscillators Oscillators are used as VCOs or DCOs, depending on the control being driven by a voltage amplitude or a digital word. There are two types of oscillators which are used in GHz PLLs in CMOS – LC-oscillator and ring oscillator. A LC-oscillator uses the resonance of a LC-tank to set the oscillation frequency (Figure 2-3(a)). Compared to a ring oscillator, an LC-oscillator has the advantage of low phase noise due to the high quality factor (Q-factor) of inductors. However, the inductor occupies much larger area than active circuits. A state-of-art die photo is shown in Figure 2-3(b) [20]. To reduce loss and obtain a high Q-factor, a thick top metal layer is mandatory, which is often not available in a standard digital CMOS process. The extra mask 11  increases the cost. Furthermore, the inductor may lead to coupling and interactions with other inductors, substrate and adjacent circuits.  Figure 2-3 (a) A conventional LC-VCO topology. (b) LC-tanks occupy large on-chip area, as shown in this representative die micrograph [20]. On the contrary, ring oscillators are composed of a chain of active delay cells in positive feedback. Figure 2-4 (a) shows a 3-stage inverter-based ring oscillator.  Each inverter has a 180° phase shift due to its inverting functionality. Each inverter stage also has a pole created by the parasitic resistor and the loading capacitor. The parasitic resistor comes from the series resistance of the transistor in the ON state. Figure 2-4 (b) shows how a transistor can be modeled as a simple switch with an ON-resistance. The loading capacitor can be from the parasitics, or varactors added explicitly to each cell. Figure 2-4 (c) shows the charging and discharging process of an inverter. As the waveforms propagate in the ring, the pole at each stage contributes a frequency-dependent phase shift, from 0°  at DC to 90°  at very large ( ) frequencies. According to Barkhausen’s criteria, the loop phase shift should be an integer multiple of 360° to sustain oscillation at the desired oscillation frequency [21] . Therefore, the phase shift due to 12  each pole should be 60° such that the total phase shift of the loop is (60° + 180°)×3 = 720°. Figure 2-4 (d) shows the oscillation waveform at the output node of each stage. The time period for the oscillation is set by the sum of total time delay in the loop, and therefore proportional to the RC delay per stage.    Figure 2-4 (a) Single-ended ring oscillator. (b) Oscillation waveform at each node. (c) Switching model of transistors. (d) Charging & discharging of an inverter.  13  2.3 Supply-Noise Sensitivity of Ring-Based ADPLLs The parasitic on-resistance and capacitance of a transistor varies with the voltage at its gate (G), source (S) and drain (D). According to (1), the parasitic on-resistance resistance of a transistor in triode-region, Ron, decreases when its gate to source voltage, VGS, increases:  𝑅𝑜𝑛 =1𝜇𝑛𝐶𝑜𝑥𝑊𝐿(𝑉𝐺𝑆−𝑉𝑡)                                                             (1) where  is the carrier mobility, 𝐶𝑜𝑥 is the oxide capacitance, and Vt, W and L are the threshold voltage, channel width and length of the transistor, respectively. Figure 2-5 shows the variation in the parasitic capacitance of a transistor as a function of the terminal voltages, where Cgb, Cgs, Cgd represent gate-to-body, gate-to-source, and gate-to-drain capacitance, respectively. Cgc = Cgb + Cgs + Cgd is the total intrinsic gate capacitance. C0 = WLCox is a simple approximation for total gate capacitance. As shown in Figure 2-4 (a), the source voltages of the transistors are directly affected by variation or noise on the power rails. Thus, the delay of the inverter varies with the supply voltage, and presence of noise on the supply can perturb the output clock signal of ring oscillators and induce jitters. In a large digital system, the switching of digital circuits results in large ripples on the supply rail. The ripples may interfere with the clock circuitry as supply noise, as shown in Figure 2-6.  14   Figure 2-5 Intrinsic gate capacitance as a function of (a) gate-source bias, Vgs, and (b) drain-source bias, Vds [22].  Figure 2-6 Impact of supply noise on ADPLL. Without proper regulation techniques, the supply sensitivity of ring oscillator can be very high. Figure 2-7 shows the simulated output frequency of a three-stage inverter-based ring oscillator. When the supply changes by 50 mV from a nominal VDD = 1 V, the output frequency changes by 125 MHz from a nominal oscillation frequency of 1.3 GHz.  15   Figure 2-7 Supply sensitivity of 3-stage inverter ring oscillator. In addition to the supply-noise-sensitive ring oscillator, a TDC, composed of delay cells, is also sensitive to supply-noise [23]. Thus, without proper regulation, the supply noise degrades the clock signal quality and hence the overall system performance. Therefore, techniques to mitigate supply-noise are necessary for PLLs. 16  2.4 Prior Art 2.4.1 Supply-Noise Suppression/Regulation  Figure 2-8 ADPLL supply-noise suppression with LDOs. LDOs can be used to regulate the supply of the ADPLL, as shown in Figure 2-8. However, fully integrated CMOS LDOs degrade the overall jitter performance of the PLL and require 200~300 mV supply headroom to achieve regulation performance comparable with off-chip (stand-alone) LDOs [7], [17]. It should be noted that it is still challenging for commercial stand-alone LDOs, often fabricated in BiCMOS process to achieve superior performance, to simultaneously achieve high bandwidth for power supply rejection ratio (PSRR) and low output noise. PSRR is defined as the ratio of supply voltage variation over induced output voltage variation. An excellent comparison on the impact of supply noise from two LDOs on the phase noise of a frequency synthesizer is presented in [5]. One [6] has lower output noise and does not degrade the PLL phase noise under a clean linear laboratory supply, while the other [24] degrades the PLL in-band phase noise by 15 dB. However, the former also suffers from 15 dB lower PSRR than the latter at 10 MHz, which may not be sufficient to regulate the PLL under a noisy supply with high frequency 17  ripples. Standalone LDOs and decoupling capacitors increase the overall board area and cost. Furthermore, the bond wires in the supply rail can create ripples as well, because of the fast switching in ring oscillators.  Some ADPLLs use regulation techniques embedded inside the ADPLL to isolate the supply noise from the supply rail of the oscillators as well as the control node [9]–[12]. A simplified schematic is shown as Figure 2-9.  However, similar to LDOs, CMOS process scaling poses challenges to the design of analog regulation circuits and degrades the regulation performance. To properly regulate the control voltage, the bandwidth of regulation circuits should be much larger than the loop bandwidth of the PLL. This creates a trade-off between regulator bandwidth and loop bandwidth. Increasing the regulator bandwidth comes at an expense of power consumption. Limiting the PLL loop bandwidth can affect the suppression of oscillator phase noise. The embedded regulator also has a certain drop-out voltage and limits the maximum achievable control voltage and hence the tuning range of the oscillator. Furthermore, the regulator needs a large decoupling capacitor, which may occupy an area larger than that of the active circuits [9], [10].   Figure 2-9 ADPLL supply noise suppression with embedded regulation techniques.  18  2.4.2 Supply-Noise Cancellation Apart from supply noise regulation, several supply noise cancellation techniques have also been investigated [13]-[19]. Delay cells in conventional ring oscillators have a given sign and magnitude for supply sensitivity, where supply sensitivity can be quantified as frequency pushing – the ratio of relative oscillation frequency variation to relative supply voltage change. It is defined as   Frequency Pushing =  ∂𝑓∂V𝑆𝑢𝑝𝑝𝑙𝑦V𝑆𝑢𝑝𝑝𝑙𝑦𝑓                                              (2) where f is the oscillation frequency, and VSupply is the power supply voltage. For example, an inverter has a positive supply sensitivity. Adding circuitry with sufficient sensitivity, of equal and opposite magnitude, can cancel the overall supply sensitivity. In an analog PLL, a voltage-to-current (V-I) converter following the charge pump is implemented in [13], and this current is fed into a current controlled oscillator (CCO). With a cancellation circuit at the output node of the V-I converter compensating current fluctuations caused by supply noise, the CCO experiences a constant supply current. However, without a calibration, the effectiveness of cancellation is limited by PVT, and the design efficacy is further exacerbated by CMOS process scaling. A similar technique of a V-I converter driving a CCO is also adopted in a digital PLL in [14], but it also lacks any calibrations. A digital background calibration technique is added in [15] to the supply-noise cancellation circuitry (similar to [14]) to overcome PVT variations. But the stacked analog cancellation circuitry has voltage headroom issues and is not suitable for low supply voltage implementation.  Another method to introduce negative supply sensitivity is to shunt the output node of the delay cells to ground using additional transistors in saturation [16]. As shown in Figure 2-10(a), when 19  VDD increases, the current in M1 increases and therefore VB increases accordingly. Consequently, Mn at the output nodes of the delay cells sink more current, resulting in a negative sensitivity due to Mn. If Mn is sized properly, the programmable IB can be adjusted to match the negative sensitivity with the positive sensitivity of the delay cell and achieve supply insensitivity. A similar cancellation circuitry is adopted in the ring oscillator [17], [18] to implement an ADPLL, as shown in Figure 2-10(b). The digital calibration logic controls a digitally controlled resistor (DCR) to generate a deterministic test signal for calibration. The fluctuation in the integral path output of DLF reflects the supply sensitivity of the DCO under injected test signal, and is used by the calibration logic to tune the noise-cancelling current source IB. This approach can ensure the supply insensitivity of ADPLL under various PVT conditions. However, the always-on test signal itself degrades the jitter performance and power consumption. Table 2-1 summarizes the three approaches to address supply noise issue in ring-oscillator based ADPLLs.   Figure 2-10 (a) Ring VCO with current-source based cancellation. (b) Ring ADPLL with supply-noise cancellation and calibration.   20  Table 2-1 Comparison of supply-noise mitigating techniques in ring oscillators  LDO-based regulation/ suppression Embedded  regulation/suppression Noise cancellation Pros Good PSRR  Fully integrated, without  packaging issues  Fully integrated, without packaging issues  Cons Jitter degradation analog-intensive power and area penalty reduced voltage headroom Analog intensive reduced tuning range PLL bandwidth trade-off power overhead Requires calibration analog intensive  21  Chapter 3: Proposed Supply-Noise-Insensitive DCO 3.1 Evolution of the Oscillator Core Consider a 2-stage differential ring oscillator with quadrature outputs as shown in Figure 3-1 (a). Each stage contains a pair of complementary-phase inverters and a latch consisting of two back-to-back inverters [19], [25]. Unlike conventional single-ended ring oscillator with odd-number of inverter stages, this 2-stage ring oscillator can be regarded as a 4-stage single-ended ring oscillator where each stage is coupled to another by the latch, as shown in Figure 3-1 (b). Without the latches, the delay caused by parasitic resistance (Rpar) and capacitance (Cpar) of each stage cannot be 90 at a finite frequency, prohibiting oscillations. Extra delay per stage is provided by the latches to enable 90 phase shift and initiate oscillation. The latch resists the state change below the threshold voltage and accelerates the toggling above the threshold voltage. Its positive feedback can reduce the transition time and thereby reduce phase noise [25]. Furthermore, the latch provides negative supply sensitivity. Increase in the supply of the latch increases the threshold for the latch to change its status. This increases the transition time and reduces the oscillation frequency [19]. The inverter delay cells have positive supply sensitivity, because the RparCpar product of the simple inverter decreases when the supply voltage increases. Unfortunately, the negative sensitivity of latch is much lower than the positive sensitivity of the inverter, as shown in Figure 3-2, and therefore, inadequate for overall supply insensitivity.  22   Figure 3-1 A 2-stage differential ring oscillator with inverter delay cells and latches: (a) Conventionally-drawn, and (b) redrawn for clarity.  Figure 3-2 Supply sensitivity analysis of differential ring oscillator. Further reduction in supply sensitivity can be made by adding a passive resistor, Rpas, at the output node of each inverter, as shown in Figure 3-3 (a) [19]. When the supply voltage increases, the resistance of the inverter decreases while the passive resistor stays constant. The total delay,  (Rpas + Rpar)Cpar, therefore, decreases at first and then tends to saturate. In other words, the positive sensitivity of resistively loaded inverter decreases and then saturates with supply voltage. With Rpar loading the latch, the latch effect results in a larger frequency change, thereby, increasing the negative sensitivity.  An optimal point for the supply voltage can be obtained where the negative 23  supply sensitivity cancels positive supply sensitivity. A drawback of this one-point cancellation technique is that the frequency pushing degrades soon after the deviation of VDD from the optimal point. The frequency pushing degradation calculated from reported data is shown in Figure 3-4, which can be as large as 40% with only 30 mV of excursions from the optimal operating point. A larger supply-insensitive range is needed for variations and noise that is seen on the supply in practical scenarios.    Figure 3-3 (a) A 2-stage ring oscillator with inverter delay cells and latches loaded by passive resistors,  and (b) achieving supply insensitivity at an optimal VDD. 24   Figure 3-4 Simulated frequency pushing versus supply voltage for oscillator  with resistive-loaded inverter-latch delay cells. A background calibration ensures that the DCO works at an optimal supply voltage near zero pushing. The calibration circuity is shown in Figure 3-5, where a digitally controlled resistor is added to tune the supply voltage of DCO, i.e., VDD_DCO. Upon sweeping the resistance of DCR in open-loop operation of the ADPLL, the maximum frequency of DCO can be obtained, where the frequency pushing is also zero. Then the ADPLL closes the loop to start locking process, and the optimal point does not change with the frequency tuning of the DCO.  25   Figure 3-5 (a) Supply insensitive ADPLL with background calibration.  (b) Open-loop supply sensitivity calibration. (c) Closed-loop locking process. To enhance the range of supply insensitivity, the oscillation frequency should be increased when the supply voltage exceeds the zero pushing point. Realizing that it is the load resistor (Rpar) that increases the negative sensitivity of the latch and reduces the positive sensitivity of the inverter, reducing Rpar with increasing supply voltage beyond the optimal point can make the supply sensitivity curve flatter. According to (3), the resistance of a PMOS in triode-region decreases when its gate to source voltage, VGS, increases:  𝑅𝑜𝑛 =  1𝜇𝑝𝐶𝑜𝑥𝑊𝐿(𝑉𝐺𝑆−𝑉𝑇)                                                             (3) 26  where 𝜇𝑝 is the hole mobility, 𝐶𝑜𝑥 is the oxide capacitance, and Vt, W and L are the threshold voltage, channel, width and length of the PMOS, respectively. Thus, a poly resistor–PMOS–poly resistor is added in shunt to the poly resistor Rpar, leading to the proposed DCO design as shown in Figure 3-6 (a), and an equivalent resistance that decreases with increasing supply voltage, as shown in Figure 3-6 (b). Therefore, a supply sensitivity curve which is insensitive over a large excursion of supply voltage is obtained, as shown in Figure 3-7 (a). The PMOS gate bias (VDD) can be tuned digitally to compensate for PVT variations and ensure that the zero pushing point matches the desired supply voltage over a large range, as shown in Figure 3-7 (b). The proposed design does not have supply voltage headroom issue, and is hence suitable for low supply voltage and low power applications. Figure 3-8 shows the simulation results of phase noise of a 2-stage oscillator with and without the resistor-triode load, at the same output frequency (1.25 GHz) and power consumption. At low frequency offset, the phase noise values are identical, being dominated by the flicker noise of active transistors in the delay cells. The thermal noise of additional resistor-triode load affects the phase noise at high frequency offsets - 3 dB and 6 dB at 1 MHz and 10 MHz, respectively. With typical loop bandwidth of PLLs being 100s of kHz to a few MHz, the impact of additional noise to the overall integrated jitter of the PLL remains less than 10%.  27   Figure 3-6 (a) Proposed supply-noise-insensitive oscillator with a resistor-triode load.  (b) Resistance variation of the resistor-triode combination as a function of supply voltage.  Figure 3-7 Supply sensitivity curve of the proposed oscillator (a) in comparison to an oscillator with resistor-loaded inverter latch delay cells, and (b) as a function of bias setting .. 28   Figure 3-8   Phase noise of proposed DCO in comparison to the conventional DCO shown in Figure 3-1. 3.2 Capacitor Bank with Bridging Capacitor To achieve fine tuning, high resolution (DACs) are usually adopted to tune DCOs [4], [10], [14], [15], [17], [18], [19]. However, DACs with high resolutions, i.e., above 13bits are challenging to design, especially in advanced CMOS technology, as well as consume considerable power and area [14], [19]. DACs are also sensitive to supply noise, requiring regulated supply voltage [19].  Therefore, DCOs without DACs can reduce power, area and supply noise sensitivity. A capacitor bank can be used to tune the DCO by switching on different amounts of capacitors in the bank according to input digital bits [7], [26]. To reduce spurs and phase noise, a fine resolution for frequency tuning is required, which needs the capacitance step to be extremely small, sometimes impractical to implement. A sigma-delta modulator can be used to dither the least significant control bits [19], [27], but the quantization noise from dithering may degrade the jitter performance  [28].  A bridging capacitor is used to increase the frequency resolution without reducing the capacitance of the unit capacitor (Cu) [29]. The complete capacitor bank is shown in Figure 3-9 (a), and the 29  schematic and layout of a single unit are shown in Figure 3-9 (b). The capacitor bank is composed of a 6-bit coarse tuning bank and 7-bit fine tuning bank. Due to the bridging capacitor, the equivalent capacitance step of fine bank is reduced by 100, as given by (4): ∆Cfine =CBridge2(Ctotal+CBridge)Cu                                                     (4)      where ∆Cfine, CBridge, and Ctotal are the minimum resolution of the fine-tuning bank, bridging capacitance, and total capacitance including parasitics, respectively. Both banks use identical metal-oxide-metal (MOM) capacitors, with a Cu = 2.5 fF in 1.9  1.7 m2 area. The MOM capacitor has stacked metal layers from M5 to M7, with a floating poly layer to shield coupling with the substrate. A floating, instead of grounded, shielding layer is used to reduce parasitic capacitance [30] and further increase the immunity to substrate noise. A polysilicon shielding layer, with lower conductivity than metal layers, is used to reduce eddy current loss as well as coupling capacitance [31]. The finalized DCO design covers 400 MHz frequency range by coarse tuning and achieve less than 300 kHz frequency resolution by fine tuning. The tuning range can be easily increased by adding more bits of Cu if needed.  Figure 3-9 (a) DCO schematic with capacitor bank. (b) Detailed illustration of the capacitor bank. 30  3.3 Digitally Controlled Resistor Bank The gate voltage of shunt PMOS is biased by a DCR bank [15]. The resistor bank is composed of 64-bits of coarse and 16-bits of fine bank, thermometer-weighted. The gate voltage can be biased from 13 mV to 478 mV with less than 1 mV of resolution. The -3dB bandwidth of the DCR bank is above 383 MHz and thereby sufficient to permit the supply noise fluctuation.   Figure 3-10 (a) Schematic and (b) AC-response of the DCR used to generate VDD. 31  Chapter 4: Supply-Noise-Insensitive ADPLL As shown in Figure 4-1, the proposed supply-noise-insensitive ADPLL is composed of a bang-bang phase detector (BBPD), a DLF, the noise-insensitive DCO, a divider, and a DCR bank to generate the optimal bias voltage for the DCO.  Figure 4-1 Block diagram of proposed supply-noise-insensitive ADPLL. 4.1 Bang-Bang Phase Detector ADPLLs with ultra-low in-band phase noise requirement often employ TDC due to their superior noise performance. However, the delay cells in TDC are sensitive to supply noise. On the other hand, a BBPD has one bit output – if the reference clock is leading, then the output is one, otherwise the output is zero. Therefore, the output of a BBPD is not affected by supply noise. Designing a BBPD also reduces complexity and trade-offs associated with TDC in terms of resolution, mismatch, power and area. In this design, a BBPD is chosen for a low power, supply-noise-insensitive design. The BBPD is designed using standard cells, and the schematic is shown in Figure 4-2 (a). As shown in Figure 4-2(b), the output of BBPD changes its status every rising edge of Div signal. If Ref is leading, then the output of BBPD will be high for the following Div 32  clock cycle starting with the rising edge of Div signal. If Div is leading, then the output of BBPD will be low for this Div clock cycle.   Figure 4-2 (a) Block diagram of a BBPD. (b) Timing diagram for BBPD input and output. 4.2 Proportional-Integral Based Digital Loop Filter A proportional-integral (P-I) based DLF is implemented using the standard digital design flow. Its transfer function can be expressed as in (5). The loop coefficients Kp and Ki are reconfigurable. The internal integrator has 20 bits of which the 13 most significant bits (MSBs) are fed into the DCO as 6 bits of coarse and 7 bits of fine control, as shown in Figure 4-1. H(z) =  𝐾𝐼1−𝑧−1+ 𝐾𝑃                                                             (5) 4.3 Multi-Modulus Divider A multi-modulus divider (MMD) is implemented with a division ratio from 32 to 63, using standard cell latches and AND gates, as shown in Figure 4-3 [32]. The MMD has 5-stages of 2/3 divider cells. Each stage receives a modulus control from the next stage and gives a modulus control to the previous stage to toggle between a division of 2 or 3. All the stages have the same schematic and layout. The modular design reduces the design and layout complexity, as well as increases design flexibility and reusability. With a 5-bit control word, the divider ratio can be 33  expressed as in (6).  A D flip-flop (DFF) is used to re-time the divider output to reduce jitter accumulation.  𝑁 = 25 + 𝐷[4] ∙ 24 + 𝐷[3] ∙ 23 + 𝐷[2] ∙ 22 + 𝐷[1] ∙ 21 + 𝐷[0]                          (6)  Figure 4-3 A 5-stage MMD with re-timing DFF. 34  Chapter 5: Measurement Results 5.1 Measurement Setup The proposed supply-noise-insensitive ADPLL was fabricated in 65 nm CMOS process, with an area of 180×210m2. Figure 5-1 shows the die micrograph of the prototype. The prototype is bonded in a CQFP 44 pin package and soldered on a printed circuit board (PCB) to perform measurements. The measurement setup is shown in Figure 5-2. A source signal analyzer (SSA) provides a clean DC supply, and sinusoidal supply noise generated from an RF signal generator is coupled into the supply through a bias-Tee. This noise-coupled supply is buffered and monitored using an oscilloscope. The reference clock is provided by a signal generator. The output phase noise, jitter and the spectrum are measured using an SSA, a high-speed oscilloscope, and a spectrum analyzer, respectively. An FPGA controls the scan to reconfigure the ADPLL.  Figure 5-1 Die micrograph of the proposed supply-noise-insensitive ADPLL. 35   Figure 5-2 Measurement setup. 5.2 PCB Design A PCB is used to mechanically support and electrically connect chips and passive components such as resistors and capacitors. The pads are used to solder components on the PCB and conductive tracks are used to provide electrical connection. In addition to the packaged prototype soldered on the board, there are also many other components and chips to serve the measurement. LDOs are used to regulate the noisy supply voltages from DC sources and convert them to desired supply voltages for the measurement. Level shifters and Schmitt triggers are used to interface the prototype with the FPGA board for reconfiguration. Since the FPGA board has 3.3 V IO (input/output) ports, while the prototype can only stand 1 V input signal, the level shifters are necessary. The hysteresis feature of a Schmitt trigger is used to prevent metastability due to the inductive bond wires. Headers and subminiature version A connectors (SMAs) are used for the 36  board to exchange signals and power with test equipment. The 2-layer fabricated board is shown in Figure 5-3.   Figure 5-3 Designed PCB for prototype measurements.  5.3 DCO Measurement The performance of stand-alone DCO is measured first. The DLF can be reconfigured as open-loop and digital control bits of the DCO can be set externally. The DCO output frequency ranges 37  from 979 MHz to 1.435 GHz. The measured phase noise (PN) plots at different output frequencies are shown in Figure 5-4 and summarized in Table 5-1: Table 5-1 DCO phase noise (PN) with clean VDD Offset Frequency  (Hz) PN @1.43 GHz (dBc/Hz) PN @1.25 GHz (dBc/Hz) PN @980 MHz (dBc/Hz) 1 k -7.92 -9.45 -10.97 10 k -38.65 -40.38 -42.34 100 k -67.43 -69.43 -70.70 1 M -94.67 -96.50 -97.34 10 M -117.50 -119.77 -120.81 100 M -134.80 -137.71 -137.31       38   Figure 5-4 Measured phase noise plots at minimum and maximum oscillation frequency. 39  The supply sensitivity of DCO is measured by capturing the frequency variation with the supply voltage swept. As shown in Figure 5-5 (a), at the optimal supply voltage of 855 mV, the frequency variation is ~ 0.1% with voltage excursions of 25mV in both directions. As shown in Figure 5-5 (b), the optimal point for the supply sensitivity does not change with frequency tuning using the digital control bits, as long as the gate bias of PMOS remains the same. Figure 5-5 (c) and (d) show the change in the supply sensitivity curve when the gate bias of the PMOS is swept digitally. The optimal point can be adjusted to compensate for PVT variations. As shown in Figure 5-6, there is a 50 mV of supply voltage range where the frequency pushing is less than 10%. 40    41   Figure 5-5 Supply sensitivity measurement with varying (a) supply voltage for a specific DCR bit supporting maximum insensitivity range, (b) DCO frequency tuning bits, (c) supply voltage for another DCR bit supporting minimum insensitivity range, (d) DCR bits.   Figure 5-6 Calculated frequency pushing based on measurement results. 42  The closed-loop characteristics of the ADPLL are measured next. Figure 5-7 shows the phase noise plots under different supply-noise conditions – a and b are phase noise plots at 0% and 20% pushing point, respectively, with 50 mVpp of sinusoidal supply-noise at 10 MHz, and c is the phase noise plot with a clean supply. It can be concluded that when operating at the supply insensitive point, the phase noise plot remain unaffected from its counterpart with the clean supply, except the spurs at the supply noise frequency and its harmonics. The integrated jitter only increases from 16.51 ps to 18.93 ps. But when the ADPLL is operating at the 20% pushing point, a dramatic increase in phase noise as well as integrated jitter is observed, as shown in Table 5-2.   Figure 5-7 Impact of supply-noise on closed-loop ADPLL phase noise.   43  Table 5-2 PN measurements under different supply noise conditions Offset Frequency (Hz) PN @ 20% pushing point (dBc/Hz) PN @ 0% pushing point (dBc/Hz) PN without supply noise (dBc/Hz) 1 k -80.73 -81.51 -85.59 10 k -81.74 -90.54 -90.54 100 k -81.54 -91.44 -90.96 1 M -81.36 -89.01 -89.66 10 M -70.12 -88.52 -104.06 100 M -133.74 -137.10 -136.05 Int. Jitter (ps) (10 k-100 M) 57.08 18.93  16.51  Jitter analysis is done using the Keysight EZJIT plus jitter analysis tool in a DSA-X 93204A high speed oscilloscope. The injected sinusoidal supply noise can be regarded as a deterministic jitter (DJ). With a clean supply, the baseline DJ is 520 fs. When the supply voltage is at the desired 0% pushing point with 50 mVpp of sinusoidal supply noise injected at 10 MHz, the DJ is obtained as 1.2 ps. DJ is degraded to 8.1 ps at the 20% pushing point. The supply noise spur changes from  –10.17 dB to –28.54 dB when the operating point is changed from 20% to 0% pushing, respectively, leading to 18 dB of improvement. This comparison of jitter histogram and spectrum is shown in Figure 5-8. The spur level comparison for different frequencies of supply noise are shown in Figure 5-9 (a). When operating at 0% pushing point, the worst spur level of 15.94 dB is 44  observed when the supply noise frequency is 2 MHz. When operating at 20% pushing point, below 1 MHz, the spectrum indicates that the ADPLL cannot lock in the presence of the supply noise, while it works well when operating at the 0% pushing point. The negative spur level means the spur is higher than the fundamental tone. A good spur suppression is observed when operating the ADPLL at 0% pushing in comparison to 20% pushing. Figure 5-9 (b) shows a similar improvement in period jitter. Table 5-3 gives a summary of the measured performance for the ADPLL prototype, and a comparison to the state-of-the-art is given is shown in Table 5-4.  Figure 5-8 Effect of 50 mVpp sinusoidal supply noise at 10 MHz on measured jitter and spurs: jitter histogram at (a) 0% and (b) 20% pushing; output spectrum at (c) 0% and (d) 20% pushing.  45   Figure 5-9 (a) Supply noise spurs and (b) period jitter, as a function of the supply noise frequency.  Table 5-3 ADPLL performance summary Technology 65 nm Dimension (m2) 210180 Tuning Range (GHz) 1– 1.4 Fout (GHz) 1.25 Supply voltage (mV) 850 Power consumption  DCO: 2.25 Digital: 0.196 Int. Jitter (ps) Clean Supply 16.5 10 MHz, 50 mVpp 18.9 PJ (ps) Clean Supply 1.3 10 MHz, 50 mVpp 1.3 Reference Spur (dBc) 55.94  46  Table 5-4 Comparison to prior-art ring-based ADPLLs   47  Chapter 6: Conclusion A supply-noise-insensitive ADPLL is presented in this thesis. A 2-stage differential ring-oscillator with inverter-based delay cell and weak latches is augmented by a resistor-triode load per stage to attain cancellation of supply sensitivity. The proposed technique does not require analog design techniques, does not reduce voltage headroom, and minimally affects the phase noise only at large frequency offset, where the contribution to the integrated jitter is minimal. A proof-of-concept prototype can withstand 50 mVpp excursions on the supply with less than 10% frequency pushing. 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