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Transformer-enhanced high-performance voltage-controlled oscillators Lightbody, Samuel 2018

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Transformer-enhancedHigh-performance Voltage-controlledOscillatorsbySamuel LightbodyA THESIS SUBMITTED IN PARTIAL FULFILLMENT OFTHE REQUIREMENTS FOR THE DEGREE OFMASTER OF APPLIED SCIENCEinThe Faculty of Graduate and Postdoctoral Studies(Electrical and Computer Engineering)THE UNIVERSITY OF BRITISH COLUMBIA(Vancouver)August 2018c© Samuel Lightbody 2018The following individuals certify that they have read, and recommend tothe Faculty of Graduate and Postdoctoral Studies for acceptance, the thesisentitled:Transformer-enhanced High-performance Voltage-controlled Os-cillatorssubmitted by Samuel Lightbody in partial fulfillment of the requirementsforthe degree of Master of Applied Sciencein Electrical and Computer EngineeringExamining CommitteeSudip Shekhar, Electrical and Computer EngineeringSupervisorShahriar MirabbasiSupervisory Committee MemberChristine ChenSupervisory Committee MemberiiAbstractWe show that, in comparison to an inductor, an asymmetric transformercan improve the quality factor (Q) of an inductor-capacitor (LC) tank whenthe tank loss is dominated by the varactor. Near, and at mm-wave fre-quencies, varactors in complementary metal-oxide-semiconductor (CMOS)processes have significantly lower Q than inductors and transformers. Di-rectly connecting a varactor to the core of an LC oscillator lowers tank Q,and the increased ratio of parasitic capacitance to total tank capacitancelimits frequency tuning range (FTR). Instead, magnetically coupling a var-actor to the oscillator core using an asymmetric transformer, where the coreis connected to the primary and varactor to the secondary, increases tankQ. Furthermore, it permits doubling the varactor bias range and reduc-ing the parasitic capacitance seen at the varactor. Thus, both FTR andPhase Noise (PN) are improved simultaneously. Measurement results fortwo prototypes in 65nm CMOS are presented. A 25 GHz Voltage-controlledOscillator (VCO) shows an FTR of 29.8%, a PN of -106.6 dBc/Hz at 1 MHzoffset, and an FTR-inclusive Figure of Merit (FoMT ) of -195.04 dBc/Hz. A60 GHz self-mixing VCO, where the VCO core at 20 GHz is mixed with itscommon-mode 40 GHz tone, shows an FTR of 18.5%, a PN of -98.9 dBc/Hzat 1 MHz offset, and an FoMT of -193.4 dBc/Hz.iiiLay SummaryThis thesis outlines the design of a new type of Voltage-controlled Oscillator(VCO) using complementary metal-oxide semiconductor (CMOS) technol-ogy. The VCO uses a transformer in its design in place a standard inductorto connect some of its components magnetically. It is shown that this hassome advantages over a normal design in terms of the tuning range of theoscillator as well as the noise generated at frequencies close to the generatedsignal. Two designs are chosen to operate at around 25 GHz and 60 GHz.These designs are then fabricated and measured, and compared to otherpublished works.ivPrefaceAll chapters concerning work on the 20.77 - 28 GHz VCO are based onwork which has been submitted for publication at the Radio FrequencyIntegrated Circuits (RFIC) Conference. Amir. H Masnadi Shirazi, Hor-moz Djahanshahi, Rod Zavari and Shahriar Mirabbasi helped take part infruitful discussions about the direction of the design. I was responsible forthe schematic design, layout and measurement with the help of Dr. SudipShekhar.vTable of ContentsAbstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiiLay Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ivPreface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vTable of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . viList of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viiiList of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ixList of Abbreviations . . . . . . . . . . . . . . . . . . . . . . . . . xiAcknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . xii1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 Prior Art . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21.3 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 Transformer-Based Resonators . . . . . . . . . . . . . . . . . 52.1 Prior Art . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52.2 Asymmetric Transformer Load Operation . . . . . . . . . . . 62.3 Transformer Q-Enhancement . . . . . . . . . . . . . . . . . . 82.3.1 Theory . . . . . . . . . . . . . . . . . . . . . . . . . . 82.3.2 Inductor vs Transformer Q . . . . . . . . . . . . . . . 82.3.3 Optimum condition for transformer-Q enhancement . 112.3.4 Q-enhancement Implementation . . . . . . . . . . . . 142.4 FTR Reduction . . . . . . . . . . . . . . . . . . . . . . . . . 16viTable of Contents3 Varactor Performance Enhancement . . . . . . . . . . . . . . 193.1 Voltage Range Extension . . . . . . . . . . . . . . . . . . . . 193.2 Varactor Q . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203.3 Parasitic Capacitance Reduction . . . . . . . . . . . . . . . . 213.4 Conventional VCO vs Transformer-enhanced VCO . . . . . . 213.5 Low-Frequency Noise to Phase Noise Conversion . . . . . . . 234 Design Considerations and Measurement Results . . . . . 254.1 General Considerations . . . . . . . . . . . . . . . . . . . . . 254.2 Design of 25 GHz VCO . . . . . . . . . . . . . . . . . . . . . 264.3 Design of 60 GHz VCO . . . . . . . . . . . . . . . . . . . . . 274.4 Measurement Results . . . . . . . . . . . . . . . . . . . . . . 295 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36viiList of Tables4.1 Performance Summary and Comparison . . . . . . . . . . . . 30viiiList of Figures1.1 Spectrum showing the necessary (a) clock frequencies for com-mon wireline baudrates, and range covered by 20-28 GHzVCO when combined with a ÷2 and ÷4, (b) wide rangesneeded for 5G NR and 60 GHz wireless communication . . . 22.1 Circuit schematic of a dual-mode VCO . . . . . . . . . . . . . 52.2 (a) Conventional LC resonator, and (b) transformer-enhancedresonator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62.3 Coupled inductor resonators in a (a) series, (b) parallel, and(c) transformer configuration . . . . . . . . . . . . . . . . . . 92.4 Comparison of loaded Q normalized to QP for coupled in-ductors placed in series, parallel, and transformer (XFMR)configurations for (a) QP = QS (b) QP =12QS (c) QP = 2QS 102.5 Comparison of Ψ - Q-enhancement in transformer configura-tion for (a) QP = QS (b) QP =12QS (c) QP = 2QS . . . . . . 122.6 Plots showing the ratio of loaded Q to primary winding Q,QTQp, and of primary winding Q to secondary winding Q,QpQs,as well as ξ for (a) the 25GHz VCO design and (b) the 60GHzVCO design . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152.7 Plot ofΩL,HIGHΩL,LOWvs. fs for (a) the 25 GHz VCO and (b) the60 GHz SMV, showing the placement of fp in each case . . . 173.1 Simulated normalized capacitance of the varactor vs. gate-source voltage across the varactor . . . . . . . . . . . . . . . . 203.2 Loaded Q vs. oscillation frequency for a transformer-enhancedresonator in an VCO operating near 25GHz, a conventionalresonator, and a conventional resonator with an inductor Qincreased by (1 + k) . . . . . . . . . . . . . . . . . . . . . . . 22ixList of Figures3.3 Loaded Q vs. oscillation frequency for a transformer-enhancedresonator in an SMV operating near 60GHz, a conventionalresonator, and a conventional resonator with an inductor Qincreased by (1 + k) . . . . . . . . . . . . . . . . . . . . . . . 223.4 Schematic of simplified transformer network stimulated by avoltage source . . . . . . . . . . . . . . . . . . . . . . . . . . . 244.1 Schematic for the 20 - 28 GHz Class-C VCO . . . . . . . . . 264.2 Schematic for the 51.5 - 62 GHz Class-C Self-Mixing VCO . . 274.3 Plot of simulated QP , QS and QV AR vs. frequency for (a)the 25 GHz VCO and (b) the 60 GHz SMV . . . . . . . . . . 284.4 Plot of simulated k vs. frequency between the primary andsecondary windings of the transformers used in the 25 GHzVCO and the 60 GHz SMV . . . . . . . . . . . . . . . . . . . 294.5 Chip micrographs: (a) 20 - 28 GHz VCO with core area of246 x 473 µm2, and (b) 51.5 - 62 GHz SMV with core area of340 x 500 µm2 . . . . . . . . . . . . . . . . . . . . . . . . . . 314.6 Measured oscillation frequency vs. control voltage for (a) the25 GHz VCO and (b) the 60 GHz SMV . . . . . . . . . . . . 324.7 Measured phase noise of (a) the 25 GHz VCO at 26.45 GHzand (b) the 60 GHz SMV at 59.63 GHz . . . . . . . . . . . . 334.8 Plot of Phase Noise measurements and simulation results at1 MHz offset across the tuning range for the 25 GHz VCOand the 60 GHz SMV . . . . . . . . . . . . . . . . . . . . . . 34xList of AbbreviationsAM Amplitude ModulationCMOS Complementary Metal-Oxide-SemiconductorFOM Figure of MeritFTR Frequency Tuning RangeLO Local OscillatorPM Phase ModulationPN Phase NoiseQ Quality FactorRF Radio FrequencySMV Self-Mixing VCOTR Tuning RatioVCO Voltage Controlled OscillatorXFMR TransformerxiAcknowledgementsI would like to acknowledge my supervisor, Dr. Sudip Shekhar, for hissupport while working on this thesis. Without his guidance this work wouldnot have been possible.I would also like to acknowledge Dr. Hormoz Djahanshahi, Dr. AmirMasnadi Shirazi for many helpful discussions and input into the VCO design.Finally, I would like to acknowledge Rohde & Schwarz for lending testequipment for my measurements, and Roozbeh Mehrabadi and Dr. RobertoRosales for providing CAD and test support.xiiChapter 1Introduction1.1 MotivationNew communication standards to support wireline data rates up to 56Gbaud/s and wireless radios operating at 5G NR and 60 GHz bands re-quire high frequency LO sources with low phase noise (PN). For wirelinestandards, there is often a need to support lower speeds such as 28/10/5Gbaud/s, for which various clock frequencies must be generated using acombination of multiple Voltage-controlled Oscillatiors (VCOs), frequencydividers and/or multipliers [17]. Unfortunately, multiple LC VCOs requiremultiple inductors and frequency synthesizers, and increase silicon area, de-sign, routing and simulation complexity [24].As illustrated in Fig. 1.1(a), a single low-PN LO source with an FTRfrom 20-28 GHz could support data rates at 10/25/28/56 Gbaud/s withonly two frequency dividers. Fig. 1.1(b) shows that similar requirements forlarge frequency tuning range (FTR) with low PN are necessary for wirelesscommunication in the 5G NR bands as well as the 60 GHz ISM band.Low PN and wide FTR are difficult to achieve simultaneously in Comple-mentary metal-oxide-semiconductor (CMOS) VCOs operating at very highfrequencies [24]. Large varactors are needed for wide FTR, but at frequencieshigher than 20 GHz, varactors in CMOS processes suffer from low qualityfactor (Q) [23]. Varactor Q, QV AR, scales inversely to its operating fre-quency, i.e, the oscillation frequency of the VCO, f0, as well as to its size thatdictates the capacitive tuning range CmaxCmin [23]. Switchable capacitor banks,often used to increase the FTR with a smaller varactor [22], do not workwell at high frequencies due to switch loss. Furthermore, while the parasiticcapacitance may remain constant or even increase from larger transistorsfor power gain needed at these frequencies, the total tank capacitance (andinductance) must be decreased to sustain larger oscillation frequencies. Assuch, a higher ratio of parasitic capacitance to variable capacitance becomesnecessary in the tank. These, and other factors detailed in [23], reduce FTRwith low PN, or degrade PN with good FTR. Overall, these VCOs exhibitlower Figure of Merit (FoM) and tuning range inclusive FoMT , defined as11.2. Prior ArtFigure 1.1: Spectrum showing the necessary (a) clock frequencies for com-mon wireline baudrates, and range covered by 20-28 GHz VCO when com-bined with a ÷2 and ÷4, (b) wide ranges needed for 5G NR and 60 GHzwireless communication[23]:FoM = PN − 20log( f0∆f) + 10log(PDC1mW) (1.1)FoMT = FoM − 20log(FTR10%) (1.2)where ∆f is the frequency offset from f0 at which PN is measured, andPDC is the power consumption of the oscillator.In this thesis, we will focus on a transformer enhanced LC-VCO topologyto achieve a better tradeoff between PN and FTR and thus a better FoMT1.2 Prior ArtThere have been multiple attempts to address these issues at mm-wave andnear mm-wave frequencies [1] [8] [9] [28] [23].In [8], the available power gain of the transistors is increased by distribut-ing the gm-cells across a λ/4 transmission line, which acts like a resonant21.3. Overviewload. Excellent PN is achieved, but varactors are still necessary for tuningand only a small FTR is achieved. In [28], a triple-coil transformer-basedload is implemented and two separate oscillator cores are switched in andout to increase the FTR, but the varactors still limit the overall tank-Q. Sim-ilarily, in [1], the tank inductance is switched by changing the eddy currentsin a floating substrate-shield to obtain a large FTR as well as an excellentPN at 10 MHz offset, but the switchable inductor shows a degraded Q inone of the two switched modes, and more importantly, the overall tank-Qis still limited by the varactor. In [9], a magnetically coupled LC networkis excited into odd or even modes by switching negative resistances, anda large FTR is achieved. The PN performance is limited by the Q of thenetwork, which in turn is limited by the QV AR. In [23], the switching coreis operated at 1/3 of the desired frequency to alleviate the issue of low Qpassives, and a self-mixing VCO (SMV) topology to mix the fundamentalfrequency with the second harmonic is used. But the performance is stillburdened by the QV AR.In this work, we propose a method to address the issue of the poor QV AR.There has been an on-going debate regarding the advantage of trans-formers over inductors in terms of Q. Earlier works [14], [3] suggest thata transformer, in comparison to an inductor, can boost the energy storageby virtue of the additional magnetic coupling factor (without adding extraseries resistance), and thus the Q of the spiral. These claims were later re-futed in [11], [2], [16], which proved that transformer based resonators havethe same performance as inductors for the same area, because the spiral in-ductor Q can be boosted using magnetic coupling as well. A formal proof in[16] showed that the PN or FoM remains the same in either case. However,these proofs were provided for a symmetric network, where the Q of theprimary (Qp) or secondary side (Qs) of the transformer were assumed to beequal (Qp = Qs), because the two windings share the same trace width andsimilar metal layers. In this paper, we prove that if the transformer networkis asymmetric because one side is loaded by a varactor (which reduces theeffective Q of that side), a transformer based resonator is indeed superiorin performance to an LC resonator comprising of the same high-Q inductorand low-Q varactor.1.3 OverviewTwo designs are proposed using the transformer topology for the VCO core,one tunable from 20-28 GHz, and the other from 52-62 GHz using an SMV31.3. Overviewtopology. The Thesis is organized as follows: Chapter 2 briefly summa-rizes the theory behind transformer-coupled resonators, highlighting thedifference of our topology from prior-art. Chapter 3 provides the detailsof proposed transformer Q-enhancement technique, followed by the detailsof varactor performance enhancement in Chapter 4. Chapter 5 describes thesuppression in low-frequency noise to PN conversion in the proposed design.The design and measurement results for the two prototypes are presented inChapter 6 and 7, respectively. Chapter 8 provides the concluding remarks.4Chapter 2Transformer-BasedResonators2.1 Prior ArtCVAR2CVAR2LSVCtrl2LPKVDDLP LSCVAR1VCtrlM1M2M3VTAIL2CVAR1 M4VDDM6M5VTAIL1Figure 2.1: Circuit schematic of a dual-mode VCOTransformer-based resonators have been studied thoroughly in recentyears [4], [16] [26]. In previous works, focus has been primarily on thetransformer as a fourth order LC network, with techniques to leverage bothresonant modes to increase the tunable range of the VCO. A schematic ofthis dual-mode VCO can be seen in 2.1.The primary and secondary of the transformer are designed as loadswhich are approximately identical in terms of Q and resonant frequency. Bycoupling the two inductors magnetically, the two resonant tanks combineto make a fourth order resonant network with two resonant frequencies. Inthe lower frequency mode, the phase shift of voltage across the primary tothe voltage across the secondary will be 0, while in the higher frequencymode it will be pi. The switched current sources in the dual-mode VCO takeadvantage of this fact to control start-up in either the high or lower frequencyresonant mode of the transformer network. When M5 is turned on (and M6off) the VCO acts like a normal cross-coupled NMOS VCO and starts up52.2. Asymmetric Transformer Load OperationCVARCVARLSVCTRLVc (0/1)LPCPARCPAR KVDDLP LSCVARCVARCPARCPARVCTRL VDDLPLP(a) (b)𝜔𝑠 = 1  𝐿𝑠𝐶𝑉𝐴𝑅  𝜔𝑝 = 1  𝐿𝑃𝐶𝑃𝐴𝑅    wL,QTFigure 2.2: (a) Conventional LC resonator, and (b) transformer-enhancedresonatorin the lower frequency mode, and when M6 is turned on (and M5 off) thepi phase-shifted voltage is fed back to the gates of the transistors, allowingstartup. In this way, either frequency mode can be easily selected. Byproperly selecting the resonant frequencies of the two tanks, and tuning thevalues of CV AR1 and CV AR2, the two modes can overlap across their tuningrange, significantly boosting effective FTR. However, this design suffers fromdecreased performance in the higher frequency mode and is not able to takeadvantage of the magnetic decoupling of passive components.2.2 Asymmetric Transformer Load OperationIn this work, we investigate the several benefits of magnetically couplingpurposely-imbalanced loads (in both frequency and Q) by moving all low-Q varactance onto the secondary node of the transformer, away from theprimary switching core and power supply in an effort to maximize FTRwhile also improving the loaded Q and PN. Only the lower frequency modeof the resonator is used, but significantly large and gapless FTR is achieved.Fig. 2.2(a) shows a conventional LC resonator tank with tank inductor,varactor CV AR, and parasitic capacitance CPAR. Fig. 2.2(b) shows thetransformer-enhanced resonator tank used in our VCOs.The natural resonant frequency ωp on the primary side of the tank isdefined by the inductance of the primary winding LP and the parasitic ca-pacitance CPAR associated with the VCO switching core and buffers, whilethe natural resonant frequency ωs of the secondary is defined by the induc-tance LS of the secondary along with CV AR.When a current is applied to the primary winding of the transformer, itwill induce a current to flow in the secondary winding proportional to the62.2. Asymmetric Transformer Load Operationcoupling factor k. We know from [4], [26] that the magnetic fields producedby either side of the transformer will couple in phase at the lower frequencymode, or anti-phase in the higher frequency mode, increasing or decreasingthe total inductance and thus energy stored in the resonator. These twoconditions will cause the VCO (with a high-Q) to oscillate at either ωL orωH given by [4]:ωL,H = ΩL,H(ξ, k)ωs (2.1)whereΩL,H =√1 + ξ ∓√(1− ξ)2 − 4ξ(1− k2)2(1− k2) (2.2)andξ = (ωpωs)2 (2.3)For this design it is important to note that because of the effect ofincreased and decreased inductance seen at ωL and ωH respectively, ωLwill always be lower than both ωp and ωs and ωH will always be greaterthan both, regardless of the value ξ and k [4].The oscillator will start-up in the frequency mode with enough transcon-ductance to satisfy the Barkhausen criteria. In our one-port transformerimplementation the lower frequency mode is heavily favoured [4], given thatthe transconductance is not excessively large as to allow multi-mode oscil-lations [26], [7], [21]. Also, it has been shown in [4] that in the high-Q casethe frequency mode that will experience start-up is a function of only ξ andk. The majority of combinations of ξ and k will result in oscillation at ωLas long as ξ stays sufficiently low and k sufficiently high. As k is increased,the maximum ξ allowed before initiating start-up at ωH is also increased.It is therefore desirable to maximize k in the transformer design in orderto increase the range of ξ. For k = 0.75, ξ can reach up to a value of ap-proximately 3.5 before oscillations will start up at ωH . Proper choices forthe transformer and transconductance therefore ensures that our VCO onlyoperates at ωL.72.3. Transformer Q-Enhancement2.3 Transformer Q-Enhancement2.3.1 TheoryThe extra magnetic energy storage added to the tank from in-phase couplingof the primary and secondary currents can act to increase the loaded qualityfactor QT at ωL of the transformer beyond either Qp or Qs, respectively[16], [4]. Since this in-phase coupling is only present in the ωL case, theload is designed to always start up in the ωL mode by controlling the designparameter ξ in order to increase QT .The equation forQT of a transformer load as a function of the parametersof the two coupled resonant tanks is given as [16]:QT = Ψ(ξ, k,QPQS)QP (2.4)whereΨ =[2Ω4L,H(1− k2)− Ω2L,H(1 + ξ)][Ω2L,H(1− k2)− 1]ξ[Ω4L,H(1 +QPQSk2)− 2Ω2L,H + 1](2.5)From (2.4), we can see that to optimize QT for a given QP , we need tomaximize Ψ.Ψ scales with k and is a function of QPQS as well as ξ. Ψ increases mono-tonically with Qs and is maximized for identical loads, i.e QP = QS andωp = ωs (or ξ = 1) but improvement can be achieved for non-identical loadsas long as the value of ξ is chosen intelligently according to the ratio of QPQS[16].2.3.2 Inductor vs Transformer QIt has been pointed out in [16], [2] that the increased Q due to mutualcoupling between windings also exists when the inductors are in a parallelor series configuration (as shown in Fig. 2.3), and that for the same area thetransformer configuration itself offers no intrinsic benefit in terms of Q. Inother words, the factor that is increasing energy storage while not increasingloss (the magnetic coupling) is not specific to the transformer configuration,and similar benefits can be obtained in multi-spiral inductors.While the result seems intuitive (that an inductor network with thesame geometry and metal layers should have the same ratio of stored todissipated energy regardless of its configuration) it is only proven to be validfor symmetric windings, i.e the case where ωp = ωs (or ξ = 1) and the quality82.3. Transformer Q-EnhancementFigure 2.3: Coupled inductor resonators in a (a) series, (b) parallel, and (c)transformer configurationfactor of the two windings are the same [16], [2]. When this restriction isremoved and the two windings are allowed to vary in both resonant frequencyand quality factor, we see different behavior between the series, parallel andtransformer implementations of the network. The equations for the loadedQ for the series and parallel configuration shown in Fig. 2.3(a) and (b) aregiven by (2.6) and (2.7) [16], respectively:Qseries = QP1 + 2nk + n21 + n2QPQS(2.6)Qparallel = QPQSQP+ n21 + n21− k21− 2nk1+n2, (2.7)where n is the turns ratio is given by n =√LSLP.Using (2.4)-(2.7), Fig. 2.4 shows a simulated comparison of the threeconfigurations shown in Fig. 2.3 in terms of the loaded Q normalized toQP as a function of n2 and for different values of QS relative to QP . Allcases are simulated with k = 0.8, and the transformer case is plotted forCP = CS , where CP and CS are the total capacitance seen by the primaryand secondary winding, respectively.The simulations in Fig. 2.4 show that the Q of the three tanks are indeedthe same for the case of n = 1 and QP = QS and that it is boosted by afactor of 1 + k over QP , consistent with [11], [16]. However, for asymmetriccases, each configuration responds differently to different ratios of inductanceas well as Q. These asymmetric cases arise, for example, when one side ofthe tank is loaded by a varactor, wherein the loss of the varactor can betranslated to the series resistance of the inductor it is connected to.92.3. Transformer Q-EnhancementFigure 2.4: Comparison of loaded Q normalized to QP for coupled inductorsplaced in series, parallel, and transformer (XFMR) configurations for (a)QP = QS (b) QP =12QS (c) QP = 2QSIt is important to note that this comparison only concerns the changein loaded Q and does not take into account the changes that would have tobe made in the capacitor in order to have the same resonant frequency or102.3. Transformer Q-Enhancementtuning range for the three cases. For example, the capacitor in the seriescase would need to be much smaller for the same resonant frequency, andgiven that the parasitic capacitance is constant, would have a reduced FTR.In this paper, we are purposely aiming to implement an imbalance inthe two quality factors and resonant frequencies while still achieving anincrease in QT , and also take advantage of the benefits offered by decouplingcomponents from the circuit magnetically.2.3.3 Optimum condition for transformer-Q enhancementFig. 2.5 shows simulation plots of Ψ (defined in (2.5)) as a function ofξ for different values of QPQS . The shape of the curves is consistent withresults in Fig. 2.4, which is unsurprising when considering from (2.3) thatξ = LSCSLPCP = n2 CSCP. For the case when CP = CS , these plots reduce to thoseof the transformer configuration in Fig. 2.4. However, in this case ξ can betuned easily post-fabrication with a varactor while n2 cannot.We can observe three things from the plots in Fig. 2.5: (i) For a givenvalue of QPQS , Ψ has an optimum (maximum) point at a specific ξ, and thatthis optimum value is achieved whenξ =QSQP(2.8)(ii) QT > max(QP , QS) can be achieved near the optimum point, and (iii)at this peak Ψ has a value ofΨopt =1ΩL2QPQS(2.9)Therefore, at this peak we can say:Ψopt =ξΩ2L(2.10)From (2.1), (2.3) and (2.4), we can now write:Ψopt =QT,optQP=ωp2ωL2(2.11)andQT,opt = QPωp2ωL2= QSωs2ωL2(2.12)which reduces to Qp(1 + k) for identical loads, which is consistent withderivations in [16].112.3. Transformer Q-EnhancementFigure 2.5: Comparison of Ψ - Q-enhancement in transformer configurationfor (a) QP = QS (b) QP =12QS (c) QP = 2QS122.3. Transformer Q-EnhancementFor any resonant LC network, sinceω =1√LC(2.13)and the energy stored in either the capacitor or inductor at resonance isgiven byEstored =12CV 2 (2.14)we can say the square of the angular resonant frequency ω2 is inverselyproportional to the energy stored in the resonator. Therefore, for identi-cal input voltage (or current) the ratio of two resonant frequencies can beequivalently expressed as the ratio of stored energy in the two resonators:ω22ω21=Estored,1Estored,2(2.15). Recalling the fundamental equation for quality factor asQ = 2piEstoredEdiss(2.16)where Ediss is the energy dissipated in the tank per cycle, we can rewrite(2.12) as:QT,opt =Estored,PEdiss,PEstored,totalEstored,P=Estored,SEdiss,SEstored,totalEstored,S(2.17)and finally,Ediss,P = Ediss,S (2.18)giving the interesting result that the optimum Ψ is achieved when thesame amount of energy is dissipated in both windings each cycle, and thetwo tanks are balanced in loss per cycle.For a given ratio of primary and secondary quality factorsQpQs, thereexists an optimum distribution of stored energy ξ between the primary andsecondary windings that results in a maximum loaded quality factor of thetransformer QT .For example, if QP > QS , and thus the primary tank dissipates lessenergy per cycle for the same amount of energy stored, conventional wisdomtells us that it is more efficient for a larger portion of the total energy in thetank to be stored in the components on the primary winding than in thesecondary.132.3. Transformer Q-EnhancementEquivalently, it would be more efficient for ωp to be much lower than ωs.In the limit case where ωp << ωs, ξ = 0 and the secondary stores a negligibleamount of the total energy in the tank, giving ωL = ωp and QT = QP , whilefor ξ = ∞ the reverse is true and QT = Qs. This can be observed in bothFig. 2.4 and 2.5.However, as ωs is pushed higher relative to ωp, and the secondary windingholds less and less of the total stored energy, it also contributes less addedenergy storage, which was the original source of the Q increase. Thus, someoptimum point emerges for QT between the maximum added stored energyand minimum added energy lost per cycle. As shown in (2.8), this optimumpoint is when ξ and QPQS are the inverse of eachother. Equivalently, from(2.18), this optimum point occurs when both coupled resonators dissipatean equal amount of energy per cycle.2.3.4 Q-enhancement ImplementationIn prior arts, the oscillation frequencies were less than 10 GHz, so the mainfocus was centered on the Q due to the geometry of the inductor windings[11], [2], [4], [26]. Since our designs are operating at a much higher frequency,the Q of each inductor winding becomes large relative to the capacitor,and the loaded Q becomes dominated by the loading of the varactor andcapacitive parasitics. Fortunately, (2.4) still holds if we model all loss to bedue to the inductor, but now we have some control of the distribution of theQ unrelated to the inductor geometry.From (2.1), (2.2) and (2.3), there are multiple combinations of resonantfrequencies ωp and ωs which when coupled will oscillate at a particular choiceof ωL. This allows ξ to be also varied somewhat independently as a designparameter in order to optimize QT at a given frequency.However, in this design, since the resonant frequency on only one sideis being tuned, ξ will also vary and is chosen to stay in a range reasonablyclose to its optimum point such that while QT is not perfectly optimized ateach frequency, it can still be boosted beyond QP .Moving the varactor away from the primary and onto the secondaryresults in QS 6= QP . For the case of QPQS > 1, the optimum ξ for Ψ shiftsbelow unity, and for QPQS < 1 it shifts above. As ωs is tuned, ξ varies withit (from (2.1)), so Ψ > 1 is limited to a certain frequency range, and variesacross the range.For a proper choice of ωp and ωs and reasonable sizing of varactor andsecondary transformer winding, Ψ is held above 1 for the required FTR ofωs. If QP > QS , we can design ωs to be at a higher frequency, causing QT142.3. Transformer Q-EnhancementFigure 2.6: Plots showing the ratio of loaded Q to primary winding Q, QTQp ,and of primary winding Q to secondary winding Q,QpQs, as well as ξ for (a)the 25GHz VCO design and (b) the 60GHz VCO design152.4. FTR Reductionto be boosted near or above QP . This is useful for lower frequencies in therange, where QV AR is very low [25]. Fig. 2.6(a) shows the ratioQTQPof the20-28 GHz VCO due to the transformer action as well as the ratio of thetwo tank quality factors QPQS and the value of ξ at each frequency, while Fig.2.6(b) shows the same for the 50-62 GHz VCO.In Fig. 2.6(a), QPQS is below 1 across the FTR due to the relative sizingof the varactors and switching transistors. In the lower half of the frequencyrange, ξ > 1 causing a boost in the Q relative to QP . In the upper half ofthe range ξ is not optimized, but QV AR becomes so large that QT is stillincreased relative to QP , as Ψ is monotonic with QS . In Fig. 2.6(b),QPQS> 1in the lower half of the frequency range, but in this case ξ < 1 across thewhole range, so Ψ > 1. Similar to Fig. 2.6(a), Ψ is not optimized in theupper half but QV AR becomes high enough that it is not an issue. It shouldbe noted that the core of the 60 GHz VCO oscillates at a third of the outputfrequency.2.4 FTR ReductionThe enhancement in QT due to the transformer coupling comes with a trade-off in FTR reduction. As the effect of the varactor on the whole tank isreduced, the effect of its capacitance variation on FTR is reduced as well.From (2.1)-(2.2) we know that ωL is ωs scaled by ΩL, which is a function of ξand k. Since ξ will vary as ωs varies (and k is approximately constant acrossthe range), the scaling of ωs to ωL will be different at different frequencies.For example, if ΩL decreases as ωs increases, a ”compression” effect onthe FTR of ωL from the FTR of ωs will be observed. It can be easily shownthat:TRωL =ΩL,HIGHΩL,LOW∗ TRωs (2.19)whereΩL,HIGHΩL,LOWis the ratio of ΩL calculated at the highest and lowestfrequencies in the tuning range, and TR is the ratio of those highest andlowest frequencies.Simulation results plotted in Fig. 2.7 show that ΩL decreases with in-creasing ωs (or decreasing ξ), with the decrease becoming more pronouncedthe further ωs is tuned for both the 25 GHz and the 60 GHz SMV design.This is an expected result, as a simple rearrangement of (2.1) shows thatΩL is inversely proportional to ωs.162.4. FTR Reduction(a)(b)Figure 2.7: Plot ofΩL,HIGHΩL,LOWvs. fs for (a) the 25 GHz VCO and (b) the 60GHz SMV, showing the placement of fp in each caseThis means as fs is tuned higher, the oscillation frequency of the trans-former tank becomes a smaller fraction of fs than it was at lower frequencies,causing a diminishing returns effect on the tuning range.Equivalently, as fs is increased the stored energy in the secondary wind-172.4. FTR Reductioning decreases as well as its proportion to the total stored energy in the tank,reducing the effect of its tuning on the total tank. For fs to have a largeeffect on the oscillation frequency, it needs to be storing a significant frac-tion of the total energy in the tank, so that changes in its energy have alarger effect on the total tank. In fact, we can observe in 2.7 thatΩL,HIGHΩL,LOWis larger and has a smaller slope when fs < fp (in the case of the 25GHzVCO) and drops off very quickly when fs > fp (in the case of the 60GHzVCO). The reduced ratio of ΩL,HIGHΩL,LOW has the result of a reduced FTR of ωLas compared to ωs.This trade-off limits the frequency range over which the loaded Q, QTcan be boosted, especially when considering that fs can not be tuned somuch lower than fp that ξ becomes very large and oscillation starts up atωH .After a certain point, the benefits of increasing the size of the varactor onthe secondary diminish significantly. However, there are benefits that comefrom decoupling the varactor from the supply and core transistors using thetransformer which are not captured by a simple load analysis. Next, weshow that FTR can be also simultaneously enhanced in our design.18Chapter 3Varactor PerformanceEnhancement3.1 Voltage Range ExtensionIn a conventional LC-VCO design, a varactor is usually connected to thecontrol voltage VCTRL on one terminal and some supply-dependent voltage(e.g: VDD,VDD2 or GND) on the other, depending on the implementation ofthe switching transistors (see Fig. 2.2(a)). VCTRL can be varied arbitrarilyto control capacitance, but the other node must be held constant to allowoperation of active components in the circuit.Capacitance variation can be increased by increasing the range of VCTRLto reach above VDD or below GND, but large bias voltages and negativevoltages can be difficult to produce on-chip.By magnetically coupling the varactor to the tank, we remove the powersupply constraint from the passives on the secondary and free the secondterminal of the varactor to be biased through the center tap of the secondarywinding with an arbitrary voltage VC (see Fig. 2.2(b)).Fig. 3.1 shows simulated values of capacitance normalized to the max-imum capacitance for different values of the gate source voltage Vgs acrossthe varactor. If VCTRL is a voltage bounded between GND and VDD and thecapacitance of the varactor is a function of the voltage difference betweengate and source nodes VC − VCTRL, then the total voltage range measuredacross the varactor terminals can be doubled by switching VC between VDDand GND in a discrete fashion. Fig. 3.1 illustrates this effect, showing howtwice the range of Vgs is achieved for only a binary implementation of Vc,thus increasing the capacitance variation. Arbitrary amounts of frequencyoverlap can also be introduced between the frequency bands by implement-ing intermediate levels of VC between GND and VDD using a voltage DAC.193.2. Varactor QFigure 3.1: Simulated normalized capacitance of the varactor vs. gate-sourcevoltage across the varactor3.2 Varactor QIn addition to doubling the available voltage range across the varactor, whena varactor is biased with a negative gate-source voltage, a depletion layeris formed underneath the gate [25]. This causes QV AR to be significantlyhigher at higher frequencies (see Fig. 4.3). This phenomenon cannot beduplicated in a conventional NMOS LC-VCO topology by simply reversingthe terminals and connecting the source-drain to the output node (and thus acommon-mode of VDD), as this will load the output with a very low-Q, largeparasitic capacitive path to ground through the bulk junction capacitanceof the surrounding n-well. Therefore, the benefit of a negative gate-sourcebias on the accumulation-mode MOS varactor can only be achieved if thecommon-mode voltage of the gate node is set below the level of VCTRL, asis the case here.203.3. Parasitic Capacitance Reduction3.3 Parasitic Capacitance ReductionSeparating the varactor from the active circuitry also improves the varactorperformance by significantly reducing the amount of parasitic capacitanceseen by the varactor. Any fixed parasitic capacitance on the secondaryattenuates the relative effect of CV AR to overall FTR. Ifωres =1√L(CPAR + CV AR)(3.1)Where ωres is the resonant angular frequency of an LC network, then wecan easily see that as CPAR becomes comparable to CV AR in magnitude, thevarying capacitance becomes a smaller percentage of the total capacitanceand has a significantly dampened effect when tuning the frequency.This is generally a problem for high frequency VCOs, as the the totalreactance in the tank becomes smaller to accommodate higher frequencies,and the core transistor parasitics become a larger portion of the total tankcapacitance [23].By disconnecting the varactor from the core transistors we are able toreduce the parasitic capacitance to just its own overlap capacitance as wellas metal trace capacitance. This allows the FTR of ωs to reach extremelyhigh percentages for the same varactor sizing, or the same FTR for a muchhigher Q, as can be seen in Fig. 2.7. Of course, as previously mentioned,there is also a partial reduction in FTR when translated to ωL caused bythe transformer coupling.3.4 Conventional VCO vs Transformer-enhancedVCOFigs. 3.2 and 3.3 show simulated comparisons for FTR and Q using (2.1)-(2.5) between a transformer-enhanced VCO and a conventional VCO thatuses the same varactor, varying VCTRL from 0 to 1 V, for both the 20-28GHz VCO as well as the 51.5-62 GHz SMV. For the 51.5-62 GHz SMV, itshould be noted that the Q listed is the measured at 1/3 of the frequency,where the VCO core is operating.In the conventional VCO load, the secondary winding is removed andthe varactor is connected in parallel with the primary inductor while allother components are kept constant (see Fig. 2.2(a)). The blue and redportion of the transformer tuning curve correspond to VC set to 1 V and 0V, respectively. We observe that both Q of the transformer load and FTR are213.4. Conventional VCO vs Transformer-enhanced VCOFigure 3.2: Loaded Q vs. oscillation frequency for a transformer-enhancedresonator in an VCO operating near 25GHz, a conventional resonator, anda conventional resonator with an inductor Q increased by (1 + k)Figure 3.3: Loaded Q vs. oscillation frequency for a transformer-enhancedresonator in an SMV operating near 60GHz, a conventional resonator, anda conventional resonator with an inductor Q increased by (1 + k)223.5. Low-Frequency Noise to Phase Noise Conversionlarger than a conventional VCO with the same varactor. This observationholds true even if the Q of the inductor in the conventional VCO is increasedby 1+k (to take into account the potential gain of designing a better inductorwith the same area footprint as the primary [2]) because the Q is dominatedby the varactor and parasitic capacitances at these frequencies.3.5 Low-Frequency Noise to Phase NoiseConversionA persistent source of PN in LC-VCOs comes from low-frequency noiseacross the varactors, either at VC from noise sources within the VCO (e.gflicker noise) or at VCTRL from noise sources within the PLL. Voltage noisemodulating VC−VCTRL in turn modulates the capacitance, which modulatesthe frequency and appears as PN. The power spectral density at a frequencyoffset fm from the carrier due to a noise component at fm is given by [18][20]:S(fm) = (KV COVm2fm)2 (3.2)where KV CO is the frequency gain of the VCO (as a function of controlvoltage) and Vm is the amplitude of the noise component at fm. Althoughthe change in secondary frequency ∆ωs due to change in voltage ∆VC willbe larger than KV CO in this design, the transfer function∆ωL∆ωswill be thesame as ωLωs , making KV CO an appropriate coefficient.Since almost all of the low-frequency voltage noise will be produced byactive components on the primary side of the transformer, we are interestedin the voltage gain from the primary to secondary. Assuming large Q and op-eration below the resonant frequency of the transformer tank, the gain fromthe primary voltage Vp to the secondary voltage Vs can be approximated as:VsVp≈ nk (3.3)Since both n and k are frequency independent to the first-order, in theideal case this gain should be constant across all frequencies below resonance.However, at low frequencies the Q of each winding is very low. As theQ drops, the impedance of the winding becomes dominated by the seriesresistance of the coil and thus the voltage Vp across the inductive part of thecoil is only a fraction of the applied voltage. In this case, even though thevoltage gain due to the flux linkage between the two inductors is unchanged,233.5. Low-Frequency Noise to Phase Noise Conversionthe amount of flux, and thus the effective gain from the input port of theprimary winding to the secondary winding, is significantly reduced. Thevoltage gain in this scenario can be expressed as:VsVp=ωLP√ω2LP2 +RP2nk =nk√1 + 1QP2(3.4)where RP is the series resistance of the primary winding. A schematicto help illustrate this effect is shown in Fig. 3.4CVARVSNOISE SOURCEKLP LSRPVPVCTRLVCFigure 3.4: Schematic of simplified transformer network stimulated by avoltage sourceWhen QP << 1, the voltage transmission from primary to secondarybecomes very small. From EM simulations, QP of both VCOs (see Fig.4.3) is more than an order of magnitude below unity around 10 kHz - 10MHz, making noise components at these frequencies significantly attenuated.This high-pass filter effect is very helpful in reducing the conversion of low-frequency noise to PN through the varactor, and offsets some of the negativeeffects associated with increasing KV CO and thus FTR.Unfortunately, this effect will not reduce the effect of AM-PM conversiondue to low-frequency noise upconverting to f0 and modulating the varac-tor capacitance [12] and, depending on n and k, may in fact increase thisconversion.24Chapter 4Design Considerations andMeasurement Results4.1 General ConsiderationsTwo separate VCOs, shown in Fig. 4.1 and Fig. 4.2 are designed to testthe viability of the transformer topology. The former is designed to tunefrom 20 - 28 GHz and the latter effectively from 51.5 - 62 GHz. In bothdesigns a Class-C VCO [15] [6] is implemented with a resonator made up ofa transformer coupling two LC-tanks with a coupling constant k. The 51.5- 62GHz VCO utilizes a self-mixing architecture outlined in [23].A Class-C VCO topology is chosen for both designs due to its 3.9 dB re-duction in PN for the same power consumption [15]. It is also has a superiordc-to-2f0 efficiency, which is useful for increasing swing in the SMV design,and it contributes less parasitic capacitance to the tank than a standardVCO [23].Bias voltages for the tail current source as well Class-C switching tran-sistors are implemented with externally generated analog voltages VBIASand VG, respectively. Inductively loaded common source amplifiers tunedto the output frequency are used as buffers with a separate power supplyVBUFF to ensure rail to rail swing and enable measurement on a 50-ohmload. Frequency control is achieved by setting the voltage across the var-actors CV AR with the pins VCTRL and VC . VCTRL is varied continuouslyfrom 0 to VDD in the same way as a conventional VCO, while VC can beswitched in a discrete fashion between 0 and VDD to extend the capacitancevariation. Since the capacitance CV AR is set by the voltage difference acrossits positive and negative terminals, switching VC allows the entire capaci-tance range of CV AR to be used without the need to generate any negativevoltages, or voltages above VDD. Similarly, by adding intermediate voltagelevels for VC between 0 and VDD (such as with a voltage DAC), any amountof frequency overlap between bands can be achieved. Such a switching iseasily realizable in frequency synthesizers, in a fashion similar to switchable254.2. Design of 25 GHz VCOCVAR CVARLSLPCG CGRG RGM1 M2VBIAS CBIASVGVDDM3M4 M5VDD_BUFF VDD_BUFFLBUFF LBUFFVCTRLVC (0/1)Figure 4.1: Schematic for the 20 - 28 GHz Class-C VCOcapacitor banks, but without the associated performance degradation of thelatter.4.2 Design of 25 GHz VCOThe 25GHz VCO is designed for a large FTR while maintaining a good PN.To accomplish this, ωs is designed to be lower than ωp for half of the FTRand higher in the other half. This optimizes the effect of tuning ωs on theentire tank, as it holds a large share of the total tank energy for a largerportion of the FTR. This is made clear in Fig. 2.7(a) as compared to (b).Because ωL < ωp, ωs [4], ωp is designed to be slightly higher than thehighest frequency desired in the range. At the same time, the lower limit ofωs is set by the startup factor and can not go so low that the oscillator will264.3. Design of 60 GHz VCOstart up in the high frequency mode.Consequently, since ωs is lower than ωp and ξ > 1 for the lower half of therange, the tank is designed such that QP < QS in this range, to maximizeQT . In the upper half, the varactor is operated in the depletion region andits quality factor increases significantly, reducing the necessity to optimizeQT .EM simulation results for Q and k of the transformer used in the 25 GHzdesign is shown in Fig. 4.3(a) and Fig. 4.4, respectively. QS is larger in thelower frequency range, which as previously mentioned, is beneficial for thisdesign. k is designed to be as high as possible and is simulated to be around0.71.CVAR CVARLSLPCG CGRG RGM1 M2VBIAS CBIASVGVDDM3M5VDD_BUFFLBUFFVCTRLVC (0/1)VB_MIX VB_MIXLO+ LO-LO+ LO-VDD_BUFFVout+ Vout-M4M6 M7λ/4 @ 2f0LBIASFigure 4.2: Schematic for the 51.5 - 62 GHz Class-C Self-Mixing VCO4.3 Design of 60 GHz VCOThe 60 GHz prototype uses an SMV topology, mixing the output of a stan-dard VCO core with its second harmonic, tapped from the transformercommon-mode node connected to the supply and fed into a mixer, to get alarge 3rd harmonic component [23]. This allows the core transformer to bedesigned around 20 GHz instead of 60 GHz where the quality factor of thevaractor is higher, as well as relaxing the self-resonant frequency requirementfor the transformer.274.3. Design of 60 GHz VCO(a)(b)Figure 4.3: Plot of simulated QP , QS and QV AR vs. frequency for (a) the25 GHz VCO and (b) the 60 GHz SMVThe 60GHz VCO core is designed to optimize the Q boosting due to thetransformer coupling while maintaining a good FTR. For this reason, ωs isdesigned to always be greater than ωp, and QP is designed to be greaterthan QS . ThereforeQPQS> 1 and ξ > 1 for the lower frequencies and QT isboosted above QP . Similar to the 25 GHz design, at higher frequencies, QSincreases significantly and the optimization is not as crucial.EM simulation results for Q and k of the transformer used in the 60GHz design is shown in Fig. 4.3 (b) and Fig. 4.4, respectively. k is againdesigned to be as high as possible and is simulated to be around 0.79.284.4. Measurement ResultsFigure 4.4: Plot of simulated k vs. frequency between the primary andsecondary windings of the transformers used in the 25 GHz VCO and the60 GHz SMV4.4 Measurement ResultsThe die micrographs of the 20 - 28 GHz VCO and the 51.5 - 62 GHz VCOdesigned in 65 nm CMOS process are shown in Fig. 4.5(a) and Fig. 4.5(b),respectively. In both designs, LP is a single large winding. LS is imple-mented with two windings in order to decrease the varactor size while stillkeeping ωs to reasonable values.Measurements are done using an R&S FSWP-50 spectrum and PN an-alyzer. Fig. 4.6(a) shows the FTR plot of the 20 - 28 GHz VCO, achievinga range of 20.77 GHz to 28.02 GHz (FTR of 29.8%) while consuming a corepower PDC of 12.65 mW to 15.12 mW from a 1 V supply. An overlap of480 MHz is achieved between the two frequency bands without any inter-mediate levels of VC by altering the bias. Fig. 4.7(a) shows the PN plot at26.45 GHz with a PN of -106.6 dBc/Hz at ∆f = 1 MHz offset. Fig. 4.8plots the measurements for PN at ∆f = 1 MHz across the FTR.Fig. 4.6(b) shows the FTR plot of the 51.5 - 62 GHz SMV, achievinga range of 51.46 GHz - 61.96 GHz (FTR of 18.5%) while consuming a corepower of 4.1m mW to 5.4 mW from 1 V supply. An overlap of 1.38 GHzis achieved between the two bands again without any intermediate levels ofVC by altering the bias, but it should be noticed that the frequency tripling294.4. Measurement ResultsTable 4.1: Performance Summary and ComparisonArchitecture Frequency (GHz) FTR % VDD(V) PN (dBc/Hz) PDC(mW) FOMT (dBc/Hz)XFMR-Coupled [19] 14.8 - 17.6 16.5 1 -110 @ 1MHz 5 -191.94 @ 1MHzAsymmetric XFMR 20.77 - 28.02 29.8 1 -106.6 @ 1MHz 12.65 - 15.12 -195 @ 1MHzSwitched Inductor [1] 20.9 - 29.7 34.8 1 -115.8 @ 10MHz 4.1 -194.6 @ 10MHzStanding Wave [8] 26.3 - 27.6 4.8 1.8 -115 @ 1MHz 17.7 -184.62 @ 1MHzSwitched Cap [18] 34.29 - 39.88 15.1 1.2 -101 @ 1MHz 14.4 -183.6 @ 1MHz3f0 Extractor [27] 48.4 - 62.5 25 0.7 -100.1 @ 1MHz 13.5 -189.6 @ 1MHzDigital Varactors [10] 51 - 60.5 17 1.2 -99.4 @ 1MHz 15 -186.8 @ 1MHzAsymmetric XFMR SMV 51.5 - 62 18.5 1 -98.9 @ 1MHz 4.1 - 5.4 -193.4 @ 1MHzSMV [23] 52.8 - 62.5 16.8 1.2 -100.57 @ 1MHz 7.6 -190.85 @ 1MHzMag-Coupled [9] 47.6 - 71 39 1 -113.4 @ 10MHz 8.9-10.4 -190.6 @ 10MHzSwitched Cores [28] 55.7 - 66 17.2 1.2 -93.5 @ 1MHz 19.1/11.2 -181 @ 1MHzShielded Inductor [5] 59 - 65.2 10 1 -95 @ 1MHz 3.9 -185 @ 1MHzCapacitor Splitting [13] 61.1 - 66.7 8.75 0.6 -95 @ 1MHz 3.16 -185 @ 1MHzeffect of the SMV also triples the frequency overlap. Fig. 4.7(b) shows thePN plot at 59.63 GHz with a PN of -98.9 dBc/Hz at ∆f = 1 MHz offset. Fig.4.8 plots the measurement data and simulation results for PN at ∆f = 1MHz across the FTR.Table 4.1 provides a performance comparison of the two prototypes toother state-of-the-art high frequency VCO designs. As the performance ofvarious prior-art topologies are limited by varactors, the proposed topologymay be incorporated into those topologies as well for further performanceimprovement.304.4. Measurement Results(a)(b)Figure 4.5: Chip micrographs: (a) 20 - 28 GHz VCO with core area of 246x 473 µm2, and (b) 51.5 - 62 GHz SMV with core area of 340 x 500 µm2314.4. Measurement Results(a)(b)Figure 4.6: Measured oscillation frequency vs. control voltage for (a) the 25GHz VCO and (b) the 60 GHz SMV324.4. Measurement Results(a)(b)Figure 4.7: Measured phase noise of (a) the 25 GHz VCO at 26.45 GHz and(b) the 60 GHz SMV at 59.63 GHz334.4. Measurement ResultsFigure 4.8: Plot of Phase Noise measurements and simulation results at 1MHz offset across the tuning range for the 25 GHz VCO and the 60 GHzSMV34Chapter 5ConclusionConnecting a varactor to the secondary of a transformer increases the tankQ, significantly reduces the parasitics in the secondary tank and therebyenables the varactor to control most of the frequency tuning, and enablesflexible biasing for the varactor. Thus, PN and FTR can be simultaneouslyimproved, significantly relaxing the tradeoff associated with high-frequencyVCO designs. Both a 20.77-28.02 GHz and a 51.5 - 62 GHz prototypedemonstrate the benefits of the proposed techniques and achieve state ofthe art FoMT of -195.04 dBc/Hz and -193.4 FoMT respectively, which arethe highest reported for VCOs in high-frequency range. The techniques aresuitable for multi-rate wireline/optical transceivers as well as attractive forhigh-frequency 5G radio bands.In future works, improvements could be made to reduce the variationof phase noise across the tuning range. This could be accomplished bytaking more effort to optimize ξ vs. the quality factor ratio over a smallertuning range. It could also be done by reducing KV CO, possibly by addinga switched capacitor bank on the secondary.Efforts could also be made to design the transformer to attenuate voltagefrom primary to secondary at high frequencies (e.g, n < 1) in order to reducethe AM-PM noise conversion due to the varactor.35Bibliography[1] P. Agarwal, Partha Pratim Pande, and D. Heo. 25.3 GHz, 4.1 mW VCOwith 34.8% tuning range using a switched substrate-shield inductor. In2015 IEEE MTT-S International Microwave Symposium, pages 1–4,May 2015.[2] P. Andreani and J. R. Long. Misconception regarding use of transformerresonators in monolithic oscillators. 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