Design of Relaxation Oscillator in Buck Converter

For buck converter application, when the switching frequency is working in MHz range, RC relaxation oscillator can work well in buck converter compared to the crystal oscillator and the voltage-controlled oscillator. The crystal oscillator has the disadvantage of consuming large volume. The voltage-controlled oscillator has the disadvantage of voltage instability and the disadvantage of temperature instability. While the RC relaxation oscillator not only consume little chip area but also have good temperature stability and voltage stability. So, it is the best choice in buck converter working in MHz range. In recent years, many theses have been proposed to improve the temperature coefficient of the RC relaxation oscillator or to improve the power consumption. In this thesis, two topology of relaxation oscillator have been introduced. Both of them focused on how to save the power consumption and how to improve the temperature stability. The techniques on improving the start-up time, saving chip area, and simplifying control logic circuit has also been shown.

       The first RC relaxation oscillator topology is the delay-compensation relaxation oscillator. It focuses on compensating the delay time of the comparators used in relaxation oscillator. Because the delay time is one of the factors that would affect the relaxation oscillator in frequency temperature stability. With the delay time of the comparator compensated, the relaxation oscillator can achieve good temperature coefficient. The voltage reference and current reference in this relaxation oscillator also been improve by integrated them into one simple circuit. So, the chip area consumption and the power consumption of the voltage reference and current reference can all be saved. The control logic circuit is simplified by reducing the numbers of the comparators, which reduced to two comparators from four comparators. A low dropout regulator also is used to improve the voltage stability of the relaxation oscillator. The working principal of the voltage reference, current reference and oscillator control logic circuit are all described in this thesis. The simulation results and testing results of this delay-compensation topology are also shown. The testing results indicates that this relaxation oscillator has good performance. It only consumes 5.72μW, start in only one cycle, has the temperature coefficient about 60 ppm/℃, and the chip area of the oscillator is only 9000 μm2. The good performances of this relaxation oscillator indicates that it can be used in buck converter.

       The second RC relaxation oscillator topology is the improved feedforward period control relaxation oscillator. It also focuses on compensating the delay time of the comparators while the compensation techniques and the logic control circuits are different from the first relaxation topology. The voltage and current reference block is same as the block used in the first oscillator. Because using the different compensation technique, it uses less switches and charging current and not discharging current is used in it. It also has the advantages of good temperature coefficient, power voltage stability, less power consumption, and less chip area consumption. The simulation results shows that it consumes about 5μW when working in 5 Mhz frequency, while the first one working in 1 Mhz frequency using the same power, so its power efficiency is better. The simulation results also shows that it has the temperature coefficient of 30 ppm/℃, which close to the theoretical limitation. It also can be used in buck converter.

对于降压变换器的应用而言，当它的开关频率工作在Mhz的工作频率内时，RC松弛振荡器相比晶体振荡器和压控振荡器具有更高的性价比。晶体振荡器的缺点是体积大、成本高，压控振荡器的缺点是具有电压不稳定性和温度不稳定性。而RC松弛振荡器不仅占用芯片面积小，而且具有良好的温度稳定性和电压稳定性。因此，它非常适合用于工作在MHz范围内的降压变换器中，作为它的时钟信号源。近年来，许多论文提出了提高RC松弛振荡器的温度稳定性或降低功耗的方法。本文介绍了两种松弛振荡器的拓扑结构。它们都着眼于如何节省功耗和提高温度稳定性。文中还介绍了提高启动时间，节省芯片面积和简化控制逻辑电路的技术。

第一个RC松弛振荡器是延迟补偿松弛振荡器。它的设计特点是可以补偿松弛振荡器中比较器的延迟时间。因为比较器延迟时间是影响松弛振荡器频率的温度稳定性的关键因素之一。通过补偿比较器的延迟时间，松弛振荡器可以获得更好的温度系数。通过将电压基准源和电流基准源集成到一个简单的电路中，该松弛振荡器中的电压基准和电流基准可以得到改进。因此，可以节省芯片面积以及电压基准源和电流基准源的功耗。通过减少比较器的数量，简化了控制逻辑电路，从四个比较器减少到两个比较器。此设计中还用到了低压差线性稳压器，用于改善松弛振荡器的电压稳定性。本文介绍了电压基准、电流基准和振荡器控制逻辑电路的工作原理。文中还给出了该延迟补偿拓扑结构的仿真结果和测试结果。

第二种RC松弛振荡器是改进的前馈周期控制松弛振荡器。和第一种振荡器的设计重点一样，它也着眼于补偿比较器的延迟时间，但是补偿技术和逻辑控制电路与第一种松弛振荡器不同。电压和电流参考源与第一振荡器中使用的参考源相同。由于采用了不同的补偿技术，它使用了更少的开关和充电电流，而不使用放电电流。它还具有温度系数好、电源电压稳定、功耗小、芯片面积小等优点。仿真结果表明，在5Mhz频率下工作时功耗约为5μW，而第一个振荡器工作在1Mhz下就要消耗掉相同的功耗。因此其功率效率更高。仿真结果还表明，其温度系数为30ppm/℃，接近理论极限。它也可用于作为降压转换器的时钟信号源。

[1] Choe K, Bernal O D, Nuttman D, et al. A precision relaxation oscillator witha self-clocked offset-cancellation scheme for implantable biomedical SoCs[C].2009 IEEE International Solid-State Circuits Conference-Digest of TechnicalPapers. IEEE, 2009: 402-403,403 a.
[2] Zheng Y, Zhou L, Tian F, et al. A 51-nW 32.7-kHz CMOS relaxation oscillatorwith half-period pre-charge compensation scheme for ultra -low powersystems[C]//2016 IEEE International Symposium on Circuits and Systems(ISCAS). IEEE, 2016: 830-833.
[3] Tokairin T, Nose K, Takeda K, et al. A 280nW, 100kHz, 1 -cycle start-up time,on-chip CMOS relaxation oscillator employing a feedforward period controlscheme[C]//2012 Symposium on VLSI Circuits (VLSIC). IEEE, 2012: 16 -17.
[4] Wang J, Goh W L. A 13.5-MHz relaxation oscillator with±0.5% temperaturestability for RFID application[C]//2016 IEEE International Symposium onCircuits and Systems (ISCAS). IEEE, 2016: 2431 -2434.
[5] Tsubaki K, Hirose T, Osaki Y, et al. A 6.66 -kHz, 940-nW, 56ppm/° C, fullyon-chip PVT variation tolerant CMOS relaxation oscillator[C]//2012 19th IEEEInternational Conference on Electronics, Circuits, and Systems (ICECS 2012).IEEE, 2012: 97-100.
[6] Mikulić J, Schatzberger G, Barić A. A 1 -MHz on-chip relaxation oscillatorwith comparator delay cancelation[C]//ESSCIRC 2017 -43rd IEEE EuropeanSolid State Circuits Conference. IEEE, 2017: 95-98.
[7] Wang J, Goh W L, Liu X, et al. A 12.77-MHz 31 ppm/° C on-chip RC relaxationoscillator with digital compensation technique[J]. IEEE Transactions onCircuits and Systems I: Regular Papers, 2016, 63(11): 1816 -1824.
[8] Cimbili B, Wang D, Zhang R C, et al. A PVT -tolerant relaxation oscillator in65nm CMOS[C]//2016 IEEE Region 10 Conference (TENCON). IEEE, 2016:2315-2318.
[9] Tokunaga Y, Sakiyama S, Matsumoto A, et al. An on -chip CMOS relaxationoscillator with voltage averaging feedback[J]. IEEE Journal of Solid -StateCircuits, 2010, 45(6): 1150-1158.
[10] Cao Y, Leroux P, De Cock W, et al. A 63,000 Q -factor relaxation oscillatorwith switched-capacitor integrated error feedback[C]//2013 IEEE InternationalSolid-State Circuits Conference Digest of Technical Papers. IEEE, 2013: 186 -187.
[11] Tsai Y K, Lu L H. A 51.3-MHz 21.8-ppm/° C CMOS relaxation oscillator withtemperature compensation[J]. IEEE Transactions on Circuits and Systems II:Express Briefs, 2016, 64(5): 490-494.
[12] Paidimarri A, Griffith D, Wang A, et al. An RC oscillator with comparatoroffset cancellation[J]. IEEE Journal of Solid -State Circuits, 2016, 51(8): 1866-1877.
[13] Sebastiano F, Breems L J, Makinwa K A A, et al. A low -voltage mobility-basedfrequency reference for crystal-less ULP radios[J]. IEEE journal of solid-statecircuits, 2009, 44(7): 2002-2009.
[14] Tsubaki K, Hirose T, Kuroki N, et al. A 32.55 -kHz, 472-nW, 120ppm/° C, fullyon-chip, variation tolerant CMOS relaxation oscillator for a real -time clockapplication[C]//2013 Proceedings of the ESSCIRC (ESSCIRC). IEEE, 2013:315-318.
[15] Gürleyük Ç, Pedalà L, Pan S, et al. A CMOS dual-RC frequency referencewith±200-ppm inaccuracy from− 45° C to 85° C[J]. IEEE Journal of Solid -State Circuits, 2018, 53(12): 3386-3395.
[16] Zhang G, Yayama K, Katsushima A, et al. A 3.2 ppm/° C second -ordertemperature compensated CMOS on -chip oscillator using voltage ratioadjusting technique[J]. IEEE Journal of Solid-State Circuits, 2017, 53(4):1184-1191.
[17] Choi M, Jang T, Bang S, et al. A 110 nW resistive frequency locked on-chiposcillator with 34.3 ppm/° C temperature stability for system -on-chipdesigns[J]. IEEE Journal of Solid-State Circuits, 2016, 51(9): 2106-2118.
[18] Hsiao K J. A 32.4 ppm/° C 3.2-1.6 V self-chopped relaxation oscillator withadaptive supply generation[C]//2012 Symposium on VLSI Circuits (VLSIC).IEEE, 2012: 14-15.
[19] Lee J, George A, Je M. 5.10 A 1.4 V 10.5 MHz swing -boosted differentialrelaxation oscillator with 162.1 dBc/Hz FOM and 9.86 psrms period jitter in0.18 µm CMOS[C]//2016 IEEE International Solid-State Circuits Conference(ISSCC). IEEE, 2016: 106-108.
[20] Griffith D, Røine P T, Murdock J, et al. 17.8 A 190nW 33kHz RC oscillatorwith±0.21% temperature stability and 4ppm long -term stability[C]//2014 IEEEInternational Solid-State Circuits Conference Digest of Technical Papers(ISSCC). IEEE, 2014: 300-301.
[21] Mikulić J, Schatzberger G, Barić A. Post-Manufacturing Process andTemperature Calibration of a 2 -MHz On-Chip Relaxation Oscillator. IEEETransactions on Circuits and Systems I: Regular Papers, 2021, 68(10): 4076-4089.REFERENCES93
[22] Liu N, Agarwala R, Dissanayake A, et al. A 2.5 ppm/° C 1.05 -MHz relaxationoscillator with dynamic frequency -error compensation and fast start-up time[J].IEEE Journal of Solid-State Circuits, 2019, 54(7): 1952-1959.
[23] Liu N, Agarwala R, Dissanayake A, et al. A 2.5 ppm/° C 1.05 MHz RelaxationOscillator with Dynamic Frequency-Error Compensation and 8 µs Start-upTime[C]//ESSCIRC 2018-IEEE 44th European Solid State Circuits Conference(ESSCIRC). IEEE, 2018: 150-153.
[24] Chen C Q, Zhan C, Zhang Z, et al. A 5.72 -μW, 1.02-MHz,-40~ 125° C, 1μsStartup Time Relaxation Oscillation with Fully-on-Chip Voltage Reference andLDO Regulator[C]//2021 IEEE International Conference on Integrated Circuits,Technologies and Applications (ICTA). IEEE, 2021: 237-238.
[25] Savanth A, Weddell A S, Myers J, et al. A sub -nW/kHz relaxation oscillatorwith ratioed reference and sub-clock power gated comparator[J]. IEEE Journalof Solid-State Circuits, 2019, 54(11): 3097-3106.
[26] Nadeau P M, Paidimarri A, Chandrakasan A P. Ultra low -energy relaxationoscillator with 230 fJ/cycle efficiency[J]. IEEE Journal of Solid -State Circuits,2016, 51(4): 789-799.
[27] Lei K M, Mak P I, Martins R P. A 0.35-V 5,200-μm 2 2.1-MHz TemperatureResilient Relaxation Oscillator With 667 fJ/Cycle Energy Efficiency Using anAsymmetric Swing-Boosted RC Network and a Dual-Path Comparator[J]. IEEEJournal of Solid-State Circuits, 2021, 56(9): 2701 -2710.
[28] Cicalini M, Marchetti D, Ria A, et al. A 10 MHz Relaxation Oscillator with anovel Jitter Suppression Comparator Autozeroing technique[C]//2020 27thIEEE International Conference on Electronics, Circuits and Systems (ICECS).IEEE, 2020: 1-4.
[29] Barkley A, Santi E. Improved online identification o f a DC–DC converter andits control loop gain using cross-correlation methods[J]. IEEE Transactions onpower electronics, 2009, 24(8): 2021 -2031.
[30] Miao B, Zane R, Maksimovic D. System identification of power converterswith digital control through cross-correlation methods[J]. IEEE Transactionson Power Electronics, 2005, 20(5): 1093-1099.
[31] Miao B, Zane R, Maksimovic D. Practical on-line identification of powerconverter dynamic responses[C]//Twentieth Annual IEEE Applied PowerElectronics Conference and Exposition, 2005. APEC 2005. IEEE, 2005, 1: 57-62.
[32] Roinila T, Helin T, Vilkko M, et al. Circular correlation based identificationof switching power converter with uncertainty analysis using fuzzy densityapproach[J]. Simulation Modelling Practice and Theory, 2009, 17(6): 1043-1058.
[33] Choi J Y, Cho B H, VanLandingham H F, et al. System identification of powerconverters based on a black-box approach[J]. IEEE Transactions on Circuitsand Systems I: Fundamental Theory and Applications, 1998, 45(11): 1148 -1158.
[34] Mikulić J, Schatzberger G, Barić A. A 1-MHz relaxation oscillator coreemploying a self-compensating chopped comparator pair[J]. IEEE Transactionson Circuits and Systems I: Regular Papers, 2019, 66(5): 1728 -1736.
[35] Wang L, Zhan C. A 0.7-V 28-nW CMOS subthreshold voltage and currentreference in one simple circuit[J]. IEEE Transactions on Circuits and SystemsI: Regular Papers, 2019, 66(9): 3457 -3466.
[36] Liu Y, Zhan C, Wang L, et al. A 0.4-V wide temperature range all-MOSFETsubthreshold voltage reference with 0 .027%/V line sensitivity[J]. IEEETransactions on Circuits and Systems II: Express Briefs, 2018, 65(8): 969 -973.
[37] Huang C, Zhan C, He L, et al. A 0.6-V minimum-supply, 23.5 ppm/° Csubthreshold CMOS voltage reference with 0.45% variation coefficient[J].IEEE Transactions on Circuits and Systems II: Express Briefs, 2018, 65(10):1290-1294.
[38] Ji Y, Jeon C, Son H, et al. A 9.3 nW all -in-one bandgap voltage and currentreference circuit using leakage-based PTAT generation and DIBLcharacteristic[C]//2018 23rd Asia and South Pacific Design AutomationConference (ASP-DAC). IEEE, 2018: 309-310.
[39] Zhou W, Goh W L, Gao Y. A 3 -MHz 17.3-$\mu $ W 0.015% Period JitterRelaxation Oscillator With Energy Efficient Swing Boosting[J]. IEEETransactions on Circuits and Systems II: Express Briefs, 2019, 67(10): 1745-1749.
[40] Lee J, George A K, Je M. An ultra -low-noise swing-boosted differentialrelaxation oscillator in 0.18-μm CMOS[J]. IEEE Journal of Solid-State Circuits,2020, 55(9): 2489-2497.
[41] Savanth A, Myers J, Weddell A, et al. 5.6 A 0.68 nW/kHz supply-independentRelaxation Oscillator with±0.49%/V and 96ppm/° C stability[C]//2017 IEEEInternational Solid-State Circuits Conference (ISSCC). IEEE, 2017: 96-97.
[42] Wang L, Zhan C, Tang J, et al. A 0.9 -V 33.7-ppm/° C 85-nW sub-bandgapvoltage reference consisting of subthreshold MOSFETs and single BJT[J].IEEE Transactions on Very Large Scale Integration (VLSI) Systems, 2018,26(10): 2190-2194.
[43] Gomez H, Arenas J, Rojas C, et al. A 68/36ppm/○ C Tc 32.768 Khz-To-1MhzRc-Based Oscillator With 72/6Pj Start-Up Energy[C]//2019 IEEE CustomIntegrated Circuits Conference (CICC). IEEE, 2019: 1 -4