A relaxation oscillator exploits a noise filtering technique implemented with a switched-capacitor circuit to minimize phase noise. A 65nm CMOS design produces a sawtooth waveform, has a frequency tuning range of 1 to 12MHz and a constant frequency-tuning gain. By minimizing and balancing noise contributions from charge and discharge mechanisms, a FOM of -162dB is achieved, which is a 7dB improvement over state-of-the-art

Geraedts, P.F.J.

Klumperink, E.A.M.

Nauta, B.

Tuijl, A.J.M. van

Wienk, G.J.M.

English

van Tuijl, Adrianus Johannes Maria

Klumperink, Eric A.M.

Wienk, Gerhardus J.M.

Nauta, Bram

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A 90μW 12MHz Relaxation Oscillator with a -162dB FOM

University of Twente Research Information

348 •  2008 IEEE International Solid-State Circuits ConferenceISSCC 2008 / SESSION 19 / PLLs & OSCILLATORS / 19.519.5 A 90µW 12MHz Relaxation Oscillator with a –162dB FOMPaul F. J. Geraedts, Ed van Tuijl, Eric A. M. Klumperink, Gerard J. M. Wienk, Bram NautaUniversity of Twente, Enschede, NetherlandsBoth ring oscillators and relaxation oscillators are subsets of RCoscillators featuring large tuning ranges and small areas. Figure19.5.1 shows a typical relaxation oscillator with a capacitor andtwo switched current sources. Such relaxation oscillators havetwo advantages with respect to ring oscillators: 1) they have aconstant frequency tuning gain; and 2) their phase can be readout continuously due to their triangular (or sawtooth) waveform.A major disadvantage of practical relaxation oscillators is theirpoor phase-noise compared to ring oscillators [1,2,4].The 1/f2 phase-noise performance of oscillators can be comparedusing the FoM definition given in Fig. 19.5.3 [1]. Navid et al. haveshown that at 290K thermodynamics limits the FoM of ring oscil-lators and relaxation oscillators to -165.3dB and -169.1dB,respectively [2]. Interestingly, they have also shown that the FoMof practical ring oscillators is generally better than about -160dB,while the FoM of practical relaxation oscillators is about 10dBworse. So in theory relaxation oscillators can be better, but inpractice they are not. Part of the explanation is given in [2]; thenoise added by the comparator, which is present in relaxationoscillators (cmposc in Fig. 19.5.1) but not in ring oscillators,increases the phase-noise. We will show below that filtering thisnoise by exploiting a switched-capacitor discharge mechanism,the FoM of a practical relaxation oscillator can be as good as theFoM of ring oscillators.Figure 19.5.2 shows the new relaxation oscillator. As in Fig.19.5.1, I1 charges capacitor C1. However, C1 is not grounded, butconnected across an OTA, and the discharge process exploits aswitched capacitor, C2, which is reversed periodically. The opera-tion of the circuit is described in the next sentences. The initialvoltage across C2 is Vref,OTA. At t0, I1 is charging C1 at a constantrate via the OTA, resulting in a linearly decreasing voltage V-. Att1, V- crosses Vref,osc and cmposc reverses C2. C2 is then beingcharged from –Vref,OTA to +Vref,OTA by I1 and the OTA. At t2, C2 ischarged to +Vref,OTA and, as a result, a fixed charge packet equalto 2C2Vref,OTA has been subtracted from C1. V3 = V+ - V- is a saw-tooth waveform. Subtracting this fixed charge packet filters outthe noise of the oscillator comparator. The operation is illustrat-ed in Fig. 19.5.3, which shows the control signal X, V3 and theoutput of the comparator cmpout, Vout, is also shown, which pro-duces an edge whenever voltage V3 reverses polarity. Supposenow that cmposc is noisy and C2 is reversed at t4 instead of at t3.Although the duty cycle of Vout is changed (at t5), the active edgeof Vout at t6 is unaffected and so is the phase-noise. This filter tech-nique is similar to the anti-jitter circuit (AJC) technique used inopen-loop jitter filters [3]; note that we apply a switched-capaci-tor circuit to subtract the charge packet, which is very power-effi-cient.  Filtering out the noise of the oscillator comparator has two con-sequences: 1) the power dissipated by the oscillator comparatorand its reference can be reduced without deteriorating the phase-noise; and 2) the two remaining contributions to the 1/f2 phase-noise are the white noise of the charging and discharging mecha-nisms. It can be shown that the resulting FoM of such a relax-ation oscillator is given by the equation in Fig. 19.5.3, where k isthe Boltzmann constant, T the absolute temperature and Pcore isthe power dissipated in the oscillator core: Pcore = VDDIcore (in W).I1 is the charge current and ΔV1 and ΔV2 (also shown in Fig.19.5.2) are the voltage headroom reserved for the charging andthe discharging mechanisms, respectively. For a good FoM wewant ΔV1 and ΔV2 to be high and about equal, while we also wanta large V3 swing to reduce the phase-noise floor contribution ofcmpout.In Fig. 19.5.1 this is not possible, since the sum ΔV1 + ΔV2 + ΔV3has to fit in the supply VDD. In Fig. 19.5.2 the voltage swing of V3mainly occurs at the output of the OTA, leaving the full VDD forΔV1 + ΔV2.Instead of reversing C2, C2 could be discharged to ground beforeconnecting it to V+, which would be easier to implement.Reversing C2 has some advantages though: 1) ΔV2 can be doubledwithout increasing power dissipation; and 2) the time allowed forsettling is doubled (C2 needs to settle only once instead of twiceevery period). By reversing C2, both a near optimal and a practi-cal choice would be ΔV1 = ΔV2 = 2VDD/3. In the case of a sawtoothwaveform, the total core current, Icore, is at least 2I1 in steadystate (= I1 + I2); the discharge current has to be equal to thecharge current. This implies a theoretical FoM of 163.2dB at290K, which is similar to that of ring oscillators.Figure 19.5.4 shows the actual implementation of the switched-capacitor relaxation oscillator. I1 is implemented by a resistivelydegenerated PMOST to increase control linearity and decreasethermal noise. M2 could be biased continuously by I2, but thiswould worsen the FoM dramatically. Only when C2 is reversed, S2is closed briefly (during tosc·I1/I2) and I2 discharges C1 through C2during this time. When S2 is opened, C2 starts settling to Vref,OTA.Note that the accuracy of the charge packet with which C1 is dis-charged is only a function of the settling of C2; noise on I2 does notaffect the accuracy. Vref,OTA is implemented as the gate-source volt-age of M2 biased at current I1.The relaxation oscillator of Fig. 19.5.4 has been designed in astandard 65nm CMOS process (VDD = 1.2V). The main designchoices are: Vref,OTA = VDD/3, Vref,osc = VDD/6, ΔV1 = ΔV2 = ΔV3 =2VDD/3, I1 = I2 = I2/4 = 25µA, C1 = C2 = 2.5pF. The measurementbuffers, oscillator comparator and its reference are designed toconsume about 2.5mA, 10µA and 5µA, respectively. The circuitryto switch I2 and reverse C2 reliably consumes about 5µA. As aresult, fosc = 12.5MHz, Icore = 2.8I1 = 70µA. According to the equa-tion in Fig. 19.5.3, the FoM is expected to be -161.7dB at 290K,which is similar to the -161.4dB predicted by simulation.Simulation also predicts a lower oscillation frequency and lowerpeak voltages than calculated, mainly due to the gate-source andgate-drain capacitances of M2. Figures 19.5.5 and 19.5.6 show the measurement results. The cir-cuit is measured using a battery supply. It is fully functional andthe performance is similar for supply voltages between 1.0 and1.3V. Unfortunately, S2 is closed for somewhat less than tosc·I1/I2,so the waveform is slightly deformed; this can be easily correctedin a re-design. The measured FoM is -162dB, which is similar toboth analysis and simulation results. Ten samples have beenmeasured and all have similar FoMs. Measurements illustrate the advantages of a relaxation oscilla-tor: the phase can be read out continuously and the tuning rangeis both large and linear. Measurements also show an outstandingphase-noise performance; the FoM is at least 7dB better thanstate-of-the-art relaxation oscillators [1,2,4] and similar to state-of-the-art ring oscillators [2]. Note that we include all the corecurrent consumption. As it seems to be increasingly more difficultto reach the minimal FoM for ring oscillators in smaller CMOStechnologies [2], relaxation oscillators could well become the pre-ferred choice of RC oscillators in low-power applications, like sen-sor networks.References:[1] S. L. J. Gierkink, A. J. M. van Tuijl, “A Coupled Sawtooth OscillatorCombining Low Jitter with High Control Linearity,” IEEE J. Solid-StateCircuits, pp. 702-710, June 2002.[2] R. Navid, T. H. Lee, R. W. Dutton, “Minimum Achievable Phase Noiseof RC Oscillators,” IEEE J. Solid-State Circuits, pp. 630-637, March 2005.[3] M. J. Underhill, “The Adiabatic Anti-Jitter Circuit,” IEEE T. Ultrasonic,Ferroelectrics, and Frequency Control, vol. 48, no. 3, pp. 666–674, May2001.[4] L. B. Oliveira, et al., “Experimental Evaluation of Phase-Noise andQuadrature Error in a CMOS 2.4 GHz Relaxation Oscillator,” ISCAS, pp.1461-1464, 2007.978-1-4244-2010-0/08/$25.00 ©2008 IEEESession_19_Penmor.qxp:Session_  12/29/07  11:42 AM  Page 348349DIGEST OF TECHNICAL PAPERS  •Continued on Page 618ISSCC 2008 / February 5, 2008 / 3:45 PMFigure 19.5.1: Relaxation oscillator based on current sources (which is part ofthe general class of relaxation oscillators based on resistors, like in [2]).Figure 19.5.2: Block-level schematic of a switched-capacitor relaxation oscillator.Figure 19.5.3: Technique to filter out the noise of the oscillator comparator(cmposc).Figure 19.5.5: Measured waveforms, frequency tuning range and frequencytuning gain (Agilent DSO6104A oscilloscope and LeCroy AP033 active differ-ential probe, R&S FSP spectrum analyzer).Figure 19.5.6: Measured phase-noise (Agilent E4440A spectrum analyzer,Keithley 2000 multimeter).Figure 19.5.4: Actual implementation of a switched-capacitor relaxation oscillator.⋅Δ⋅ΔΔ+Δ⋅⋅=⋅= +++===19Session_19_Penmor.qxp:Session_  12/29/07  11:42 AM  Page 349618 •  2008 IEEE International Solid-State Circuits Conference 978-1-4244-2010-0/08/$25.00 ©2008 IEEEISSCC 2008 PAPER CONTINUATIONSFigure 19.5.7: Die micrograph of 65nm CMOS design.

https://doi.org/10.1109/ISSCC.2008.4523200

A 90μW 12MHz Relaxation Oscillator with a -162dB FOM

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