Noise Analysis and Simulation of Chopper Amplifier

Tao Yin' 2, Haigang Yang1 Quan Yuan' 2 and Guoping Cuil,21 The State Key Lab of Transducer Technology, Institute of Electronics, CAS

2 Graduate University of the Chinese Academy of SciencesBeijing, China

(*Corresponding Author: yanghgWmail.ie.ac.cn)

Abstract Conventional SPICE-like simulators are notadequate for the noise simulation of the chopper amplifier, whichtypically has no DC operating point. This paper discusses thenoise properties of the chopper amplifier in both time domainand frequency domain and presents a method of simulatingchopper amplifier noise behavior with the RF simulator-SpectreRF. The simulation results for a designed circuit are given.A comparison between the simulation and the calculation resultsshows effectiveness and efficiency of this method in dealing withchopper amplifier noise simulation.

Keywords chopper amplifier, low noise, noise simulation

I. INTRODUCTIONThe Chopper technique is widely used in precision

amplifier design for its low noise and low offset characteristics.What's more, its continuous signal level and low noise foldingcompared to the autozero/CDS techniquel'l make it suitable inthe sensor readout applications such as capacitive sensing.

References [1-3] have discussed in depth about somedesign considerations of the chopper amplifier and have alsogiven the measured performance. However, none of them haveincluded the noise simulation of the chopper amp. A chopperamp transfers its low frequency noise and DC offset onto thehigh frequency by modulation. The modulation is normallyimplemented with four MOSFET switches that are open andclosed alternatively. Therefore, there exist strong nonlinearitiesand no DC operating point in this kind of circuit. As a result,the noise effect can hardly be simulated using conventionalSPICE-like simulators because of their algorithms limitingthem to do the noise analysis only based on a DC operatingpoint of the circuit. But in practice, an effective noisesimulation of the chopper amplifier is usually required todetermine the non-ideal influence on the system performance,which should give more accurate prediction than the calculatedone where some degree of approximation is assumed.

SpectreRF is known for its RF simulation capacity and isavailable as an option in Spectre, a SPICE-like simulator fromCadence Design Systems[4]. SpectreRF provides a powerful andunique way of analysis that offers designers the ability topredict the performance of the switched capacitor filters whileincluding all of the important second-order effects [5]. But untilnow there is no report with regard to a noise simulation methodespecially for chopper amplifiers.

This paper first briefly presents the principle of the chopperamplifier technique in Section II. It is followed, in Section III,by a discussion of the effect of chopping on the amplifier noisein both time and frequency domain. Then a noise simulationexample of a transistor level chopper amplifier is described inSection IV, based on commercial tools such as SpectreRF withthe help of conventional SPICE-like simulators. Thissimulation method is also useful in the noise simulation of theconventional capacitive sensing readout circuit, which alsoextensively uses the chopper technique to reduce the offset and1/f noise. Finally, a brief discussion and a summary arepresented in Section V.

II. PRINCIPLE OF CHOPPER AMPLIFIER TECHNIQUE

Suppose that the input signal V,, has a spectrum limited tohalf of the chopper frequency so no signal aliasing occurs. Theprinciple of the chopper technique is shown in Fig. 1.The inputsignal is modulated to the chopping frequency, amplified andmodulated back to the baseband. The offset and 1/f noise ismodulated only once and appears at the chopping frequencyand its odd harmonics. These frequency components can beremoved through a low-pass filter.

m(t) Tr 17

x(t) + Y(t) Vout

J_signal Cg alvnos Sga1 i1noise

5,@htil) tAlmo f3 fhop 5,X

Vi. V V

sinal g nosAVi Vos siCalI signalV I *tVA(VJ-u AftlsVnJo,2TV T 2T T ST

Figure 1. Principle of chopping technique including signals in frequencyand time domain.

Apart from the frequency domain, the chopping principlecan also be explained in the time-domain. In that case, the inputsignal is periodically inverted by the first multiplier or thechopper. After amplification, the inverted and amplified signalis inverted for the second time, resulting again in a dc signal.The offset is periodically inverted only once and thereforeappears as a square wave at the output [3], which will be filtered

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out by the output low-pass filter. This way, a chopper amplifiercan suppress the DC offset and low frequency noise to achievea high precision.

III. EFFECT OF CHOPPING ON THE NOISE OF AMPLIFIER

The thermal noise and low frequency 1/f noise is the mainlimit on the low noise amplifier design. Chopping techniquecan effectively reduce the low frequency noise of the amplifierwithout significant folding of the thermal noise . Asmentioned earlier, the effect of chopping on the amplifier noisecan also be analyzed in time and frequency domainrespectively.

A. Time domain analysis

m

Figure 2. A simple noise chopping process diagram

A simple noise chopping process is described in fig.2. Thenoise voltage VNO(t) after modulation can be derived as follows,in which co, stands for the chopping frequency of m(t).

VOt

VNo(t) = E - VN(t) sin(kilt) (1)k=l kik=odd

1) Narrowband noise:For a Gaussian distributed narrowband noise V"(t) with zero

mean value, which has a No12 power spectral density (PSD) in(wan-B12- 0)n+B12), it can be decomposed into two separate lowfrequency Stationary Stochastic Processes n,(t) and ns(t)j6', asshown in Fig.3.

V, (t) = n, (t) cos wvt- ns (t) sin 0wnt (2)After chopping, the noise voltage

4VNO (t= E[k (n, (t) cos0),t-ns(t) sin ojt)

k=l kik=odd

* sin(kwi1t)] (3)Then after low-pass filter, the sum-frequency term in form

equation is filtered out and the final noise voltage is

2VNout (t) = - [n, (t). sin(wol - (0n )t

if

N(2

Is _ Oi

0 K812 0

Figure 3. Narrowband noise and its orthogonal sinusoidal and cosinusoidalPSD

2) Wideband noise:If noise is wideband such as thermal noise, then for the

VnCOs('wnt+q) component in the wideband noise, the choppedresult is

VNO (t) = x V, sin(cwt + yp)x sin(kw1t)k=l krk=odd

2 1= V, i cos[(kwl-won )t-y]

f k=l kk=odd

-cos [(kw1 +wvn )t +Q]} (6)Then after low-pass filter, the sum-frequency term in (6) is

filtered out and the final noise voltage is

VNOUt =-VIk l Cos[(ow -kwoil)t+y])Z k=l k

k=odd

(7)

So the output noise is not only appear around COn= o1 butaround wo,=(2n -)w)1 (n is integer). This is like a comb filterwhose magnitude frequency response is shown in Fig.4. Whenthe noise component whose frequency is (2n -)w)1 multiplieswith correspond harmonic component of the chopper signal, itwill produce a DC output after the low-pass filter. This outputwill increase the output noise and add harmonic component inthe output signal, too.

delative m agnitude

Figure 4. Output noise hannonics response

(4)So when w,zcoj, which is the usual case after the noise

passes through a band-pass selective amplifier, the first term in(4) can be neglected. So the output noise voltage is reduced.

2VNoUt(t) -- n (t) (5)

if

B. Frequency domain analysisNoise characteristics of a chopper amp in frequency domain

have been discussed in [1-3] in details. This process is shownin Fig.5 with the amplifier. We directly present the results. Theequivalent amplifier input noise PSD can be expressed as (8),in which SNO stands for the thermal noise PSD and fk for thecorner frequency of 1/f noise.

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"'k-N(a

11 VI' I- aco,,-N2 'o It,ll+..

+ n, (t) - cos(w, w')t]

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(8)SNJ, = SNO (1+ fk)m(f1

VN VoutA(h x

Figure 5. Noise chopping process diagram with internal amplifier

If the bandwidth of the amplifier is far larger than thechopper frequency, then the final output low frequency noisePSD after low-pass filter is

2f 22 fk)(9SNoUw= SNO A° (L42 2 (9)odd

So the input equivalent noise PSD is

SNin ' SNO (1 + 2 fkh) (10)

Equation (10) shows that when the bandwidth of theamplifier is infinite, the thermal noise stays constant afterchopper modulation. In contrast to an autozero amplifier, whichis also widely used in the high precision design, the thermalnoise in chopper amplifier isn't aliased. Then, a chopperamplifier can obtain a very low low-frequency noise. And the1/f noise is reduced obviously when fchop>>fk. But the fchopcannot be too high, because high fchop will induce substantialresidual offset, which will degrade the accuracy of the chopperamplifier [1,2]

IV. NOISE SIMULATION WITH SPECTRERFAs discussed before, chopper amplifier uses modulation to

reduce the low frequency noise. The modulator is implementedwith four MOSFET switches, as shown in Fig.6. Theyalternatively open and close to chop the signal added with noise.Noise calculations in conventional SPICE-like simulators arebased on a small-signal linearized model of the circuit at its DCoperating point[7]. Because of the linearization, frequencytranslation of noise due to the switch modulation cannot bedirectly determined in these simulators. For example, SPICEcan only calculate the noise of a circuit based on the DCoperating point when 0 and Ob are fixed but cannot calculatewhen 0 and Ob are constantly changing. Thus, the traditionalSPICE-like analysis cannot be used for estimating noise inchopper amplifiers.

The SpectreRF simulator extends the traditional time-domain algorithms to handle RFIC simulation. It uses theNewton shooting method[7] to calculate the periodic steady-state (PSS) response of those circuits including oscillators. Theperiod of the chopper amplifier is the time when a modulationswitch is opened once and closed once. What's more,SpectreRF can efficiently handle the circuits with strongnonlinearities.

-lp+ 7T v +~~~~

Vin H M Vout

Figure 6. Chopper modulator

The first step to simulate a chopper amplifier withSpectreRF is to calculate the periodic steady-state (PSS)response of the circuit to determine the periodical operatingpoint. With the PSS analysis, the input of a circuit is biased to acommon input voltage with only the chopper clock applied.The chopper clock will help to determine the period of thecircuit's PSS response. Based on the calculated periodicaloperating point, SpectreRF can simulate the noise of thechopper amplifier. There are two numerical parameters thatwill affect the simulation accuracy and time [4' 'I. They are'maxacfreq' and 'maxsideband'.

Parameter maxacfreq specifies the maximum frequency thatwill be used in any subsequent small-signal analysis such as thenoise analysis. This helps the PSS analysis choose a time stepaccurate for the small-signal analysis. Its value is affected byboth the maximum small-signal analysis frequency (generallythe simulation stop frequency) and the maximum number ofthesidebands of interest, such that maxacfreq > ftop +fchopxmaxsideband where fchop is the clock frequency. Forexample, in our simulation the ftop is chosen to be 10kHz,larger than the 1kHz bandwidth of the whole chopper amplifier,fchop to 62.5kHz, larger than the 1/f noise corner frequency ofthe amplifier and maxsideband to 15. So the maxacfreq must belarger than 947.5 kHz. Higher values can actually increase theaccuracy, but will also result in slower simulation.

Maxsideband is used in our SpectreRF's noise simulation todetermine how much noise aliasing of the chopping modulationshould be considered. The noise aliasing of the chopperamplifier is small in contrast to that of the autozero counterpart[1]* Yet we still compare the simulation results for differentmaxsideband values in order to choose an optimalmaxsideband value in simulation.

Vin+Vin-

Vein

Figure 7. Preamplifier schematic

A SpectreRF simulation is performed on a simple chopperamplifier whose block diagram is similar to Fig.1. Differencelies in that the amplifier is composed of low-noise wide-bandpreamplifier and a middle-staged amplifier. Preamplifierconsists of a transconductance input stage and a linearizedtransimpedance in a folded cascode configuration which is

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shown in Fig.7. Elaborate work is done to ensure the amplifierhas a wide bandwidth far larger than the chopping frequency.In this way we can predict the final noise performance of thechopper amplifier through (9) to (10).

200-

Without chopper tech.

increases, however the simulation time will increasesignificantly when maxbandside reach 100 and 500. Thesimulation results also show the noise aliasing of the chopperamplifier is small in contrast to that of the autozerocounterpart[1, 5]. We can choose maxbandside to be as smallas 10-15 which will sufficiently ensure a good simulationaccuracy (<0.7%) and at the same time a less simulation time.

TABLE I. SIMULATION RESULTS WITH DIFFERENT MAXBANDSIDES'

0~

With chopper tech.

10 100 Ik 10kFrequency(Hi)

Figure 8. The simulation results of input equivalent noise at 62.5kHzchopping frequency.

The simulation results of the amplifier with and withoutchopping are shown in Fig.8. The Spectre simulation resultshows that the low-frequency noise of the amplifier is veryhigh due to the 1/f noise whose corner frequency is about 32kHz and the input equivalent thermal noise is 8.2nVN1Hz. Afterapplying the chopper technique with a 62.5 kHz choppingfrequency, SpectreRF simulation shows that the low-frequencynoise becomes almost flat with only 10.23nVThHz inputequivalent noise. The calculated input noise from (10) is about9.85 nVN1Hz. The simulation result is a bit larger than thecalculated result because the calculation neglects the noisecontribution of the modulation switches and output low-passfilter.

Other simulations with different chopping frequencies arealso performed using SpectreRF and the results are shown inFig.9. The simulation input equivalent noise decreases with theincreasing chopping frequency, which agrees with the noisepredicted from (10). The simulation and calculation result areless consistent at higher chopper frequencies because the realbandwidth of the amplifier is not infinite, which will reduce thegain of the amplifier and lead to an increase in the simulationinput equivalent noise.

1: o=

Q

In - IJ=|t

0 20 40 60 W 100 120Choppiog f-jqo-y{kHz)

Figure 9. The input equivalent noise at different chopping frequency.

The simulation results with different maxbandsideparameters are shown in Table.1. It shows that the noisesimulation results are almost constant as the maxbandside

Maxband-sides

510152050100500

Time Simulation Simulated inputsteps time (s) noise (n V\I$Hz)966968968984104011983062

91.8103.2115.5126.3211.4409.54062.5

10.1110.1910.2310.2410.25210.25310.253

Calculated inputnoise (n V\I$Hz)

9.7189.7909.8149.8269.8479.8549.859

V. CONCLUSION

This paper discussed how RF simulator--SpectreRF can beused to simulate the noise effect of the chopper amplifier whichhas no DC operation point. In order to compare the simulationresults with the theory, we also describe the principle and noisecharacteristics of the chopper amplifier separately from timeand frequency domain. It has been shown that the noisesimulation of the chopper amplifier with RF simulator--SpectreRF is an effective and efficient way of analysis. Thissimulation method can also be applied to the noise simulationof the conventional capacitive readout circuits, which also usethe chopper technique to reduce the 1/f noise. A chip for furtherverifying the analysis and simulation described in this paper isbeing fabricated in Chartered 0.35,um CMOS 2P4M process.

REFERENCES[1] C. C. Enz and G. C. Temes, "Circuit techniques for reducing the effects

of op-amp imperfections: Autozeroing, correlated double sampling, andchopper stabilization," Proc. IEEE, vol. 84, pp. 1584-1614, Nov. 1996.

[2] C. Menolfi and Q. Huang, "A low-noise CMOS instrumentationamplifier for thermoelectric infrared detectors," IEEE JSSC, vol. 32, pp.968-976, July 1997.

[3] A. Bakker, K. Thiele, and J. Huijsing, "A CMOS Nested-ChopperInstrumentation Amplifier with 100-nV Offset", IEEE JSSC, vol. 35, no.12, pp. 1877-1883, Dec. 2000.

[4] Cadence Design Systems. (2000) Affirma RF Simulator User Guide.[Online]. Available: http://www.cadence.com

[5] K. Kundert, "Simulating Swiched-Capacitor Filters with SpectreRF",[Online] http://www.designer- guide.org, 2005.

[6] Jinzhan Gao, "Weak Signal Detection", China,Beijing, Tsinghua Univ.Press, pp. 21-27, 2004.

[7] K. Mayaram, D. C. Lee, S. Moinian, D. A. Rich, and J. Roychowdhury"Computer-Aided Circuit Analysis Tools for RFIC Simulation:Algorithms, Features, and Limitations", IEEE Trans. on Circ. and Syst.-II: ADSP, vol. 47, no. 4, pp. 274-286, Apr. 2000.

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