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Course - ECE 1352 Analog Integrated Circuits I Professor – K. Phang Chopper Stabilized Amplifiers -- term paper Yiqian Ying 930360680 Department of Electrical and Computer Engineering University of Toronto Nov. 12, 2001 Chopper Stabilized Amplifiers by Yiqian Ying Page 2 of 17 Chopper Stabilized Amplifiers Abstract— In this paper, historical background and fundamental concept of chopper stabilized amplifiers are first introduced. Then effects of noise and residual offset are analyzed. Several techniques to reduce the residual offset are proposed. Also some of the disadvantages of chopper stabilization technique, as compared to correlated double sampling technique, are stated. Applications of chopper stabilized amplifiers, some latest research findings, and some new products utilizing chopper stabilization technique are given in the last two sections. I. Introduction and Historical Background Chopper stabilization (CHS) is a modulation technique that can be employed to reduce the effects of op-amp imperfections including noise (mainly 1/f and thermal noise) and the input-referred dc offset voltage. Other techniques include autozeroing (AZ), which is a sampling technique, and correlated double sampling (CDS), which is a particular case of AZ. Ideally, a chopper stabilized amplifier can eliminate dc offset and low-frequency (primarily 1/f) noise. The CHS approach was first developed by E. A. Goldberg in 1948 [1]. Actual implementations have evolved from tube types through silicon hybrids [2]. As IC technologies advance, chopper stabilization can easily be realized on-chip. Early chopper efforts involved switched ac coupling of the input signal and synchronous demodulation of the ac signal to re-establish the dc signal. While these amplifiers achieved very low offset, low offset drift, and very high gain, they had limited bandwidth and required filtering to remove the large ripple voltages generated by chopping. Chopper stabilized Chopper Stabilized Amplifiers by Yiqian Ying Page 3 of 17 amplifiers solved the bandwidth limitations by combining the chopper amplifier with a conventional wideband amplifier that remained in the signal path. However, simple chopper stabilized designs are capable of inverting operation only since the stabilizing amplifier is connected to the non-inverting input of the wideband amplifier [2]. II. Basic Principle The CHS technique uses an ac carrier to amplitude modulate the input signal. The principle of chopper amplification is illustrated in Fig. 1 with input Vin, output Vout, and A is the gain of a linear memoryless amplifier. The signal m1(t) and m2(t) are modulating and demodulating carriers with period T=1/fchop where fchop is the chopper frequency. Also, VOS and VN denote deterministic dc offset and noise. It is assumed that the input signal is bandlimited to half of the chopper frequency fchop so no signal aliasing occurs. Fig. 1. The Chopper amplification principle Chopper Stabilized Amplifiers by Yiqian Ying Page 4 of 17 Basically, amplitude modulation using a square-wave carrier transposes the signal to higher frequencies where there is no 1/f noise, and then the modulated signal is demodulated back to the baseband after amplification. For the periodic carrier with a period of T and 50% duty cycle, its Fourier representation is k sin 2 m(t ) 2 cos(2f chop kt) . k 1 k 2 (1) Its k-th Fourier-coefficients, Mk, have the property: M 0 M 2 M 4 ... 0 . (2) The modulated signal is the product of the initial signal and equation (1). The spectrum of the product Vinm1(t) in Fig. 1 shows that the signal is transposed to the odd harmonic frequencies of the modulating signal. After amplification, the modulated signal is then demodulated by multiplying m2(t) to obtain k l sin sin 2 2 Vd (t ) 4 AVin (t ) cos2f chop kt cos( 2f choplt ) l k 1 k l 1 2 2 Fig. 2 shows the Fourier transform of this noiseless demodulated output signal. Fig. 2. Fourier transform of the ideal noiseless output signal (3) Chopper Stabilized Amplifiers by Yiqian Ying Page 5 of 17 To recover the original signal in amplified form, the demodulated signal is applied to a low-pass filter with a cut-off frequency slightly above the input signal bandwidth, in this case, half of the chopper frequency. Noise and offset are modulated only once. If SN(f) denotes the power spectral density (PSD) of the noise and offset, then the PSD of (VOS + VN)m2(t) is: S CS ( f ) k M 2 k 1 S N ( f 2 2k 1 2 ) T 2 1 (2k 1) k 2 SN ( f 2k 1 ) T (4) So noise and offset are translated to the odd harmonic frequencies of the modulating signal, leaving the chopper amplifier ideally without any offset or low-frequency noise. Assume the input signal Vin is a dc signal, if the amplifier has an infinite bandwidth and no delay, the signal at its output, VA, is simply the same square wave with an amplitude AVin and the signal after demodulation is again a dc signal of value AVin. In a less ideal situation, the amplifier would have a limited bandwidth, say up to twice the chopper frequency with a constant gain of A and is zero elsewhere (ideal low-pass). As shown in Fig. 3 [3], the amplifier output signal VA(t) is now a sinewave corresponding to the fundamental component of the chopped dc signal with an amplitude (4/)(AVin). The output Vout of the second modulator is then a rectified sinewave containing even-order harmonic frequencies components. The output will have to be low-pass filtered to recover the desired amplified signal. After low-pass filtering, the dc value is (8/2)(AVin), thus an approximately 20% degradation on dc gain. So a larger bandwidth of the main amplifier results in a bigger dc gain. Chopper Stabilized Amplifiers by Yiqian Ying Page 6 of 17 Fig. 3. Effect of limited bandwidth of the amplifier on a dc input signal Delay introduced by the main amplifier could also cause degradation on overall dc gain. For example, if the amplifier has an infinite bandwidth but introduces a constant delay of T/4 while the input and output modulators are in phase, the output signal would be a chopped cosinewave, without a dc component and containing only odd harmonics, i.e., the overall dc gain of the chopper stabilized amplifier is zero. If there is the same constant delay between the input and output modulators, i.e., t in Fig. 1 equals T/4, the output signal is a rectified sinewave. These conclude that in order to maximize dc gain of the chopper amplifier, the phase shift between the two modulators needs to match precisely the phase shift introduced by the main amplifier [3]. III. Effect of Chopping on Amplifier Noises The effect of chopping on both thermal white noise and flick noise is analyzed in this section. First, let fc be the cut-off frequency of the main amplifier in Fig. 1. Note that the definition for cutoff frequency widely used is the frequency for which the transfer function magnitude is decreased by the factor 1/ 2 from its maximum value [4]. Typically, fc equals five times the chopper frequency fchop = 1/T. In baseband ( f 0.5 f chop ), SCS in equation (4) can be approximated by a white noise PSD Chopper Stabilized Amplifiers by Yiqian Ying Page 7 of 17 tanh( 2 f cT ) S CS white ( f ) S CS white ( f 0) S 0 1 f cT 2 (5) And for f c f chop , S CS white can be further approximated to S CS white ( f ) S 0 for f 0.5 f chop and f c f chop . (6) So the baseband PSD of the noise is nearly constant for large fc of the main amplifier. And the chopped-modulated PSD is smaller than but asymptotically approaches the PSD of the original white noise. For 1/f noise, the input PSD is given by S N 1/ f ( f ) S 0 fk f (7) where fk is the amplifier corner frequency. If we substitute this input PSD into equation (2), i.e., when the low-frequency noise is translated higher frequencies, the odd harmonics of fchop, the 1/f noise pole disappears from the baseband. Simulation shows that the chopped 1/f noise PSD in baseband can be approximated by [3] S CS 1 / f ( f ) 0.8525S 0 f k T . (8) The total input-referred residual noise in the baseband for a typical amplifier is the sum of equation (6) and equation (8), given by SCS ( f ) S 0 (1 0.8525 f k T ) for f 0.5 f chop and f c f chop . (9) It is reasonable to choose the chopper frequency fchop equal to the amplifier corner frequency fk. The resulting white noise PSD increase is less than 6dB. This has been verified experimentally according to [3]. Chopper Stabilized Amplifiers by Yiqian Ying Page 8 of 17 IV. Effect of Chopping on Residual Offset If the modulators are realized with MOS switches, every time a switch turns off, the charges in its conducting channel exit through the source and drain terminals. This nonideality is called charge injection, also known as clock feedthrough. It causes spikes at the input of the main amplifier. This residual offset voltage will be amplified then modulated by the output modulator. A typical spike signal in time domain is shown in Fig. 4(a) where represents the time constant of the parasitic spikes, T again is the chopper period. Since only the odd harmonics of the chopper frequency contributes to the residual offset, the spike signal has an odd symmetry. Fig. 4. (a) Spike signal at the input of the amplifier (b) spectra of spike signal of chopper-modulated signal with amplifier bandwidth characteristics The time constant in general is much smaller than T/2, so the energy of the spike signal concentrates at frequencies higher than the chopper frequency. The spectra of the spikes and the chopper-modulated signal at the input of the main amplifier are shown in Fig. 4(b). The input-referred offset can be calculated as [3]: VOS 2 Vspike T (10) Chopper Stabilized Amplifiers by Yiqian Ying Page 9 of 17 Using an amplifier with a bandwidth much larger than the chopper frequency fchop results in a dc gain approaching maximum gain A, as discussed in section II. However, this also leads to a maximum output offset voltage since almost all of the spectral components of the spike signal will contribute. A good compromise is to limit the bandwidth of the amplifier to twice the chopper frequency. The overall dc gain will be (8/2)A = 0.81A, only 19% degradation while the offset voltage is reduced drastically. The new value is [3] 2 Vspike . T 2 VOS (11) V. Techniques to Reduce Residual Offset Voltage There are several circuit techniques to reduce the residual offset voltage caused by charge injection. A simple MOS switch is shown in Fig. 5 to help the analysis. Fig. 5. Basic MOS switch Ch corresponds to the total capacitance at the switch drain (the hold capacitor) and Cp corresponds to the total parasitic capacitance at the source. Chopper Stabilized Amplifiers by Yiqian Ying Page 10 of 17 A. Complementary Switches This is the simplest technique. The theory is that the charges released by one switch are absorbed by the complementary switch to build its channel. However, it is difficult to match precisely channel charges of an n-MOS device and a p-MOS device. Phase jitter between the two complementary clocks further degrades the charge mismatch. B. Larger Capacitance A more efficient technique is to make Cp much larger than Ch and choose a slow clock transition. Most of the channel charges will be attracted to the larger capacitor Cp, leaving almost zero charges to Ch on the output side. Disadvantage of this technique is that it sets a limit on the maximum clock frequency. C. Fully Differential Structure An example of a fully differential structure is shown in Fig. 6. If we purposely set Cp = Ch, the resulting voltage appears as a common-mode voltage and is rejected. This usually requires the generation of delayed-cutoff clock phases [3]. Fig. 6. Fully differential structure Chopper Stabilized Amplifiers by Yiqian Ying Page 11 of 17 D. Multistage Cascading Several single-stage amplifiers can be cascaded to achieve high gain and speed. A sample circuit is shown in Fig. 7. Fig. 7. Multistage offset cancellation circuit Switches S1, S2, …, SN are opened successively. The effective offset voltage is only determined by charge injection of switch SN into capacitor CN in the last stage. Offset voltages at earlier stages get cancelled. The equivalent input-referred offset is VOS qinj N 1 A1 A2 ... AN C N (12) where qinj is the injected charge. This offset voltage is much smaller than that obtained for a single-stage low-gain amplifier. VI. Disadvantages of Chopper Stabilization Chopper stabilization technique aids low frequency amplifier noise performance and eliminates many of the careful design and layout procedures necessary in a classic differential approach. The most significant trade-off is increased complexity. The chopping circuitry requires significant attention for good results. Additionally, the ac Chopper Stabilized Amplifiers by Yiqian Ying Page 12 of 17 dynamics of chopper stabilized amplifiers are complex if input bandwidths greater than the carrier chopping frequency are required. Comparing to correlated double sampling (CDS) technique which can be used to enhance the effective gain of the op-amps, CHS technique causes the op-amp to amplify a higher-frequency signal, hence its effective gain is usually reduced as discussed in section II. Also the dc offset of a chopper stabilized amplifier is not eliminated, only modulated to higher frequencies. CDS is the method of choice when high dc gain and maximum signal swing are desired; In contrast, CHS is preferable for continuous-time systems and when low baseband noise is a critical requirement. VII. A Practical Implementation of Chopper Modulator A practical realization of input and output chopper modulators is presented in Fig. 8 below [3]. The four switches are controlled by complementary phases. Capacitance Cin represents the differential input capacitance of the main amplifier. Fig. 8. Implementation of the input and output chopper modulators Chopper Stabilized Amplifiers by Yiqian Ying Page 13 of 17 VIII. Applications Chopper stabilized amplifiers are a part of the design for A/D converters that are immune from the influence of low-frequency noise at the modulator input. The comparators have been realized by chopper-stabilized amplifiers to reduce the effect of the offset voltage of the MOS amplifiers since the 70’s [5]. In general, chopper stabilized amplifiers are low-noise continuous-time amplifiers useful for amplifying dc and very low frequency signals, mainly used for instrumentation application such as biomedical electronics and optoelectronics. Often the design objective is to reach the microvolt level for both offset and noise, with a bandwidth limited to a few hundred Hz while maintaining the power consumption below 100 W [3]. One typical application example is capacitive sensors for measurement of acceleration and pressure. Utilization of chopper stabilization removes the effects of offset, 1/f noise and switch charge injection. High resolution and low drift can be achieved [6]. Edge detector of image-sensors can also be chopped-stabilized. With CDS readout technique, two dimensional photodiode array can be efficiently build with only one readout circuit providing a bi-directional edge detection capability for high resolution image sensing applications operating at high frequencies [7]. IX. Latest Research and Products A latest research paper introduced generalized chopper stabilization. Traditional chopper stabilization is used in continuous-time and switched capacitor filtering [8]. The concept of CHS can be extended to linear dynamical and certain types of nonlinear circuits proved by [9]. Chopper Stabilized Amplifiers by Yiqian Ying Page 14 of 17 Switched capacitors are often sensitive to parasitic capacitances from either terminal of the capacitors to the ground. A parasitic insensitive solution for a fully balanced circuit is shown in Fig. 9 [9]; The symbol for the chopper and a traditional chopper stabilized fully balanced amplifier are shown in Fig. 10. Fig. 9. A parasitic-insensitive implementation for fully balanced circuits containing op-amps Fig. 10. (a)circuit symbol for the chopper, ( b) traditional chopper stabilized fully balanced amplifier Another paper proposed substitution of track-and-hold (T/H) for the demodulator of a conventional chopper stabilized amplifier. The advantage consists in the cancellation of the amplifier input offset, low-frequency input noise components, and residual offsets Chopper Stabilized Amplifiers by Yiqian Ying Page 15 of 17 due to input switching spikes, without requiring any low-pass filtering. One requirement is that the input signal spectrum bandwidth is smaller than 0.2 times the Nyquist frequency. However, this approach suffers a white-noise degradation due to the hold function; this degradation is minimized when maximum allowable duty cycle is 0.5 and the amplifier bandwidth is at its minimum [10]. This year, many companies released new products utilizing CHS technique. For example, The A3425LK dual chopper-stabilized, ultra-sensitive, bipolar Hall-effect switch of Allegro Microsystems is an extremely temperature-stable and stress-resistant sensor. Its superior high-temperature performance is made possible through dynamic offset cancellation by CHS, which reduces the residual offset voltage caused by device overmolding, temperature dependencies, and thermal stress [11]. In July of 2001, company Intersil released its new product ICL7650. It is said to bring “a new era in glitch-free chopper stabilized amplifiers” [12]. A single full-time main amplifier is used to avoid any output glitches; And input switching glitches are minimized by careful area- and charge-balancing on the network of input switches. The chopper operation is performed by means of a nulling amplifier which shares on input with the main amplifier [12]. X. Conclusion Chopping stabilization is one of the two major techniques for suppression of the low-frequency noise. Chopping stabilization is preferred over the other technique, autozeroing, when the system is linear and low baseband noise is the most important requirement. Chopper stabilized amplifiers are best suited for low-power, portable, very low-noise, very small offset and offset drift, high performance applications such as Chopper Stabilized Amplifiers by Yiqian Ying Page 16 of 17 electronic sensors. New products that apply chopping stabilization technique are available every year. Usage of this technique will continue to be broadened as more researches are made on this topic. Chopper Stabilized Amplifiers by Yiqian Ying Page 17 of 17 References 1. Jim Williams, Application Consideration and Circuits for a New Chopper-Stabilized Op Amp, Linear Technology online publications, March 1985, Available at: http://www.linear-tech.com/pub/document.html?pub_type=app&document=16 2. Auto-Zero Amplifiers, Products and Datasheets Whitepapers, Nov. 2001, [cited Nov. 8, 2001], Available at: http://www.analog.com/support/standard_linear/white_autozero.html 3. C. C. Enz and G. C. Temes, Circuit techniques for reducing the effects of op-amp imperfections: autozeroing, correlated double sampling, and chopper stabilization. Proceedings of the IEEE, Vol. 84, No. 11, pp. 1584-1614, November 1996 4. J. W. Nilsson and S. A. Riedel, Electric Circuits, fifth edition, Addison Wesley, 1996 5. Kh. Hadidi, V. S. Tso and G. C. Temes, Fast successive-approximation A/D converters, IEEE 1990 Custom Integrated Circuits Conference, pp. 6.1.1-6.1.4 6. B. K. Marlow, D. C. Greager, R. kemp and M. B. Moore, Highly sensitive capacitance measurement for sensors, Electronics Letters, Vol. 29, No. 21, pp. 18441845, October 1993 7. J. B. Kuo, T. L. Chou, and E. J. Wong, BiCMOS edge detector with correlateddouble-sampling readout circuit for pattern recognition neural network, Electronics Letter, Vol. 27, No. 14, pp. 1248-1250, July 1991 8. K-C. Hsieh, P. R. Gray, D. Senderowicz, and D. G. Messerschmitt, A low-noise chopper-stabilized differential switched-capacitor filtering technique, IEEE Journal on Solid-state Circuits, Vol. SC-16, No. 6, December 1981 9. L. Toth and Y. Tsividis, Generalized chopper stabilization, IEEE, I-540 to I-543, September 2001 10. A. Bilotti and G. Monreal, Chopper-stabilized amplifiers with a track-and-hold signal demodulator, IEEE Transactions on Circuits and Systems—I: Fundamental Theory and Applications, Vol. 46, No. 4, pp. 490-495, April 1999 11. 3425 datasheet, Allegro Microsystems, January. 2001, Available at: http://www.allegromicro.com/datafile/3425.pdf 12. P. Bradshaw, The ICL7650S: a new era in glitch-free chopper stabilized amplifiers, Application Note, Intersil, July 2001, Available at: http://www.intersil.com/data/AN/AN0/AN053/AN053.pdf