# The Chopper Stabilized Amplifiers Biology Essay

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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.

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. Actual implementations have evolved from tube types through silicon hybrids. 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 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.

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

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

Its k-th Fourier-coefficients, Mk, have the property:

The modulated signal is the product of the initial signal and equation . The spectrum of the product Vinïƒ-m1(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

Fig. 2 shows the Fourier transform of this noiseless demodulated output signal.

Fig. 2. Fourier transform of the ideal noiseless output signal

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)ïƒ-m2(t) is:

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 Aïƒ-Vin and the signal after demodulation is again a dc signal of value Aïƒ-Vin. 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, the amplifier output signal VA(t) is now a sinewave corresponding to the fundamental component of the chopped dc signal with an amplitude (4/ï°)(Aïƒ-Vin). 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/ï°2)(Aïƒ-Vin), thus an approximately 20% degradation on dc gain. So a larger bandwidth of the main amplifier results in a bigger dc gain.

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 cosine wave, 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., ï„t in Fig. 1 equals T/4, the output signal is a rectified sine wave. 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 .

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/from its maximum value. Typically, fc equals five times the chopper frequency fchop = 1/T. In baseband (), SCS in equation can be approximated by a white noise PSD

(5)

And for ï€¾ï€¾ , can be further approximated to

for

and .

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

where fk is the amplifier corner frequency. If we substitute this input PSD into equation, 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

The total input-referred residual noise in the baseband for a typical amplifier is the sum of equation and equation , given by

for and .

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 .

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 ï´ 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 ï´ 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:

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/ï°2)ïƒ-A = 0.81A, only 19% degradation while the offset voltage is reduced drastically. The new value is

## .

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.

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.

Fig. 6. Fully differential structure

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, â€¦, 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

where qinj is the injected charge. This offset voltage is much smaller than that obtained for a single-stage low-gain amplifier.

V1.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 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. 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 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.

VIII. ACKNOWLEDGEMENT

I would like to pronounce my profound gratitude and indebtness to my project guide Prof.Dipesh Panchal who has always been a source of constant motivation and support throughout the term paper.

IX. REFERENCES

Jim Williams, Application Consideration and Circuits for a New Chopper-Stabilized Op Amp, Linear Technology online publications, March 1985, Available at:

http://www.lineartech.com/pub/document.html?pub_type=app&document=16

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

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

J. W. Nilsson and S. A. Riedel, Electric Circuits, fifth edition, Addison Wesley, 1996

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

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. 1844-1845, October 1993

J. B. Kuo, T. L. Chou, and E. J. Wong, BiCMOS edge detector with correlated-double-sampling readout circuit for pattern recognition neural network, Electronics Letter, Vol. 27, No. 14, pp. 1248-1250, July 1991