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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
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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
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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
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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(2f 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 Vin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
 k 
 l 
sin  
sin  

2
2
Vd (t )  4 AVin (t )   cos2f chop kt   cos( 2f 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)
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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 AVin and the signal after demodulation is again a dc signal of value A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 [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/)(A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/2)(AVin), thus
an approximately 20% degradation on dc gain. So a larger bandwidth of the main
amplifier results in a bigger dc gain.
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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
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


 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].
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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)
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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.
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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
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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
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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
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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].
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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
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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
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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.
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References
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Op Amp, Linear Technology online publications, March 1985, Available at:
http://www.linear-tech.com/pub/document.html?pub_type=app&document=16
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8, 2001], Available at:
http://www.analog.com/support/standard_linear/white_autozero.html
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imperfections: autozeroing, correlated double sampling, and chopper stabilization.
Proceedings of the IEEE, Vol. 84, No. 11, pp. 1584-1614, November 1996
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Letter, Vol. 27, No. 14, pp. 1248-1250, July 1991
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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
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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