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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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2

of 17





Chopper Stabilized Amplifie
rs

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 so
me 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 o
f 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 a
chieved 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

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amplifiers solved the bandwidth limitations by combining the chop
per 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 wideban
d 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 V
in
, output V
out,

and A
is the gain of a linear memoryless amplif
ier. The signal m
1
(t) and m
2
(t) are modulating
and demodulating carriers with period T=1/f
chop
where f
chop

is the chopper frequency.
Also, V
OS

and V
N

denote deterministic dc offset and noise. It is assumed that the input
signal is bandlimited to half of t
he chopper frequency f
chop

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 modulate
d 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

.






(1)


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

.







(2)

The modulated signal is the product of the initial signal and equation (1). The spectrum of
the product V
in

m
1
(t) in Fig. 1 shows that the signal is transposed to the odd harmonic
frequencies of the modulating signal. After amp
lification, the modulated signal is then
demodulated by multiplying m
2
(t) to obtain



(3)


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






Fig. 2.

Fourier transform of the

ideal noiseless output signal


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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 a
nd offset are modulated only once. If S
N
(f) denotes the power spectral
density (PSD) of the noise and offset, then the PSD of (V
OS
+ V
N
)

m
2
(t) is:














(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 V
in
is a dc signal, if the amplifier has an infinite
bandwidth and no delay, the signal at its output, V
A
, is simply the same
square wave with
an amplitude A

V
in

and the signal after demodulation is again a dc signal of value A

V
in
.
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 V
A
(t) is now a sinewave corresponding to
the fundamental component of the chopped dc signal with an amplitude (4/

)(A

V
in
). The
output V
out

of the second modulator is then a re
ctified 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

V
in
), 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 exampl
e, 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 ov
erall 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 ga
in 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 fli
ck noise is analyzed in
this section.


First, let f
c

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 [4].
Typically, f
c

equals five times the chopper frequency f
chop
= 1/T. In baseband
(
), S
CS

in equation (4) can be approximated by a white noise PSD


Chopper Stabilized Amplifiers

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(5)

And
for



,

can be further approximated to




for

and
.


(6)

So the baseband PSD of the noise is nearly constant for l
arge f
c
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










(7)

where f
k

is the amplifier corner f
requency. If we substitute this input PSD into equation
(2), i.e., when the low
-
frequency noise is translated higher frequencies, the odd
harmonics of f
chop
, the 1/f noise pole disappears from the baseband. Simulation shows
that the chopped 1/f noise PSD i
n baseband can be approximated by [3]









(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



for

and
.


(9)

It is reasonable to choose the chopper frequency f
chop

equal to the amplifier corner
frequency f
k
. 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, al
so 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 ti
me 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) s
pectra 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 spec
tra 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]:











(10)


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Using an amplifier with a bandwidth much larger than th
e chopper frequency f
chop

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 compr
omise 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]


.







(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

C
h
corresponds to
the total capacitance at the switch drain (the hold capacitor) and C
p
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 absorb
ed 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 Capaci
tance


A more efficient technique is to make C
p

much larger than C
h

and choose a slow
clock transition. Most of the channel charges will be attracted to the larger capacitor C
p
,
leaving almost zero charges to C
h

on the output side. Disadvantage of this tec
hnique 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
C
p

= C
h
, the resulting voltage appears as a common
-
mode voltage and is re
jected. 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 sho
wn in Fig. 7.


Fig. 7.
Multistage offset cancellation circuit


Switches S
1
, S
2
, …, S
N

are opened successively. The effective offset voltage is
only determined by charge injection of switch S
N

into capacitor C
N

in the last stage.
Offset voltages at earlier

stages get cancelled. The equivalent input
-
referred offset is









(12)

where q
inj

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


VI. Disadvantages of Choppe
r 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 complex
ity. 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 do
uble 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 o
f 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 n
oise 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 C
in

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 ampl
ifiers 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 le
vel 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 choppe
r 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 i
ntroduced 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
cho
pper 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 bala
nced 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 degradat
ion 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 n
ulling 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,
autozer
oing, 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

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elect
ronic 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

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/s
upport/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. 15
84
-
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. 1844
-
1845, October 1993

7.

J. B. Kuo, T. L. Chou, and E. J. Wong, BiCMOS edge detector with correlated
-
do
uble
-
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
-
capaci
tor 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