Chopper Stabilization. iabraham 22 jan 2009. 22 jan 2009. So what is Chopper Stabilization?. Probably better described as Offset Stabilization in Opamps by using a Chopper Circuit Minimize the input offset voltage  and possibly any lowfrequency noise voltage in an opamp.
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22 jan 2009
1948: First chopperstabilized opamp
In 1949, Edwin A. Goldberg designed a chopperstabilized opamp. This setup uses a normal opamp with an additional AC amplifier that goes alongside the opamp. The chopper gets an AC signal from DC by switching between the DC voltage and ground at a fast rate (60Hz or 400Hz). This signal is then amplified, rectified, filtered and fed into the opamp's noninverting input. This vastly improved the gain of the opamp while significantly reducing the output drift and DC offset. Unfortunately, any design that used a chopper couldn't use their noninverting input for any other purpose. Nevertheless, the much improved characteristics of the chopperstabilized opamp made it the dominant way to use opamps. Techniques that used the noninverting input regularly would not be very popular until the 1960s when opamp ICs started to show up in the field.
In 1953, vacuum tube opamps became commercially available with the release of the K2W from GAP/R. It sold in an octal package and had a (K2P) chopper addon available that would effectively "use up" the noninverting input. This opamp was based on a descendant of Loebe Julie's 1947 design and, along with its successors, would start the widespread use of opamps in industry.
Source: http://en.wikipedia.org/wiki/Operational_amplifier#1948:_First_chopperstabilized_opamp
22 jan 2009
Gain is the traditional
Av = (R/R1)
CaseII:
Av = Er + (R/R1) (ei  Er)
22 jan 2009
Applications Manual for Computing Amplifiers for Modeling, Measuring, Manipulating & Much Else
22 jan 2009
circuit2
circuit3
CC
RB
Circuit1 : primary amplifier
Circuit2 : chopper amplifier and passive envelope detector
Circuit3 : LPF
CC : Coupling B’ to B
RB : Biasing B to signal GND
25 jan 2009
circuit2
circuit3
Visualize the chopper circuit in “stuck” one of its states.
Eliminate all but the most necessary components incircuit to develop the first level of understanding.
25 jan 2009
circuit2
circuit3
The simple and intuitive “idea” is to have net B’ mirror a scaled copy of OS(main_amp). The stabilizer will amplifiy and invert this value to cancel the offset at input A of the main_amp.
25 jan 2009
R2
vnet00

vo
A1,U1
+
OS1 +
OS2 +
A2, U2
Assume chopper (switch) is locked onto vnet00 implying absence of chop.
Let vnet00 be the voltage contribution by the U2loop.
Now write the loop equation by inspection after breaking the loop at the “x”.
(vnet00OS1)(A1)+OS2)(A2)*(R1/(R1+R2))=vnet00
Algebraic manipulation yields:
vnet00 = A2*R*(OS2+A1*OS1)/(1A1*A2*R) where R=R1/(R1+R2)
25 jan 2009
vnet00 = A2*R*(OS2+A1*OS1)/(1A1*A2*R) where R=R1/(R1+R2)
Case 1: OS1=0, (A1,A2)
vnet00 = +OS2/A1
V_U2+ = (vnet00OS1)*(A1)+OS2
= ( OS2  0 ) + OS2
= 0 OFFSET FULLY CANCELED
Case 2: OS1=OS2=OS, (A1,A2)
vnet00 OS+
V_U2+ = (vnet00OS1)*(A1)+OS2
= (OS+  OS)*(A1)+OS
= some residual (small,big) number OFFSET PARTIALLY CANCELED
Case 3: OS1 != OS2, (A1,A2)
vnet00 = (OS2+A1*OS1)/A1 ~ OS1
V_U2+ = (vnet00OS1)*(A1)+OS2
= (OS1  OS1)*(A1)+OS2
= OS2 OFFSET FULLY RETAINED
Conclusion:
The simple nonchopped scheme did not conclusively eliminate the offset under all conditions. Case 2 was the fuzzy boundary between full cancellation and full retention.
25 jan 2009
V2( 1/R)* t
0.5 B2(1/µ0)* t
Energy
0.5 (E2)* t
Energy manifests in various forms such as voltage, current, electric field, magnetic field, force etc, over time.
25 jan 2009
t
v
1
E=V2tR1
E=12*1*1=1J
R=1
1s
_
V _ _
E = [V2(t/2) + (V)2(t/2)] R1
= V2tR1
E = 12*0.5*1+(1)2*0.5*1
= 1J
Total energy is conserved* but something remarkable happens…
V
1
R=1
1s
0.5s
t
1
30 jan 2009
Chopping (or modulation with a square wave) has now mapped the energy from the DCdomain into multiple frequency domains.
! Remember  The total energy in the harmonics must be equal to the energy in the square wave by virtue of conservation of energy
30 jan 2009
Should we do this (a very lowLPF)?
Refer to the circuit to decide.
30 jan 2009
a sizable (offset) power remains in circuit at LF
LPF
30 jan 2009
A significant HF power could remain (depending on application)
HPF
30 jan 2009
small HF power content remains
30 jan 2009
For a fixed bandpass filter, the OSpower content removed from the circuit increased with the harmonic content in the square wave increased.
! In order to distribute the power to all available frequencies, the best possible ideal square wave is desired.
30 jan 2009
R1
R2
vi’+OS2

sw
U2, A2
vo
FILTER
n00
n01
U1,A1
+
OS1 +
OS2 +
By virtue of the loop around Opamp –A2, the negative input of U2, has a very small copy of vi, and OS2.
EQN 1: Vn01 = A1*vi’+ A1*n{(OS1+OS2*)}+OS2 ( term1+term2+term3)
EQN 1 shows two ways to cancel the offset
Case 1: Eliminate filtering altogether and set A1<1 (cancelling term 2 against term3)
ie –A1(OS1+OS2*) = OS2
Unfortunately,
(i) A1<1 means that the amplifier U1 does not benefit the signal at all.
(ii)A1<1 also means that we’re planning to leave all the harmonics in, making for a very noisy circuit
(iii) Attenuation is not a substitute for elimination
Case 2: A1 > 1 such that
ie A1*n*(OS1+OS2*)=OS2
For A1>1, there is the benefit that vi’ gets to be amplified first by U1, then by U2.
2 feb 2009
See below for Sample numbers showing the effect of chopper Stabilization. These are taken from a prelayout testbench. Courtesy Hong Chan, Intel Corp.
Ustabilized opamp : 27mV
Stabilized opamp circuit with clock stopped : 19mV
Stabilized opamp with clock running : 0.5mV
U2,A2
U1,A1
2 feb 2009
Recognize that voltage in time, (V,t) is yet another manifestation of energy. It is energy we’re going to deal with fundamentally  in the (V,t) domain in this case.
U2,A2
U1,A1
2 feb 2009
Ingrained the fundamental notion that while design deals with (V,t), energy is the true quantity we’re after.
Associated “chopping” with a Fourier Decomposition from an energy perspective.
Worked through our own ideas of how we could implement offset cancellation intuitively, and identified it’s weaknesses with simple equations.
Developed a decent “feel” for how the harmonics can be eliminated from the product of chopping.
Identified the function of each component in one implementation of chopper stabilization as practiced by George A Philbrick Researches Inc..
Developed rudimentary equations to understand how the different loops work.
Generated a “flowchart” understanding of chopper based stabilization as applicable to opamps.
This should pave the way to understanding more complex styles and implementations of chopper stabilization of which there must be a wide variety.
U2,A2
U1,A1
2 feb 2009
George A Philbrick Researches
Applications Manual for Computing Amplifiers for Modeling, Measuring, Manipulating & Much Else
Ideal Amplifiers: pp11
Amplifier Limitations: pp15
Philbrick’s archive : An extensive and wonderful collection.
http://www.philbrickarchive.org/
Philbrick’s book on computing amplifiers, as stored at Analog.
http://www.analog.com/library/analogdialogue/archives/philbrick/computing_amplifiers.html
U2,A2
U1,A1
2 feb 2009
MATLAB>> chopper_energy(harmonic_length,begin_passband, end_passband))
harmonic_length is the number of harmonics desired in the square wave
begin_passband is the pth harmonic at which passband opens up.
end_passband is the qth harmonic at which passband closes down.
U2,A2
U1,A1
2 feb 2009