Transcript What is Chopper Stabilization?

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 low-frequency noise voltage in an opamp.
•
Chopping is effective in combating “drift” in the offset voltage(OSV).
•
Also referred to as CHS in literature.
The “technique” expressly “chops” or “modulates” the input signal using a
square wave and somehow eliminates or minimizes the offset voltage
appearing at the output.
In this presentation, we try to understand the “how” in somehow.
Aside: The CHS approach was first developed by E. A. Goldberg in 1948.
22 jan 2009
First CHS Amplifier
1948: First chopper-stabilized op-amp
In 1949, Edwin A. Goldberg designed a chopper-stabilized op-amp. This set-up
uses a normal op-amp 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 op-amp's non-inverting input. This vastly
improved the gain of the op-amp 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 chopper-stabilized op-amp made it the dominant way to use
op-amps. Techniques that used the non-inverting input regularly would not be very
popular until the 1960s when op-amp ICs started to show up in the field.
In 1953, vacuum tube op-amps became commercially available with the release of
the K2-W from GAP/R. It sold in an octal package and had a (K2-P) chopper addon available that would effectively "use up" the non-inverting input. This op-amp
was based on a descendant of Loebe Julie's 1947 design and, along with its
successors, would start the widespread use of op-amps in industry.
Source: http://en.wikipedia.org/wiki/Operational_amplifier#1948:_First_chopperstabilized_op-amp
22 jan 2009
Effect of offset Voltage Er
Case-I:
Gain is the traditional
Av = (R/R1)
Case-II:
Av = Er + (R/R1) (ei - Er)
22 jan 2009
General Schematic & Results
Courtesy: Philbrick’s
Applications Manual
for Computing
Amplifiers for
Modeling, Measuring,
Manipulating & Much
Else
22 jan 2009
Dissembling the Schematic
CC
RB
circuit-1
circuit-2
circuit-3
Circuit-1
Circuit-2
Circuit-3
CC
RB
: primary amplifier
: chopper amplifier and passive envelope detector
: LPF
: Coupling B’ to B
: Biasing B to signal GND
25 jan 2009
Barebones OS Cancellation-1
circuit-1
circuit-2
circuit-3
Visualize the chopper circuit in “stuck” one of its states.
Eliminate all but the most necessary components in-circuit to develop the first
level of understanding.
25 jan 2009
Barebones OS Cancellation-2
circuit-1
circuit-2
circuit-3
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
Barebones OS Cancellation-3
R1
R2
vnet00
OS1 +
-A1,U1
OS2 +
-A2, U2
+
vo
Assume chopper (switch) is locked onto vnet00 implying absence of chop.
Let vnet00 be the voltage contribution by the U2-loop.
Now write the loop equation by inspection after breaking the loop at the “x”.
(vnet00-OS1)(-A1)+OS2)(-A2)*(R1/(R1+R2))=vnet00
Algebraic manipulation yields:
vnet00 = -A2*R*(OS2+A1*OS1)/(1-A1*A2*R) where R=R1/(R1+R2)
25 jan 2009
Barebones OS Cancellation-3
vnet00 = -A2*R*(OS2+A1*OS1)/(1-A1*A2*R) where R=R1/(R1+R2)
Case 1: OS1=0, (A1,A2)
vnet00
= +OS2/A1
+
V_U2
= (vnet00-OS1)*(-A1)+OS2
= ( -OS2 - 0 ) + OS2
=0
OFFSET FULLY CANCELED
Case 2: OS1=OS2=OS, (A1,A2)
vnet00
 OS+
V_U2+
= (vnet00-OS1)*(-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+
= (vnet00-OS1)*(-A1)+OS2
= (OS1 - OS1)*(-A1)+OS2
= OS2
OFFSET FULLY RETAINED
Conclusion:
The simple non-chopped 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
ToolBox- Tool 1: Energy Centric World View
(F )* t
V2( 1/R)* t
Energy
0.5 B2(1/µ0)* t
0.5 (E2)* t
Energy manifests in various forms such as voltage, current,
electric field, magnetic field, force etc, over time.
25 jan 2009
ToolBox- Tool 2: Energy in DC State
v
V
1
E=V2tR-1
E=12*1*1=1J
R=1
1s t
E = [V2(t/2) + (-V)2(t/2)] R-1
= V2tR-1
V
1
0.5s
-1
_
V _| |_
R=1
E = 12*0.5*1+(-1)2*0.5*1
= 1J
1s
Total energy is conserved*
t
but something remarkable
happens…
30 jan 2009
ToolBox- Tool 3: Fourier Transform
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
Graph of Power Distribution across Harmonics
Harmonics
= 111
PassBand
% Improvement
= 5,9
= 94%
02 feb 2009
Eliminating unwanted energy - LPF Method - i
signal
Should we do this (a very low-LPF)?
Refer to the circuit to decide.
30 jan 2009
LPF Method i …continued
- a sizable (offset) power remains in circuit at LF
+ No HF noise to content with
+ eliminating radiated power
+ less spikes on power supply
+ need less on-die power decoupling
LPF
30 jan 2009
Eliminating unwanted energy - HPF Method
- A significant HF power could remain (depending on application)
- HF content could prove noisy and radiate
+ The more significant low power content are eliminated
HPF
30 jan 2009
Eliminating unwanted energy - PassBand
- small HF power content remains
- needs some on-die power decoupling
+ the significant lower portion is eliminated
+ selective passband possible to accommodate available
decoupling, tolerance to readiated noise etc
30 jan 2009
Characteristic of the desired Square Wave
For a fixed bandpass filter, the OS-power content removed from the circuit increased with
the harmonic content in the square wave increased.
#
# of Harmonics
PassBand
(begin,end)
Improvement%
(in OS power)
1
11
5,9
93.90
2
111
5,9
94.08
3
1111
5,9
94.10
Notes
! In order to distribute the power to all available frequencies, the best possible ideal
square wave is desired.
30 jan 2009
Loop Performance
vi
R1
R2
vi’+OS2
-
sw
OS1 +
U1,-A1
n00 FILTER
n01
OS2 +
U2, -A2
+
vo
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
A final look at the Chopper Stabilized Opamp
Primary Opamp
& Feedback
DC BLOCK
BLEEDER
U2,-A2
U1,-A1
HPF
DC BLOCK
LPF
2 feb 2009
Example Chopper Stabilization
See below for Sample numbers showing the effect of chopper Stabilization. These are
taken from a pre-layout testbench. Courtesy Hong Chan, Intel Corp.
Ustabilized opamp
: U2,-A2
27mV
Stabilized opamp circuit with U1,-A1
clock stopped
: 19mV
Stabilized opamp with clock running
: 0.5mV
2 feb 2009
The Chopper Algorithm
1.
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.
2.
Chopping or “modulation” transfers energy from DC domain to odd-sine-harmonics. So
chop the energy content of the offset voltage.
i.
The best chopping occurs with an ideal square wave
U2,-A2
3.
Filter out the undesireable energy contents (harmonics) with a BandPass filter
U1,-A1
i.
Choice of pass-band
will dictate residual noise, power decoupling needed etc
ii.
About 80% of the offset-power is concentrated in the fundamental
4.
Simultaneously amplify the incoming signal which will thus benefit from being amplified
in two amplifiers.
2 feb 2009
Summary
In this presentation we have:
(1)
(2)
(3)
(4)
(5)
(6)
(7)
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,
U2,-A2
and identified it’s weaknesses with simple equations.
Developed a decent “feel” for how the harmonics can be eliminated from the product of
U1,-A1
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 “flow-chart” 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.
2 feb 2009
References
George A Philbrick Researches
Applications Manual for Computing Amplifiers for Modeling, Measuring, Manipulating & Much Else
(i)
Ideal Amplifiers: pp11
(ii) Amplifier Limitations: pp15
Philbrick’s archive : An extensive and wonderful collection.
http://www.philbrickarchive.org/
U2,-A2
U1,-A1
Philbrick’s book on computing amplifiers, as stored at Analog.
http://www.analog.com/library/analogdialogue/archives/philbrick/computing_amplifiers.html
2 feb 2009
MATLAB CODE
1.
2.
3.
U2,-A2
Rename and save as chopper_energy.m
Instructions are in the file at the header, and also find repeated below.
U1,-A1
Call as a function from
MATLAB prompt
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.
2 feb 2009