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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.

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Chopper stabilization l.jpg

Chopper Stabilization

iabraham

22 jan 2009

22 jan 2009


So what is chopper stabilization l.jpg

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 l.jpg

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 op-amp. 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 non-inverting 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 add-on 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_chopper-stabilized_op-amp

First CHS Amplifier

22 jan 2009


Effect of offset voltage er l.jpg

Case-I:

Gain is the traditional

Av = (R/R1)

Effect of offset Voltage Er

Case-II:

Av = Er + (R/R1) (ei - Er)

22 jan 2009


General schematic results l.jpg

Courtesy: Philbrick’s

Applications Manual for Computing Amplifiers for Modeling, Measuring, Manipulating & Much Else

General Schematic & Results

22 jan 2009


Dissembling the schematic l.jpg

circuit-1

circuit-2

circuit-3

Dissembling the Schematic

CC

RB

Circuit-1 : primary amplifier

Circuit-2 : chopper amplifier and passive envelope detector

Circuit-3 : LPF

CC : Coupling B’ to B

RB : Biasing B to signal GND

25 jan 2009


Barebones os cancellation 1 l.jpg

circuit-1

circuit-2

circuit-3

Barebones OS Cancellation-1

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 l.jpg

circuit-1

circuit-2

circuit-3

Barebones OS Cancellation-2

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 l.jpg

R1

R2

vnet00

-

vo

-A1,U1

+

OS1 +

OS2 +

Barebones OS Cancellation-3

-A2, U2

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 310 l.jpg

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.

Barebones OS Cancellation-3

25 jan 2009


Toolbox tool 1 energy centric world view l.jpg

(F )* t

ToolBox- Tool 1: Energy Centric World View

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


Toolbox tool 2 energy in dc state l.jpg

V

t

v

ToolBox- Tool 2: Energy in DC State

1

E=V2tR-1

E=12*1*1=1J

R=1

1s

_

V _| |_

E = [V2(t/2) + (-V)2(t/2)] R-1

= V2tR-1

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


Toolbox tool 3 fourier transform l.jpg

ToolBox- Tool 3: Fourier Transform

Chopping (or modulation with a square wave) has now mapped the energy from the DC-domain 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 l.jpg

Harmonics = 111

PassBand = 5,9

% Improvement = 94%

Graph of Power Distribution across Harmonics

02 feb 2009


Eliminating unwanted energy lpf method i l.jpg

signal

Eliminating unwanted energy - LPF Method - i

Should we do this (a very low-LPF)?

Refer to the circuit to decide.

30 jan 2009


Lpf method i continued l.jpg

LPF

LPF Method i …continued

30 jan 2009


Eliminating unwanted energy hpf method l.jpg

  • 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

Eliminating unwanted energy - HPF Method

30 jan 2009


Eliminating unwanted energy passband l.jpg

  • 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

Eliminating unwanted energy - PassBand

30 jan 2009


Characteristic of the desired square wave l.jpg

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.

! In order to distribute the power to all available frequencies, the best possible ideal square wave is desired.

30 jan 2009


Loop performance l.jpg

vi

R1

R2

vi’+OS2

-

sw

U2, -A2

vo

FILTER

n00

n01

U1,-A1

+

OS1 +

OS2 +

Loop Performance

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 l.jpg

Primary Opamp & Feedback

DC BLOCK

BLEEDER

HPF

DC BLOCK

LPF

A final look at the Chopper Stabilized Opamp

U2,-A2

U1,-A1

2 feb 2009


Example chopper stabilization l.jpg

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 : 27mV

Stabilized opamp circuit with clock stopped : 19mV

Stabilized opamp with clock running : 0.5mV

U2,-A2

U1,-A1

2 feb 2009


The chopper algorithm l.jpg

  • 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.

  • Chopping or “modulation” transfers energy from DC domain to odd-sine-harmonics. So chop the energy content of the offset voltage.

    • The best chopping occurs with an ideal square wave

  • Filter out the undesireable energy contents (harmonics) with a BandPass filter

    • Choice of pass-band will dictate residual noise, power decoupling needed etc

    • About 80% of the offset-power is concentrated in the fundamental

  • Simultaneously amplify the incoming signal which will thus benefit from being amplified in two amplifiers.

  • The Chopper Algorithm

    U2,-A2

    U1,-A1

    2 feb 2009


    Summary l.jpg

    In this presentation we have: manifestation of energy. It is energy we’re going to deal with fundamentally - in the (V,t) domain in this case.

    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 “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.

    Summary

    U2,-A2

    U1,-A1

    2 feb 2009


    References l.jpg

    References manifestation of energy. It is energy we’re going to deal with fundamentally - in the (V,t) domain in this case.

    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 code l.jpg

    MATLAB CODE manifestation of energy. It is energy we’re going to deal with fundamentally - in the (V,t) domain in this case.

    • Rename and save as chopper_energy.m

    • Instructions are in the file at the header, and also find repeated below.

    • 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.

    U2,-A2

    U1,-A1

    2 feb 2009


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