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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.

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Chopper Stabilization

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  1. Chopper Stabilization iabraham 22 jan 2009 22 jan 2009

  2. 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

  3. 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

  4. 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

  5. Courtesy: Philbrick’s Applications Manual for Computing Amplifiers for Modeling, Measuring, Manipulating & Much Else General Schematic & Results 22 jan 2009

  6. 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

  7. 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

  8. 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

  9. 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

  10. 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

  11. (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

  12. 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

  13. 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

  14. Harmonics = 111 PassBand = 5,9 % Improvement = 94% Graph of Power Distribution across Harmonics 02 feb 2009

  15. signal Eliminating unwanted energy - LPF Method - i Should we do this (a very low-LPF)? Refer to the circuit to decide. 30 jan 2009

  16. 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 LPF Method i …continued 30 jan 2009

  17. 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

  18. 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

  19. 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

  20. 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

  21. 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

  22. 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

  23. 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

  24. In this presentation we have: 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

  25. References 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

  26. MATLAB CODE • 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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