2 Outline Definitions Differentialinput amplifier Commonmode voltage Commonmode rejection ratio CMRR Commonmode rejection CMR CMRR in Operational Amplifiers CMRR in Difference Amplifiers ID: 1030890
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1. 1Fully Understanding CMRR in DAs, IAs, and OAs
2. 2OutlineDefinitionsDifferential-input amplifierCommon-mode voltageCommon-mode rejection ratio (CMRR)Common-mode rejection (CMR)CMRR in Operational AmplifiersCMRR in Difference AmplifiersCMRR in Instrumentation AmplifiersCMRR in ‘Hybrid’ Amplifiers
3. 3Differential Input AmplifierDifferential input amplifiers are devices/circuits that can input and amplify differential signals while suppressing common-mode signalsThis includes operational amplifiers, instrumentation amplifiers, and difference amplifiersDifferenceAmplifierInstrumentation AmplifiersOperationalAmplifier
4. 4Common-Mode VoltageFor a differential input amplifier, common-mode voltage is defined as the average of the two input voltages. [2]
5. 5Common-Mode Voltage (Alternate defn.)For a differential amplifier, common-mode voltage is defined as the average of the two input voltages. [2]
6. 6Common-Mode VoltageIdeally a differential input amplifier only responds to a differential input voltage, not a common-mode voltage.
7. 7CMRR and CMRCommon-Mode Rejection Ratio is defined as the ratio of the differential gain to the common-mode gainCMR is defined as follows [2]:CMR and CMRR are often used interchangeably
8. 8Ideal Differential Amplifier CMRRWhat is the CMRR of an ideal differential input amplifier (e.g. op-amp)?Recall that the ideal common-mode gain of a differential input amplifier is 0.Voltage Amplifier Model [1]Also recall the differential gain of an ideal op-amp is infinity.So
9. 9Real Op-Amp CMRRIn an operational amplifier, the differential gain is known as the open-loop gain. The open-loop gain of an operational amplifier is fixed and determined by its design
10. 10Real Op-Amp CMRRHowever, there will be a common-mode gain due to the followingAsymmetry in the circuitMismatched source and drain resistorsSignal source resistancesGate-drain capacitancesForward transconductancesGate leakage currents Output impedance of the tail current sourceChanges with frequency due to tail current source’s shunt capacitanceThese issues will manifest themselves through converting common-mode variations to differential components at the output and variation of the output common-mode level. [4]
11. 11Resistor MismatchLet’s look at the case of a slight mismatch in drain resistances [4] in the input stage (diff-in, diff-out) of an op-ampWhat happens to Vx and Vy as Vin,cm changes?Assuming M1 and M2 are identical, Vx and Vy will change by different amounts:This imbalance will introduce a differential component at the outputSo changes in the input common-mode can corrupt the output signal
12. 12Transistor MismatchWhat about mismatches with respect to M1 and M2?Threshold mismatchesDimension mismatchesThese mismatches will cause the transistors to conduct slightly different currents and have unequal transconductances.We find the conversion of input common mode variations to a differential error by the following factor [4]
13. 13Tail Current Source CapacitanceAs the frequency of the CM disturbance increases the capacitance shunting the tail current source will introduce larger current variations. [4]OPA333
14. 14Modeling CMRRNow that we understand what CMRR is and what affects it in operational amplifiers, let’s see how it can affect a circuit.First, however, we need to understand the modelTo be useful, CMRR needs to be referred-to-input (RTI)We can therefore represent it as a voltage source (aka offset voltage) in series with an input. The magnitude (RTI) is Vcm/CMRR [2]
15. 15OA CMRR ErrorExample: non-inverting buffer
16. 16Real CMRR ExampleTo understand the effects CMRR can have at the output of a device, let’s look at an example.OPA376 PDSNotice the Vcm is specified at the top of the pageDeviation from this value will induce an offset errorRemember CMRR is RTI
17. 17Real CMRR ExampleRememberIn reality, CMRR is measured by changing the input common-mode voltage and observing the output change.For an operational amplifier, this is usually done with a composite amplifierIt is then referred-to-input by dividing by the gain and can be though of as an offset voltageFrom reference [3], in TI datasheets CMRR is defined as follows so that the value is positive
18. 18Real CMRR ExampleFor the OPA376, CMRR(min)=76dB. Note this is really CMR!
19. 19CMRR of Difference AmplifiersA difference amplifier is made up of a differential amplifier (operational amplifier) and a resistor network as shown below.The circuit meets our definition of a differential amplifierThe output is proportional to the difference between the input signals
20. 20DA CMRRLet’s replace V1 and V2 with our alternate definition of the inputs (in terms of differential-mode and common-mode signals)It is readily observed that an ideal difference amplifier’s output should only amplify the differential-mode signal…not the common-mode signal.
21. 21DA CMRRThis assumes that the operational amplifier is ideal and that the resistors are balanced.Keeping the assumption that the operational amplifier is ideal, let’s see what happens when an imbalance factor (ε) is introduced.
22. 22DA CMRRUsing superposition we find thatAfter some algebra we find that [1]As expected, an imbalance affects the differential and common-mode gains, which will affect CMRR!As the error->0, Adm->R2/R1 and Acm->0.
23. 23DA CMRRSince we have equations for Acm and Adm, let’s look at CMRIf the imbalance is sufficiently small we can neglect its effect on AdmWith that and some algebra we find [1]
24. 24DA CMRRThis equation shows two very important relationshipsAs the gain of a difference amplifier increases (R2/R1), CMR increasesAs the mismatch (ε) increases, CMR decreasesPlease remember that this just shows the effects of the resistor network and assumes an ideal amplifier
25. 25DA CMRRAnother possible source for CMRR degradation is the impedance at the reference pin.So far we have connected this pin to low-impedance ground.Placing and impedance here will disturb the voltage divider we come across during superposition analysis.This will negatively affect CMR
26. 26Real DA CMRR Example (INA149 PDS)
27. 27Why not make our own DA?If a DA is simply an operational amplifier and 4 resistors, I can save money by making my own, right?Should be well-matched Should have low temperature drift
28. 28Why not make our own DA?Let’s assume an ideal amplifier and just look at resistor mismatches using TINA (only changing R2)Monte Carlo analysisGaussian distribution (6σ), 100 casesValues are negative due to TINAAssuming 0% tolerance for R1, R3, and R4 and only 0.1% tolerance for R2 this network can degrade CMRR to 66dB (calculated), 69.16dB (simulated).
29. 29Why not make our own DA?What if all resistors are 0.01% or 0.1%?Worse performance than all of our DAs
30. 30Why not make our own DA?0.5%: 52dB (calc), 53.64dB (sim)1.0%: 46dB (calc), 46.85dB (sim)5.0%: 32dB (calc), 33.34dB (sim)
31. 31Why not make our own DA?80dB: Lowest cost of one 0.01%, 10ppm/C resistor (1k pricing)1206 package: $0.45 ($1.80 total cost)0805 package: $0.53 ($2.12 total cost)0603 package: $0.53 ($2.12 total cost)0402 package: $0.50 ($2.00 total cost, 10k pricing!)60dB: Lowest cost 4-pack 0.1%, 25ppm/C resistor (1k pricing)SO-8 package: $0.98 ($0.98 total cost)Footprint size comparison:4 required1 required(need op amp)
32. 32Why not make our own DA?Now that we understand how the resistor matching can affect CMRR and the related cost, what about an integrated solution?TI can trim resistors to within 0.01% relative accuracy INA152 CMR(min)=80dBGE=10ppm/˚C (max)On-chip resistors will drift togetherMSOP-81k price on www.ti.com: $1.20Includes amplifier!Some DA’s can give CMR(min)=74dB @ $1.05!Customer will require 2 suppliers (1 for OA, 1 for precision resistors)Op amp included!
33. 33DA GainWe learned that the gain of a difference amplifier is set by R2 and R1.What if we wanted variable gain?We would have to adjust 2 resistors due to the topology.To retain good CMR they would have to be tightly matched, too.This is difficult and expensiveAlternately, you could use an external operational amplifier (with very low output impedance so as not to degrade CMR) to drive the reference pin as shown below [4]
34. 34DA GainBut, R3 should be a precision resistor. Its error will be seen as a gain error.You also need to purchase an external operational amplifier and potentiometer.If you need variable gain, there are better optionsInstrumentation amplifiers (IAs) usually have an external resistor that can be used to set the gainProgrammable Gain Amplifiers (PGAs) can be programmed (either with pin settings or digitally) with a particular gainIn summary, difference amplifiers are typically manufactured with a set gain so as to preserve CMR and since there are alternate (better) solutions for variable gainSince difference amplifiers come with a fixed gain, you will only see 1 CMR curve in the datasheet
35. 35Difference Amplifiers-SummaryPros:Difference amplifiers amplify differential signals and reject common-mode signalsThe common-mode rejection is based mainly resistor matchingMaking your own difference amplifier will not yield the same performanceDifference amplifiers can be used to protect against ground disturbancesCons:Externally changing the gain of a difference amplifier is not worthwhileThe input impedance is finiteThis means that a difference amplifier will load the input signalsIf the input signal source’s impedances are not balanced, CMR could be degradedIs there a way we can amplify differential signals, change the gain, retain high CMR, and not load our source?Yes! Buffer the inputs…this creates an Instrumentation Amplifier (IA).
36. 36Instrumentation AmplifierThere are 2 common types of instrumentation amplifiers2 op-amp (e.g. INA122)3 op-amp (e.g. INA333)
37. 37Instrumentation AmplifierNotice both have gain equations so you can vary the gainNotice the input impedance is that of the non-inverting terminal of a non-inverting amplifier Difference AmpHigh-Z NodesHigh-Z NodesVariable Gain
38. 38IA CMRRSo, what is the CMRR of an instrumentation amplifier?Instrumentation amplifiers reject common-mode signals (Acm->0)RecallCMRR is directly related to differential gain. Since we can change the differential gain of an IA, we also change the CMRR.
39. 39INA826 CMRR Model Verification
40. 40INA826-Effects of Rg Tolerance on CMRRNow that we see our INA826 model is accurate, let’s look at the effects of Rg’s tolerance on CMRRSet G=100, 6σ resistors, 100 cases.Note that due to the number of cases, no post-processing was performedNormally this would be Gain/Waveform. Therefore we have to mentally subtract 20dB from this cluster of waveforms.Notice the gain setting resistor tolerance does not significantly affect the CMR.
41. 412-OA Instrumentation AmplifiersWhat are the properties of 2-OA Instrumentation Amplifiers?ProsLower cost (only 2 op-amps), less trimmingHigh impedance inputCan be placed in a smaller packageConsCompare signal path to Vo for Vin+ and Vin-Vin+ has a shorter path than V-This delay does not allow the common-mode components to cancel each other as well as frequency increasesTherefore CMR degradation occurs earlier in frequency than the 3-OA designsSince we can change the differential gain, the CMR also changes.
42. 42‘Hybrid’ Difference AmplifiersSome devices have unique topologies (e.g. INA321).How do we determine whether CMRR will change with the ‘gain’ of this device?2OA Instrumentation AmpOp-amp (has fixed differential gain)
43. 43‘Hybrid’ Difference AmplifiersDepends on what ‘gain’ you’re talking about.With respect to CMRR, it’s all about the differential gain since the common-mode gain of all differential amplifiers is ideally 0.When you place resistors for R1 and R2, are you changing the differential gain?
44. 44No. The differential gain of the device is set internally! If you can’t change the differential gain of the device, the CMRR will not change with gain.Remember the differential gain of an op-amp (A3) is fixed (it’s the open-loop gain)‘Hybrid’ Differential Amplifiers
45. 45Real IA CMR Competitive Analysis
46. 46SummaryA ‘differential amplifier’ amplifies differential signals, not common-mode signalsExamples include operational amplifiers, difference amplifiers, and instrumentation amplifiersCMRR is defined as the ratio of differential gain to common-mode gainAll differential amplifiers have an ideal common-mode gain of 0To determine if a circuit’s CMRR is going to change with gain, you must look at the differential gain. Remember an op-amp’s differential gain is fixed.If you can change the differential gain of the device/circuit, the CMRR will also change
47. 47References[1] Franco, “Design with Operational Amplifiers and Analog Integrated Circuits”, 3rd Edition, McGraw-Hill, 2002.[2] Tobey, Graeme, Huelsman, “Operational Amplifiers: Design and Applications”, McGraw-Hill, 1971.[3] Karki, “Understanding Operational Amplifier Specifications”, White Paper: SLOA011, Texas Instruments, 1998.[4] Razavi, “Design of Analog CMOS Integrated Circuits”, McGraw-Hill, 2001.
48. 48Questions?