*Fully Understanding CMRR in DAs, IAs, and OAsPete SemigAnalog Applications Engineer-Precision Linear

*OutlineDefinitionsDifferential-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

*Differential 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

*Common-Mode VoltageFor a differential input amplifier, common-mode voltage is defined as the average of the two input voltages. [2]

*Common-Mode Voltage (Alternate defn.)For a differential amplifier, common-mode voltage is defined as the average of the two input voltages. [2]

*Common-Mode VoltageIdeally a differential input amplifier only responds to a differential input voltage, not a common-mode voltage.

*CMRR and CMRCommon-Mode Rejection Ratio is defined as the ratio of the differential gain to the common-mode gain

CMR is defined as follows [2]:

CMR and CMRR are often used interchangeably

*Ideal 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

*Real 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

*Real 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 sources 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]

*Resistor MismatchLets 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

*Transistor 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]

*Tail Current Source CapacitanceAs the frequency of the CM disturbance increases the capacitance shunting the tail current source will introduce larger current variations. [4]

OPA333

*Modeling CMRRNow that we understand what CMRR is and what affects it in operational amplifiers, lets 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]

*OA CMRR ErrorExample: non-inverting buffer

*Real CMRR ExampleTo understand the effects CMRR can have at the output of a device, lets 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

*Real 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

*Real CMRR ExampleFor the OPA376, CMRR(min)=76dB. Note this is really CMR!

*CMRR 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

*DA CMRRLets 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 amplifiers output should only amplify the differential-mode signalnot the common-mode signal.

*DA CMRRThis assumes that the operational amplifier is ideal and that the resistors are balanced.Keeping the assumption that the operational amplifier is ideal, lets see what happens when an imbalance factor () is introduced.

*DA CMRRUsing superposition we find that

After 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.

*DA CMRRSince we have equations for Acm and Adm, lets look at CMR

If the imbalance is sufficiently small we can neglect its effect on AdmWith that and some algebra we find [1]

*DA CMRRThis equation shows two very important relationships

As the gain of a difference amplifier increases (R2/R1), CMR increasesAs the mismatch () increases, CMR decreasesPlease remember that this just shows the effects of the resistor network and assumes an ideal amplifier

*DA 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

*Real DA CMRR Example (INA149 PDS)

*Why 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

*Why not make our own DA?Lets assume an ideal amplifier and just look at resistor mismatches using TINA (only changing R2)Monte Carlo analysisGaussian distribution (6), 100 casesValues are negative due to TINA

Assuming 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).

*Why not make our own DA?What if all resistors are 0.01% or 0.1%?Worse performance than all of our DAs

*Why 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)

*Why 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)

0402

0603

0805

1206

SO-8

*Why 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 DAs can give CMR(min)=74dB @ $1.05!Customer will require 2 suppliers (1 for OA, 1 for precision resistors)Op amp included!

MSOP-8

SO-8

*DA 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]

*DA 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

*Difference 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 sources 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 inputsthis creates an Instrumentation Amplifier (IA).

*Instrumentation AmplifierThere are 2 common types of instrumentation amplifiers2 op-amp (e.g. INA122)3 op-amp (e.g. INA333)

*Instrumentation 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

*IA CMRRSo, what is the CMRR of an instrumentation amplifier?Instrumentation amplifiers reject common-mode signals (Acm->0)Recall

CMRR is directly related to differential gain. Since we can change the differential gain of an IA, we also change the CMRR.

*INA826 CMRR Model Verification

*INA826-Effects of Rg Tolerance on CMRRNow that we see our INA826 model is accurate, lets look at the effects of Rgs tolerance on CMRRSet G=100, 6 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.

*2-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.

*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)

*Hybrid Difference AmplifiersDepends on what gain youre talking about.With respect to CMRR, its 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?

*No. The differential gain of the device is set internally!

If you cant 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 (its the open-loop gain)Hybrid Differential Amplifiers

*Real IA CMR Competitive Analysis

*SummaryA 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 circuits CMRR is going to change with gain, you must look at the differential gain. Remember an op-amps differential gain is fixed.If you can change the differential gain of the device/circuit, the CMRR will also change

*References[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.

*Questions?

*A differential input amplifier is the same as an operational amplifier.

A difference amplifier is an operational amplifier with surrounding resistors.***