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Fully Understanding CMRR in DAs, IAs, and OAs

Fully Understanding CMRR in DAs, IAs, and OAs. Outline. Definitions Differential-input amplifier Common-mode voltage Common-mode rejection ratio (CMRR) Common-mode rejection (CMR) CMRR in Operational Amplifiers CMRR in Difference Amplifiers CMRR in Instrumentation Amplifiers

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Fully Understanding CMRR in DAs, IAs, and OAs

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  1. Fully Understanding CMRR in DAs, IAs, and OAs

  2. Outline • Definitions • Differential-input amplifier • Common-mode voltage • Common-mode rejection ratio (CMRR) • Common-mode rejection (CMR) • CMRR in Operational Amplifiers • CMRR in Difference Amplifiers • CMRR in Instrumentation Amplifiers • CMRR in ‘Hybrid’ Amplifiers

  3. Differential Input Amplifier • Differential input amplifiers are devices/circuits that can input and amplify differential signals while suppressing common-mode signals • This includes operational amplifiers, instrumentation amplifiers, and difference amplifiers Instrumentation Amplifiers Operational Amplifier Difference Amplifier

  4. Common-Mode Voltage • For a differential input amplifier, common-mode voltage is defined as the average of the two input voltages. [2]

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

  6. Common-Mode Voltage • Ideally a differential input amplifier only responds to a differential input voltage, not a common-mode voltage.

  7. CMRR and CMR • Common-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

  8. Ideal Differential Amplifier CMRR • What 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. Real Op-Amp CMRR • In 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. Real Op-Amp CMRR • However, there will be a common-mode gain due to the following • Asymmetry in the circuit • Mismatched source and drain resistors • Signal source resistances • Gate-drain capacitances • Forward transconductances • Gate leakage currents • Output impedance of the tail current source • Changes with frequency due to tail current source’s shunt capacitance • These 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. Resistor Mismatch • Let’s look at the case of a slight mismatch in drain resistances [4] in the input stage (diff-in, diff-out) of an op-amp • What 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 output • So changes in the input common-mode can corrupt the output signal

  12. Transistor Mismatch • What about mismatches with respect to M1 and M2? • Threshold mismatches • Dimension mismatches • These 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. Tail Current Source Capacitance • As the frequency of the CM disturbance increases the capacitance shunting the tail current source will introduce larger current variations. [4] OPA333

  14. Modeling CMRR • Now 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 model • To 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. OA CMRR Error • Example: non-inverting buffer

  16. Real CMRR Example • To understand the effects CMRR can have at the output of a device, let’s look at an example. • OPA376 PDS • Notice the Vcm is specified at the top of the page • Deviation from this value will induce an offset error • Remember CMRR is RTI

  17. Real CMRR Example • Remember • In 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 amplifier • It is then referred-to-input by dividing by the gain and can be though of as an offset voltage • From reference [3], in TI datasheets CMRR is defined as follows so that the value is positive

  18. Real CMRR Example • For the OPA376, CMRR(min)=76dB. Note this is really CMR!

  19. CMRR of Difference Amplifiers • A 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 amplifier • The output is proportional to the difference between the input signals

  20. DA CMRR • Let’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. DA CMRR • This 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. DA CMRR • Using 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.

  23. DA CMRR • Since we have equations for Acm and Adm, let’s look at CMR • If the imbalance is sufficiently small we can neglect its effect on Adm • With that and some algebra we find [1]

  24. DA CMRR • This equation shows two very important relationships • As the gain of a difference amplifier increases (R2/R1), CMR increases • As the mismatch (ε) increases, CMR decreases • Please remember that this just shows the effects of the resistor network and assumes an ideal amplifier

  25. DA CMRR • Another 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. Real DA CMRR Example (INA149 PDS)

  27. 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

  28. Why not make our own DA? • Let’s assume an ideal amplifier and just look at resistor mismatches using TINA (only changing R2) • Monte Carlo analysis • Gaussian distribution (6σ), 100 cases • Values 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).

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

  30. 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)

  31. 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: 1 required (need op amp) 4 required

  32. 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)=80dB • GE=10ppm/˚C (max) • On-chip resistors will drift together • MSOP-8 • 1k price on www.ti.com: $1.20 • Includes 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. DA Gain • We 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 expensive • Alternately, 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. DA Gain • But, 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 options • Instrumentation amplifiers (IAs) usually have an external resistor that can be used to set the gain • Programmable Gain Amplifiers (PGAs) can be programmed (either with pin settings or digitally) with a particular gain • In summary, difference amplifiers are typically manufactured with a set gain so as to preserve CMR and since there are alternate (better) solutions for variable gain • Since difference amplifiers come with a fixed gain, you will only see 1 CMR curve in the datasheet

  35. Difference Amplifiers-Summary • Pros: • Difference amplifiers amplify differential signals and reject common-mode signals • The common-mode rejection is based mainly resistor matching • Making your own difference amplifier will not yield the same performance • Difference amplifiers can be used to protect against ground disturbances • Cons: • Externally changing the gain of a difference amplifier is not worthwhile • The input impedance is finite • This means that a difference amplifier will load the input signals • If the input signal source’s impedances are not balanced, CMR could be degraded • Is 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. Instrumentation Amplifier • There are 2 common types of instrumentation amplifiers • 2 op-amp (e.g. INA122) • 3 op-amp (e.g. INA333)

  37. Instrumentation Amplifier • Notice both have gain equations so you can vary the gain • Notice the input impedance is that of the non-inverting terminal of a non-inverting amplifier High-Z Nodes Difference Amp High-Z Nodes Variable Gain

  38. IA CMRR • So, 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.

  39. INA826 CMRR Model Verification

  40. INA826-Effects of Rg Tolerance on CMRR • Now that we see our INA826 model is accurate, let’s look at the effects of Rg’s tolerance on CMRR • Set G=100, 6σ resistors, 100 cases. • Note that due to the number of cases, no post-processing was performed • Normally 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. 2-OA Instrumentation Amplifiers • What are the properties of 2-OA Instrumentation Amplifiers? • Pros • Lower cost (only 2 op-amps), less trimming • High impedance input • Can be placed in a smaller package • Cons • Compare 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 increases • Therefore CMR degradation occurs earlier in frequency than the 3-OA designs Since we can change the differential gain, the CMR also changes.

  42. ‘Hybrid’ Difference Amplifiers • Some devices have unique topologies (e.g. INA321). • How do we determine whether CMRR will change with the ‘gain’ of this device? Op-amp (has fixed differential gain) 2OA Instrumentation Amp

  43. ‘Hybrid’ Difference Amplifiers • Depends 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. ‘Hybrid’ Differential Amplifiers • No. 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)

  45. Real IA CMR Competitive Analysis

  46. Summary • A ‘differential amplifier’ amplifies differential signals, not common-mode signals • Examples include operational amplifiers, difference amplifiers, and instrumentation amplifiers • CMRR is defined as the ratio of differential gain to common-mode gain • All differential amplifiers have an ideal common-mode gain of 0 • To 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. 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.

  48. Questions?

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