The differential amplifier (diff amp) addressed in an earlier article was considered with an ideal operational amplifier (op amp), that is, one with infinite common mode rejection. Real world op amps display less-than-perfect common-mode rejection. This specification is either common mode rejection (CMR) or common mode rejection ratio (CMRR).

To appreciate the difference between the CMR and the CMRR, consider the circuit shown in Figure 1.

Figure 1: Differential amplifier with gain of 100.
(Click on image to enlarge)

Here, Vcm is the common mode voltage, and Vdm1 and Vdm2 are the differential mode voltages. The intent of the circuit is to amplify the differential mode voltage (Vdm1 + Vdm2) while rejecting the common mode voltage.

With the change in resistor values from an earlier article (Part 3, link below), this is now a gain stage. The transfer function is:

The CMR also could be called the common-mode gain or:

Since CMR is determined by the op amp input-stage device match, in a circuit with ratio-matched resistors, the value of CMR also depends on the gain of the circuit. To normalize the gain, or refer the reading to the input, the CMRR is defined as:

Both of these terms usually are expressed in dB. CMRR becomes:

While the basic diff amp is useful, it has two weak spots. The input impedance is relatively low, and changing the gain requires changing two matched resistors.

To address the input impedance issue, two buffer amplifiers are added at the diff amp inputs, Figure 2.

Figure 2: Input buffer stages
(Click on image to enlarge)

This configuration provides high input impedance with the gain and CMRR set by the output-stage resistors. Adding matched resistors around the input op amps moves the gain set to the front end.

Figure 3: Classical three op-amp instrumentation amp
(Click on image to enlarge)

In the general case the gain expression becomes:

For the circuit in Figure 3, this is reduced to:

(Click on image to enlarge)

Adding this front end gives high input impedance, single-resistor gain-set capability, and keeps the CMRR adjustment at the output-stage resistor-ratio match. In IC manufacturing, it is easier to adjust the resistor ratio than be concerned with the absolute value of the resistor.

About the author

William P. (Bill) Klein is a Senior Applications Engineer with the High Performance Analog group at Texas Instruments. Bill joined TI through its acquisition of Burr-Brown in August 2000. His experience as an analog circuit designer covers over 40 years in fields ranging from mineral exploration to medical nuclear imaging. One current role Bill has is hosting the Analog e-LAB Web Cast, presenting real world solutions to real world problems in analog circuit design. In addition to a BSEE from Arizona State University and registration as a Professional Engineer in the State of Arizona, he has authored numerous magazine articles, application notes and conference papers.

Previous installments of this series:

• "SIGNAL CHAIN BASICS Series (Part 4): Introduction to analog/digital converter (ADC) types", www.planetanalog.com/features/showArticle.jhtml;?articleID=204803631, click here
• "SIGNAL CHAIN BASICS Series (Part 3): Analog and the digital world", www.planetanalog.com/features/showArticle.jhtml;?articleID=204400376, click here
• "SIGNAL CHAIN BASICS Series (Part 2): Op Amp--Basic operations", www.planetanalog.com/features/showArticle.jhtml;?articleID=203101699, click here
• "SIGNAL CHAIN BASICS: Operational Amplifier--The Basic Building Block", www.planetanalog.com/features/showArticle.jhtml;?articleID=202801320, click here