CM rejection condition; isolation amp applications

Condition to reject common-mode signal (single op-amp IA)

            R1           R2
 V1 ----/\/\/----+----/\/\/----+
                 |             |
                (-)\           |
                    >----------+--> Vo
                (+)/
            R3   |
 V2 ----/\/\/----+---[R4]---GND

Step 1, output by superposition:

V+ = V2 · R4/(R3 + R4)
Vo = (1 + R2/R1)·V+ − (R2/R1)·V1
   = [R4(R1 + R2) / (R1(R3 + R4))]·V2 − (R2/R1)·V1

Step 2, apply a pure common-mode input, V1 = V2 = Vcm:

Vo = Vcm [ R4(R1 + R2)/(R1(R3 + R4)) − R2/R1 ]
   = Vcm (R1R4 + R2R4 − R2R3 − R2R4) / (R1(R3 + R4))
   = Vcm (R1R4 − R2R3) / (R1(R3 + R4))

So the common-mode gain is:

Acm = (R1R4 − R2R3) / [R1(R3 + R4)]

Step 3, condition for rejection. Acm = 0 requires R1R4 = R2R3, that is:

R4/R3 = R2/R1   (resistor ratios matched)

Usually R3 = R1 and R4 = R2. Then:

Vo = (R2/R1)(V2 − V1),   Ad = R2/R1,   CMRR → ∞

With mismatched resistors, Acm ≠ 0 and CMRR = Ad/Acm is finite. Even a 1 % mismatch limits CMRR to about 40 dB. For this reason the resistors are trimmed (for example R4 made adjustable) or laser-trimmed in IC form.

Applications of isolation amplifiers

• Medical electronics (ECG, EEG, patient monitoring): protect the patient from leakage and fault currents
• High-voltage sensing in power electronics, motor drives and power systems
• Breaking ground loops between remote sensors and the data acquisition system
• Industrial process control: thermocouples and 4–20 mA loops at high common-mode voltage
• Protecting low-voltage control or computer circuits from high-voltage transients. They are also used in nuclear and chemical plant instruments.