What condition ensures proper common-mode rejection in a classic four-resistor difference amplifier?

What condition ensures proper common-mode rejection in a classic four-resistor difference amplifier?

• A. R1/R2 = R3/R4
• B. All four resistors equal
• C. R1 = R2
• D. R3 = R4

Answer: (A)

The key idea is that to cancel the same voltage appearing on both inputs (common-mode), the amplifier must treat both input paths equally. In this four-resistor difference amplifier, the inverting path provides a gain of -R2/R1 for Vin1, while the non-inverting path feeds back a contribution from Vin2 through a divider formed by R3 and R4. If the resistor ratios match, specifically R1/R2 = R3/R4, the output becomes Vout = (R2/R1)(Vin2 − Vin1). That means the common-mode part (where Vin1 and Vin2 move together) cancels out, giving good common-mode rejection. If the ratios aren’t equal, the two inputs aren’t amplified by the same factor, and some common-mode voltage leaks into the output, reducing CMRR. Special cases like all four resistors being equal also satisfy the ratio condition, but the essential requirement is the ratio equality, not just equality of individual resistors.

The key idea is that to cancel the same voltage appearing on both inputs (common-mode), the amplifier must treat both input paths equally. In this four-resistor difference amplifier, the inverting path provides a gain of -R2/R1 for Vin1, while the non-inverting path feeds back a contribution from Vin2 through a divider formed by R3 and R4. If the resistor ratios match, specifically R1/R2 = R3/R4, the output becomes Vout = (R2/R1)(Vin2 − Vin1). That means the common-mode part (where Vin1 and Vin2 move together) cancels out, giving good common-mode rejection. If the ratios aren’t equal, the two inputs aren’t amplified by the same factor, and some common-mode voltage leaks into the output, reducing CMRR.

Special cases like all four resistors being equal also satisfy the ratio condition, but the essential requirement is the ratio equality, not just equality of individual resistors.