An engineer builds a difference amplifier to measure a 5 mV sensor signal riding on 2 V of common-mode noise. The circuit uses 1% tolerance resistors and measures poor noise rejection. What is the most likely cause?
AThe op-amp's open-loop gain is too low for differential inputs
BResistor mismatch from 1% tolerance breaks the equal ratio condition, reducing CMRR dramatically
CThe sensor signal is too small for the difference amplifier architecture to handle
DCommon-mode rejection requires the inputs to be driven from the same source impedance
The CMRR of a difference amplifier depends entirely on the resistor ratio R_f/R_1 = R_g/R_2 being exactly equal on both sides. Even 1% resistor tolerance mismatch can reduce CMRR to roughly 40 dB (factor of 100 rejection), which may be completely insufficient for millivolt-level signals sitting on volt-level common-mode noise. This is the defining weakness of the basic difference amplifier — the CMRR is limited by passive component matching, not the op-amp. Option A is incorrect: op-amp open-loop gain is typically very high and not the limiting factor. Option D is partially related but describes a secondary effect of different input impedances, not the primary CMRR mechanism.
Question 2 Multiple Choice
In a summing amplifier, three input signals V₁, V₂, V₃ are applied through equal resistors R to the inverting input. Why do the three signals not interact with each other or affect each other's contribution to the output?
AThe op-amp's high input impedance blocks current from flowing between inputs
BThe virtual ground at the inverting node forces each input to see 0V regardless of the others, making each current independent
CThe resistors are large enough that mutual coupling between them is negligible
DThe non-inverting input is grounded, which prevents any signal from propagating backward
Virtual ground is the key: the inverting node is held at 0V by the op-amp feedback regardless of what the other inputs are doing. Each input only sees the voltage drop from its own source to 0V across its own resistor, contributing current V_n/R_n. Because each input always sees the same 0V node, changing one input's voltage does not change the voltage seen by any other input's resistor. The inputs are completely decoupled at the summing junction. Option A is incorrect — op-amp input impedance refers to the inputs of the op-amp chip itself, not the summing node. Option D is a distraction; the grounded non-inverting input sets the common-mode reference but doesn't explain input independence.
Question 3 True / False
In a basic difference amplifier, the CMRR can degrade severely even when the op-amp itself is ideal, if the resistors are not perfectly matched.
TTrue
FFalse
Answer: True
Common-mode rejection in a difference amplifier works by cancellation: the signal that appears identically on both inputs is amplified with equal and opposite gain factors that sum to zero. This cancellation requires R_f/R_1 = R_g/R_2 exactly. Any mismatch — even 1% — breaks the cancellation, allowing some common-mode signal to appear at the output. An ideal op-amp with mismatched resistors will have poor CMRR. This is fundamentally different from the op-amp's own CMRR specification, which describes the chip's ability to reject differential input offset. The circuit-level CMRR and the op-amp CMRR are separate and independently limiting.
Question 4 True / False
An instrumentation amplifier achieves high CMRR primarily because it uses a more precise op-amp chip than a standard difference amplifier.
TTrue
FFalse
Answer: False
The instrumentation amplifier's CMRR advantage comes from its architecture, not from a better op-amp. The INA adds two non-inverting buffer stages before the difference amplifier output stage. These buffers provide high, equal input impedance on both inputs (eliminating asymmetric loading) and the differential gain is set by a single external resistor R_G, which does not affect CMRR. Critically, the internal resistors in the output difference amplifier stage are laser-trimmed on a single chip to match to very high precision — achieving 80–120 dB CMRR that is independent of source impedance variation. The benefit is architectural and manufacturing precision, not a fundamentally different op-amp technology.
Question 5 Short Answer
Why does the instrumentation amplifier solve the two main weaknesses of the basic difference amplifier, and what specific design features accomplish this?
Think about your answer, then reveal below.
Model answer: The basic difference amplifier has two weaknesses: (1) low and unequal input impedances (the inverting input sees R₁, the non-inverting input sees R₂ + Rg), which causes asymmetric loading from source impedances that degrades CMRR; and (2) CMRR limited by external resistor matching, which is difficult to control in discrete circuits. The instrumentation amplifier solves both. First, two unity-gain non-inverting buffer stages at the inputs provide very high and equal input impedances, eliminating loading asymmetry. Second, all resistors in the output stage are laser-trimmed on a single integrated circuit, achieving precise matching (and thus high CMRR) that is impossible with discrete resistors. The differential gain is set by a single external resistor R_G in the input stage, which controls gain without affecting CMRR.
A complete answer identifies both problems and maps each to the specific design solution. The input buffer stages solve the impedance problem; the laser-trimmed integrated resistors solve the matching problem. Students who only say 'it has buffers for high input impedance' have captured half the insight. The key is that CMRR in the basic difference amp is limited by an external, uncontrolled factor (resistor tolerance), while the INA moves that sensitive component inside the chip where it can be trimmed to high precision.