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An ideal differential amplifier responds to the voltage difference between its two inputs and rejects any voltage shared equally by both. That model explains common-mode rejection and provides a useful starting point for understanding the familiar four-resistor op-amp difference amplifier—but real circuits only approach the ideal, with resistor matching, input range, and frequency all affecting performance.
What is a differential amplifier?
A differential amplifier has two inputs, and its output depends on the difference between their voltages. For inputs V1 and V2, define the differential input and common-mode input as:
Vd = V2 − V1
Vcm = (V1 + V2)/2
The differential input is the signal difference; the common-mode input is the average voltage shared by the pair. In the ideal model, the output is Vout = Ad(V2 − V1), where Ad is differential gain. There is no output contribution from Vcm. Reversing which input is designated positive reverses the sign of the equation.
Analog Devices defines a differential amplifier as a two-input circuit that amplifies only the difference between its inputs. This behavior is useful when the wanted signal is a voltage difference and interference appears similarly on both leads. Analog Devices’ differential amplifier glossary describes the distinction and the role of common-mode rejection.
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How does common-mode rejection work?
Suppose the two inputs contain a wanted difference plus the same unwanted voltage. If the unwanted component raises both inputs equally, their difference is unchanged. An ideal differential amplifier therefore rejects that shared component while amplifying the difference.
Common-mode rejection ratio (CMRR) expresses differential gain relative to common-mode gain. A higher CMRR means less output response to a common-mode input relative to the response to a differential input. In a real circuit, rejection is finite: some common-mode voltage can appear as output error.
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- Common-mode rejection can reduce interference coupled similarly onto both signal leads.
- It does not cancel noise that differs between the leads.
- It does not make an out-of-range input safe or ensure the output can swing to the requested voltage.
Low-amplitude ECG sensing is one application class: a front end may amplify signals on the order of a few millivolts before digitization. That example does not mean a basic difference-amplifier circuit alone meets medical-device safety or performance requirements. Analog Devices’ glossary gives the ECG example.
How does the ideal op-amp assumption apply?
A common way to build a differential amplifier is with an operational amplifier and negative feedback. In the simplified ideal op-amp model, open-loop gain is infinite. While the circuit is operating linearly with negative feedback, the feedback drives the op amp’s inverting and non-inverting input voltages toward equality.
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This is often called a virtual short: the input voltages are treated as nearly equal for analysis, but the terminals are not physically connected. The approximation depends on the circuit’s feedback and operating conditions; it is not a universal property of every amplifier. The output must remain within its available range, and the inputs must remain within their permitted operating range. Analog Devices University Program’s introduction to op-amp assumptions explains these conditions.
How does a four-resistor difference amplifier work?
The standard single-op-amp difference amplifier uses four resistors: one pair around the inverting input and another pair forming a divider at the non-inverting input. To state a transfer equation unambiguously, let V1 connect through R1 to the inverting input, with feedback resistor R2 from output to that input; let V2 connect through R3 to the non-inverting input, with R4 from that input to ground. When the resistor ratios match, R2/R1 = R4/R3, the ideal transfer is:
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Vout = (R2/R1)(V2 − V1)
With equal ratios of 1, the circuit is a voltage subtractor; with other matched ratios, it applies differential gain. The equation is not a guarantee for arbitrary resistor values. For the topology and practical error discussion, see Harry Holt’s Analog Devices article on difference amplifiers.
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Why resistor matching matters
The circuit rejects common-mode voltage only when the ratios match. Ratio mismatch causes some shared input voltage to become output error, which can be mistaken for a genuine differential signal. The relevant property is ratio accuracy, not simply whether each resistor has a low nominal resistance.
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Analog Devices illustrates the effect for a unity-gain difference amplifier with an ideal op amp: 1% resistors limit CMRR to 50 V/V, about 34 dB, while 0.1% resistors limit it to 500 V/V, about 54 dB. These are illustrative calculations under those stated assumptions, not guaranteed values for every resistor set or real amplifier. A matched precision resistor network can help control ratio error.
Independent reader supportYour contribution helps us test, update, and keep practical guides available for everyone.What limits performance in a real circuit?
Real CMRR is limited both by resistor-ratio mismatch and by amplifier imperfections. It can also decline as frequency rises, so a CMRR value at one frequency should not be assumed to apply across the signal band. The manufacturer’s precision-amplifier topology guide identifies frequency-dependent CMRR and highlights source impedance, signal type, gain accuracy, and required CMRR as selection factors.
Input common-mode range and output swing are separate constraints from CMRR. Even a circuit with excellent common-mode rejection can fail to operate correctly if the input voltages exceed the amplifier’s permitted range or the output would need to exceed its available swing. Source impedance also matters because unequal source impedances can undermine common-mode performance and affect loading.
How should you choose a differential-amplifier topology?
Choose around the signal and operating conditions, rather than treating the ideal equation as the whole design. Check:
- Differential gain and accuracy: establish the gain required and how much gain error the application can tolerate.
- CMRR across frequency: evaluate rejection at the actual signal and interference frequencies, not only at a low-frequency headline value.
- Input common-mode range and output swing: confirm the input voltages and expected output remain within the amplifier’s operating limits.
- Source impedance and loading: account for the source resistance on each input and whether the circuit loads the source too heavily.
- Resistor matching and drift: use ratios with suitable accuracy and stability for the required common-mode rejection and gain consistency.
- Supply and bandwidth: verify that supply conditions and bandwidth accommodate the signal without leaving the intended operating range.
A four-resistor difference amplifier is a straightforward choice when its source impedances, gain, and resistor matching suit the job. For demanding input impedance or CMRR requirements, assess the complete topology and amplifier specifications rather than assuming that the ideal difference equation guarantees real-world performance.
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