Electronics Guide

Common-Mode and Differential Signals

Any pair of input voltages can be decomposed into two parts. The differential signal is the difference between them, V_diff = V₊ − V₋, and it carries the information to be measured. The common-mode signal is the average of the two, V_cm = (V₊ + V₋)/2, and it is usually interference: ground-potential differences, capacitively coupled mains hum, or the bias voltage on which a sensor's output happens to sit. A measurement front end must amplify V_diff while producing as little output as possible from V_cm.

The Shortcomings of a Single-Op-Amp Difference Amplifier

The one-op-amp difference amplifier fails the measurement task on two counts. First, its input impedance is low and unequal: each input looks into a resistor, and the two input resistances differ, so the amplifier loads the source and, worse, loads the two sides unequally. A sensor with any meaningful source resistance is therefore both attenuated and unbalanced by the very act of connecting it. Second, its rejection of common-mode voltage depends entirely on the precise matching of its four resistors. The common-mode rejection ratio is limited by resistor tolerance, and ordinary resistors hold the ratio to only modest levels; achieving high rejection demands tightly trimmed matched networks. The instrumentation amplifier overcomes both problems by buffering the inputs with high-impedance amplifiers and by taking the gain in a way that does not rely on matching for its accuracy.

The Defining Specifications

An instrumentation amplifier is characterized by a small set of figures that follow directly from its purpose: very high differential and common-mode input impedance, so it does not disturb the source; high common-mode rejection ratio, so it ignores shared interference; low input offset voltage and low offset drift, so it does not add error to small signals; low input bias current and noise; and an accurately settable gain. The remainder of this article examines how the topology achieves each of these and where the practical limits lie.

The Input Stage

Each input connects directly to the non-inverting input of one op-amp, so the two inputs see the enormous input impedance of those amplifiers, balanced and typically in the gigaohm range. The two input amplifiers are cross-coupled through a network of three resistors: a single gain resistor R_G between their two inverting inputs, with a feedback resistor R from each output back to the corresponding inverting input. Because each op-amp forces its inverting input to follow its non-inverting input, the full differential input voltage appears across R_G. That voltage drives a current through R_G, and the same current flows through both feedback resistors, so the difference between the two stage outputs is amplified while any common-mode voltage passes through both buffers unchanged.

The Difference-Amplifier Output Stage

The two outputs of the input stage feed a conventional one-op-amp difference amplifier, which subtracts them to produce a single-ended output and rejects the common-mode voltage they still carry in common. The output is measured with respect to a reference terminal, which can be tied to ground or driven to shift the output level, a useful feature for setting the zero point of a single-supply system. Crucially, the common-mode rejection of the whole amplifier still depends on the matching of this output stage's resistors, but because the input stage has already applied differential gain, any residual mismatch is referred to the input divided by that gain, so the overall rejection is far better than a bare difference amplifier of the same resistors would give.

The Overall Gain Expression

For the standard three-op-amp instrumentation amplifier with input feedback resistors R, gain resistor R_G, and a unity-gain output difference stage, the overall gain is:

G = 1 + (2R / RG)

The "1 +" term and the factor of two arise because the differential input voltage is impressed across R_G and the resulting current develops a voltage across both feedback resistors. Integrated instrumentation amplifiers print this formula, with their particular internal resistor value, on the data sheet; widely used industry-standard forms are G = 1 + (50 kΩ / R_G) and G = 1 + (49.4 kΩ / R_G), the latter chosen by several parts so that a given R_G yields the same gain across pin-compatible families. Setting R_G to infinity (an open circuit) gives a gain of one, while smaller R_G gives larger gain.

Common-Mode Rejection Ratio

The common-mode rejection ratio (CMRR) is the ratio of the differential gain to the common-mode gain, almost always quoted in decibels:

CMRR = 20 log (Adiff / Acm)

It states how thoroughly the amplifier ignores a voltage common to both inputs. A CMRR of 120 dB means the amplifier responds to a common-mode signal one million times more weakly than to a differential signal of the same size. The figure is not constant: it is highest at DC and low frequencies and degrades as frequency rises, because the matching that produces rejection is undone by stray capacitance and finite amplifier bandwidth. Data sheets therefore plot CMRR against frequency, and they show it improving with gain, since higher first-stage gain refers the output stage's residual mismatch to a smaller equivalent input error.

What Sets the Rejection

In the three-op-amp circuit the common-mode signal passes through both input buffers with a gain of one, so the input stage itself adds no common-mode error and contributes its full differential gain to the rejection. The remaining common-mode error comes almost entirely from the output difference amplifier, whose rejection depends on how well its four resistors are matched. This is why integrated parts, with laser-trimmed on-chip resistors, achieve CMRR figures that are impractical to reach with discrete resistors, and why a discrete instrumentation amplifier built from three separate op-amps and ordinary resistors rarely matches a monolithic one. The source impedance also matters: an imbalance between the two source resistances converts common-mode voltage into a differential error, so even a perfect amplifier is limited by the balance of what it is connected to.

Gain Accuracy and Matching

Because the differential gain is set by the ratio 2R/R_G, its accuracy depends on the absolute value and stability of R_G together with the matching and tracking of the two internal feedback resistors. The matching and temperature tracking of the on-chip resistors are excellent in a monolithic part, so the gain accuracy and gain drift are dominated by the external gain resistor when one is used. This separation is the practical payoff of the topology: the user sets the gain with one resistor, and the rejection, which lives in the trimmed output stage, is unaffected by that choice.

One Resistor Sets the Gain

In the three-op-amp topology the entire gain is programmed by R_G, through G = 1 + (2R/R_G). A single resistor changes the gain without touching any other part of the circuit and, critically, without affecting the common-mode rejection, which resides in the trimmed output stage. This is the central practical advantage over the difference amplifier, where changing the gain means changing matched resistors and re-trimming the rejection. The designer chooses one resistor value and reads the gain from the data-sheet formula.

Why the Gain Resistor Dominates Gain Error

Since the internal resistors are trimmed and tracked while R_G is an ordinary external component, the gain error and gain drift of the finished amplifier are governed chiefly by R_G. Its absolute tolerance sets the initial gain error, and its temperature coefficient sets the gain drift; a resistor with a large or poorly specified temperature coefficient will introduce gain drift that no quality of the integrated part can remove. Precision designs therefore use a low-tolerance, low-temperature-coefficient resistor for R_G, and they account for the fact that the "1 +" term means the fractional gain error from R_G is slightly diluted at low gains and most pronounced at high gains where 2R/R_G dominates.

Practical Cautions

Several practical issues attend the gain resistor. The connection to R_G carries the full differential current, so trace and contact resistance in series with it adds directly to the effective R_G and corrupts the gain, an argument for short connections and, at the highest precision, a Kelvin connection. Because high gain demands a small R_G, the relative effect of these stray resistances grows with gain. Some integrated instrumentation amplifiers avoid the external resistor altogether by offering pin-selectable fixed gains set entirely by trimmed internal resistors, trading flexibility for the best possible gain accuracy and drift. The choice between a user-set R_G and a fixed-gain part is one of the first decisions in a design.

The Two-Op-Amp Instrumentation Amplifier

The two-op-amp instrumentation amplifier uses one fewer amplifier by cascading two stages so that the second both amplifies and performs the subtraction. It retains high input impedance at both inputs and sets its gain with a small group of resistors including a single gain resistor, and it costs and consumes less than the three-op-amp version. Its limitations follow from its asymmetry: the two inputs traverse different numbers of stages, so their paths have unequal delay and bandwidth, which degrades common-mode rejection as frequency rises more severely than in the symmetric three-op-amp circuit. Its common-mode input voltage range is also more restricted and gain-dependent. The two-op-amp design suits cost- and power-sensitive applications that need moderate, mostly low-frequency rejection rather than the highest performance.

The Current-Feedback Instrumentation Amplifier

The current-feedback instrumentation amplifier, sometimes called a current-mode or indirect-current-feedback topology, takes a different route to the difference. Rather than processing the signal as voltages through a resistor bridge, it converts the input differential voltage into a current with a transconductance stage, mirrors that current into a second stage, and converts it back to a voltage across a feedback resistor that sets the gain. The gain is the ratio of the feedback resistor to the input transconductance resistor.

Its advantage is that the common-mode rejection does not rely on the matching of a four-resistor bridge as in the classic output stage; it is set instead by the matching of transconductance stages and current mirrors, which can be made excellent on-chip and which hold up better at high common-mode voltage and over frequency. Many modern integrated instrumentation amplifiers, including those rated for large common-mode voltages such as high-side current sensing, use this architecture for precisely that reason.

Choosing an Architecture

The selection follows the application. The three-op-amp topology remains the standard for general precision measurement, balancing high CMRR, high input impedance, and accurate single-resistor gain. The two-op-amp topology is chosen where cost, board area, and power must be minimized and the rejection requirement is modest. The current-feedback topology is chosen where the common-mode voltage is large or varies quickly, or where the best CMRR-versus-frequency behavior is needed, as in current-shunt sensing and high-side monitoring. In integrated form all three are available off the shelf, so the architectural decision is usually a matter of selecting the right part rather than designing the internal circuit.

Overvoltage and Transient Threats

The inputs face several hazards: voltages that swing beyond the supply rails when the amplifier powers up after the source, inductive transients and electrostatic discharge coupled in through cabling, and fault conditions that apply a large voltage across the inputs. Without protection these can drive destructive current into the input devices or latch the part. The challenge is that the obvious protective measures, series resistance and shunt clamps, also introduce the very errors the instrumentation amplifier is built to avoid.

Series Resistance and Clamps

The common protection scheme places a resistor in series with each input to limit fault current, followed by clamping diodes that conduct to the supply rails when an input tries to exceed them. The series resistors must be equal in the two inputs, because any imbalance between them converts common-mode voltage into differential error and degrades CMRR; they also add Johnson noise and, with the input bias current, a small offset, so their value is a compromise between protection and precision. The clamp diodes must have very low leakage, since leakage current flowing in the source impedance produces an offset; low-leakage diodes or the amplifier's own internal protection are preferred. Many instrumentation amplifiers include integrated input protection rated to some voltage beyond the rails, reducing the external components required.

Filtering and Common-Mode Considerations

Input networks frequently combine protection with filtering, adding capacitors to roll off radio-frequency interference and to suppress the common-mode-to-differential conversion that out-of-band energy can cause through input nonlinearity. As with the series resistors, the two input paths must be matched: an RC filter on each input must use well-matched components, because a mismatch in the filter time constants degrades high-frequency CMRR exactly as a resistance imbalance does. Careful designers therefore make the differential capacitor across the inputs larger than the two common-mode capacitors to ground, so that any mismatch in the latter is swamped and high-frequency rejection is preserved.

Input-Referred and Output-Referred Offset

An instrumentation amplifier has two offset components, and a complete specification gives both. One scales with gain and is properly thought of as an input offset; the other is fixed and is an output offset. The total output offset is the input-referred offset multiplied by the gain plus the output offset term:

Vos,out = (Vos,in × G) + Vos,out(fixed)

At high gain the input term dominates and the amplifier's usefulness for tiny signals is governed by how small that input offset is; at low gain the fixed output term can matter more. Referring all errors to the input by dividing by the gain lets the designer compare them directly with the signal and with the sensor's own offset.

Drift Over Temperature

Offset that could be nulled at one temperature reappears as the temperature changes, and this drift, specified in microvolts per degree Celsius referred to the input, is often the limiting error in precision work because it cannot be removed by a one-time calibration. Both the input and output offset terms have temperature coefficients. For the slowly varying signals typical of bridge and thermocouple measurement, the most effective remedy is to choose an instrumentation amplifier built on a zero-drift, chopper-stabilized, or auto-zero input stage, which continuously cancels its own offset and so achieves input offset drift below a fraction of a microvolt per degree. Such parts trade a little broadband noise for a dramatic reduction in DC error and drift.

Bias Current and Noise

Input bias current flows in the source resistance and produces an offset equal to the current times the resistance; any imbalance between the two source resistances turns the bias current into a differential error, which is why balanced source impedances matter. The amplifier's voltage noise and current noise, both referred to the input, set the resolution floor; over a measurement bandwidth they combine with the source's thermal noise to determine the smallest distinguishable signal. Because gain is taken at the input stage, the input-referred noise of that stage dominates, so selecting a part for its input noise density at the relevant frequencies, and limiting the bandwidth to no more than the measurement requires, are the levers that control the noise floor.

The Wheatstone Bridge Front End

A Wheatstone bridge excited by a fixed voltage produces a differential output proportional to the imbalance of its arms, but that small differential signal sits on a common-mode voltage near half the excitation. With a 5 V excitation and a few-millivolt full-scale output, the common-mode voltage is hundreds to thousands of times the signal, so resolving the signal accurately demands very high CMRR, often well above 100 dB. The instrumentation amplifier's high, balanced input impedance also keeps it from loading the bridge arms and unbalancing the bridge, a loading error that a low-impedance difference amplifier would introduce. For these two reasons together, high CMRR and non-loading inputs, the instrumentation amplifier is the natural and standard bridge amplifier.

Strain, Pressure, and Force Sensors

Strain gauges, load cells, and pressure transducers are almost universally bridge-based, delivering on the order of one to a few millivolts per volt of excitation at full scale. The instrumentation amplifier raises this to a usable level, while its reference terminal sets the output's zero point to suit the following analog-to-digital converter. Ratiometric operation, in which the same reference that excites the bridge also serves as the converter's reference, cancels excitation drift and is a common companion technique. The amplifier's low offset drift is critical here, since the signals are small and the systems often operate over wide temperature ranges.

Thermocouples, Shunts, and Biopotentials

Beyond bridges, the instrumentation amplifier serves wherever a small difference rides on interference. It amplifies the tens of microvolts of a thermocouple while rejecting the ground-loop and mains pickup that contaminate long sensor leads. It measures the millivolt drop across a current-sense shunt that may sit at a high common-mode potential, the application that especially favors high-voltage current-feedback parts. And in biomedical instrumentation it extracts microvolt-level biopotentials such as the electrocardiogram from the large common-mode interference coupled into the body, an application that prizes both very high CMRR and high input impedance. In every case the same theme recurs: keep the difference, reject the common, and add as little offset, drift, and noise as the measurement can tolerate.