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Small sensor signals are often difficult to measure because they can be affected by electrical noise, long wires, changing temperatures, and voltage shared by both input lines. An instrumentation amplifier solves this problem by accurately amplifying the small difference between two input voltages while rejecting unwanted common-mode signals. Its high input impedance also prevents it from placing a heavy load on sensitive sensors.
An instrumentation amplifier, often called an in-amp or INA, is a precision amplifier designed to measure and amplify very small voltage differences between two input signals. At the same time, it rejects common-mode signals, such as electrical noise that appears equally on both inputs. This makes it suitable for accurate sensor and measurement systems.
The instrumentation amplifier is based on the differential amplifier principle. A differential amplifier produces an output according to the voltage difference between its inputs:
VOUT ∝V2-V1
However, a basic differential amplifier may load high-impedance sensors, and its accuracy and common-mode rejection depend strongly on precisely matched resistors. An instrumentation amplifier improves this basic circuit by adding high-input-impedance amplifier stages before the differential output stage.
A standard instrumentation amplifier normally uses three operational amplifiers. The first two op-amps buffer and amplify the input signals without drawing significant current from the source. The third op-amp subtracts the two signals and produces a single-ended output. In many designs, the gain can be adjusted using one external gain resistor, RG.
Because of this structure, instrumentation amplifiers provide high input impedance, accurate gain, low signal-source loading, and a high common-mode rejection ratio (CMRR).
The circuit shown is a standard three-op-amp instrumentation amplifier. It contains two input amplifiers, A1 and A2, followed by a differential output amplifier, A3. This arrangement amplifies the small voltage difference between V1 and V2 while rejecting voltage and noise common to both inputs.
Operational amplifiers A1 and A2 form the high-input-impedance gain stage. Because the input signals connect to their non-inverting terminals, the circuit draws very little current from the signal source. This prevents loading of low-level sensors such as strain gauges, pressure sensors, and bridge transducers.
The outputs of A1 and A2, labelled V(O(A1)) and V(O(A2)), feed the differential amplifier A3. This final stage subtracts the two amplified signals and converts them into the single-ended output voltage VOUT.
Assuming ideal op-amps operating with negative feedback, the voltage at each inverting input is approximately equal to the voltage at its corresponding non-inverting input. Therefore, the circuit maintains:
VA≈V1
VB≈V2
The voltage across the gain-setting resistor RG is therefore:
V(RG)=VA-VB=V1-V2
Using Ohm’s law, the current through RG is:
The op-amp inputs ideally draw no current. As a result, the same current magnitude flows through RG and the two feedback resistors R5 and R6. When these resistors have equal values,
R5=R6=RF
the differential voltage produced between the outputs of A1 and A2 is:
This equation gives the differential gain of the input stage:
The equation shows that RG controls the input-stage gain. A smaller RG produces a higher gain, while a larger RG produces a lower gain. This allows the gain to be adjusted without changing the high input impedance of the circuit.
Operational amplifier A3 and resistors R1 to R4 form the differential output stage. For proper subtraction and effective common-mode rejection, the resistor ratios must be matched:
If R1=R3 and R2=R4, the gain of this stage is:
The output of A3 is therefore:
The final stage removes most of the voltage common to both signal paths and amplifies the remaining differential component. Precise resistor-ratio matching is important because mismatch reduces the circuit’s common-mode rejection ratio, or CMRR.
Combining the gains of the input and output stages gives the complete instrumentation amplifier equation:
The total differential gain is:
where:
• AD is the total differential voltage gain.
• RF is the value of each equal input-stage feedback resistor, R5 and R6.
• RG is the gain-setting resistor.
• R2/R1 is the gain of the differential output stage.
• V2-V1 is the differential input voltage.
For example, if R2=R1, the output stage has unity gain. The complete equation becomes:
If RF=10 kΩ and RG=2 kΩ, the total gain is:
For a differential input of 10 mV :
VOUT =11(10mV)=110mV
The circuit shows a three-op-amp instrumentation amplifier used to amplify the small differential voltage produced by a strain-gauge bridge. The sensor provides a maximum differential input of 50mV, while the required overall differential gain is 100. The design must determine the resistor values and the expected maximum output voltage.
In the circuit, A1 and A2 form the high-input-impedance gain stage. Resistors R5, R6, and RG control the gain of this stage. The third op-amp forms the differential output stage, whose gain is set by R1, R2, R3, and R4.
The required gain of the differential output stage is 2. Its voltage gain is:
If R2 is selected as 2 kΩ, the required value of R1 is:
The resistor ratios on both sides of the differential amplifier must be equal:
The circuit therefore uses:
R1=R3=1kΩ
R2=R4=2kΩ
Matching these resistor ratios is important because any mismatch can reduce the amplifier’s common-mode rejection and introduce output error. In a practical precision circuit, low-tolerance matched resistor networks are preferable to separate standard resistors.
The complete differential gain of the instrumentation amplifier is:
Here, RF represents the two equal input-stage feedback resistors:
R5=R6=RF=5kΩ
To calculate RG, rearrange the gain equation:
Substituting RF=5 kΩ, R2/R1=2, and AD=100:
The nearest practical value is approximately:
RG≈204Ω
Using 204Ω gives a gain very close to 100. The slight difference comes from rounding the calculated resistor value.
The output voltage is the differential input voltage multiplied by the overall gain:
VOUT =AD VIN
For a maximum differential input of 50 mV :
VOUT =100(50 mV)
VOUT =5 V
Therefore, the circuit produces a maximum output magnitude of 5V from a 50 mV differential input.
The output polarity depends on which input is higher. In the circuit shown, A1 feeds the inverting side of the final amplifier, while A2 feeds its non-inverting side. Therefore:
VOUT=100(V2-V1)
If V2 is 50 mV higher than V1, the ideal output is +5V. If V1 is 50 mV higher than V2, the ideal output is -5 V . For this reason, the diagram should label the input as V2-V1=50 mV if it intends to show a positive 5 V output.
The fixed 204 Ω resistor can be replaced by a fixed resistor in series with a potentiometer when adjustable gain is required. For example, a 20Ω fixed resistor combined with a 2.5 k Ω potentiometer provides an approximate gain range of 10 to 1000:
At RG=2520Ω:
AD≈9.94
At RG=20"Ω:
AD=1002
The fixed resistor prevents R_Gfrom reaching zero, which would demand extremely high gain. In a real circuit, the usable gain and output voltage are also limited by the op-amps’ supply voltage, bandwidth, input common-mode range, noise, and output-swing capability.
The performance of an instrumentation amplifier depends on more than its gain equation. Several electrical specifications determine how accurately it amplifies small differential signals under real operating conditions. These parameters affect measurement precision, noise immunity, temperature stability, and compatibility with different sensors.
The common-mode rejection ratio (CMRR) measures how effectively an instrumentation amplifier rejects voltages that appear equally on both input terminals while amplifying only the voltage difference between them. Common-mode signals are often caused by electromagnetic interference, power-line noise, or ground-potential differences. Since these unwanted signals appear on both inputs, a high CMRR prevents them from affecting the output.
CMRR is usually specified in decibels (dB). A higher value indicates better noise rejection and more accurate measurements. For example, instrumentation amplifiers with CMRR values above 100 dB are commonly used for strain gauges, bridge sensors, medical electrodes, and other applications where the desired signal may be only a few millivolts but electrical noise is much larger.
Input impedance describes how much the instrumentation amplifier loads the connected signal source. Most instrumentation amplifiers have extremely high input impedance, often ranging from megaohms (MΩ) to gigaohms (GΩ). Because very little current flows into the input terminals, the amplifier has minimal effect on the sensor output.
High input impedance is especially important for high-resistance sensors such as strain gauges, load cells, thermocouples, and pH probes. It allows the amplifier to measure the original sensor voltage accurately without reducing or distorting the signal.
An ideal instrumentation amplifier produces zero output when both input voltages are equal. In practice, small internal mismatches create a tiny input offset voltage, causing a non-zero output even when the differential input is zero. This offset becomes more noticeable when high gain is used because the error is amplified together with the signal.
Offset drift describes how the input offset voltage changes with temperature. A low offset drift improves long-term measurement accuracy, especially in systems that operate over a wide temperature range or require precise calibration.
Every amplifier generates a small amount of internal electrical noise. This noise is commonly specified as input voltage noise and input current noise. When amplifying very weak signals, the amplifier's own noise can become comparable to the sensor output, reducing measurement accuracy.
Low-noise instrumentation amplifiers are preferred for applications involving thermocouples, strain gauges, medical electrodes, and other low-level sensors. Reducing amplifier noise improves the signal-to-noise ratio and allows small signal changes to be measured more reliably.
Gain accuracy indicates how closely the actual amplifier gain matches its specified or calculated value. Manufacturing tolerances and internal resistor matching can cause small differences between the expected gain and the actual gain.
Gain drift describes how the amplifier gain changes as temperature varies. A low gain drift helps maintain consistent measurement accuracy without frequent recalibration.
Bandwidth defines the range of signal frequencies that the instrumentation amplifier can amplify accurately. As the gain increases, the available bandwidth usually decreases because of the amplifier's gain-bandwidth limitation. Designers must ensure that the bandwidth is sufficient for the highest signal frequency in the application.
Settling time is the time required for the output voltage to stabilize within a specified error after a sudden change in the input signal. Fast settling time is important in high-speed data acquisition systems, multiplexed sensor measurements, and precision analog-to-digital converter (ADC) interfaces.
The input common-mode range specifies the allowable average voltage level of the two input signals while the amplifier operates correctly. Even if the differential voltage is very small, both input voltages must remain within this permitted range. Exceeding the common-mode range can increase measurement error, reduce CMRR, or cause the amplifier output to become inaccurate or saturate.
When selecting an instrumentation amplifier, both the expected differential signal and the sensor's common-mode voltage should be checked against the datasheet specifications.
The maximum output voltage of an instrumentation amplifier is limited by its supply voltage and output-stage design. The output cannot exceed the positive or negative supply rails, and many devices require a small voltage margin from each rail unless they are designed for rail-to-rail operation.
This limitation should always be considered during circuit design. For example, in the worked example, the calculated maximum output is ±5 V. The selected instrumentation amplifier and its power supply must support this output range without clipping or saturation.
Instrumentation amplifiers are used to amplify small sensor signals while rejecting common electrical noise. Their high input impedance and accurate gain make them suitable for precision measurement systems.
Instrumentation amplifiers amplify the small differential output of Wheatstone-bridge sensors. They are commonly used in weighing scales, torque sensors, and structural monitoring systems.
Pressure and force sensors often produce weak bridge signals. An instrumentation amplifier raises these signals to a level suitable for an ADC or control circuit.
Instrumentation amplifiers can condition signals from thermocouples, RTDs, and bridge-based temperature sensors. Low offset and drift help maintain measurement accuracy.
ECG, EMG, and EEG systems use instrumentation amplifiers to detect very small body signals. High CMRR helps reject power-line interference and other common-mode noise.
Instrumentation amplifiers are placed between sensors and ADCs to provide gain and noise rejection. They are useful in factories where motors, relays, and long cables can introduce interference.
Instrumentation amplifiers measure small voltages across shunt resistors and monitor differential voltages in batteries, power supplies, and motor-control systems.
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