Instrumentation Amplifier

The signal-on-noise problem

A typical strain gauge sitting on a steel beam outputs a few millivolts when the beam bends — but it's wired with twisted-pair cable running ten metres across a factory floor full of motor drives, transformers, and 60 Hz radiation. Common-mode noise picked up along that cable pair can be several volts; the differential signal you actually care about is a millivolt. If you naively measure single-ended (one wire against ground), the noise is 1000× the signal.

The answer is differential measurement: measure the voltage between the two wires, ignore the voltage between either wire and ground. As long as the noise hits both wires equally (which it largely does for nearby pickup), differential subtraction kills it. The art is doing that subtraction without disturbing the source — and that's where the 3-op-amp instrumentation amplifier comes in.

The 3-op-amp architecture

                              R                R
   V_in+ ──┐                ┌──/\/\──┐      ┌──/\/\──┐
            │                │         │      │         │
            │  op1           │   op3   │      │         │
            ├── + ───────────┤ −       ├──────┤ +       ├── V_out
            │                │         │      │         │
   R_G ─────┤ −              │ +       │      │ −       │
            │                └─────┬───┘      └─────┬───┘
            │                      │                │
   V_in- ──┤  op2                  │                │
            ├── − ───────────┐  R_REF         R_REF │
            │                │                      │
            ├──/\/\──────────┤        difference amp │
            │   R            │                      │
            │                ─                      ─
            └── + ─────GND   GND                    GND

   G = 1 + (2R / R_G)
   For INA128/AD620: R ≈ 25 kΩ, so R_G = 50 Ω → G ≈ 1000

The two input op-amps (op1, op2) buffer the inputs — their non-inverting terminals see the raw V_in+ and V_in-, so the input impedance is essentially infinite. The single gain-setting resistor R_G ties their inverting inputs together. Whatever differential voltage exists across the inputs appears across R_G (by the golden rule that the op-amp's two inputs are at the same voltage), driving a current that flows through both R feedback resistors. The two buffer outputs therefore swing in opposite directions by an amount that depends on R_G — that's the gain stage.

The third op-amp (op3) is a unity-gain difference amplifier with four matched resistors. It subtracts the two buffer outputs, killing whatever common-mode voltage they share and outputting the amplified differential as a single-ended voltage referenced to ground (or to a reference pin, for level-shifted designs).

The gain equation

With the standard topology (R inside the chip, R_G external), the closed-loop differential gain works out to:

G = 1 + (2R / R_G)

For the INA128:   R = 25 kΩ
                  R_G = 50 Ω    → G = 1001
                  R_G = 500 Ω   → G = 101
                  R_G = 5 kΩ    → G = 11
                  R_G = ∞ (open) → G = 1

For the AD620:    R = 24.7 kΩ
                  R_G = 49.4 Ω  → G = 1000

One resistor sets gain. No matched pairs needed (because both R values are on the same silicon die — they match within 0.01%). This is the architectural win: the in-amp's gain is more accurate than the user's external resistor.

Worked example: ECG front-end

An ECG signal at the body surface is roughly 1 mV peak-to-peak. The two electrodes (right arm, left arm) connect through long wires that pick up 60 Hz mains hum at common-mode levels of several volts. The differential biosignal must be amplified to about 1 V to feed a 12-bit ADC at full scale.

Required gain. 1 V / 1 mV = 1000. Use AD620: R_G = 49.4 Ω + a small trim for exactly 1000.

CMRR requirement. Common-mode of 2 V mains; differential of 1 mV. CMRR must reduce common-mode contribution to well below the signal: aim for <0.1 mV from 2 V → CMRR > 86 dB. The AD620 spec at G=1000 is 130 dB — three orders of magnitude of margin.

Input bias current. AD620 input bias is 0.5 nA typical. Through a 1 MΩ skin-electrode impedance, that's 0.5 mV of offset — comfortably below the 1 mV signal. Good enough.

Bandwidth. At G=1000 the AD620's −3 dB bandwidth is 12 kHz. ECG bandwidth is 0.05–150 Hz, so plenty of room. A separate active filter strips DC drift and high-frequency noise.

Driven right leg. A second AD620 (in unity gain) buffers the body's common-mode voltage and feeds it through a current-limiting resistor back to the body as the "DRL" (driven right leg) signal. This active common-mode feedback adds another 20–30 dB of effective CMRR by forcing the body's common-mode to track the amplifier's reference.

Total bill of materials for the front end: two AD620s, one R_G, a few bias-return resistors, a couple of bypass caps. About $10 retail. Bedside ECG monitors and consumer wearables alike start with exactly this circuit.

In-amp family comparison

Part	CMRR @ G=100	Input bias	Offset	Supply	Use case
INA128	120 dB	5 nA	50 μV	±2.25 to ±18 V	Industrial sensors
AD620	120 dB	1 nA	50 μV	±2.3 to ±18 V	Bio-signal, low-power
AD8221	110 dB	0.4 nA	40 μV	±2.3 to ±18 V	High-precision DAQ
INA333	110 dB	0.2 nA	25 μV	+1.8 to +5.5 V	Battery, rail-to-rail
AD8429	130 dB	120 nA	50 μV	±4 to ±18 V	Low-noise, audio band
LT1167	120 dB	0.35 nA	40 μV	±2.3 to ±18 V	Bridge sensors, RTDs

In-amp + Wheatstone bridge

The textbook pairing: a 350 Ω strain-gauge Wheatstone bridge excited at 5 V. Three resistors are nominally 350 Ω, one is a strain gauge varying from 350 Ω to 350 Ω + ΔR with applied force. The bridge output is:

V_diff ≈ (ΔR / 4R) × V_exc

For a typical 2 mV/V load cell at full scale:
   V_diff = 2 mV/V × 5 V = 10 mV at full scale

Common-mode at each output = V_exc / 2 = 2.5 V
We need G ≈ 200 to fill a ±2 V ADC range.

R_G = 2R / (G − 1) = 50000 / 199 ≈ 251 Ω

The in-amp ignores the 2.5 V common-mode pedestal and gives a clean amplified signal in the 0–2 V range that the ADC can digitise. Total signal-conditioning components beyond the in-amp: an R_G, two supply bypass caps, optionally a single-pole RC low-pass. That's the whole sensor front-end.

Why CMRR collapses if you skip the in-amp

The temptation is to build a "discrete" in-amp from a quad op-amp and four matched resistors. It can work — but precision-resistor mismatch dominates CMRR. The classic single-op-amp difference amp:

CMRR ≈ (1 + R_f / R_in) × 1 / (4 × (ΔR/R))

R_f / R_in = 100 (gain of 100)
Matched 0.1% resistors → ΔR/R = 0.001
CMRR = 101 / (4 × 0.001) = 25,250 = 88 dB

Even with 0.1% resistors (relatively expensive), you only reach 88 dB. Get to 1% and CMRR drops to 68 dB — your sensor signal is buried in mains hum. The 3-op-amp in-amp gets around this by having the difference stage operate at unity gain, with internal laser-trimmed resistor pairs that match to 0.01% or better. That's where the 120 dB CMRR comes from.

Critical layout notes

• Star ground at the in-amp. The reference pin (op3's non-inverting reference) is the analog measurement ground. Don't route motor currents through it.
• Twisted-pair the differential inputs. The whole CMRR story assumes the two wires pick up the same noise. Untwisted pairs guarantee a CMRR floor.
• Bias-current return paths. Even 1 nA × 10 MΩ source = 10 mV offset. AC-coupled or floating sources need a high-value resistor to ground at each input.
• R_G placement. Mount close to the in-amp pins; long traces add stray capacitance and parasitic inductance that affect bandwidth and stability.
• Shielding. Drive cable shields with the in-amp's reference or a unity-buffered common-mode signal to eliminate shunt capacitance effects on CMRR.
• Input protection. Series resistors (1 kΩ) and Schottky clamps to the supply rails protect against ESD and accidental overvoltage; many in-amps already include internal protection FETs.

Where in-amps live

• Industrial weighing scales. 4-wire load-cell bridge, 24-bit ADC, an in-amp doing the first 100×.
• Medical bedside monitors. ECG, EEG, blood-pressure transducers, pulse-oximeters — every analog channel begins with an in-amp.
• Temperature loggers. Type-K thermocouple outputs 41 μV/°C; an in-amp at G=200 turns each degree into 8 mV — directly readable.
• Battery-management systems. Current-shunt sensing on the negative rail of a 48 V or 400 V battery uses a high-voltage common-mode in-amp (INA240, MAX9923) to measure tens of millivolts across a milliohm shunt at hundreds of volts common-mode.
• 4–20 mA loop transmitters. A bridge sensor's output, in-amped, drives a precision voltage-to-current converter that modulates 4–20 mA on a two-wire loop running hundreds of metres of industrial cable.
• Automotive sensor interfaces. Hall-effect, magneto-resistive, and piezo sensors with single-supply rail-to-rail in-amps (INA333) handle 12 V/24 V common-mode and low offset across automotive temperature range.

A 1969 invention that aged well

The 3-op-amp instrumentation amplifier topology was first formally described by George Tucker in a 1969 IEEE paper as an improvement on Robert Pease's earlier discrete-transistor sensor amplifiers. The first monolithic in-amp, the AD521 from Analog Devices in 1977, integrated the topology onto a single die with laser-trimmed resistors — pushing CMRR from the 70 dB ballpark of discrete designs to over 110 dB. The AD620 (1994) became the industry's reference part: pin-compatible variants and clones are produced by TI, Linear, Maxim, and many smaller vendors thirty years later, with the basic 3-op-amp architecture essentially unchanged.