Free Instrumentation Amplifier Gain Resistor Calculator
Calculate external gain-setting resistance (Rg), voltage gain, output swing, input common-mode voltage range, and resistor-tolerance CMRR for in-amp ICs and discrete circuits.
⚡ Amplifier Architecture & Specifications
Calculated Differential Gain: 100.00 V/V (40.00 dB)
✓ Pre-amp stage operates well inside supply rails without clipping.
Design Note: In-amp gain resistors should always be high-stability metal-film with low thermal TCR (≤ 25 ppm/°C). Long PCB traces between pins 1 and 8 add stray resistance and degrade high-frequency CMRR.
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Three-Op-Amp Instrumentation Amplifier Anatomy
A classic monolithic or discrete instrumentation amplifier (such as the industry-standard AD620, INA128, INA118, or AD623) consists of a buffered differential input stage followed by a subtractor (difference) stage:
Gain Resistor Formula: R_g = 49.4 kΩ / (G - 1)
Output Voltage: V_out = G × (V_in+ - V_in-) + V_ref
Unlike a standard single op-amp differential amplifier, the instrumentation amplifier presents extremely high input impedance (10 GΩ to 1 TΩ) on both inputs simultaneously. This eliminates source-loading imbalances that degrade Common-Mode Rejection Ratio (CMRR) in sensor bridge applications like strain gauges, thermocouples, RTDs, and load cells.
The In-Amp "Diamond Plot" Common-Mode Trap
A common design pitfall occurs when beginners assume that because the differential output ($V_{out} = G cdot V_{diff}$) is within the power supply rails, the amplifier will function linearly. However, the internal first-stage buffer op-amps must carry both the common-mode voltage and half the differential gain:
V_o2 = V_cm + (V_diff / 2) × (1 + 2 × R1 / R_g)
If $V_{o1}$ or $V_{o2}$ hits within 1.2V to 1.5V of the positive or negative supply rails (on non-rail-to-rail parts), the input stage saturates, causing catastrophic gain compression and total loss of CMRR even though $V_{out}$ appears normal.
CMRR vs Resistor Tolerance
In a discrete 3-op-amp topology, the CMRR of the difference stage is heavily dominated by the relative matching of the four difference resistors ($R_3$ and $R_4$):
With 1% resistors, worst-case CMRR drops to roughly 54 dB regardless of the op-amp's internal capability. This is why monolithic laser-trimmed in-amps (with internal $0.01%$ matching) achieve 100 to 120 dB of real-world common-mode rejection.
Frequently Asked Questions
Why does leaving Rg disconnected set the gain to exactly 1?
When Rg is open-circuit (infinite resistance), the term 2*R1/Rg becomes zero. The two input buffer op-amps act as simple unity-gain voltage followers, passing Vin+ and Vin- directly to the difference stage, yielding a net differential gain of exactly 1.
Why should I connect the Vref pin to a low-impedance source?
The Vref pin sets the output baseline voltage. Any resistance in series with Vref unbalances the internal difference stage resistor network, degrading CMRR by several tens of decibels. Always drive Vref with an op-amp buffer or low-impedance ground reference.
Can I use a potentiometer for Rg?
While possible for prototyping, potentiometers have poor temperature coefficients (100-200 ppm/°C) and parasitic wiper capacitance. For stable production designs, use a fixed 0.1% or 0.5% metal film resistor or a digitally controlled resistor with specified TCR.