Instrumentation Amplifier Gain Calculator

Instrumentation Amplifier Gain Calculator results cover gain in V/V and dB, output and clipping. Choose a 3 op-amp circuit or an IC like the INA128, then enter RG or a target gain.

Instrumentation Amplifier Gain Calculator Formula

The Instrumentation Amplifier Gain Calculator uses the standard three op-amp gain formula. Two input op-amps share one gain resistor, RG, and each has a feedback resistor, R2. A third op-amp subtracts their outputs through four resistors, two R3 and two R4.

$$G=\left(1+\frac{2R_2}{R_G}\right)\times \frac{R_4}{R_3}$$

RG is in the denominator, so a smaller gain resistor means more gain. With RG = 1 kΩ and all other resistors at 10 kΩ, the first term is 1 + 20 and the second is 1. The gain is 21.00 V/V, which the result shows alongside 26.44 dB.

The output is that gain times the difference between the two inputs, plus whatever voltage sits on the REF pin. With REF grounded, the output is measured from circuit ground.

$$V_{OUT}=G\times (V_{+}-V_{-})+V_{REF}$$

Take V+ at 2.52 V, V- at 2.5 V and REF grounded. The differential input is 20.00 mV, so the output is 420.0 mV. The same card shows the common-mode input, 2.510 V here, which is the average of the two inputs and the part the amplifier is meant to reject.

Instrumentation Amplifier Gain Derivation

The instrumentation amplifier gain derivation starts at RG. Each input op-amp holds its inverting input at the same voltage as its signal input. The two ends of RG therefore sit at V- and V+, and the whole differential input appears across RG.

That voltage drives a current through RG. No current enters the op-amp inputs, so the same current flows through both R2 resistors. The voltage between the two op-amp outputs is that current times RG plus twice R2.

$$V_{A2}-V_{A1}=(V_{+}-V_{-})\times \left(1+\frac{2R_2}{R_G}\right)$$

A common-mode voltage puts the same level on both ends of RG, so no current flows and the first stage passes it at a gain of 1. Analog Devices sets this out in its MT-063 tutorial on the three op-amp in-amp. Each input op-amp is wired like the stage in the Non-Inverting Op-Amp Resistor Calculator, with RG shared between the two.

The third op-amp then subtracts the two outputs and multiplies the result by R4 ÷ R3. That step removes the common mode and leaves a single output measured from the REF pin, which gives the full formula used by the Instrumentation Amplifier Gain Calculator.

Instrumentation Amplifier Gain Calculator for ICs

An IC instrumentation amplifier has R2, R3 and R4 built in, so only RG is left to choose. Pick an INA128, AD620, INA333 or another listed part under Amplifier, and the gain switches to the maker's equation. The table shows each one with the E96 resistor for a gain of 100.

The equations come from the TI INA128 and INA129 data sheet, the TI INA333 page and the Analog Devices AD620 data sheet. TI explains that the 50 kΩ term is the sum of the two internal feedback resistors.

The 49.4 kΩ parts and the 50 kΩ parts are not interchangeable without a new RG. A 499 Ω resistor gives 100.0 V/V on an AD620 or INA129 and 101.2 V/V on an INA128. The exact values for 100 V/V are 505.1 Ω, 499.0 Ω and 1.010 kΩ in table order.

Instrumentation Amplifier Design for a Target Gain

Most instrumentation amplifier design work runs backward from a gain to a resistor. Set Solve For to RG for a Target Gain and enter the gain in V/V or dB. The Instrumentation Amplifier Gain Calculator rearranges the gain formula for RG.

$$R_G=\frac{2R_2}{G/(R_4/R_3)-1}$$

A 100 V/V target with R2 = 10 kΩ and equal R3 and R4 needs exactly 202.0 Ω. The nearest E96 part is 200 Ω, and it gives 101.0 V/V, or 40.09 dB. The tolerance setting picks the series, with E192 for ±0.1%, E96 for ±1% and E24 for ±5%.

The Gain Resistor for Common Gains table repeats this for gains from 2 to 1,000 V/V. With R2 at 10 kΩ, a gain of 10 needs 2.222 kΩ and lands on 2.21 kΩ. A gain of 50 needs 408.2 Ω and lands on 412 Ω, and 1,000 needs 20.02 Ω and lands on 20 Ω.

High gains call for very small RG values, and stray resistance starts to count. TI notes that wiring and socket resistance add gain error at gains of about 100 or more. Keep RG close to the pins and avoid sockets for those builds.

Voltage Gain in Decibels

The Instrumentation Amplifier Gain Calculator gives the voltage gain both as a ratio and in decibels. To calculate gain in dB, take 20 times the base-10 log of the V/V figure. The default 21.00 V/V comes out at 26.44 dB.

$$G_{dB}=20{\log }_{10}(G)$$

A 20 dB gain multiplies the voltage by 10, and 40 dB means the output is 100 times the input. Every further 20 dB is another factor of ten. The same rule applies to the single op-amp stages in the Op Amp Gain Calculator.

What Happens if Gain Is Too High

When the gain is too high for the supply, a stage runs into its rail and the output stops following the input. With RG = 20 Ω in the default circuit the gain is 1,001 V/V. A 20 mV input asks for 20.02 V, and on a ±15 V supply with 1.4 V of headroom the output clips at 13.60 V.

The input stage can clip first, and that failure is harder to see. Each input op-amp swings half of the amplified difference above or below the common mode. The clipping card in the Instrumentation Amplifier Gain Calculator shows both of those internal voltages.

$$V_{A1}=V_{CM}-\frac{G_1\times V_D}{2}$$

$$V_{A2}=V_{CM}+\frac{G_1\times V_D}{2}$$

G1 is the first-stage gain, 1 + 2R2 ÷ RG. VD is the differential input and VCM is the common mode. In the default example the two outputs sit at 2.300 V and 2.720 V, far inside the ±13.60 V swing.

Now take an INA333 on a 5 V single supply with a sensor that sits at ground. V- is 0 V, V+ is 10 mV and the target gain is 40. The E96 resistor is 2.55 kΩ for 40.22 V/V, so the expected output is 402.2 mV.

The card turns red and reads Inputs Outside INA333 Range. TI keeps the INA333 inputs 0.1 V inside each rail, which is 100.0 mV to 4.900 V on this supply, and one input sits at 0 V. The output card reads Output Not Valid, Inputs Out of Range.

Lifting the sensor to 200 mV clears the pin limit and exposes the next one. With V- at 0.2 V and V+ at 0.21 V, one input op-amp would need 3.922 mV and can only reach 100.0 mV. The card now reads Input Stage Clips at 100.0 mV.

TI warns in the INA128 data sheet that an input overload can produce an output that appears normal. Moving the common mode fixes both problems. With the inputs at 2.5 V and 2.51 V and REF at 2.5 V, the internal outputs sit at 2.304 V and 2.706 V. The output is then a valid 2.902 V.

The fourth card turns the same limits into design numbers. In the default example it shows a ±647.6 mV input range and names the output stage as the first to clip. It also gives 680.0 V/V as the highest clean gain for a 20 mV input.

The input-pin check covers the INA128, INA129, AD620 and INA333, using each maker's stated range. The INA128 and INA129 need both inputs 2 V inside each rail. An INA128 on ±15 V with inputs at 13.5 V and 13.51 V therefore goes red, because the limit is ±13 V.

The other listed parts and a discrete build use the textbook three op-amp model alone, with one headroom figure for every stage. An instrumentation amplifier simulation in TI's TINA-TI, or the Analog Devices Diamond Plot Tool, checks a specific chip in more detail.

Resistor Tolerance, Gain Spread and CMRR

Real resistors move the gain, and the third card shows by how much. With every resistor at its ±1% limit, the default 21.00 V/V can land anywhere from 20.20 to 21.84 V/V, a spread of -3.8% to +4.0%. For an IC only RG counts, so an INA128 with a ±1% 5.62 kΩ resistor stays within 0.9% of its 9.897 V/V.

Mismatch in the difference stage does more damage, because it lets part of the common mode through. Analog Devices gives the worst case for four resistors of the same tolerance in its MT-061 tutorial. The first-stage gain multiplies that figure, since the first stage amplifies the signal and not the common mode.

$$CMRR=20{\log }_{10}\left(\frac{G_1\times (1+R_4/R_3)}{4t}\right)$$

The tolerance t is a fraction, so ±1% is 0.01. Analog Devices notes that four ±1% resistors at unity gain can be no better than 34 dB. The table shows the default circuit, where a first-stage gain of 21 helps, against its 2.510 V common mode and 420.0 mV signal.

With an IC selected the card reads Set by the IC, because the internal resistors are laser trimmed. TI lists a 120 dB minimum for the standard INA128 grade at a gain of 100. The REF pin still matters, and TI notes that 8 Ω in series with it drops a typical INA128 to about 80 dB at a gain of 1.

Analog Devices points out that the usual interference is 50 Hz or 60 Hz power-line noise arriving equally on both inputs. Whatever gets past the amplifier can be narrowed down afterward with a filter sized in the Bandpass Filter Calculator.

Gain of Instrumentation Amplifier FAQ

How do you calculate the gain of an instrumentation amplifier?

Multiply the first-stage gain by the difference-stage ratio. For a three op-amp circuit that is (1 + 2R2 ÷ RG) × (R4 ÷ R3). For an IC the maker fixes the internal resistors, so RG is the only value needed.

An INA128 with RG = 5.62 kΩ gives 1 + 50 kΩ ÷ 5.62 kΩ, which is 9.897 V/V or 19.91 dB. A 20 mV differential input then produces 197.9 mV at the output with REF grounded. The Instrumentation Amplifier Gain Calculator does this in its Gain From Resistors mode.

What is the gain of an instrumentation amplifier?

It is whatever RG sets, within the range the part supports. Analog Devices describes typical in-amp gains as 1 to 1,000. TI rates the INA128 and INA129 for 1 to 10,000, and lists the INA333 up to 1,000. The AD620 also covers 1 to 10,000. Above a part's rating the result still shows, with an amber alert such as Above the INA333 Rated Gain.

With RG left out, the first stage has a gain of 1. An IC then has an overall gain of 1 V/V, or 0 dB. A three op-amp circuit is left with the gain of its difference stage, R4 ÷ R3.

What is the formula for the gain of a difference amplifier?

A difference amplifier, also called a differential amplifier, uses one op-amp and four resistors and has a gain of R4 ÷ R3. It is the last stage of the three op-amp circuit, and its resistors go under Difference Stage and Tolerance. Changing R4 to 20 kΩ with R3 at 10 kΩ doubles the default gain from 21 to 42 V/V.

A fully differential amplifier is a different part. It has two outputs that move in opposite directions, so the single-output formula and the REF pin used in the Instrumentation Amplifier Gain Calculator do not describe it.

How do you reduce amplifier gain?

Raise RG. In the default circuit, going from 1 kΩ to 2.21 kΩ drops the gain from 21 to 10.05 V/V. Removing RG altogether takes the first stage down to a gain of 1, which is the lowest it can go.

A discrete build can also lower R2. With RG at 1 kΩ, changing both R2 resistors from 10 kΩ to 4.99 kΩ gives 10.98 V/V. An IC has fixed internal resistors, so RG is its only gain control.

How much gain should I use?

Use enough to fill the range of whatever reads the output, and no more than the supply allows. The Highest Clean Gain row gives the ceiling for the entered input, common mode, REF and supply. In the default example that ceiling is 680.0 V/V.

Working right at the ceiling leaves no margin for a larger input or for part tolerance. With ±1% parts the default gain can run 4.0% high, so the gain chosen in the Instrumentation Amplifier Gain Calculator should sit at least that far below the limit.