Instrumentation amplifier gain calculator: R_G, drift and common-mode range

The gain resistor for an instrumentation amplifier gain, or the gain a resistor gives, from the gain formula G = 1 + K/R_G with each part's own K; the nearest 1 % value and the gain it really gives; the gain drift budget the vendors use; and the voltages on the in-amp's internal nodes, checked against its common-mode limits, as ADI's AN-1401 diamond plot does. The defaults are TI's INA128 at a gain of 100, 505.1 Ω exact and 511 Ω from its own table, G = 98.85; the page's tests hold the calculation to the R_G tables and worked examples printed in ten datasheets.

Fig 1 — TI INA128 as the classic three-op-amp in-amp: R_G = 511 Ω between two 25 kΩ feedback resistors sets G = 1 + K/R_G = 98.85. The input amplifiers' outputs sit at V_CM ± G·V_DIFF/2: A1 at −4.94 V, A2 at 4.94 V; the subtractor removes the common-mode voltage and gives V_OUT = 9.88 V.

Fig 2 — TI INA128 at G = 98.85, V_REF = 0.00 V, on −15.0 V and 15.0 V: the shaded region is every output voltage and common-mode voltage the amplifier handles without a node saturating (AN-1401's diamond plot). At V_OUT = V_REF the common-mode range is −13.0 V to 13.0 V; it narrows with slope 1/2 as the preamp outputs swing. The operating point, V_OUT = 9.88 V at V_CM = 0.00 V, is inside it.

Calculate

In-amp

Target gain G (V/V)

R_G series

R_G temperature coefficient (ppm/°C)

In-amp gain drift, G > 1 (ppm/°C)

Temperature change ΔT (°C)

Positive supply V+ (V)

Negative supply V− (V)

Reference voltage V_REF (V)

Common-mode voltage V_CM (V)

Differential input V_DIFF (mV)

Input range headroom to V+ (V)

Input range headroom to V− (V)

Input amplifier output headroom to V+ (V)

Input amplifier output headroom to V− (V)

Output swing headroom to V+ (V)

Output swing headroom to V− (V)

Exact gain resistor R_G = K/(G − 1): 505.1 Ω
Nearest E96 R_G · the gain it gives · error: 511 Ω · 98.85 · −1.15 %
Gain drift, in-amp + R_G tempco (the vendors' worst case): 120 ppm/°C · 7200 ppm (0.720 %) over 60 °C
Root-sum-square of the two, as TI SBAA314A combines them: 110 ppm/°C
R_G's share, ((G − 1)/G)·α_RG (derived): 9.9 ppm/°C
Output V_OUT = G·V_DIFF + V_REF: 9.88 V
Input amplifier outputs A2 · A1 = V_CM ± G·V_DIFF/2: 4.94 V · −4.94 V
Common-mode range for this V_DIFF: −8.06 V to 8.06 V
Output range, V_OUT limits: −13.6 V to 13.6 V

At G = 98.85, R_G is 511 Ω: wiring and socket resistance in series with it add gain error, which TI's INA128 datasheet flags "in gains of approximately 100 or greater".

TI INA128 (SBOS051G): K = 50 kΩ (p. 7; Eq 1, p. 20). The table gives ±10 ppm/°C gain drift at its default G = 1 and ±100 ppm/°C for the 50 kΩ term (CSO: SHE, max, p. 7); at G > 1 both apply, so the default is their sum. Input: "approximately 2V less than the positive supply voltage to 2V greater than the negative supply", limited by the output swing of A1 and A2 (p. 18). Output: (V+) − 1.4 V, (V−) + 1.4 V, CSO: SHE (p. 7).

How this is calculated

Standard: TI INA128/INA129 (SBOS051G), INA333 (SBOS445C), INA821 (SBOS893D), INA826 (SBOS562G), INA828 (SBOS792A) datasheets; ADI AD620 (Rev. H), AD8221 (Rev. C), AD8421 (Rev. A), AD8422 (Rev. C) datasheets; ADI AN-1401, The Diamond Plot; ADI, A Designer's Guide to Instrumentation Amplifiers, 3rd ed.; TI SBAA314A

$G = 1 + \frac{K}{R_G}, \qquad R_G = \frac{K}{G - 1}$: The gain equation on every datasheet here, with K = 50 kΩ (INA128, INA828), 49.4 kΩ (INA129, INA821, INA826, AD620, AD8221), 100 kΩ (INA333), 9.9 kΩ (AD8421) or 19.8 kΩ (AD8422). The AD620 prints the inverse, "RG = 49.4 kΩ/(G − 1)" (p. 15). G = 1 is R_G left open: "for G = 1, the RG pins are unconnected (RG = ∞)".
$V_{OUT} = (V_{+IN} - V_{-IN})\left(1 + \frac{2R_F}{R_G}\right) + V_{REF}$: AN-1401 Figure 6 (p. 4). K is 2R_F, the two input amplifiers' feedback resistors in series; TI's INA828 datasheet: "The 50-kΩ term in Equation 1 comes from the sum of the two internal 25-kΩ feedback resistors" (p. 17). ADI's in-amp guide writes the general form with a subtractor gain R2/R1, VOUT = (VIN2 – VIN1)(1 + 2R5/RG)(R2/R1) (p. 2-3); AN-1401 notes the subtractor gain "is typically 1".
$V_{A2,\,A1} = V_{CM} \pm \frac{G\,V_{DIFF}}{2}, \qquad V_{CM} = \frac{V_{+IN} + V_{-IN}}{2}$: AN-1401 p. 4: "the two outputs of the preamplifier stage are at VCM ± G × VIN_DIFF/2". With the input range and the output swing, these are the three limits of the diamond plot; on V_CM against V_OUT axes the input limit has slope ±1/(2G) and the preamp limit ±1/2.
$\alpha_G = |\alpha_{INA}| + |\alpha_{R_G}|, \qquad \Delta G/G = \alpha_G\,\Delta T$: The vendors' worst case: the in-amp's gain drift for G > 1, which every datasheet here specifies without R_G, plus R_G's tempco. AD620 Table 4 (p. 13): "(50 ppm + 10 ppm) × 60°C", 3600 ppm. INA821 Table 5 (p. 25) lists 35 ppm/°C × 80 °C and R_G's 10 ppm/°C × 80 °C as separate rows of a worst-case sum. TI SBAA314A (p. 6) combines the same terms as a root-sum-square instead.
$\frac{1}{G}\frac{dG}{dT} = \frac{G - 1}{G}\left(\alpha_K - \alpha_{R_G}\right)$: Derived here by differentiating G = 1 + K/R_G, not printed in the sources: R_G's tempco reaches the gain in proportion (G − 1)/G, half at G = 2 and nearly all at G = 100, and an R_G that tracks the internal resistors would cancel. The calculator reports R_G's share from it, labelled derived.
$V_D = V_{IN}\,\frac{R_2}{R_1 + R_2}, \qquad \frac{V_{OUT} - V_{REF}}{V_{IN}} = G\,\frac{R_2}{R_1 + R_2}$: TI INA821 Equations 4 and 5 (pp. 29–30): a divider ahead of the in-amp, the one route to a net gain below 1. The calculator sizes R2 for a target net gain with R1 = 100 kΩ, as TI's example uses, and R_G open; that inversion, R2 = t·R1/(G − t), is derived.

Assumptions

The in-amp is the three-op-amp type that AN-1401 and ADI's guide describe, with its gain set by one resistor. Two-op-amp in-amps and indirect-current-feedback parts have other limits.
The nearest standard R_G is the E96 or E24 value closest in ratio to the exact one, the rule the datasheets' "nearest 1 %" columns follow. Resistor tolerance, and wiring or socket resistance in series with R_G, are not included.
Gain drift figures are datasheet maxima. The in-amp and R_G terms are added as magnitudes, the vendors' worst case; the root-sum-square beside it assumes they are independent. At G = 1 no R_G is fitted and the datasheet's G = 1 figure is used.
For the INA128 and INA129 the datasheet gives ±10 ppm/°C gain drift at its default G = 1 and ±100 ppm/°C for the 50 kΩ (49.4 kΩ) term, both for the CSO: SHE die; the G > 1 default is their sum, 110 ppm/°C. The CSO: FRE die is specified tighter.
The input amplifiers' output swing is not published for most parts. Their presets take it equal to the input range, the narrowest swing consistent with the datasheet, so the check leans towards a warning; the INA826 preset uses its datasheet's "approximately 100 mV" swing and 0.8 V level shift. The datasheet's V_CM vs V_OUT plots are the authority.
Limits are the datasheet figures at its own test conditions (mostly ±15 V, 25 °C, 2 kΩ or 10 kΩ load); several are "approximately". Over temperature and at other loads they move. The subtractor's own input limit, which AN-1401 notes "typically does not affect the circuit", is not modelled.

How the instrumentation amplifier gain formula arises

ADI's AN-1401 notes that "Most instrumentation amplifiers are based on the traditional 3-op-amp architecture" (p. 4), and ADI's A Designer's Guide to Instrumentation Amplifiers calls it "the most popular configuration for instrumentation amplifier design" (p. 2-2), building it in steps. Two input amplifiers, A1 and A2, buffer the inputs, and "a single gain resistor, RG, is connected between the summing junctions of the two input buffers". Each op amp holds its inverting input at the voltage on its non-inverting input, so "The full differential input voltage will now appear across RG", and the current that difference drives through R_G also flows through the two feedback resistors on either side of it. The differential voltage between the two amplifier outputs is therefore the input difference multiplied by (R_F + R_G + R_F)/R_G, which is 1 + 2R_F/R_G.

The third amplifier, A3, is a subtractor. It takes the difference of the two outputs and refers it to the REF pin; the guide writes the whole thing as V_OUT = (V_IN2 – V_IN1)(1 + 2R5/RG)(R2/R1) (p. 2-3), where R2/R1 is the subtractor's gain; AN-1401 notes that the subtractor gain "is typically 1" and writes the integrated version (Figure 6): V_OUT = V_DIFF(1 + 2R_F/R_G) + V_REF. A common-mode voltage, by contrast, puts the same voltage on both ends of R_G, so no current flows and, in the guide's words, "amplifiers A1 and A2 will operate as unity-gain followers". Only the difference is amplified; that is the whole point of the circuit.

The datasheets fold 2R_F into one constant, K, and print the instrumentation amplifier gain formula as G = 1 + K/R_G. TI's INA828 datasheet says what K is: "The 50-kΩ term in Equation 1 comes from the sum of the two internal 25-kΩ feedback resistors" (p. 17). Solving for the resistor gives the form this calculator uses in the gain-to-R_G direction, R_G = K/(G − 1), which the AD620 datasheet prints as "RG = 49.4 kΩ/(G − 1)" (p. 15).

K is not the same for every part

The formula has the same shape everywhere, but K is a property of the chip, and the families differ by a factor of ten:

Part	K	Where it is printed	Gain range
TI INA128	50 kΩ	SBOS051G, p. 7; Eq 1, p. 20	1 to 10000
TI INA129	49.4 kΩ	SBOS051G, p. 7; Eq 2, p. 20	1 to 10000
TI INA333	100 kΩ	SBOS445C, p. 5; Eq 1, p. 15	1 to 1000
TI INA821	49.4 kΩ	SBOS893D, p. 6	1 to 10000
TI INA826	49.4 kΩ	SBOS562G, Eq 1, p. 20	1 to 1000
TI INA828	50 kΩ	SBOS792A, p. 5; Eq 1, p. 17	1 to 1000
ADI AD620	49.4 kΩ	Rev. H, p. 3; p. 15	1 to 10000
ADI AD8221	49.4 kΩ	Rev. C, p. 4; p. 18	1 to 1000
ADI AD8421	9.90 kΩ	Rev. A, p. 4; p. 22	1 to 10000
ADI AD8422	19.8 kΩ	Rev. C, p. 4; p. 22	1 to 1000

The same R_G therefore gives very different gains. 499 Ω is G = 100.0 on an AD620 but G = 20.84 on an AD8421 and 201.4 on an INA333. Copying a gain resistor from one datasheet into a design around another part is the commonest way to get the gain wrong, and the calculator's part list exists to prevent it.

R_G for common gains: the derived table

The table runs R_G = K/(G − 1) for the three commonest values of K, with the nearest E96 (1 %) value and the gain error that value gives. At G = 1 the pins are left open. The error is never more than 1.15 % in these rows, because E96 steps are 2.4 % apart and G − 1 moves in proportion to 1/R_G.

G	K = 50 kΩ INA128, INA828	K = 49.4 kΩ INA129, INA821, INA826, AD620, AD8221	K = 100 kΩ INA333
1	open	open	open
2	50 kΩ → 49.9 kΩ, +0.10 %	49.4 kΩ → 49.9 kΩ, −0.50 %	100 kΩ → 100 kΩ, +0.00 %
5	12.5 kΩ → 12.4 kΩ, +0.65 %	12.35 kΩ → 12.4 kΩ, −0.32 %	25 kΩ → 24.9 kΩ, +0.32 %
10	5.556 kΩ → 5.62 kΩ, −1.03 %	5.489 kΩ → 5.49 kΩ, −0.02 %	11.11 kΩ → 11 kΩ, +0.91 %
20	2.632 kΩ → 2.61 kΩ, +0.79 %	2.6 kΩ → 2.61 kΩ, −0.36 %	5.263 kΩ → 5.23 kΩ, +0.60 %
50	1.02 kΩ → 1.02 kΩ, +0.04 %	1.008 kΩ → 1 kΩ, +0.80 %	2.041 kΩ → 2.05 kΩ, −0.44 %
100	505.1 Ω → 511 Ω, −1.15 %	499 Ω → 499 Ω, −0.00 %	1.01 kΩ → 1.02 kΩ, −0.96 %
200	251.3 Ω → 249 Ω, +0.90 %	248.2 Ω → 249 Ω, −0.30 %	502.5 Ω → 499 Ω, +0.70 %
500	100.2 Ω → 100 Ω, +0.20 %	99 Ω → 100 Ω, −1.00 %	200.4 Ω → 200 Ω, +0.20 %
1000	50.05 Ω → 49.9 Ω, +0.30 %	49.45 Ω → 49.9 Ω, −0.90 %	100.1 Ω → 100 Ω, +0.10 %

The vendors print the same table for their own parts, and checking them against the equation finds four rows that are not the nearest 1 % value. TI's INA128/INA129 table (SBOS051G, p. 19) gives 9.76 Ω for the INA129 at G = 5000, which is +1.25 % out, where 10 Ω is also E96 and gives −1.18 %; at G = 10 000 it gives 4.87 Ω (+1.45 %) where 4.99 Ω gives −0.99 %. The INA128 column beside them is right in every row. The INA828's Table 1 (SBOS792A, p. 17) gives 5.49 kΩ at G = 10 (+1.07 %) where 5.62 kΩ gives −1.03 %; 5.49 kΩ is the 49.4 kΩ family's value, and the INA128, with the same 50 kΩ, prints 5.62 kΩ in that row. The INA333's Table 1 (SBOS445C, p. 15) gives 1 kΩ at G = 100 (+1.00 %) where 1.02 kΩ gives −0.96 %, a near tie; the same table prints its G = 50 value as "2.05" without the k. The page's tests hold the calculator to every other row of all four tables.

Worked example: the INA128 at a gain of 100

TI's INA128 datasheet gives the gain as G = 1 + 50 kΩ/R_G(Equation 1, p. 20) and its table (p. 19) lists 505.1 Ω exact and 511 Ω as the nearest 1 % value at G = 100. The calculator's defaults are this row, with a 100 mV full-scale differential input on ±15 V and REF grounded:

exact     R_G = 50 kΩ / (100 − 1)            = 505.1 Ω
E96       neighbours 499 Ω and 511 Ω
          G(511 Ω) = 1 + 50 000/511          = 98.85  (−1.15 %)
          G(499 Ω) = 1 + 50 000/499          = 101.2  (+1.20 %)
output    98.85 × 100 mV + 0 V               = 9.88 V
A2, A1    0 V ± 98.85 × 100 mV / 2           = 4.94 V, −4.94 V
drift     (110 + 10) ppm/°C × 60 °C          = 7200 ppm

511 Ω and 499 Ω straddle the exact value almost equally, and 511 Ω wins by a hair: −1.15 % against +1.20 %. Either way the gain is about 1 % off before resistor tolerance. The datasheet leaves that part to the designer: "The contribution of RG to gain accuracy and drift can be directly inferred from Equation 1 and Equation 2" (p. 20). If 1 % matters, calibrate it out or pick R_G from a finer series.

With the input amplifiers' outputs at 4.94 V and −4.94 V, the INA128's approximately 2 V of input headroom on ±15 V leaves a common-mode range of −8.06 V to 8.06 V at this signal. The drift line is the calculator's default sum for this part, explained below: 120 ppm/°C is large, and most of it is the tempco of the INA128's own 50 kΩ term.

Worked example: the AD620's Table 5, and the AD8421

The AD620 datasheet (Rev. H, p. 15) lists the 1 % and 0.1 % standard R_G values for round gains and the gain each gives. Every printed gain is 1 + 49.4 kΩ/R_G to the digits shown:

1 % R_G	AD620 prints	1 + 49.4 kΩ/R_G	0.1 % R_G	AD620 prints	1 + 49.4 kΩ/R_G
49.9 kΩ	1.990	1.990	49.3 kΩ	2.002	2.002
12.4 kΩ	4.984	4.984	12.4 kΩ	4.984	4.984
5.49 kΩ	9.998	9.998	5.49 kΩ	9.998	9.998
2.61 kΩ	19.93	19.93	2.61 kΩ	19.93	19.93
1 kΩ	50.40	50.40	1.01 kΩ	49.91	49.91
499 Ω	100.0	100.0	499 Ω	100.0	100.0
249 Ω	199.4	199.4	249 Ω	199.4	199.4
100 Ω	495.0	495.0	98.8 Ω	501.0	501.0
49.9 Ω	991.0	991.0	49.3 Ω	1,003.0	1003

The 0.1 % column earns its place at the extremes: 49.3 Ω gives 1003 where the 1 % 49.9 Ω gives 991.0, because the exact value for G = 1000 is 49.45 Ω. The AD8221, with the same K, prints the same 1 % column as its Table 6 (Rev. C, p. 18).

The AD8421's K is 9.9 kΩ, a fifth of the AD620's, so its resistors are a fifth the size: G = 10 is exactly 1.1 kΩ and its Table 7 (Rev. A, p. 22) prints 1.1 kΩ for "10.00" (10.000); G = 1000 needs 9.91 Ω against the AD620's 49.45 Ω, and the table's last row, 4.99 Ω, gives "1985" (1985.0). At a few ohms, the trace and any socket in series with R_G are part of the resistor.

Unity gain, and a gain less than 1

Unity gain needs no resistor: with R_G open, K/R_G is zero and G = 1. The AD620 datasheet: "for G = 1, the RG pins are unconnected (RG = ∞)" (p. 15). This is also where the in-amps are most accurate, because the internal resistors alone set the gain. TI's INA821 datasheet: "The best gain drift of 5 ppm/℃ (maximum) is achieved when the INA821 uses G = 1 without RG connected" (p. 21).

A gain less than 1 is out of reach of R_G: 1 + K/R_Gis at least 1 for every positive resistor. The route is to attenuate before the in-amp, and TI's INA821 datasheet works one (Figure 69, pp. 29–30): a programmable-logic-controller input that accepts ±10 V through a 100 kΩ/4.17 kΩ divider on −IN, with +IN grounded, and drives "2.5 V ±2.3 V". Its equations, recomputed:

Eq 5      R2 = 100 kΩ × 0.4 V / (10 V − 0.4 V) = 4.167 kΩ
Eq 6      G = (4.8 V − 2.5 V) / 400 mV       = 5.75
Eq 7      R_G = 49.4 kΩ / (5.75 − 1)         = 10.4 kΩ
fitted    R_G = 10.5 kΩ: G = 1 + 49.4/10.5   = 5.705
net       G × R2/(R1 + R2), 4.17 kΩ and 100 kΩ = 0.2284
output    2.5 V + 0.2284 × 10 V              = 4.78 V

TI computes 4.167 kΩ and 10.4 kΩ and fits 4.17 kΩ and 10.5 kΩ, "a standard 0.1% resistor value"; the schematic in Figure 69 still labels R_G 10.4 kΩ. The net gain from the ±10 V terminal is 0.230 as designed and 0.2284 as built, well below 1, while the in-amp itself runs at G = 5.70. When the calculator is given a target gain below 1 it sets R_G open and sizes this divider with TI's 100 kΩ R1. The divider changes what the source sees: "R1 sets the input impedance of the voltage input mode" (p. 30).

Gain drift and choosing R_G

Every datasheet here specifies the in-amp's gain drift at G > 1 without the external resistor. The AD620's footnote reads "Does not include effects of external resistor RG" (p. 3), and the TI parts say "The values specified for G > 1 do not include the effects of the external gain-setting resistor, RG" (INA821, p. 7). R_G's own tempco has to be added, and the vendors add it straight. The AD620's error budget (Table 4, p. 13) writes "(50 ppm + 10 ppm) × 60°C" and gets 3,600 ppm, which the calculator reproduces as 3600 ppm. TI's INA821 budget (Table 5, p. 25) carries the two as separate rows over 80 °C, 2800 ppm from the in-amp and 800 ppm from a 10 ppm/°C R_G, in a worst-case sum. The calculator shows that sum, and beside it the root-sum-square that TI's SBAA314A (p. 6) uses for an INA828 with a 20 ppm/°C resistor and an ADC's 6 ppm/°C: √(50² + 20² + 6²) = 54.2 ppm/°C, against 76 ppm/°C added.

Two things are easy to miss in the INA821's Table 5. Its column headers say G = 1, G = 100 and G = 1000, but the text above it describes the cases as "G = 1 (no external resistor) and G = 10 (5.49-kΩ external resistor) and G = 100 (499-Ω external resistor)", and the numbers in the columns (an input offset of 35 µV giving 35, 350 and 3500 ppm of a 1 V output) fit 1, 10 and 100. And its G = 1 column still carries the external resistor's 100 ppm tolerance and 800 ppm drift, although at G = 1 no resistor is fitted.

What matters most is the resistor's tempco, and ADI's guide is blunt about the usual choice. Through-hole 1 % metal film and 1 % chip resistors "typically have a 100 ppm/°C temperature coefficient", and "An in-amp with a standard 1% metal film gain resistor should never be used ahead of even a 12-bit converter: It would destroy the accuracy of a 14-bit or 16-bit converter" (p. 5-10). The arithmetic is short: at G = 100, 100 ppm/°C moves the gain 990 ppm over 10 °C, while one LSB of a 12-bit converter is 244 ppm of full scale and of a 16-bit one 15.3 ppm (the ADC resolution calculator gives the LSB for any width). The AD620 asks for R_G "less than 10 ppm/°C" (p. 15); SBAA314A's design notes use "0.1% 20ppm/°C film resistors or better" (p. 2).

Gain softens the resistor's effect only at low gain. Differentiating G = 1 + K/R_G gives the share of R_G's tempco that reaches the gain as (G − 1)/G: for a 100 ppm/°C resistor, 50 ppm/°C at G = 2, 90 ppm/°C at G = 10 and 99 ppm/°C at G = 100. That is a derivation, not a vendor figure, and the calculator labels it so. The same derivation says why the INA128 and INA129 defaults are high. Their datasheet (p. 7) gives ±10 ppm/°C gain drift under a table whose default condition is G = 1, and a separate ±100 ppm/°C (CSO: SHE, maximum) for "the 50-kΩ or 49.4-kΩ term in the gain equation"; at high gain K's tempco reaches the gain in full, so the calculator's default for G > 1 is the sum, 110 ppm/°C. The other die source, CSO: FRE, is specified at ±5 and ±50.

Common-mode range: the internal nodes and the diamond plot

An in-amp can saturate inside while its inputs and output both look legal. AN-1401 explains why: "In the 3-op-amp in-amp, the gain is taken in the first stage, but the common-mode voltage is removed in the second stage. Because of this, the two outputs of the preamplifier stage are at VCM ± G × VIN_DIFF/2" (p. 4). The input amplifiers carry the full common-mode voltage and half the amplified signal each. TI's INA826 datasheet calls exceeding their swing "The most commonly overlooked overload condition", adding that A1 and A2 "are internal circuit nodes that cannot be measured" (p. 21), and the INA128's warns that "Input overload can produce an output voltage that appears normal" (p. 18).

ADI's guide gives the canonical case (pp. 2-3 to 2-4): at a gain of 1000, a 10 mV differential input puts one input amplifier's output at +5 V "plus the common-mode voltage" and the other at −5 V plus the same. The calculator gives 5.00 V and −5.00 V above V_CM. On ±15 V with the INA128's approximately 2 V of headroom, the common-mode range for that signal shrinks from −13.0 V to 13.0 V at G = 1 to −8.00 V to 8.00 V at G = 1000; the guide's own estimate for its example is "an 8 V common-mode voltage".

AN-1401 draws all of this as the diamond plot, the second figure above: common-mode voltage against output voltage, with the valid region bounded by three limits. The output swing gives vertical edges. The input range gives edges of slope ±1/(2G), nearly flat at high gain ("a slope of ±1/200" for the AD8221 at G = 100). The preamplifier outputs give edges of slope ±1/2 that do not flatten with gain, which is why the region narrows as the output moves away from V_REF. The calculator draws the diamond for the part, gain, supplies and V_REF entered and marks the operating point; a node outside its limit turns red in both figures. For comparison at G = 100 with a 100 mV input on ±15 V, the AD620's limits leave −8.10 V to 8.60 V and the AD8421's −7.70 V to 8.20 V.

The limits are the datasheets' own: TI's INA128 gives its linear input range as "approximately 2V less than the positive supply voltage to 2V greater than the negative supply" (p. 18), the INA821 and INA828 specify (V−) + 2 V to (V+) − 2 V, the AD620 −V_S + 1.9 V to +V_S − 1.4 V (p. 3). Only the INA826 states the swing of its input amplifiers, "within approximately 100 mV of the power-supply rails", with their outputs shifted "by approximately 0.8 V" (p. 21). For the others the calculator takes the input amplifiers' swing equal to the input range, which is the least it can be, and the datasheet's V_CM vs V_OUT plots remain the authority. Every limit is an editable field.

Common instrumentation amplifier gain mistakes

Using the wrong K. 49.4 kΩ, 50 kΩ, 100 kΩ, 9.9 kΩ and 19.8 kΩ are all current; a 499 Ω resistor gives G = 100.0 on an AD620 and G = 20.84 on an AD8421. Take K from the datasheet of the part on the board.
Trusting a vendor table without the equation. Four rows above, in three TI tables, are not the nearest 1 % value; the equation is the authority, and it takes one line to check.
Fitting a 1 % metal-film R_G. At about 100 ppm/°C it swamps the in-amp's own drift and, in ADI's words, "should never be used ahead of even a 12-bit converter". Budget R_G's tempco with the in-amp's, as the AD620 and INA821 datasheets do.
Expecting G < 1. No R_G gives it. Divide the input first, as the INA821's PLC example does.
Checking only the input and output ranges. The input amplifiers carry V_CM ± G·V_DIFF/2 and can saturate while the output looks normal; check the internal nodes, which is what the diamond plot is for.
Driving REF from a resistor divider. The INA128 datasheet: "if a resistor voltage divider is used to generate a reference voltage, the voltage must be buffered by an op amp to avoid CMRR degradation", and "A resistance of 8Ω in series with the REF pin causes a typical device to degrade to approximately 80 dB CMR (G = 1)" (p. 19).
Ignoring what is in series with a small R_G. At high gain R_G is tens of ohms or less; TI notes that "Sockets add to the wiring resistance, which contributes additional gain error (possibly an unstable gain error) in gains of approximately 100 or greater" (INA128, p. 20).
Copying a worked number without rechecking it. TI's SBAA314A (p. 2) designs an INA828 for G = 666.7: R_G = 50 kΩ/(G − 1) = 75.11 Ω, taken as 75.1 Ω, then "G = 1 + 50kΩ/Rg = 667.7". 1 + 50 kΩ/75.1 Ω is 666.8; 667.7 is what 75.0 Ω, the E96 value, gives. The note carries 667.7 into its offset calculation (p. 6).