SME
Bioinstrumentation · Problem type
Instrumentation amplifier gain
Use this for “Which gain resistor gives a three-op-amp instrumentation amplifier a gain of 500?”
Diagram
G
=
1
+
2R
Rg
=
1
+
2
×
25
kΩ
100
Ω
G = 501
vₒᵤₜ = G·Vd = 501 × 1 mV
vₒᵤₜ = 0.501 V
The buffers A₁ and A₂ amplify only the difference Vd; A₃ subtracts, so Vcm (the hum both electrodes share) mostly cancels.
This is an example. Type your own values to start a new problem.
G
=
1
+
2
×
R (kΩ)
Rg (Ω)
vₒᵤₜ (V)
=
G
×
Vd (mV)
Formulas
G
=
1
+
2
×
1,000
×
R
Rg
501
=
1
+
2
×
1,000
×
25
100
vₒᵤₜ
=
G
×
Vd
1,000
0.501
=
501
×
1
1,000
Assumptions
•
Ideal op-amps: no current into either input, and v₊ = v₋ (the virtual short).
•
The difference stage has four equal resistors, so its gain is 1.
•
R is in kΩ and Rg in Ω, so the steps multiply R by 1000 to put it in ohms.
Step-by-step
WE KNOW
R = 25 kΩ, Rg = 100 Ω, Vd = 1 mV
FIND
gain (G), output voltage (vₒᵤₜ)
Step 1 · Find gain (G)
Use G = 1 + 2 × 1,000 × R ÷ Rg
The
buffers
add
2
R
Rg
to
a
gain
of
1,
so
Rg
sets
the
whole
gain.
G
=
1
+
2
×
1,000
×
25
100
G
=
1
+
2,000
×
25
100
G
=
1
+
50,000
100
G
=
1
+
500
G
=
501
Step 2 · Find output voltage (vₒᵤₜ)
Use vₒᵤₜ = G × Vd ÷ 1,000
The difference times the gain; dividing by 1000 turns mV into V.
vₒᵤₜ
=
501
×
1
1,000
vₒᵤₜ = 0.501 V
Check
Put the numbers back in. Both sides should match.
501
=
1
+
2
×
1,000
×
25
100
✓
0.501
=
501
×
1
1,000
✓
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