SME
Bioinstrumentation
Biopotential amplifiers
Use this for “An ECG amplifier has a gain of 1000 and a CMRR of 100 dB. How much of 0.5 V of hum reaches the output?”
Diagram
vₒᵤₜ = Ad·Vd = 1,000 × 1 mV
vₒᵤₜ = 1 V
Ac
=
Ad
10
CMRR ÷ 20
=
1,000
10
100 dB ÷ 20
=
0.01
vₕᵤₘ = Ac·Vcm = 0.01 × 0.5 V
vₕᵤₘ = 5 mV
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.
Ac
=
Ad
10
dB
/
20
vₕᵤₘ (mV)
=
Ac
×
Vcm (V)
Vd
Difference signal
example · mV
vₒᵤₜ
Signal out
calculated · V
Formulas
Ac
=
Ad
10
CMRR ÷ 20
0.01
=
1,000
10
100 ÷ 20
vₒᵤₜ
=
Ad
×
Vd
1,000
1
=
1,000
×
1
1,000
vₕᵤₘ = Ac × Vcm × 1,000
5 = 0.01 × 0.5 × 1,000
Assumptions
•
An ideal op-amp apart from its CMRR; linear, no clipping.
•
Both electrodes carry the same mains hum Vcm; the heart’s signal is their difference Vd.
•
CMRR in dB is 20 log(Ad ÷ Ac), so each 20 dB is ten times less hum.
Step-by-step
WE KNOW
Ad = 1,000, CMRR = 100 dB, Vd = 1 mV, Vcm = 0.5 V
FIND
common-mode gain (Ac), signal out (vₒᵤₜ), hum out (vₕᵤₘ)
Step 1 · Find common-mode gain (Ac)
Use Ac = Ad ÷ 10CMRR ÷ 20
Undo the decibels: the CMRR divides the differential gain.
Ac
=
1,000
10
100 ÷ 20
Ac
=
1,000
100,000
Ac = 0.01
Step 2 · Find signal out (vₒᵤₜ)
Use vₒᵤₜ = Ad × Vd ÷ 1,000
The signal times the gain; dividing by 1000 turns mV into V.
vₒᵤₜ
=
1,000
×
1
1,000
vₒᵤₜ = 1 V
Step 3 · Find hum out (vₕᵤₘ)
Use vₕᵤₘ = Ac × Vcm × 1,000
The common mode times its small gain; times 1000 turns V into mV.
vₕᵤₘ = 0.01 × 0.5 × 1,000
vₕᵤₘ = 0.005 × 1,000
vₕᵤₘ = 5 mV
Check
Put the numbers back in. Both sides should match.
0.01
=
1,000
10
100 ÷ 20
✓
1
=
1,000
×
1
1,000
✓
5 = 0.01 × 0.5 × 1,000 ✓
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