SME
Circuit Analysis I · Problem type
Difference amplifier
Use this for “A difference amplifier has R₁ = 10 kΩ and R₂ = 50 kΩ. Find vₒᵤₜ for v₂ = 1.2 V and v₁ = 1 V.”
Diagram
vₒᵤₜ
=
(
R₂
R₁
)(v₂
−
v₁)
vₒᵤₜ
=
(50
kΩ
10
kΩ)
×
(1.2
V
−
1
V)
=
1
V
Matched
pairs:
v₊
=
v₂
R₂
R₁ + R₂
,
and
the
output
makes
v₋
equal
to
it,
so
only
v₂
−
v₁
is
amplified.
Inside the rails: |vₒᵤₜ| ≤ 15 V.
This is an example. Type your own values to start a new problem.
G
=
R₂ (kΩ)
R₁ (kΩ)
vₒᵤₜ (V)
=
G
×
(
v₂ (V)
−
v₁ (V)
)
Vₛₐₜ
Supply rail
example
Formulas
G
=
R₂
R₁
5
=
50
10
vₒᵤₜ
=
G
×
(
v₂
−
v₁
)
1 = 5 × (1.2 − 1)
Assumptions
•
Ideal op-amp: no current flows into either input, and v₊ = v₋ (the virtual short).
•
Matched pairs: both input resistors are R₁ and both of the others are R₂.
•
v₁ feeds the − input and v₂ the + input, so only their difference is amplified.
•
The output stays inside the supply rails, ±Vₛₐₜ; past them it clips.
Step-by-step
WE KNOW
v₂ = 1.2 V, v₁ = 1 V, R₁ = 10 kΩ, R₂ = 50 kΩ, Vₛₐₜ = 15 V
FIND
difference gain (G), output voltage (vₒᵤₜ)
Step 1 · Find difference gain (G)
Use G = R₂ ÷ R₁
With matched pairs, the gain on the difference is the resistor ratio.
G
=
50
10
G
=
5
Step 2 · Find output voltage (vₒᵤₜ)
Use vₒᵤₜ = G × (v₂ − v₁)
Only the difference between the inputs is amplified; a voltage both share cancels.
vₒᵤₜ = 5 × (1.2 − 1)
vₒᵤₜ = 5 × 0.2
vₒᵤₜ = 1 V
Check
Put the numbers back in. Both sides should match.
5
=
50
10
✓
1 = 5 × (1.2 − 1) ✓
Topic check
See what you know: 5 questions on this topic
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