SME
Circuit Analysis I · Problem type
Summing amplifier
Use this for “A summing amplifier has every resistor 10 kΩ. Find vₒᵤₜ for inputs of 1 V and 2 V.”
Diagram
vₒᵤₜ
=
−Rf(
v₁
R₁
+
v₂
R₂
)
vₒᵤₜ
=
−10
kΩ
×
(1
V
10
kΩ
+
2
V
10
kΩ)
vₒᵤₜ = −3 V
The − input is a virtual ground: each input’s current adds at it and flows on through Rf.
Inside the rails: |vₒᵤₜ| ≤ 15 V.
This is an example. Type your own values to start a new problem.
vₒᵤₜ (V)
=
−
Rf (kΩ)
×
v₁ (V)
R₁ (kΩ)
+
v₂ (V)
R₂ (kΩ)
Vₛₐₜ
Supply rail
example
Formulas
vₒᵤₜ
=
−Rf
×
(
v₁
R₁
+
v₂
R₂
)
−3
=
−10
×
(
1
10
+
2
10
)
Assumptions
•
Ideal op-amp: no current flows into either input, and v₊ = v₋ (the virtual short).
•
The input currents meet at the virtual ground (0 V) and all flow on through Rf.
•
The output stays inside the supply rails, ±Vₛₐₜ; past them it clips.
Step-by-step
WE KNOW
v₁ = 1 V, v₂ = 2 V, R₁ = 10 kΩ, R₂ = 10 kΩ, Rf = 10 kΩ, Vₛₐₜ = 15 V
FIND
output voltage (vₒᵤₜ)
Step 1 · Find output voltage (vₒᵤₜ)
Use vₒᵤₜ = −Rf × (v₁ ÷ R₁ + v₂ ÷ R₂)
Each
input
sends
v
R
into
the
virtual
ground;
the
sum
flows
through
Rf,
so
the
output
drops
by
Rf
times
it.
vₒᵤₜ
=
−10
×
(
1
10
+
2
10
)
vₒᵤₜ = −10 × (0.1 + 0.2)
vₒᵤₜ = −10 × 0.3
vₒᵤₜ = −3 V
Check
Put the numbers back in. Both sides should match.
−3
=
−10
×
(
1
10
+
2
10
)
✓
Topic check
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