SME
Circuit Analysis I · Problem type
Non-inverting amplifier
Use this for “A non-inverting amplifier has Rg = 10 kΩ and Rf = 30 kΩ. Find its gain and output for 0.5 V in.”
Diagram
Aᵥ
=
1
+
Rf
Rg
=
1
+
30
kΩ
10
kΩ
=
4
vₒᵤₜ = Aᵥvᵢₙ = 4 × 0.5 V = 2 V
Virtual short: v₋ = v₊ = vᵢₙ; Rf and Rg divide vₒᵤₜ down to it.
Inside the rails: |vₒᵤₜ| ≤ 15 V.
This is an example. Type your own values to start a new problem.
Aᵥ
=
1
+
Rf (kΩ)
Rg (kΩ)
vₒᵤₜ (V)
=
Aᵥ
×
vᵢₙ (V)
Vₛₐₜ
Supply rail
example
Formulas
Aᵥ
=
1
+
Rf
Rg
4
=
1
+
30
10
vₒᵤₜ = Aᵥ × vᵢₙ
2 = 4 × 0.5
Assumptions
•
Ideal op-amp: no current flows into either input, and v₊ = v₋ (the virtual short).
•
The input drives the + input; Rf and Rg divide the output down to the − input.
•
The output stays inside the supply rails, ±Vₛₐₜ; past them it clips.
Step-by-step
WE KNOW
vᵢₙ = 0.5 V, Rg = 10 kΩ, Rf = 30 kΩ, Vₛₐₜ = 15 V
FIND
voltage gain (Aᵥ), output voltage (vₒᵤₜ)
Step 1 · Find voltage gain (Aᵥ)
Use Aᵥ = 1 + Rf ÷ Rg
The
−
input
follows
the
input,
so
Rg
carries
vᵢₙ
Rg
and
Rf
adds
its
drop
on
top.
Aᵥ
=
1
+
30
10
Aᵥ = 1 + 3
Aᵥ = 4
Step 2 · Find output voltage (vₒᵤₜ)
Use vₒᵤₜ = Aᵥ × vᵢₙ
The output is the input times the gain.
vₒᵤₜ = 4 × 0.5
vₒᵤₜ = 2 V
Check
Put the numbers back in. Both sides should match.
4
=
1
+
30
10
✓
2 = 4 × 0.5 ✓
Topic check
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