SME
Circuit Analysis I
Op-amps
Use this for “An inverting amplifier has Rᵢₙ = 10 kΩ and Rf = 47 kΩ. Find vₒᵤₜ for 0.2 V in.”
Diagram
Aᵥ
=
−
Rf
Rᵢₙ
=
−47
kΩ
10
kΩ
=
−4.7
vₒᵤₜ = Aᵥvᵢₙ = −4.7 × 0.2 V
vₒᵤₜ = −0.94 V
Virtual
short:
v₋
=
v₊
=
0
V,
so
the
current
vᵢₙ
Rᵢₙ
flows
on
through
Rf;
none
enters
the
op-amp.
Inside the rails: |vₒᵤₜ| ≤ 15 V.
This is an example. Type your own values to start a new problem.
Aᵥ
=
−
Rf (kΩ)
Rᵢₙ (kΩ)
vₒᵤₜ (V)
=
Aᵥ
×
vᵢₙ (V)
Vₛₐₜ
Supply rail
example
Formulas
Aᵥ
=
−
Rf
Rᵢₙ
−4.7
=
−
47
10
vₒᵤₜ = Aᵥ × vᵢₙ
−0.94 = −4.7 × 0.2
Assumptions
•
Ideal op-amp: no current flows into either input, and v₊ = v₋ (the virtual short).
•
The + input is grounded, so the − input sits at 0 V: a virtual ground.
•
The output stays inside the supply rails, ±Vₛₐₜ; past them it clips.
Step-by-step
WE KNOW
vᵢₙ = 0.2 V, Rᵢₙ = 10 kΩ, Rf = 47 kΩ, Vₛₐₜ = 15 V
FIND
voltage gain (Aᵥ), output voltage (vₒᵤₜ)
Step 1 · Find voltage gain (Aᵥ)
Use Aᵥ = −Rf ÷ Rᵢₙ
The same current flows through Rᵢₙ and Rf, so the gain is their ratio, with the sign flipped.
Aᵥ
=
−
47
10
Aᵥ = −4.7
Step 2 · Find output voltage (vₒᵤₜ)
Use vₒᵤₜ = Aᵥ × vᵢₙ
The output is the input times the gain.
vₒᵤₜ = −4.7 × 0.2
vₒᵤₜ = −0.94 V
Check
Put the numbers back in. Both sides should match.
−4.7
=
−
47
10
✓
−0.94 = −4.7 × 0.2 ✓
Topic check
See what you know: 5 questions on this topic
New questions each time. Pass to mark it complete.
More problem types
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.”
Summing amplifier
Use this for “A summing amplifier has every resistor 10 kΩ. Find vₒᵤₜ for inputs of 1 V and 2 V.”
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.”