SME
Electronics · Problem type
Gain with source resistance
Use this for “An amplifier with Aᵥ = −60 and Rᵢₙ = 5 kΩ is driven from a 1 kΩ source. Find the overall gain.”
Diagram
vsig = vRsig + vᵢ = 2 mV + 10 mV = 12 mV
i
=
vsig
Rsig + Rᵢₙ
=
12
mV
1 kΩ + 5 kΩ
i = 2 μA
Drag the source or a resistor up or down to change it.
This is an example. Type your own values to start a new problem.
Gᵥ
=
Aᵥ
×
Rᵢₙ (kΩ)
Rᵢₙ (kΩ)
+
Rsig (kΩ)
vsig
Source signal
example
i
Signal current
calculated
vRsig
Drop across Rsig
calculated
vᵢ
Amplifier input
calculated
Formulas
i
=
vsig
Rsig + Rᵢₙ
2
=
12
1 + 5
vRsig
=
i
×
Rsig
2 = 2 × 1
vᵢ
=
i
×
Rᵢₙ
10 = 2 × 5
vsig = vRsig + vᵢ
12 = 2 + 10
Gᵥ
=
Aᵥ
×
Rᵢₙ
Rᵢₙ + Rsig
−50
=
−60
×
5
5 + 1
Assumptions
•
The source is a voltage vsig behind its own resistance Rsig, and the amplifier input looks like Rᵢₙ.
•
Aᵥ is the gain from the amplifier input to the output with the load connected (negative for a CE or CS stage, positive for a follower or a non-inverting stage).
•
Units: mV ÷ kΩ gives μA, and μA × kΩ gives mV.
Step-by-step
WE KNOW
Aᵥ = −60, Rᵢₙ = 5 kΩ, Rsig = 1 kΩ, vsig = 12 mV
FIND
signal current (i), drop across Rsig (vRsig), amplifier input (vᵢ), overall gain (Gᵥ)
Step 1 · Find signal current (i)
Use i = vsig ÷ (Rsig + Rᵢₙ)
One loop: the signal current meets Rsig and Rᵢₙ in series.
i
=
12
1 + 5
i
=
12
6
i
=
2
μA
Step 2 · Find drop across Rsig (vRsig)
Use vRsig = i × Rsig
Ohm’s law for the source resistance: this part never reaches the amplifier.
vRsig = 2 × 1
vRsig = 2 mV
Step 3 · Find amplifier input (vᵢ)
Use vᵢ = i × Rᵢₙ
Ohm’s law for the input resistance: the share the amplifier gets.
vᵢ = 2 × 5
vᵢ = 10 mV
Step 4 · Find overall gain (Gᵥ)
Use Gᵥ = Aᵥ × Rᵢₙ ÷ (Rᵢₙ + Rsig)
Only
the
share
Rᵢₙ
Rᵢₙ + Rsig
of
the
signal
reaches
the
input,
and
the
stage
multiplies
that.
Gᵥ
=
−60
×
5
5 + 1
Gᵥ
=
−60
×
5
6
Gᵥ
=
−
300
6
Gᵥ = −50
Check
Put the numbers back in. Both sides should match.
2
=
12
1 + 5
✓
2 = 2 × 1 ✓
10 = 2 × 5 ✓
12 = 2 + 10 ✓
−50
=
−60
×
5
5 + 1
✓
Topic check
See what you know: 5 questions on this topic
New questions each time. Pass to mark it complete.
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