SME
Electronics · Problem type
Common-source MOSFET amplifier
Use this for “A MOSFET biased at ID = 0.5 mA with 0.25 V of overdrive drives RD = 10 kΩ. Find gₘ and the gain.”
Diagram
gₘ
=
2·
ID
VOV
=
2
×
0.5
mA
0.25
V
gₘ = 4 mS
Aᵥ = −gₘ·RD = −4 mS × 10 kΩ
Aᵥ = −40
In saturation; a small input swing at the gate moves ID by gₘ vgs, and RD turns it into the output.
This is an example. Type your own values to start a new problem.
gₘ (mS)
=
2
×
ID (mA)
VOV (V)
Aᵥ
=
−
gₘ (mS)
×
RD (kΩ)
Formulas
gₘ
=
2
×
ID
VOV
4
=
2
×
0.5
0.25
Aᵥ = −gₘ × RD
−40 = −4 × 10
Assumptions
•
The MOSFET stays in saturation, and the signal at the gate is small next to the overdrive.
•
The source is grounded or bypassed, and the output resistance rₒ is ignored.
•
Units: mA ÷ V gives mS, and mS × kΩ is a plain ratio.
Step-by-step
WE KNOW
ID = 0.5 mA, VOV = 0.25 V, RD = 10 kΩ
FIND
transconductance (gₘ), voltage gain (Aᵥ)
Step 1 · Find transconductance (gₘ)
Use gₘ = 2 × ID ÷ VOV
The
slope
of
the
square
law
ID
=
1
2
kₙ
VOV
2
at
the
bias
point.
gₘ
=
2
×
0.5
0.25
gₘ
=
1
0.25
gₘ = 4 mS
Step 2 · Find voltage gain (Aᵥ)
Use Aᵥ = −gₘ × RD
The signal current gₘ vgs flows through RD, so the drain swings opposite to the gate.
Aᵥ = −4 × 10
Aᵥ = −40
Check
Put the numbers back in. Both sides should match.
4
=
2
×
0.5
0.25
✓
−40 = −4 × 10 ✓
Topic check
See what you know: 5 questions on this topic
New questions each time. Pass to mark it complete.
Related lessons
Amplifiers
Main lesson
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.”
Cascaded stages in decibels
Use this for “Two stages with voltage gains of 20 and 50 are cascaded. Find the overall gain, as a ratio and in dB.”