SME
Electronics · Problem type
MOSFET drain current in saturation
Use this for “An n-channel MOSFET has kₙ = 2 mA/V², Vₜ = 1 V and VGS = 3 V. Find ID in saturation.”
Diagram
Saturation: ½ × 2 × 2² = 4 mA
This is an example. Type your own values to start a new problem.
VOV (V)
=
VGS (V)
−
Vₜ (V)
ID (mA)
=
1
2
×
kₙ (mA/V²)
×
(
VOV (V)
)
2
VDS,sat
Least VDS for saturation
worked out (not typed)
Formulas
VOV = VGS − Vₜ
2 = 3 − 1
ID
=
0.5
×
kₙ
×
VOV
2
4
=
0.5
×
2
×
2
2
VDS,sat = VOV
2 = 2
Assumptions
•
kₙ = μₙCₒₓ W/L in mA/V², so ID comes out in mA (texts writing ID = KVOV² use K = kₙ ÷ 2).
•
No channel-length modulation: in saturation ID does not change with VDS.
•
Saturation holds while VDS is at least VOV; below that the MOSFET is in triode.
Step-by-step
WE KNOW
kₙ = 2 mA/V², VGS = 3 V, Vₜ = 1 V
FIND
overdrive voltage (VOV), drain current (ID), least VDS for saturation (VDS,sat)
Step 1 · Find overdrive voltage (VOV)
Use VOV = VGS − Vₜ
The overdrive is how far VGS stands above the threshold.
VOV = 3 − 1
VOV = 2 V
Step 2 · Find drain current (ID)
Use ID = 0.5 × kₙ × VOV²
Past
pinch-off
the
current
depends
on
the
overdrive
only:
mA/
V
2
×
V
2
gives
mA.
ID
=
0.5
×
2
×
2
2
ID = 0.5 × 2 × 4
ID = 4 mA
Step 3 · Find least VDS for saturation (VDS,sat)
Use VDS,sat = VOV
The channel pinches off at the drain once VDS reaches VGS − Vₜ.
VDS,sat = 2 V
Check
Put the numbers back in. Both sides should match.
2 = 3 − 1 ✓
4
=
0.5
×
2
×
2
2
✓
2 = 2 ✓
Topic check
See what you know: 5 questions on this topic
New questions each time. Pass to mark it complete.
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