SME
Electronics · Problem type
MOSFET drain current in triode
Use this for “An n-channel MOSFET has kₙ = 2 mA/V², Vₜ = 1 V, VGS = 3 V and VDS = 0.5 V. Find ID.”
Diagram
Triode: 2 × (2 × 0.5 − ½ × 0.5²) = 1.75 mA
This is an example. Type your own values to start a new problem.
VOV (V)
=
VGS (V)
−
Vₜ (V)
ID (mA)
=
kₙ (mA/V²)
×
VOV (V)
×
VDS (V)
−
1
2
×
(
VDS (V)
)
2
Formulas
VOV = VGS − Vₜ
2 = 3 − 1
ID
=
kₙ
×
(VOV
×
VDS
−
0.5
×
VDS
2
)
1.75
=
2
×
(2
×
0.5
−
0.5
×
0.5
2
)
Assumptions
•
kₙ = μₙCₒₓ W/L in mA/V², so ID comes out in mA.
•
Triode holds while VDS is below VOV = VGS − Vₜ: the channel reaches all the way to the drain.
•
For a very small VDS the MOSFET acts as a resistor of about 1 ÷ (kₙ VOV).
Step-by-step
WE KNOW
kₙ = 2 mA/V², VGS = 3 V, Vₜ = 1 V, VDS = 0.5 V
FIND
overdrive voltage (VOV), drain current (ID)
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 = kₙ × (VOV × VDS − 0.5 × VDS²)
Below
VOV
the
channel
is
open
all
along:
the
triode
formula,
mA/
V
2
×
V
2
=
mA.
ID
=
2
×
(2
×
0.5
−
0.5
×
0.5
2
)
ID = 2 × (2 × 0.5 − 0.5 × 0.25)
ID = 2 × (1 − 0.125)
ID = 2 × 0.875
ID = 1.75 mA
Check
Put the numbers back in. Both sides should match.
2 = 3 − 1 ✓
1.75
=
2
×
(2
×
0.5
−
0.5
×
0.5
2
)
✓
← Previous lesson
MOSFET drain current in saturation
Next lesson →
MOSFET regions: cutoff, triode or saturation
Topic check
See what you know: 5 questions on this topic
New questions each time. Pass to mark it complete.
Related lessons
BJTs and MOSFETs
Main lesson
Current gain: IC, IE and α from β
Use this for “A BJT with β = 100 has a base current of 20 μA. Find IC, IE and α.”
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.”
MOSFET regions: cutoff, triode or saturation
Use this for “An n-channel MOSFET with Vₜ = 1 V has VGS = 3 V and VDS = 0.5 V. Which region is it in?”