Analog CMOS Integrated Circuit Design Set 2 - Courses - University ...

SM
Small Signal Models - 1
• Small signal model is an approximation of the large-signal model
around the operation point.
• In analog circuits most MOS transistors are biased in saturation region.
• In general, I D is a function of V GS, V DS, and V BS. We can use this Taylor
series approximation:
SM
D
D
D
Taylor Expansion : I D = I D0
+ ⋅ ΔVGS
+ ⋅ ΔVDS
+ ⋅ ΔVBS
+ second order terms
∂VGS
∂VDS
∂VBS
ΔI
D
∂I
≈
∂V
D
GS
⋅ ΔV
GS
∂I
+
∂V
D
DS
• Current in Saturation:
• Taylor approximation:
• Partial Derivatives:
∂I
∂V
∂I
∂V
∂I
∂V
D
GS
D
DS
D
BS
= μ ⋅ C
n
∂I
=
∂V
g
D
TH
m
ox
1
= ⋅ μ n ⋅ C
2
= −
⋅ ΔV
∂I
DS
∂I
+
∂V
D
BS
⋅ ΔV
EECE 488 – Set 2: Background
SM 30
∂I
BS
EECE 488 – Set 2: Background
∂I
ΔV
= g m ⋅ ΔVGS
+
r
Small Signal Models - 2
W
⋅ ⋅ ( V
L
ox
∂V
⋅
∂V
TH
BS
⎡
⋅ ⎢−
⎢
⎣
2
GS
o
DS
+ g
mb
⋅ ΔV
1 W
2 1 W
2
nC
ox ( VGS
−VTH
) ≈ μ nCox
GS TH
BS
59
( V −V
) ⋅ ( + V )
I D = μ 1 λ ⋅
2 L'
2 L
Δ
W
⋅ ⋅ ( V
L
∂I
∂I
∂I
D
D
D
I D ≈ ⋅ ΔVGS
+ ⋅ ΔVDS
+ ⋅ Δ
∂VGS
∂VDS
∂VBS
−V
F
GS
TH
−V
⎡
= ⎢−
μ n ⋅ C
⎣
γ
2 ⋅ Φ
+ V
) ⋅
SB
ox
( 1+
λ ⋅V
)
2
TH
W
⋅ ⋅ ( V
L
⎤
⎥ = g
⎥
⎦
m
DS
GS
= g
−V
⋅η
= g
TH
mb
m
1
) ⋅ λ ≈ I D ⋅ λ =
r
) ⋅
o
( 1+
λ ⋅V
)
DS
V
BS
⎤
⎡
⎥ ⋅ ⎢−
⎦ ⎢
⎣
2
γ
2 ⋅ Φ
F
+ V
60
SB
⎤
⎥
⎥
⎦
DS