Post on 27-Jul-2020
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
5. MOSFET Transistrors & Circuits - II
S. S. Dan and S. R. Zinka
Department of Electrical & Electronics EngineeringBITS Pilani, Hyderbad Campus
March 16, 2016
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
Outline
1 Small-Signal Model
2 MOSFET Amplifiers
3 High Frequency Modeling
4 Frequency Response of CS Amplifier
5 Summary
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
Outline
1 Small-Signal Model
2 MOSFET Amplifiers
3 High Frequency Modeling
4 Frequency Response of CS Amplifier
5 Summary
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
LTI System
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
LTI System
Frequency domain
Time domain
LaplaceLaplace InverseLaplace
Do we study any LTI components in this course?
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
LTI System
Frequency domain
Time domain
LaplaceLaplace InverseLaplace
Do we study any LTI components in this course?
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
Taylor Series – Recap
-4
-3.5
-3
-2.5
-2
-1.5
-1
-0.5
0
0.5
1
1.5
2
-1.5 -1 -0.5 0 0.5 1 1.5
T4T7T11T16
log(1+x)
f (x) ≈ f (a) +f ′(a)
1!(x− a) +
f ′′(a)2!
(x− a)2 +f ′′′(a)
3!(x− a)3 + · · · .
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
Taylor Series – Recap
-4
-3.5
-3
-2.5
-2
-1.5
-1
-0.5
0
0.5
1
1.5
2
-1.5 -1 -0.5 0 0.5 1 1.5
T4T7T11T16
log(1+x)
f (x) ≈ f (a) +f ′(a)
1!(x− a) +
f ′′(a)2!
(x− a)2 +f ′′′(a)
3!(x− a)3 + · · · .
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
Symbol Convention – Recap
0t
iC
iC
IC
icIc
iC (t) = IC + ic (t) (1)
ic (t) = Ic sin ωt (2)
VCC, VEE, VDD, VSS, ICC, · · · (3)
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
Symbol Convention – Recap
0t
iC
iC
IC
icIc
iC (t) = IC + ic (t) (1)
ic (t) = Ic sin ωt (2)
VCC, VEE, VDD, VSS, ICC, · · · (3)
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
Symbol Convention – Recap
0t
iC
iC
IC
icIc
iC (t) = IC + ic (t) (1)
ic (t) = Ic sin ωt (2)
VCC, VEE, VDD, VSS, ICC, · · · (3)
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
Symbol Convention – Recap
0t
iC
iC
IC
icIc
iC (t) = IC + ic (t) (1)
ic (t) = Ic sin ωt (2)
VCC, VEE, VDD, VSS, ICC, · · · (3)
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
Symbol Convention – Recap
0t
iC
iC
IC
icIc
iC (t) = IC + ic (t) (1)
ic (t) = Ic sin ωt (2)
VCC, VEE, VDD, VSS, ICC, · · · (3)
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
Let’s Revisit Basic CS Amplifier ...
iD
vDS
RD
VDD
vgs+
vGS
VGS
+-
iD =12
kn (vGS −Vt)2 =
12
knv2OV
vDS = VDD − RDiD
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
Let’s Revisit Basic CS Amplifier ...
iD
vDS
RD
VDD
vgs+
vGS
VGS
+-
iD =12
kn (vGS −Vt)2 =
12
knv2OV
vDS = VDD − RDiD
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
Superimpose the AC Signal ...
The total instantaneous gate-to- source voltage, vGS = VGS + vgs, results in a total in-stantaneous drain current
iD =12
kn(VGS + vgs −Vt
)2
=12
kn (VGS −Vt)2︸ ︷︷ ︸
dc bias current
+ kn (VGS −Vt) vgs︸ ︷︷ ︸desired small signal current
+12
knv2gs︸ ︷︷ ︸
undesired small signal current
. (4)
So, to reduce non-linear distortion
12
knv2gs � kn (VGS −Vt) vgs
⇒ vgs� 2VOV . (5)
The above equation represents small-signal condition.
Equation (4) is nothing but Taylor series approximation right!
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
Superimpose the AC Signal ...
The total instantaneous gate-to- source voltage, vGS = VGS + vgs, results in a total in-stantaneous drain current
iD =12
kn(VGS + vgs −Vt
)2
=12
kn (VGS −Vt)2︸ ︷︷ ︸
dc bias current
+ kn (VGS −Vt) vgs︸ ︷︷ ︸desired small signal current
+12
knv2gs︸ ︷︷ ︸
undesired small signal current
. (4)
So, to reduce non-linear distortion
12
knv2gs � kn (VGS −Vt) vgs
⇒ vgs� 2VOV . (5)
The above equation represents small-signal condition.
Equation (4) is nothing but Taylor series approximation right!
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
Superimpose the AC Signal ...
The total instantaneous gate-to- source voltage, vGS = VGS + vgs, results in a total in-stantaneous drain current
iD =12
kn(VGS + vgs −Vt
)2
=12
kn (VGS −Vt)2︸ ︷︷ ︸
dc bias current
+ kn (VGS −Vt) vgs︸ ︷︷ ︸desired small signal current
+12
knv2gs︸ ︷︷ ︸
undesired small signal current
. (4)
So, to reduce non-linear distortion
12
knv2gs � kn (VGS −Vt) vgs
⇒ vgs� 2VOV . (5)
The above equation represents small-signal condition.
Equation (4) is nothing but Taylor series approximation right!
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
Superimpose the AC Signal ...
The total instantaneous gate-to- source voltage, vGS = VGS + vgs, results in a total in-stantaneous drain current
iD =12
kn(VGS + vgs −Vt
)2
=12
kn (VGS −Vt)2︸ ︷︷ ︸
dc bias current
+ kn (VGS −Vt) vgs︸ ︷︷ ︸desired small signal current
+12
knv2gs︸ ︷︷ ︸
undesired small signal current
. (4)
So, to reduce non-linear distortion
12
knv2gs � kn (VGS −Vt) vgs
⇒ vgs� 2VOV . (5)
The above equation represents small-signal condition.
Equation (4) is nothing but Taylor series approximation right!
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
Superimpose the AC Signal ...
The total instantaneous gate-to- source voltage, vGS = VGS + vgs, results in a total in-stantaneous drain current
iD =12
kn(VGS + vgs −Vt
)2
=12
kn (VGS −Vt)2︸ ︷︷ ︸
dc bias current
+ kn (VGS −Vt) vgs︸ ︷︷ ︸desired small signal current
+12
knv2gs︸ ︷︷ ︸
undesired small signal current
. (4)
So, to reduce non-linear distortion
12
knv2gs � kn (VGS −Vt) vgs
⇒ vgs� 2VOV . (5)
The above equation represents small-signal condition.
Equation (4) is nothing but Taylor series approximation right!
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
Superimpose the AC Signal ...
The total instantaneous gate-to- source voltage, vGS = VGS + vgs, results in a total in-stantaneous drain current
iD =12
kn(VGS + vgs −Vt
)2
=12
kn (VGS −Vt)2︸ ︷︷ ︸
dc bias current
+ kn (VGS −Vt) vgs︸ ︷︷ ︸desired small signal current
+12
knv2gs︸ ︷︷ ︸
undesired small signal current
. (4)
So, to reduce non-linear distortion
12
knv2gs � kn (VGS −Vt) vgs
⇒ vgs� 2VOV . (5)
The above equation represents small-signal condition.
Equation (4) is nothing but Taylor series approximation right!
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
Superimpose the AC Signal ...
The total instantaneous gate-to- source voltage, vGS = VGS + vgs, results in a total in-stantaneous drain current
iD =12
kn(VGS + vgs −Vt
)2
=12
kn (VGS −Vt)2︸ ︷︷ ︸
dc bias current
+ kn (VGS −Vt) vgs︸ ︷︷ ︸desired small signal current
+12
knv2gs︸ ︷︷ ︸
undesired small signal current
. (4)
So, to reduce non-linear distortion
12
knv2gs � kn (VGS −Vt) vgs
⇒ vgs� 2VOV . (5)
The above equation represents small-signal condition.
Equation (4) is nothing but Taylor series approximation right!
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
The Transconductance Parameter (gm)
If the small-signal condition is satisfied,
iD ≈12
kn (VGS −Vt)2 + kn (VGS −Vt) vgs = ID + id. (6)
So, the transconductance parameter is given as
gm =∆iD
∆vGS=
idvgs
= knVOV . (7)
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
The Transconductance Parameter (gm)
If the small-signal condition is satisfied,
iD ≈12
kn (VGS −Vt)2 + kn (VGS −Vt) vgs = ID + id. (6)
So, the transconductance parameter is given as
gm =∆iD
∆vGS=
idvgs
= knVOV . (7)
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
The Transconductance Parameter (gm)
If the small-signal condition is satisfied,
iD ≈12
kn (VGS −Vt)2 + kn (VGS −Vt) vgs = ID + id. (6)
So, the transconductance parameter is given as
gm =∆iD
∆vGS=
idvgs
= knVOV . (7)
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
The Transconductance Parameter (gm)
If the small-signal condition is satisfied,
iD ≈12
kn (VGS −Vt)2 + kn (VGS −Vt) vgs = ID + id. (6)
So, the transconductance parameter is given as
gm =∆iD
∆vGS=
idvgs
= knVOV . (7)
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
The Voltage Gain
Total instantaneous voltage is given by
vDS = VDD − RDiD.
Under the small-signal condition, we have
vDS = VDD − RD (ID + id) = VDS − RDid︸︷︷︸vds
.
So, the small-signal voltage gain is given by
Av =vdsvgs
= −RDidvgs
= −RDgmvgs
vgs= −gmRD. (8)
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
The Voltage Gain
Total instantaneous voltage is given by
vDS = VDD − RDiD.
Under the small-signal condition, we have
vDS = VDD − RD (ID + id) = VDS − RDid︸︷︷︸vds
.
So, the small-signal voltage gain is given by
Av =vdsvgs
= −RDidvgs
= −RDgmvgs
vgs= −gmRD. (8)
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
The Voltage Gain
Total instantaneous voltage is given by
vDS = VDD − RDiD.
Under the small-signal condition, we have
vDS = VDD − RD (ID + id) = VDS − RDid︸︷︷︸vds
.
So, the small-signal voltage gain is given by
Av =vdsvgs
= −RDidvgs
= −RDgmvgs
vgs= −gmRD. (8)
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
The Voltage Gain
Total instantaneous voltage is given by
vDS = VDD − RDiD.
Under the small-signal condition, we have
vDS = VDD − RD (ID + id) = VDS − RDid︸︷︷︸vds
.
So, the small-signal voltage gain is given by
Av =vdsvgs
= −RDidvgs
= −RDgmvgs
vgs= −gmRD. (8)
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
Separating the DC Analysis and the Signal Analysis
vGS
(gmRD ) V
0
vDSmax
VDS
min vGSmax - Vt
vDS
0
vGS
VGS
V
t
t
(VGS - Vt)V2 2
VDD
vDS
<<
<
<
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
Separating the DC Analysis and the Signal Analysis
vGS
(gmRD ) V
0
vDSmax
VDS
min vGSmax - Vt
vDS
0
vGS
VGS
V
t
t
(VGS - Vt)V2 2
VDD
vDS
<<
<
<
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
Why Small-Signal Models?
VSS
VDD
CC1
CS
Rsig
vsig
RL
CC2
RG
RD
vo
+-
Do we need to repeat this Taylor series analysis for each and every type of MOSFETamplifiers?
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
Why Small-Signal Models?
VSS
VDD
CC1
CS
Rsig
vsig
RL
CC2
RG
RD
vo
+-
Do we need to repeat this Taylor series analysis for each and every type of MOSFETamplifiers?
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
Why Small-Signal Models?
VSS
VDD
CC1
CS
Rsig
vsig
RL
CC2
RG
RD
vo
+-
Do we need to repeat this Taylor series analysis for each and every type of MOSFETamplifiers?
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
Differential (Small-Signal) Model of MOSFET
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
Differential (Small-Signal) Model of MOSFET
+
+
How small-signal current, id, is related to small-signal voltages, vgs and vds?
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
Differential (Small-Signal) Model of MOSFET
+
+
How small-signal current, id, is related to small-signal voltages, vgs and vds?
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
Differential (Small-Signal) Model of MOSFET
+
+
How small-signal current, id, is related to small-signal voltages, vgs and vds?
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
Differential (Small-Signal) Model of MOSFET
Since in saturation mode
iD =12
kn (vGS −Vt)2 (1 + λvDS) ,
using partial differential equation, we get
∂iD∂vGS
∣∣∣∣vGS=VGS
= kn (VGS −Vt) (1 + λvDS) = gm
and∂iD
∂vDS
∣∣∣∣vDS=VDS
=12
kn (vGS −Vt)2 × λ = r−1
o .
Using the theory of partial differentiation,
∆iD = id =∂iD
∂vGS∆vGS +
∂iD∂vDS
∆vDS =∂iD
∂vGSvgs +
∂iD∂vDS
vds = gmvgs +vdsr0
. (9)
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
Differential (Small-Signal) Model of MOSFET
Since in saturation mode
iD =12
kn (vGS −Vt)2 (1 + λvDS) ,
using partial differential equation, we get
∂iD∂vGS
∣∣∣∣vGS=VGS
= kn (VGS −Vt) (1 + λvDS) = gm
and∂iD
∂vDS
∣∣∣∣vDS=VDS
=12
kn (vGS −Vt)2 × λ = r−1
o .
Using the theory of partial differentiation,
∆iD = id =∂iD
∂vGS∆vGS +
∂iD∂vDS
∆vDS =∂iD
∂vGSvgs +
∂iD∂vDS
vds = gmvgs +vdsr0
. (9)
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
Differential (Small-Signal) Model of MOSFET
Since in saturation mode
iD =12
kn (vGS −Vt)2 (1 + λvDS) ,
using partial differential equation, we get
∂iD∂vGS
∣∣∣∣vGS=VGS
=
kn (VGS −Vt) (1 + λvDS) = gm
and∂iD
∂vDS
∣∣∣∣vDS=VDS
=12
kn (vGS −Vt)2 × λ = r−1
o .
Using the theory of partial differentiation,
∆iD = id =∂iD
∂vGS∆vGS +
∂iD∂vDS
∆vDS =∂iD
∂vGSvgs +
∂iD∂vDS
vds = gmvgs +vdsr0
. (9)
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
Differential (Small-Signal) Model of MOSFET
Since in saturation mode
iD =12
kn (vGS −Vt)2 (1 + λvDS) ,
using partial differential equation, we get
∂iD∂vGS
∣∣∣∣vGS=VGS
= kn (VGS −Vt) (1 + λvDS)
= gm
and∂iD
∂vDS
∣∣∣∣vDS=VDS
=12
kn (vGS −Vt)2 × λ = r−1
o .
Using the theory of partial differentiation,
∆iD = id =∂iD
∂vGS∆vGS +
∂iD∂vDS
∆vDS =∂iD
∂vGSvgs +
∂iD∂vDS
vds = gmvgs +vdsr0
. (9)
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
Differential (Small-Signal) Model of MOSFET
Since in saturation mode
iD =12
kn (vGS −Vt)2 (1 + λvDS) ,
using partial differential equation, we get
∂iD∂vGS
∣∣∣∣vGS=VGS
= kn (VGS −Vt) (1 + λvDS) = gm
and∂iD
∂vDS
∣∣∣∣vDS=VDS
=12
kn (vGS −Vt)2 × λ = r−1
o .
Using the theory of partial differentiation,
∆iD = id =∂iD
∂vGS∆vGS +
∂iD∂vDS
∆vDS =∂iD
∂vGSvgs +
∂iD∂vDS
vds = gmvgs +vdsr0
. (9)
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
Differential (Small-Signal) Model of MOSFET
Since in saturation mode
iD =12
kn (vGS −Vt)2 (1 + λvDS) ,
using partial differential equation, we get
∂iD∂vGS
∣∣∣∣vGS=VGS
= kn (VGS −Vt) (1 + λvDS) = gm
and∂iD
∂vDS
∣∣∣∣vDS=VDS
=
12
kn (vGS −Vt)2 × λ = r−1
o .
Using the theory of partial differentiation,
∆iD = id =∂iD
∂vGS∆vGS +
∂iD∂vDS
∆vDS =∂iD
∂vGSvgs +
∂iD∂vDS
vds = gmvgs +vdsr0
. (9)
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
Differential (Small-Signal) Model of MOSFET
Since in saturation mode
iD =12
kn (vGS −Vt)2 (1 + λvDS) ,
using partial differential equation, we get
∂iD∂vGS
∣∣∣∣vGS=VGS
= kn (VGS −Vt) (1 + λvDS) = gm
and∂iD
∂vDS
∣∣∣∣vDS=VDS
=12
kn (vGS −Vt)2 × λ
= r−1o .
Using the theory of partial differentiation,
∆iD = id =∂iD
∂vGS∆vGS +
∂iD∂vDS
∆vDS =∂iD
∂vGSvgs +
∂iD∂vDS
vds = gmvgs +vdsr0
. (9)
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
Differential (Small-Signal) Model of MOSFET
Since in saturation mode
iD =12
kn (vGS −Vt)2 (1 + λvDS) ,
using partial differential equation, we get
∂iD∂vGS
∣∣∣∣vGS=VGS
= kn (VGS −Vt) (1 + λvDS) = gm
and∂iD
∂vDS
∣∣∣∣vDS=VDS
=12
kn (vGS −Vt)2 × λ = r−1
o .
Using the theory of partial differentiation,
∆iD = id =∂iD
∂vGS∆vGS +
∂iD∂vDS
∆vDS =∂iD
∂vGSvgs +
∂iD∂vDS
vds = gmvgs +vdsr0
. (9)
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
Differential (Small-Signal) Model of MOSFET
Since in saturation mode
iD =12
kn (vGS −Vt)2 (1 + λvDS) ,
using partial differential equation, we get
∂iD∂vGS
∣∣∣∣vGS=VGS
= kn (VGS −Vt) (1 + λvDS) = gm
and∂iD
∂vDS
∣∣∣∣vDS=VDS
=12
kn (vGS −Vt)2 × λ = r−1
o .
Using the theory of partial differentiation,
∆iD = id =
∂iD∂vGS
∆vGS +∂iD
∂vDS∆vDS =
∂iD∂vGS
vgs +∂iD
∂vDSvds = gmvgs +
vdsr0
. (9)
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
Differential (Small-Signal) Model of MOSFET
Since in saturation mode
iD =12
kn (vGS −Vt)2 (1 + λvDS) ,
using partial differential equation, we get
∂iD∂vGS
∣∣∣∣vGS=VGS
= kn (VGS −Vt) (1 + λvDS) = gm
and∂iD
∂vDS
∣∣∣∣vDS=VDS
=12
kn (vGS −Vt)2 × λ = r−1
o .
Using the theory of partial differentiation,
∆iD = id =∂iD
∂vGS∆vGS +
∂iD∂vDS
∆vDS =
∂iD∂vGS
vgs +∂iD
∂vDSvds = gmvgs +
vdsr0
. (9)
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
Differential (Small-Signal) Model of MOSFET
Since in saturation mode
iD =12
kn (vGS −Vt)2 (1 + λvDS) ,
using partial differential equation, we get
∂iD∂vGS
∣∣∣∣vGS=VGS
= kn (VGS −Vt) (1 + λvDS) = gm
and∂iD
∂vDS
∣∣∣∣vDS=VDS
=12
kn (vGS −Vt)2 × λ = r−1
o .
Using the theory of partial differentiation,
∆iD = id =∂iD
∂vGS∆vGS +
∂iD∂vDS
∆vDS =∂iD
∂vGSvgs +
∂iD∂vDS
vds
= gmvgs +vdsr0
. (9)
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
Differential (Small-Signal) Model of MOSFET
Since in saturation mode
iD =12
kn (vGS −Vt)2 (1 + λvDS) ,
using partial differential equation, we get
∂iD∂vGS
∣∣∣∣vGS=VGS
= kn (VGS −Vt) (1 + λvDS) = gm
and∂iD
∂vDS
∣∣∣∣vDS=VDS
=12
kn (vGS −Vt)2 × λ = r−1
o .
Using the theory of partial differentiation,
∆iD = id =∂iD
∂vGS∆vGS +
∂iD∂vDS
∆vDS =∂iD
∂vGSvgs +
∂iD∂vDS
vds = gmvgs +vdsr0
. (9)
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
So, Small-Signal Equivalent-Circuit Model is ...
G D
S
rovgs vgsgm
+
-
ig
is
id
ig = 0
id = is = gmvgs +vdsr0
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
So, Small-Signal Equivalent-Circuit Model is ...
G D
S
rovgs vgsgm
+
-
ig
is
id
ig = 0
id = is = gmvgs +vdsr0
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
So, Small-Signal Equivalent-Circuit Model is ...
G D
S
rovgs vgsgm
+
-
ig
is
id
ig = 0
id = is = gmvgs +vdsr0
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
So, Small-Signal Equivalent-Circuit Model is ...
G D
S
rovgs vgsgm
+
-
ig
is
id
ig = 0
id = is = gmvgs +vdsr0
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
Physical Interpretation of gm and ro
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
Physical Interpretation of gm and ro
Triode Saturation
0
Slope
VOV
=1ro
vDS-VA = 1/
iD
-
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
Physical Interpretation of gm and ro
Triode Saturation
0
Slope
VOV
=1ro
vDS-VA = 1/
iD
-
vDS vGS –Vtn
vGS
vOV
Vtn
iD
0
0
= gmSlope
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
The T Equivalent-Circuit Model ... Neglecting ro
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
The T Equivalent-Circuit Model ... Neglecting ro
G D
S
is
ig = 0 id
vgs gmvgs
+
-
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
The T Equivalent-Circuit Model ... Neglecting ro
G D
S
is
ig = 0 id
vgs gmvgs
G D
S
is
ig = 0
id
vgs
gmvgs
gmvgs
X
+
-
+
-
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
The T Equivalent-Circuit Model ... Neglecting ro
gmvgs
G D
S
is
ig = 0 id
vgs gmvgs
X
G D
S
is
ig = 0
id
vgs
gmvgs
gmvgs
X
G D
S
is
id
vgs gmvgs
ig = 0
+
-
+
-
+
-
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
The T Equivalent-Circuit Model ... Neglecting ro
is
ig = 0
id
vgs
gmvgs
G D
S
is
ig = 0 id
vgs gmvgs
gmvgs
X
G D
S
is
ig = 0
id
vgs
gmvgs
gmvgs
X
G D
S
is
id
vgs gmvgs
1/gm
ig = 0
+
-
+
-
+
-
+
-
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
The T Equivalent-Circuit Model ... Including ro
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
The T Equivalent-Circuit Model ... Including ro
ro
g
G
S
D
m
1/gm
vgs
vgs
+
-
ro
1 i
G
S
D
i
1/gm
+
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
Using Small-Signal Model for Circuit Analysis
DC Analysis:
First of all, external capacitors are open circuited and inductors are short circuited.
AC voltage sources are replaced by short circuits and AC current sources are replacedby open circuits.
Perform DC analysis on the rest of the circuit to find DC operating point (i.e.,(VGS, VDS, ID)) and calculate gm and ro at that operating point.
AC Analysis:
Once DC analysis is done, DC voltage sources are replaced by short circuits and DCcurrent sources are replaced by open circuits.
All external capacitors are short circuited and inductors are open circuited.
Replace MOSFET with its small-signal circuit model.
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
Using Small-Signal Model for Circuit Analysis
DC Analysis:
First of all, external capacitors are open circuited and inductors are short circuited.
AC voltage sources are replaced by short circuits and AC current sources are replacedby open circuits.
Perform DC analysis on the rest of the circuit to find DC operating point (i.e.,(VGS, VDS, ID)) and calculate gm and ro at that operating point.
AC Analysis:
Once DC analysis is done, DC voltage sources are replaced by short circuits and DCcurrent sources are replaced by open circuits.
All external capacitors are short circuited and inductors are open circuited.
Replace MOSFET with its small-signal circuit model.
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
Using Small-Signal Model for Circuit Analysis
DC Analysis:
First of all, external capacitors are open circuited and inductors are short circuited.
AC voltage sources are replaced by short circuits and AC current sources are replacedby open circuits.
Perform DC analysis on the rest of the circuit to find DC operating point (i.e.,(VGS, VDS, ID)) and calculate gm and ro at that operating point.
AC Analysis:
Once DC analysis is done, DC voltage sources are replaced by short circuits and DCcurrent sources are replaced by open circuits.
All external capacitors are short circuited and inductors are open circuited.
Replace MOSFET with its small-signal circuit model.
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
Using Small-Signal Model for Circuit Analysis
DC Analysis:
First of all, external capacitors are open circuited and inductors are short circuited.
AC voltage sources are replaced by short circuits and AC current sources are replacedby open circuits.
Perform DC analysis on the rest of the circuit to find DC operating point (i.e.,(VGS, VDS, ID)) and calculate gm and ro at that operating point.
AC Analysis:
Once DC analysis is done, DC voltage sources are replaced by short circuits and DCcurrent sources are replaced by open circuits.
All external capacitors are short circuited and inductors are open circuited.
Replace MOSFET with its small-signal circuit model.
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
Using Small-Signal Model for Circuit Analysis
DC Analysis:
First of all, external capacitors are open circuited and inductors are short circuited.
AC voltage sources are replaced by short circuits and AC current sources are replacedby open circuits.
Perform DC analysis on the rest of the circuit to find DC operating point (i.e.,(VGS, VDS, ID)) and calculate gm and ro at that operating point.
AC Analysis:
Once DC analysis is done, DC voltage sources are replaced by short circuits and DCcurrent sources are replaced by open circuits.
All external capacitors are short circuited and inductors are open circuited.
Replace MOSFET with its small-signal circuit model.
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
Using Small-Signal Model for Circuit Analysis
DC Analysis:
First of all, external capacitors are open circuited and inductors are short circuited.
AC voltage sources are replaced by short circuits and AC current sources are replacedby open circuits.
Perform DC analysis on the rest of the circuit to find DC operating point (i.e.,(VGS, VDS, ID)) and calculate gm and ro at that operating point.
AC Analysis:
Once DC analysis is done, DC voltage sources are replaced by short circuits and DCcurrent sources are replaced by open circuits.
All external capacitors are short circuited and inductors are open circuited.
Replace MOSFET with its small-signal circuit model.
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
Using Small-Signal Model for Circuit Analysis
DC Analysis:
First of all, external capacitors are open circuited and inductors are short circuited.
AC voltage sources are replaced by short circuits and AC current sources are replacedby open circuits.
Perform DC analysis on the rest of the circuit to find DC operating point (i.e.,(VGS, VDS, ID)) and calculate gm and ro at that operating point.
AC Analysis:
Once DC analysis is done, DC voltage sources are replaced by short circuits and DCcurrent sources are replaced by open circuits.
All external capacitors are short circuited and inductors are open circuited.
Replace MOSFET with its small-signal circuit model.
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
Using Small-Signal Model for Circuit Analysis
DC Analysis:
First of all, external capacitors are open circuited and inductors are short circuited.
AC voltage sources are replaced by short circuits and AC current sources are replacedby open circuits.
Perform DC analysis on the rest of the circuit to find DC operating point (i.e.,(VGS, VDS, ID)) and calculate gm and ro at that operating point.
AC Analysis:
Once DC analysis is done, DC voltage sources are replaced by short circuits and DCcurrent sources are replaced by open circuits.
All external capacitors are short circuited and inductors are open circuited.
Replace MOSFET with its small-signal circuit model.
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
Using Small-Signal Model for Circuit Analysis
DC Analysis:
First of all, external capacitors are open circuited and inductors are short circuited.
AC voltage sources are replaced by short circuits and AC current sources are replacedby open circuits.
Perform DC analysis on the rest of the circuit to find DC operating point (i.e.,(VGS, VDS, ID)) and calculate gm and ro at that operating point.
AC Analysis:
Once DC analysis is done, DC voltage sources are replaced by short circuits and DCcurrent sources are replaced by open circuits.
All external capacitors are short circuited and inductors are open circuited.
Replace MOSFET with its small-signal circuit model.
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
DC & AC Analyses – Example
VSS
VDD
CC1
CS
Rsig
vsig
RL
CC2
RG
RD
vo
+-
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
DC & AC Analyses – Example
VSS
VDD
CC1
CS
Rsig
vsig
RL
CC2
RG
RD
vo
+-
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
DC Analysis
VSS
VDD
CC1
CS
Rsig
vsig
RL
CC2
RG
RD
vo
+-
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
AC Analysis
viRo
ii 0
Rin
vgs = vi
vd
(0 V)
VSS
VDD
CC1
CS
Rsig
vsig
RL
CC2
RG
RD
vo
+-
(0 V)
+
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
AC Analysis ... Cont’d
RG
S
Rsig
vsig
ig= 0 Gii
gmvgs
Rin= RG Ro = RD ro
vi vgs ro RD
D
RL
vo = gm vgs (RD RL ro)
+-
+
Rin = RG
Rout = RD‖ro
Gv = − RG
RG + Rsig× gm (RD‖RL‖ro)
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
AC Analysis ... Cont’d
RG
S
Rsig
vsig
ig= 0 Gii
gmvgs
Rin= RG Ro = RD ro
vi vgs ro RD
D
RL
vo = gm vgs (RD RL ro)
+-
+
Rin = RG
Rout = RD‖ro
Gv = − RG
RG + Rsig× gm (RD‖RL‖ro)
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
AC Analysis ... Cont’d
RG
S
Rsig
vsig
ig= 0 Gii
gmvgs
Rin= RG Ro = RD ro
vi vgs ro RD
D
RL
vo = gm vgs (RD RL ro)
+-
+
Rin = RG
Rout = RD‖ro
Gv = − RG
RG + Rsig× gm (RD‖RL‖ro)
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
AC Analysis ... Cont’d
RG
S
Rsig
vsig
ig= 0 Gii
gmvgs
Rin= RG Ro = RD ro
vi vgs ro RD
D
RL
vo = gm vgs (RD RL ro)
+-
+
Rin = RG
Rout = RD‖ro
Gv = − RG
RG + Rsig× gm (RD‖RL‖ro)
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
AC Analysis ... Cont’d
RG
S
Rsig
vsig
ig= 0 Gii
gmvgs
Rin= RG Ro = RD ro
vi vgs ro RD
D
RL
vo = gm vgs (RD RL ro)
+-
+
Rin = RG
Rout = RD‖ro
Gv = − RG
RG + Rsig× gm (RD‖RL‖ro)
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
Outline
1 Small-Signal Model
2 MOSFET Amplifiers
3 High Frequency Modeling
4 Frequency Response of CS Amplifier
5 Summary
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
Basic Configurations (Stripped Down Versions)
Common Source (CS) Common Gate (CG)
Common Drain (CD)
vo
vi
RL
+- +
RDvi
vo+-
+ RD vo
vi +-
+
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
Basic Configurations (Stripped Down Versions)
Common Source (CS) Common Gate (CG)
Common Drain (CD)
vo
vi
RL
+- +
RDvi
vo+-
+ RD vo
vi +-
+
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
Various Definitions of Gain – Recap
+vi
+
vo
+
R0
RiAvovi+vs RL
RSii io
Avo =vo
vI
∣∣∣∣RL→∞
Av = AvoRL
RL + Ro
Gv =vo
vs= Avo
(Ri
Ri + RS
)(RL
RL + Ro
)
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
Various Definitions of Gain – Recap
+vi
+
vo
+
R0
RiAvovi+vs RL
RSii io
Avo =vo
vI
∣∣∣∣RL→∞
Av = AvoRL
RL + Ro
Gv =vo
vs= Avo
(Ri
Ri + RS
)(RL
RL + Ro
)
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
First Let’s Analyze CS Amplifier ...
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
1. The Common-Source (CS) Amplifier
iD
vDS
RD
VDD
vgs+
vGS
VGS
+-
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
1. The Common-Source (CS) Amplifier
iD
vDS
RD
VDD
vgs+
vGS
VGS
+-
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
1. The Common-Source (CS) Amplifier – AC Analysis
Rin
vivo
Ro
vsig
Rsig
RD+-
+
+
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
1. The Common-Source (CS) Amplifier – AC Analysis
vovgs= vi gmvgsvsig
Rsig
RDro
+
+-
+
Rin
vivo
Ro
vsig
Rsig
RD+-
+
+
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
1. The Common-Source (CS) Amplifier ... Ri
vo
Rin
vgs= vi gmvgsvsig
Rsig
RDro
+
+-
+
=
Obviously,Ri = ∞. (10)
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
1. The Common-Source (CS) Amplifier ... Ri
vo
Rin
vgs= vi gmvgsvsig
Rsig
RDro
+
+-
+
=
Obviously,Ri = ∞. (10)
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
1. The Common-Source (CS) Amplifier ... Ri
vo
Rin
vgs= vi gmvgsvsig
Rsig
RDro
+
+-
+
=
Obviously,Ri = ∞. (10)
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
1. The Common-Source (CS) Amplifier ... Ro
vo
Rin
vgs= vi gmvgs
Ro=RD|| ro
vsig
Rsig
RDro
+
+-
+
=
The output resistance Ro is the resistance seen looking back into the output terminalwith vi set to zero. So,
Ro = RD ‖ ro ≈ RD. (11)
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
1. The Common-Source (CS) Amplifier ... Ro
vo
Rin
vgs= vi gmvgs
Ro=RD|| ro
vsig
Rsig
RDro
+
+-
+
=
The output resistance Ro is the resistance seen looking back into the output terminalwith vi set to zero. So,
Ro = RD ‖ ro ≈ RD. (11)
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
1. The Common-Source (CS) Amplifier ... Ro
vo
Rin
vgs= vi gmvgs
Ro=RD|| ro
vsig
Rsig
RDro
+
+-
+
=
The output resistance Ro is the resistance seen looking back into the output terminalwith vi set to zero.
So,
Ro = RD ‖ ro ≈ RD. (11)
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
1. The Common-Source (CS) Amplifier ... Ro
vo
Rin
vgs= vi gmvgs
Ro=RD|| ro
vsig
Rsig
RDro
+
+-
+
=
The output resistance Ro is the resistance seen looking back into the output terminalwith vi set to zero. So,
Ro = RD ‖ ro ≈ RD. (11)
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
1. The Common-Source (CS) Amplifier ... Avo
vo
Rin
vgs= vi gmvgs
Ro=RD|| ro
vsig
Rsig
RDro
+
+-
+
=
Since vo = −gmvgs (ro ‖ RD), and vi = vgs,
Avo = −gm (ro ‖ RD) ≈ −gmRD. (12)
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
1. The Common-Source (CS) Amplifier ... Avo
vo
Rin
vgs= vi gmvgs
Ro=RD|| ro
vsig
Rsig
RDro
+
+-
+
=
Since vo = −gmvgs (ro ‖ RD), and vi = vgs,
Avo = −gm (ro ‖ RD) ≈ −gmRD. (12)
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
1. The Common-Source (CS) Amplifier ... Avo
vo
Rin
vgs= vi gmvgs
Ro=RD|| ro
vsig
Rsig
RDro
+
+-
+
=
Since vo = −gmvgs (ro ‖ RD), and vi = vgs,
Avo = −gm (ro ‖ RD) ≈ −gmRD. (12)
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
1. The Common-Source (CS) Amplifier ... Av and Gv
vo
Rin
vgs= vi gmvgs
Ro=RD|| ro
vsig
Rsig
RDro
+
+-
+
=
When load resistance RL is attached to the output, overall impedance seen by the sourcegmvgs is (ro ‖ RD ‖ RL).So,
Av = −gm (ro ‖ RD ‖ RL) . (13)
Since Ri → ∞,
Gv = Av = −gm (ro ‖ RD ‖ RL) . (14)
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
1. The Common-Source (CS) Amplifier ... Av and Gv
vo
Rin
vgs= vi gmvgs
Ro=RD|| ro
vsig
Rsig
RDro
+
+-
+
=
When load resistance RL is attached to the output, overall impedance seen by the sourcegmvgs is (ro ‖ RD ‖ RL).So,
Av = −gm (ro ‖ RD ‖ RL) . (13)
Since Ri → ∞,
Gv = Av = −gm (ro ‖ RD ‖ RL) . (14)
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
1. The Common-Source (CS) Amplifier ... Av and Gv
vo
Rin
vgs= vi gmvgs
Ro=RD|| ro
vsig
Rsig
RDro
+
+-
+
=
When load resistance RL is attached to the output, overall impedance seen by the sourcegmvgs is (ro ‖ RD ‖ RL).
So,
Av = −gm (ro ‖ RD ‖ RL) . (13)
Since Ri → ∞,
Gv = Av = −gm (ro ‖ RD ‖ RL) . (14)
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
1. The Common-Source (CS) Amplifier ... Av and Gv
vo
Rin
vgs= vi gmvgs
Ro=RD|| ro
vsig
Rsig
RDro
+
+-
+
=
When load resistance RL is attached to the output, overall impedance seen by the sourcegmvgs is (ro ‖ RD ‖ RL).So,
Av = −gm (ro ‖ RD ‖ RL) . (13)
Since Ri → ∞,
Gv = Av = −gm (ro ‖ RD ‖ RL) . (14)
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
1. The Common-Source (CS) Amplifier ... Av and Gv
vo
Rin
vgs= vi gmvgs
Ro=RD|| ro
vsig
Rsig
RDro
+
+-
+
=
When load resistance RL is attached to the output, overall impedance seen by the sourcegmvgs is (ro ‖ RD ‖ RL).So,
Av = −gm (ro ‖ RD ‖ RL) . (13)
Since Ri → ∞,
Gv = Av = −gm (ro ‖ RD ‖ RL) . (14)
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
1. The Common-Source (CS) Amplifier ... Av and Gv
vo
Rin
vgs= vi gmvgs
Ro=RD|| ro
vsig
Rsig
RDro
+
+-
+
=
When load resistance RL is attached to the output, overall impedance seen by the sourcegmvgs is (ro ‖ RD ‖ RL).So,
Av = −gm (ro ‖ RD ‖ RL) . (13)
Since Ri → ∞,
Gv = Av = −gm (ro ‖ RD ‖ RL) . (14)
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
Now ... Common Gate (CG) Amplifier ...
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
2. The Common Gate Amplifier
Rin
vi
Rsig
vsig
voRD
Ro+-
+
+
In the right hand side of the above figure, the effect of ro is neglected.
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
2. The Common Gate Amplifier
Rin
vi
Rin
vivsig
Rsig
Rsigvsig Ro= RD
vo voRD
G
D
RD
1/gm
1/gm
Ro
i
iS+
-
+
+-
+
+
+
=
In the right hand side of the above figure, the effect of ro is neglected.
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
2. The Common Gate Amplifier
Rin
vi
Rin
vivsig
Rsig
Rsigvsig Ro= RD
vo voRD
G
D
RD
1/gm
1/gm
Ro
i
iS+
-
+
+-
+
+
+
=
In the right hand side of the above figure, the effect of ro is neglected.
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
2. The Common Gate Amplifier ... Ri
Rin
vivsig
RsigRo= RD
voRD
G
D
1/gm
1/gm
i
iS
+
+-
+
=
Ri = 1/gm (15)
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
2. The Common Gate Amplifier ... Ri
Rin
vivsig
RsigRo= RD
voRD
G
D
1/gm
1/gm
i
iS
+
+-
+
=
Ri = 1/gm (15)
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
2. The Common Gate Amplifier ... Ri
Rin
vivsig
RsigRo= RD
voRD
G
D
1/gm
1/gm
i
iS
+
+-
+
=
Ri = 1/gm (15)
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
2. The Common Gate Amplifier ... Ro
Rin
vivsig
RsigRo= RD
voRD
G
D
1/gm
1/gm
i
iS
+
+-
+
=
Ro = RD (16)
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
2. The Common Gate Amplifier ... Ro
Rin
vivsig
RsigRo= RD
voRD
G
D
1/gm
1/gm
i
iS
+
+-
+
=
Ro = RD (16)
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
2. The Common Gate Amplifier ... Ro
Rin
vivsig
RsigRo= RD
voRD
G
D
1/gm
1/gm
i
iS
+
+-
+
=
Ro = RD (16)
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
2. The Common Gate Amplifier ... Avo
Rin
vivsig
RsigRo= RD
voRD
G
D
1/gm
1/gm
i
iS
+
+-
+
=
Since i = gmvgs, vo = −gmvgsRD. Also, input voltage is vi = vsg = −vgs. So, we get
Avo = gmRD. (17)
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
2. The Common Gate Amplifier ... Avo
Rin
vivsig
RsigRo= RD
voRD
G
D
1/gm
1/gm
i
iS
+
+-
+
=
Since i = gmvgs, vo = −gmvgsRD. Also, input voltage is vi = vsg = −vgs. So, we get
Avo = gmRD. (17)
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
2. The Common Gate Amplifier ... Avo
Rin
vivsig
RsigRo= RD
voRD
G
D
1/gm
1/gm
i
iS
+
+-
+
=
Since i = gmvgs, vo = −gmvgsRD.
Also, input voltage is vi = vsg = −vgs. So, we get
Avo = gmRD. (17)
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
2. The Common Gate Amplifier ... Avo
Rin
vivsig
RsigRo= RD
voRD
G
D
1/gm
1/gm
i
iS
+
+-
+
=
Since i = gmvgs, vo = −gmvgsRD. Also, input voltage is vi = vsg = −vgs.
So, we get
Avo = gmRD. (17)
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
2. The Common Gate Amplifier ... Avo
Rin
vivsig
RsigRo= RD
voRD
G
D
1/gm
1/gm
i
iS
+
+-
+
=
Since i = gmvgs, vo = −gmvgsRD. Also, input voltage is vi = vsg = −vgs. So, we get
Avo = gmRD. (17)
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
2. The Common Gate Amplifier ... Av and Gv
Rin
vivsig
RsigRo= RD
voRD
G
D
1/gm
1/gm
i
iS
+
+-
+
=
Similar to the previous configurations
Av = gm (RD ‖ RL) . (18)
However, Gv is given by
Gv =1/gm
Rsig + 1/gmAv. (19)
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
2. The Common Gate Amplifier ... Av and Gv
Rin
vivsig
RsigRo= RD
voRD
G
D
1/gm
1/gm
i
iS
+
+-
+
=
Similar to the previous configurations
Av = gm (RD ‖ RL) . (18)
However, Gv is given by
Gv =1/gm
Rsig + 1/gmAv. (19)
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
2. The Common Gate Amplifier ... Av and Gv
Rin
vivsig
RsigRo= RD
voRD
G
D
1/gm
1/gm
i
iS
+
+-
+
=
Similar to the previous configurations
Av = gm (RD ‖ RL) . (18)
However, Gv is given by
Gv =1/gm
Rsig + 1/gmAv. (19)
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
2. The Common Gate Amplifier ... Av and Gv
Rin
vivsig
RsigRo= RD
voRD
G
D
1/gm
1/gm
i
iS
+
+-
+
=
Similar to the previous configurations
Av = gm (RD ‖ RL) . (18)
However, Gv is given by
Gv =1/gm
Rsig + 1/gmAv. (19)
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
Next, Common Drain (CD) Amplifier / Source Follower ...
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
Need For Voltage Buffers - Recap
sigR =1 MΩ
vsig=1VRL
1 kΩ+
Rsig=1 M
vsig=1V v 1 mVRL
1 k
Ω
Ω o~
++
Rin very large
Ro=100
RL1 k vo~ 0.9V
~~1VAvo=1
vsig=1V
sigR =1 MΩΩ
Ω+
+
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
Need For Voltage Buffers - Recap
sigR =1 MΩ
vsig=1VRL
1 kΩ+
Rsig=1 M
vsig=1V v 1 mVRL
1 k
Ω
Ω o~
++
Rin very large
Ro=100
RL1 k vo~ 0.9V
~~1VAvo=1
vsig=1V
sigR =1 MΩΩ
Ω+
+
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
3. The Common-Drain Amplifier or Source Follower
RoRin
vi
vo
vsig
Rsig
RL
+-
+
+
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
3. The Common-Drain Amplifier or Source Follower
RoRin
vi
vo
vsig
Rsig
RL
+-
+
+
RL
ro
vo
vi gm1 i
i
vsig
Rsig 0
+-
+
+
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
3. The Common-Drain Amplifier or Source Follower
RoRin
vi
vo
vsig
Rsig
RL
+-
+
+
RL
ro
vo
vi gm1 i
i
vsig
Rsig 0
+-
+
+
RL
Ro=
vo
vi
gm1
gm1
i
i
vsig
Rsig 0
+-
+
+
Rin =
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
3. The Common-Drain Amplifier ... Ri
RL
Ro=
vo
vi
gm1
gm1
i
i
vsig
Rsig 0
+-
+
+
Rin =
From the above figure,Ri = ∞. (20)
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
3. The Common-Drain Amplifier ... Ri
RL
Ro=
vo
vi
gm1
gm1
i
i
vsig
Rsig 0
+-
+
+
Rin =
From the above figure,Ri = ∞. (20)
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
3. The Common-Drain Amplifier ... Ri
RL
Ro=
vo
vi
gm1
gm1
i
i
vsig
Rsig 0
+-
+
+
Rin =
From the above figure,Ri = ∞. (20)
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
3. The Common-Drain Amplifier ... Ro
RL
Ro=
vo
vi
gm1
gm1
i
i
vsig
Rsig 0
+-
+
+
Rin =
Excluding RL (i.e., RL → ∞), and setting vi = 0 (i.e., by grounding the gate), we get
R0 = 1/gm. (21)
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
3. The Common-Drain Amplifier ... Ro
RL
Ro=
vo
vi
gm1
gm1
i
i
vsig
Rsig 0
+-
+
+
Rin =
Excluding RL (i.e., RL → ∞), and setting vi = 0 (i.e., by grounding the gate), we get
R0 = 1/gm. (21)
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
3. The Common-Drain Amplifier ... Ro
RL
Ro=
vo
vi
gm1
gm1
i
i
vsig
Rsig 0
+-
+
+
Rin =
Excluding RL (i.e., RL → ∞), and setting vi = 0 (i.e., by grounding the gate), we get
R0 = 1/gm. (21)
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
3. The Common-Drain Amplifier ... Avo
RL
Ro=
vo
vi
gm1
gm1
i
i
vsig
Rsig 0
+-
+
+
Rin =
Excluding RL (i.e., RL → ∞), we get
Av0 = 1. (22)
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
3. The Common-Drain Amplifier ... Avo
RL
Ro=
vo
vi
gm1
gm1
i
i
vsig
Rsig 0
+-
+
+
Rin =
Excluding RL (i.e., RL → ∞), we get
Av0 = 1. (22)
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
3. The Common-Drain Amplifier ... Avo
RL
Ro=
vo
vi
gm1
gm1
i
i
vsig
Rsig 0
+-
+
+
Rin =
Excluding RL (i.e., RL → ∞), we get
Av0 = 1. (22)
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
3. The Common-Drain Amplifier ... Av and Gv
RL
Ro=
vo
vi
gm1
gm1
i
i
vsig
Rsig 0
+-
+
+
Rin =
If we include RL, we get vo = viRL
RL+1/gm.So,
Av =RL
RL + 1/gm. (23)
Since Ri → ∞, we have Gv = Av.
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
3. The Common-Drain Amplifier ... Av and Gv
RL
Ro=
vo
vi
gm1
gm1
i
i
vsig
Rsig 0
+-
+
+
Rin =
If we include RL, we get vo = viRL
RL+1/gm.So,
Av =RL
RL + 1/gm. (23)
Since Ri → ∞, we have Gv = Av.
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
3. The Common-Drain Amplifier ... Av and Gv
RL
Ro=
vo
vi
gm1
gm1
i
i
vsig
Rsig 0
+-
+
+
Rin =
If we include RL, we get vo = viRL
RL+1/gm.
So,
Av =RL
RL + 1/gm. (23)
Since Ri → ∞, we have Gv = Av.
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
3. The Common-Drain Amplifier ... Av and Gv
RL
Ro=
vo
vi
gm1
gm1
i
i
vsig
Rsig 0
+-
+
+
Rin =
If we include RL, we get vo = viRL
RL+1/gm.So,
Av =RL
RL + 1/gm. (23)
Since Ri → ∞, we have Gv = Av.
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
3. The Common-Drain Amplifier ... Av and Gv
RL
Ro=
vo
vi
gm1
gm1
i
i
vsig
Rsig 0
+-
+
+
Rin =
If we include RL, we get vo = viRL
RL+1/gm.So,
Av =RL
RL + 1/gm. (23)
Since Ri → ∞, we have Gv = Av.
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
Finally, CS Amplifier with a Source Resistance ...
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
4. The CS Amplifier with a Source Resistance
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
4. The CS Amplifier with a Source Resistance
Rin
vivsig
Rsig
voRDRs
Ro
+-
+
+
In the above figure, the effect of ro is neglected.
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
4. The CS Amplifier with a Source Resistance
vgs
vivsig
Rsig
Ro=RD
0vo
RD
Rs
G
D
S
i
i
gm1
+-
Rin
vivsig
Rsig
voRDRs
Ro
+-
+
+
+
+
+
Rin =
In the above figure, the effect of ro is neglected.
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
4. The CS Amplifier with a Source Resistance
vgs
vivsig
Rsig
Ro=RD
0vo
RD
Rs
G
D
S
i
i
gm1
+-
Rin
vivsig
Rsig
voRDRs
Ro
+-
+
+
+
+
+
Rin =
In the above figure, the effect of ro is neglected.
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
4. CS Amplifier with a Source Resistance ... Ri
vgs
vivsig
Rsig
Ro=RD
0vo
RD
Rs
G
D
S
i
i
gm1
+-
+
+
+
Rin =
Again, from the above figure,Ri = ∞. (24)
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
4. CS Amplifier with a Source Resistance ... Ri
vgs
vivsig
Rsig
Ro=RD
0vo
RD
Rs
G
D
S
i
i
gm1
+-
+
+
+
Rin =
Again, from the above figure,Ri = ∞. (24)
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
4. CS Amplifier with a Source Resistance ... Ri
vgs
vivsig
Rsig
Ro=RD
0vo
RD
Rs
G
D
S
i
i
gm1
+-
+
+
+
Rin =
Again, from the above figure,Ri = ∞. (24)
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
4. CS Amplifier with a Source Resistance ... Ro
vgs
vivsig
Rsig
Ro=RD
0vo
RD
Rs
G
D
S
i
i
gm1
+-
+
+
+
Rin =
When vi = vsig = 0, i = 0. So,
Ro = RD. (25)
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
4. CS Amplifier with a Source Resistance ... Ro
vgs
vivsig
Rsig
Ro=RD
0vo
RD
Rs
G
D
S
i
i
gm1
+-
+
+
+
Rin =
When vi = vsig = 0, i = 0. So,
Ro = RD. (25)
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
4. CS Amplifier with a Source Resistance ... Ro
vgs
vivsig
Rsig
Ro=RD
0vo
RD
Rs
G
D
S
i
i
gm1
+-
+
+
+
Rin =
When vi = vsig = 0, i = 0. So,
Ro = RD. (25)
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
4. CS Amplifier with a Source Resistance ... Avo
vgs
vivsig
Rsig
Ro=RD
0vo
RD
Rs
G
D
S
i
i
gm1
+-
+
+
+
Rin =
Since i = vi1/gm+RS
, and vo = −iRD,
Avo = −gmRD
1 + gmRS. (26)
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
4. CS Amplifier with a Source Resistance ... Avo
vgs
vivsig
Rsig
Ro=RD
0vo
RD
Rs
G
D
S
i
i
gm1
+-
+
+
+
Rin =
Since i = vi1/gm+RS
, and vo = −iRD,
Avo = −gmRD
1 + gmRS. (26)
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
4. CS Amplifier with a Source Resistance ... Avo
vgs
vivsig
Rsig
Ro=RD
0vo
RD
Rs
G
D
S
i
i
gm1
+-
+
+
+
Rin =
Since i = vi1/gm+RS
, and vo = −iRD,
Avo = −gmRD
1 + gmRS. (26)
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
4. CS Amplifier with a Source Resistance ... Av and Gv
vgs
vivsig
Rsig
Ro=RD
0vo
RD
Rs
G
D
S
i
i
gm1
+-
+
+
+
Rin =
Av can be obtained simply by replacing RD by (RD ‖ RL). So,
Av = − gm (RD ‖ RL)
1 + gmRS. (27)
Also, since vi = vsig, Gv = Av.
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
4. CS Amplifier with a Source Resistance ... Av and Gv
vgs
vivsig
Rsig
Ro=RD
0vo
RD
Rs
G
D
S
i
i
gm1
+-
+
+
+
Rin =
Av can be obtained simply by replacing RD by (RD ‖ RL). So,
Av = − gm (RD ‖ RL)
1 + gmRS. (27)
Also, since vi = vsig, Gv = Av.
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
4. CS Amplifier with a Source Resistance ... Av and Gv
vgs
vivsig
Rsig
Ro=RD
0vo
RD
Rs
G
D
S
i
i
gm1
+-
+
+
+
Rin =
Av can be obtained simply by replacing RD by (RD ‖ RL). So,
Av = − gm (RD ‖ RL)
1 + gmRS. (27)
Also, since vi = vsig, Gv = Av.
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
4. CS Amplifier with a Source Resistance ... Why RS?
vgs
vivsig
Rsig
Ro=RD
0vo
RD
Rs
G
D
S
i
i
gm1
+-
+
+
+
Rin =
�
�RS introduces negative feedback, which provides bias stabilization and improves the
performance of the amplifier.
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
4. CS Amplifier with a Source Resistance ... Why RS?
vgs
vivsig
Rsig
Ro=RD
0vo
RD
Rs
G
D
S
i
i
gm1
+-
+
+
+
Rin =
�
�RS introduces negative feedback, which provides bias stabilization and improves the
performance of the amplifier.
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
4. CS Amplifier with a Source Resistance ... Why RS?
vgs
vivsig
Rsig
Ro=RD
0vo
RD
Rs
G
D
S
i
i
gm1
+-
+
+
+
Rin =
�
�RS introduces negative feedback, which provides bias stabilization and improves the
performance of the amplifier.
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
4. CS Amplifier with a Source Resistance ***
Since the resistor Rs is introducing negative feedback, let’s use the concept offeedback to understand CS amplifier with source resistance better!!
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
4. CS Amplifier with a Source Resistance ***
Since the resistor Rs is introducing negative feedback, let’s use the concept offeedback to understand CS amplifier with source resistance better!!
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
Feedback – Recap
Source LoadA
β
xs xi
xf
xo
+−
β =xf
x0
xo
xs=
A1 + Aβ
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
Feedback – Recap
Source LoadA
β
xs xi
xf
xo
+−
β =xf
x0
xo
xs=
A1 + Aβ
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
Amplifiers – Recap
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
Amplifiers – Recap
+vi
+
vo
+
R0
RiAvovi
ii io
vi
+
vo
+
R0RiAisii
ii io
+vi
+
vo
+
R0
RiRmii
ii io
vi
+
vo
+
R0RiGmvi
ii io
Voltage
Current
Transconductance
Transresistance
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
4. CS Amplifier with a Source Resistance ***
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
4. CS Amplifier with a Source Resistance ***
+
−
vgsgmvgs
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
4. CS Amplifier with a Source Resistance ***
+
−
vgsgmvgs
+
−
vs+
−
vf
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
4. CS Amplifier with a Source Resistance ***
+
−
vsg'mvs
whereg′m =
gm
1 + gmRs. (28)
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
4. CS Amplifier with a Source Resistance ***
+
−
vsg'mvs
whereg′m =
gm
1 + gmRs. (28)
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
4. CS Amplifier with a Source Resistance ***
+
−
vsg'mvs
whereg′m =
gm
1 + gmRs. (28)
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
4. CS Amplifier with a Source Resistance ***
+
−
vsg'mvgs
RD
So,vo
vs= −g′mRD = − gm
1 + gmRsRD =
−gmRD1 + gmRs
. (29)
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
4. CS Amplifier with a Source Resistance ***
+
−
vsg'mvgs
RD
So,vo
vs= −g′mRD = − gm
1 + gmRsRD =
−gmRD1 + gmRs
. (29)
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
4. CS Amplifier with a Source Resistance ***
+
−
vsg'mvgs
RD
So,vo
vs= −g′mRD = − gm
1 + gmRsRD =
−gmRD1 + gmRs
. (29)
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
MOSFET Amplifiers – Summary
Type Ri Ro Avo Av Gv
CS ∞ RD −gmRD −gm (RD ‖ RL) −gm (RD ‖ RL)
CG 1/gm RD gmRD gm (RD ‖ RL)RD‖RL
Rsig+1/gm
CD ∞ 1/gm 1 RLRL+1/gm
RLRL+1/gm
CS with Rs ∞ RD − gmRD1+gmRs
− gm(RD‖RL)1+gmRs
− gm(RD‖RL)1+gmRs
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
MOSFET Amplifiers – Summary
Type Ri Ro Avo Av Gv
CS ∞ RD −gmRD −gm (RD ‖ RL) −gm (RD ‖ RL)
CG 1/gm RD gmRD gm (RD ‖ RL)RD‖RL
Rsig+1/gm
CD ∞ 1/gm 1 RLRL+1/gm
RLRL+1/gm
CS with Rs ∞ RD − gmRD1+gmRs
− gm(RD‖RL)1+gmRs
− gm(RD‖RL)1+gmRs
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
Outline
1 Small-Signal Model
2 MOSFET Amplifiers
3 High Frequency Modeling
4 Frequency Response of CS Amplifier
5 Summary
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
MOSFET in Saturation Mode
Oxide (SiO2)
Gate electrode
Depletion region
n+
p-type substrate
n+
S G D
vGS
B
+
-
--------------------- - - - - - -
- - - ------ - -
- - - - - - - - - ---------------------- -
- -
--
-- - - -
--- - - -
-
vDS+
-
iD
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
MOSFET in Saturation Mode
Oxide (SiO2)
Gate electrode
Depletion region
n+
p-type substrate
n+
S G D
vGS
B
+
-
--------------------- - - - - - -
- - - ------ - -
- - - - - - - - - ---------------------- -
- -
--
-- - - -
--- - - -
-
vDS+
-
iD
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
The MOSFET Internal Capacitances
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
The MOSFET Internal Capacitances
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
The MOSFET Internal Capacitances
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
The SS Circuit Model with Internal Capacitances
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
The SS Circuit Model with Internal Capacitances
Vbs Csb
S B
Cdb
Vbs
Cgd
Cgsgmb
ro
G D
VgsVgsgm
_
+
_
+
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
The SS Circuit Model with Internal Capacitances
Vbs Csb
S B
Cdb
Vbs
Cgd
Cgsgmb
ro
G D
VgsVgsgm
_
+
_
+
CdbVgs
Cgd
Cgs gm ro
G D
Vgs
S
_
+
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
The SS Circuit Model with Internal Capacitances
Vbs Csb
S B
Cdb
Vbs
Cgd
Cgsgmb
ro
G D
VgsVgsgm
_
+
_
+
CdbVgs
Cgd
Cgs gm ro
G D
Vgs
S
_
+
VgsVgs
Cgd
Cgs gm ro
G D
S
_
+
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
The MOSFET Unity-Gain Frequency (fT)
A figure of merit for the high-frequency operation of the MOSFET as anamplifier is the unity-gain frequency, fT , also known as the transition
frequency, which gives rise to the subscript T.
This is defined as the frequency at which the short-circuit current-gain of thecommon-source configuration becomes unity.
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
The MOSFET Unity-Gain Frequency (fT)
A figure of merit for the high-frequency operation of the MOSFET as anamplifier is the unity-gain frequency, fT , also known as the transition
frequency, which gives rise to the subscript T.
This is defined as the frequency at which the short-circuit current-gain of thecommon-source configuration becomes unity.
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
The MOSFET Unity-Gain Frequency (fT)
A figure of merit for the high-frequency operation of the MOSFET as anamplifier is the unity-gain frequency, fT , also known as the transition
frequency, which gives rise to the subscript T.
This is defined as the frequency at which the short-circuit current-gain of thecommon-source configuration becomes unity.
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
The MOSFET Unity-Gain Frequency (fT)
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
The MOSFET Unity-Gain Frequency (fT)
Ii Vgs Vgs
Cgd sCgd Vgs
Cgs gm ro
Io
_
+
Applying KCL at drain node gives,
IO = gmVgs +Vdsro− sCgdVgd = gmVgs +
Vdsro− sCgdVgs = gmVgs − sCgdVgs ≈ gmVgs.
Since Ii = sCgsVgs + sCgdVgd = sCgsVgs + sCgdVgs,
Io
Ii=
gm
s(Cgs + Cgd
) . (30)
Thus unity-gain frequency, fT , at which |Io/Ii| = 1 is
fT =1
2π
gm
Cgs + Cds. (31)
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
The MOSFET Unity-Gain Frequency (fT)
Ii Vgs Vgs
Cgd sCgd Vgs
Cgs gm ro
Io
_
+
Applying KCL at drain node gives,
IO = gmVgs +Vdsro− sCgdVgd = gmVgs +
Vdsro− sCgdVgs = gmVgs − sCgdVgs ≈ gmVgs.
Since Ii = sCgsVgs + sCgdVgd = sCgsVgs + sCgdVgs,
Io
Ii=
gm
s(Cgs + Cgd
) . (30)
Thus unity-gain frequency, fT , at which |Io/Ii| = 1 is
fT =1
2π
gm
Cgs + Cds. (31)
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
The MOSFET Unity-Gain Frequency (fT)
Ii Vgs Vgs
Cgd sCgd Vgs
Cgs gm ro
Io
_
+
Applying KCL at drain node gives,
IO = gmVgs +Vdsro− sCgdVgd
= gmVgs +Vdsro− sCgdVgs = gmVgs − sCgdVgs ≈ gmVgs.
Since Ii = sCgsVgs + sCgdVgd = sCgsVgs + sCgdVgs,
Io
Ii=
gm
s(Cgs + Cgd
) . (30)
Thus unity-gain frequency, fT , at which |Io/Ii| = 1 is
fT =1
2π
gm
Cgs + Cds. (31)
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
The MOSFET Unity-Gain Frequency (fT)
Ii Vgs Vgs
Cgd sCgd Vgs
Cgs gm ro
Io
_
+
Applying KCL at drain node gives,
IO = gmVgs +Vdsro− sCgdVgd = gmVgs +
Vdsro− sCgdVgs
= gmVgs − sCgdVgs ≈ gmVgs.
Since Ii = sCgsVgs + sCgdVgd = sCgsVgs + sCgdVgs,
Io
Ii=
gm
s(Cgs + Cgd
) . (30)
Thus unity-gain frequency, fT , at which |Io/Ii| = 1 is
fT =1
2π
gm
Cgs + Cds. (31)
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
The MOSFET Unity-Gain Frequency (fT)
Ii Vgs Vgs
Cgd sCgd Vgs
Cgs gm ro
Io
_
+
Applying KCL at drain node gives,
IO = gmVgs +Vdsro− sCgdVgd = gmVgs +
Vdsro− sCgdVgs = gmVgs − sCgdVgs
≈ gmVgs.
Since Ii = sCgsVgs + sCgdVgd = sCgsVgs + sCgdVgs,
Io
Ii=
gm
s(Cgs + Cgd
) . (30)
Thus unity-gain frequency, fT , at which |Io/Ii| = 1 is
fT =1
2π
gm
Cgs + Cds. (31)
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
The MOSFET Unity-Gain Frequency (fT)
Ii Vgs Vgs
Cgd sCgd Vgs
Cgs gm ro
Io
_
+
Applying KCL at drain node gives,
IO = gmVgs +Vdsro− sCgdVgd = gmVgs +
Vdsro− sCgdVgs = gmVgs − sCgdVgs ≈ gmVgs.
Since Ii = sCgsVgs + sCgdVgd = sCgsVgs + sCgdVgs,
Io
Ii=
gm
s(Cgs + Cgd
) . (30)
Thus unity-gain frequency, fT , at which |Io/Ii| = 1 is
fT =1
2π
gm
Cgs + Cds. (31)
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
The MOSFET Unity-Gain Frequency (fT)
Ii Vgs Vgs
Cgd sCgd Vgs
Cgs gm ro
Io
_
+
Applying KCL at drain node gives,
IO = gmVgs +Vdsro− sCgdVgd = gmVgs +
Vdsro− sCgdVgs = gmVgs − sCgdVgs ≈ gmVgs.
Since Ii = sCgsVgs + sCgdVgd = sCgsVgs + sCgdVgs,
Io
Ii=
gm
s(Cgs + Cgd
) . (30)
Thus unity-gain frequency, fT , at which |Io/Ii| = 1 is
fT =1
2π
gm
Cgs + Cds. (31)
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
The MOSFET Unity-Gain Frequency (fT)
Ii Vgs Vgs
Cgd sCgd Vgs
Cgs gm ro
Io
_
+
Applying KCL at drain node gives,
IO = gmVgs +Vdsro− sCgdVgd = gmVgs +
Vdsro− sCgdVgs = gmVgs − sCgdVgs ≈ gmVgs.
Since Ii = sCgsVgs + sCgdVgd = sCgsVgs + sCgdVgs,
Io
Ii=
gm
s(Cgs + Cgd
) . (30)
Thus unity-gain frequency, fT , at which |Io/Ii| = 1 is
fT =1
2π
gm
Cgs + Cds. (31)
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
The MOSFET Unity-Gain Frequency (fT)
Ii Vgs Vgs
Cgd sCgd Vgs
Cgs gm ro
Io
_
+
Applying KCL at drain node gives,
IO = gmVgs +Vdsro− sCgdVgd = gmVgs +
Vdsro− sCgdVgs = gmVgs − sCgdVgs ≈ gmVgs.
Since Ii = sCgsVgs + sCgdVgd = sCgsVgs + sCgdVgs,
Io
Ii=
gm
s(Cgs + Cgd
) . (30)
Thus unity-gain frequency, fT , at which |Io/Ii| = 1 is
fT =1
2π
gm
Cgs + Cds. (31)
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
The MOSFET Unity-Gain Frequency (fT)
Ii Vgs Vgs
Cgd sCgd Vgs
Cgs gm ro
Io
_
+
Applying KCL at drain node gives,
IO = gmVgs +Vdsro− sCgdVgd = gmVgs +
Vdsro− sCgdVgs = gmVgs − sCgdVgs ≈ gmVgs.
Since Ii = sCgsVgs + sCgdVgd = sCgsVgs + sCgdVgs,
Io
Ii=
gm
s(Cgs + Cgd
) . (30)
Thus unity-gain frequency, fT , at which |Io/Ii| = 1 is
fT =1
2π
gm
Cgs + Cds. (31)
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
The MOSFET Unity-Gain Frequency (fT) ***
Vgsgm ro
Io
Ii Vgs Cgs_
+
From the above diagram, input voltage Vgs is
Vgs = Ii1
jωCeq= Ii
1jω(Cgs + Cgd
)because gmR′L = 0 (since RL = 0). So,
Io = gmVgs = gmIi1
jω(Cgs + Cgd
) .
Finally, we getIo
Ii=
gm
jω(Cgs + Cgd
) . (32)
The above equation is nothing but equation (30) given in the previous slide.
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
The MOSFET Unity-Gain Frequency (fT) ***
Vgsgm ro
Io
Ii Vgs Cgs_
+
From the above diagram, input voltage Vgs is
Vgs = Ii1
jωCeq= Ii
1jω(Cgs + Cgd
)because gmR′L = 0 (since RL = 0). So,
Io = gmVgs = gmIi1
jω(Cgs + Cgd
) .
Finally, we getIo
Ii=
gm
jω(Cgs + Cgd
) . (32)
The above equation is nothing but equation (30) given in the previous slide.
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
Outline
1 Small-Signal Model
2 MOSFET Amplifiers
3 High Frequency Modeling
4 Frequency Response of CS Amplifier
5 Summary
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
Frequency Response of CS Amplifier
VSS
VDD
CC1
CS
Rsig
vsig
RL
CC2
RG
RD
vo
+-
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
Frequency Response of CS Amplifier
VSS
VDD
CC1
CS
Rsig
vsig
RL
CC2
RG
RD
vo
+-
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
Frequency Response of CS Amplifier
Vo(dB)
Low-frequencyband
ViMidband
All capacitances can be neglected
High-frequency band
Gain falls offdue to the effectof Ci , CSand Co
3 dB
20 log |AM| (dB)
fL fH f (Hz)
Gain falls offdue to the internalcapacitive effectsof the MOSFET
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
Frequency Response of CS Amplifier
Vo(dB)
Low-frequencyband
ViMidband
All capacitances can be neglected
High-frequency band
Gain falls offdue to the effectof Ci , CSand Co
3 dB
20 log |AM| (dB)
fL fH f (Hz)
Gain falls offdue to the internalcapacitive effectsof the MOSFET
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
Low Frequency Analysis
Vo(dB)
Low-frequencyband
ViMidband
All capacitances can be neglected
High-frequency band
Gain falls offdue to the effectof Ci , CSand Co
3 dB
20 log |AM| (dB)
fL fH f (Hz)
Gain falls offdue to the internalcapacitive effectsof the MOSFET
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
Low Frequency Analysis
Vo(dB)
Low-frequencyband
ViMidband
All capacitances can be neglected
High-frequency band
Gain falls offdue to the effectof Ci , CSand Co
3 dB
20 log |AM| (dB)
fL fH f (Hz)
Gain falls offdue to the internalcapacitive effectsof the MOSFET
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
Lower Cutoff Frequency – fL
i
i
1gm
CS
CC1Rsig
vsig RG+-
vi
RL
CC2
vo
RD
v'o
vi = vsig ×RG
Rsig + RG + 1sCc1
i =vi
1gm
+ 1sCs
v′o = −i[
RD ‖(
RL +1
sCc2
)]vo = v′o ×
RL
RL +1
sCc2
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
Lower Cutoff Frequency – fL
i
i
1gm
CS
CC1Rsig
vsig RG+-
vi
RL
CC2
vo
RD
v'o
vi = vsig ×RG
Rsig + RG + 1sCc1
i =vi
1gm
+ 1sCs
v′o = −i[
RD ‖(
RL +1
sCc2
)]vo = v′o ×
RL
RL +1
sCc2
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
Lower Cutoff Frequency – fL
i
i
1gm
CS
CC1Rsig
vsig RG+-
vi
RL
CC2
vo
RD
v'o
vi = vsig ×RG
Rsig + RG + 1sCc1
i =vi
1gm
+ 1sCs
v′o = −i[
RD ‖(
RL +1
sCc2
)]vo = v′o ×
RL
RL +1
sCc2
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
Lower Cutoff Frequency – fL
i
i
1gm
CS
CC1Rsig
vsig RG+-
vi
RL
CC2
vo
RD
v'o
vi = vsig ×RG
Rsig + RG + 1sCc1
i =vi
1gm
+ 1sCs
v′o = −i[
RD ‖(
RL +1
sCc2
)]vo = v′o ×
RL
RL +1
sCc2
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
Lower Cutoff Frequency – fL
i
i
1gm
CS
CC1Rsig
vsig RG+-
vi
RL
CC2
vo
RD
v'o
Clubbing all the equation given in the previous slide gives,
vo
vsig=
−RL
RL +1
sCc2
[RD ‖
(RL +
1sCc2
)]1
1gm
+ 1sCs
RG
Rsig + RG + 1sCc1
=−gmRLRGRD
(RD + RL)(Rsig + RG
) sCC2 (RD + RL)
1 + sCc2 (RD + RL)
s Csgm
1 + s Csgm
sCC1(Rsig + RG
)1 + sCc1
(Rsig + RG
)
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
Lower Cutoff Frequency – fL
i
i
1gm
CS
CC1Rsig
vsig RG+-
vi
RL
CC2
vo
RD
v'o
Clubbing all the equation given in the previous slide gives,
vo
vsig=
−RL
RL +1
sCc2
[RD ‖
(RL +
1sCc2
)]1
1gm
+ 1sCs
RG
Rsig + RG + 1sCc1
=−gmRLRGRD
(RD + RL)(Rsig + RG
) sCC2 (RD + RL)
1 + sCc2 (RD + RL)
s Csgm
1 + s Csgm
sCC1(Rsig + RG
)1 + sCc1
(Rsig + RG
)
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
Lower Cutoff Frequency – fL
i
i
1gm
CS
CC1Rsig
vsig RG+-
vi
RL
CC2
vo
RD
v'o
Clubbing all the equation given in the previous slide gives,
vo
vsig=
−RL
RL +1
sCc2
[RD ‖
(RL +
1sCc2
)]1
1gm
+ 1sCs
RG
Rsig + RG + 1sCc1
=−gmRLRGRD
(RD + RL)(Rsig + RG
) sCC2 (RD + RL)
1 + sCc2 (RD + RL)
s Csgm
1 + s Csgm
sCC1(Rsig + RG
)1 + sCc1
(Rsig + RG
)
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
Lower Cutoff Frequency – fL
i
i
1gm
CS
CC1Rsig
vsig RG+-
vi
RL
CC2
vo
RD
v'o
Clubbing all the equation given in the previous slide gives,
vo
vsig=
−RL
RL +1
sCc2
[RD ‖
(RL +
1sCc2
)]1
1gm
+ 1sCs
RG
Rsig + RG + 1sCc1
=−gmRLRGRD
(RD + RL)(Rsig + RG
) sCC2 (RD + RL)
1 + sCc2 (RD + RL)
s Csgm
1 + s Csgm
sCC1(Rsig + RG
)1 + sCc1
(Rsig + RG
)
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
Lower Cutoff Frequency – fL
i
i
1gm
CS
CC1Rsig
vsig RG+-
vi
RL
CC2
vo
RD
v'o
Clubbing all the equation given in the previous slide gives,
vo
vsig=
−RL
RL +1
sCc2
[RD ‖
(RL +
1sCc2
)]1
1gm
+ 1sCs
RG
Rsig + RG + 1sCc1
=−gmRLRGRD
(RD + RL)(Rsig + RG
) sCC2 (RD + RL)
1 + sCc2 (RD + RL)
s Csgm
1 + s Csgm
sCC1(Rsig + RG
)1 + sCc1
(Rsig + RG
)
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
Lower Cutoff Frequency – fL
i
i
1gm
CS
CC1Rsig
vsig RG+-
vi
RL
CC2
vo
RD
v'o
Clubbing all the equation given in the previous slide gives,
vo
vsig=
−RL
RL +1
sCc2
[RD ‖
(RL +
1sCc2
)]1
1gm
+ 1sCs
RG
Rsig + RG + 1sCc1
=−gmRLRGRD
(RD + RL)(Rsig + RG
) sCC2 (RD + RL)
1 + sCc2 (RD + RL)
s Csgm
1 + s Csgm
sCC1(Rsig + RG
)1 + sCc1
(Rsig + RG
)5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
Lower Cutoff Frequency – fL
VoVsig
(dB)
f (Hz)(log scale)
20 dB/decade
fL
20 log AM
40 dB/decade
60 dB/decade
0fP1 fP3 fP2
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
Lower Cutoff Frequency – fL
VoVsig
(dB)
f (Hz)(log scale)
20 dB/decade
fL
20 log AM
40 dB/decade
60 dB/decade
0fP1 fP3 fP2
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
High Frequency Analysis
Vo(dB)
Low-frequencyband
ViMidband
All capacitances can be neglected
High-frequency band
Gain falls offdue to the effectof Ci , CSand Co
3 dB
20 log |AM| (dB)
fL fH f (Hz)
Gain falls offdue to the internalcapacitive effectsof the MOSFET
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
High Frequency Analysis
Vo(dB)
Low-frequencyband
ViMidband
All capacitances can be neglected
High-frequency band
Gain falls offdue to the effectof Ci , CSand Co
3 dB
20 log |AM| (dB)
fL fH f (Hz)
Gain falls offdue to the internalcapacitive effectsof the MOSFET
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
Upper Cutoff Frequency – fH
RG
Rsig
vsig +-
VgsVgs
Cgd
Cgs gm ro_
+
RD RL
Vgs = Vsig
RG ‖ 1sCeq
Rsig +(
RG ‖ 1sCeq
)
Vo = −gm (ro ‖ RD ‖ RL)Vgs
Vo
Vsig= −gm (ro ‖ RD ‖ RL)
RG ‖ 1sCeq
Rsig +(
RG ‖ 1sCeq
)
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
Upper Cutoff Frequency – fH
RG
Rsig
vsig +-
VgsVgs Cgs gm ro_
+
RD RL
Ceq = Cgs + Cgd(1 + gmR′L
)
Vgs = Vsig
RG ‖ 1sCeq
Rsig +(
RG ‖ 1sCeq
)Vo = −gm (ro ‖ RD ‖ RL)Vgs
Vo
Vsig= −gm (ro ‖ RD ‖ RL)
RG ‖ 1sCeq
Rsig +(
RG ‖ 1sCeq
)
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
Upper Cutoff Frequency – fH
RG
Rsig
vsig +-
VgsVgs Cgs gm ro_
+
RD RL
Ceq = Cgs + Cgd(1 + gmR′L
)
Vgs = Vsig
RG ‖ 1sCeq
Rsig +(
RG ‖ 1sCeq
)Vo = −gm (ro ‖ RD ‖ RL)Vgs
Vo
Vsig= −gm (ro ‖ RD ‖ RL)
RG ‖ 1sCeq
Rsig +(
RG ‖ 1sCeq
)
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
Upper Cutoff Frequency – fH
RG
Rsig
vsig +-
VgsVgs Cgs gm ro_
+
RD RL
Ceq = Cgs + Cgd(1 + gmR′L
)
Vgs = Vsig
RG ‖ 1sCeq
Rsig +(
RG ‖ 1sCeq
)Vo = −gm (ro ‖ RD ‖ RL)Vgs
Vo
Vsig= −gm (ro ‖ RD ‖ RL)
RG ‖ 1sCeq
Rsig +(
RG ‖ 1sCeq
)
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
Upper Cutoff Frequency – fH
From the previous slide,
Vo
Vsig= −gm (ro ‖ RD ‖ RL)
RG ‖ 1sCeq
Rsig +(
RG ‖ 1sCeq
)= −gm (ro ‖ RD ‖ RL)
1
1 +Rsig
(RG+
1sCeq
)RG
1sCeq
= −gm (ro ‖ RD ‖ RL)1
1 +RsigRG
RG1
sCeq+
RsigRG
= −gm (ro ‖ RD ‖ RL)1
RG+RsigRG
+sCeqRsigRG
RG
= −gm (ro ‖ RD ‖ RL)RG
RG + Rsig
1
1 +sCeqRsigRG
RG+Rsig
. (33)
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
Upper Cutoff Frequency – fH
From the previous slide,
Vo
Vsig= −gm (ro ‖ RD ‖ RL)
RG ‖ 1sCeq
Rsig +(
RG ‖ 1sCeq
)
= −gm (ro ‖ RD ‖ RL)1
1 +Rsig
(RG+
1sCeq
)RG
1sCeq
= −gm (ro ‖ RD ‖ RL)1
1 +RsigRG
RG1
sCeq+
RsigRG
= −gm (ro ‖ RD ‖ RL)1
RG+RsigRG
+sCeqRsigRG
RG
= −gm (ro ‖ RD ‖ RL)RG
RG + Rsig
1
1 +sCeqRsigRG
RG+Rsig
. (33)
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
Upper Cutoff Frequency – fH
From the previous slide,
Vo
Vsig= −gm (ro ‖ RD ‖ RL)
RG ‖ 1sCeq
Rsig +(
RG ‖ 1sCeq
)= −gm (ro ‖ RD ‖ RL)
1
1 +Rsig
(RG+
1sCeq
)RG
1sCeq
= −gm (ro ‖ RD ‖ RL)1
1 +RsigRG
RG1
sCeq+
RsigRG
= −gm (ro ‖ RD ‖ RL)1
RG+RsigRG
+sCeqRsigRG
RG
= −gm (ro ‖ RD ‖ RL)RG
RG + Rsig
1
1 +sCeqRsigRG
RG+Rsig
. (33)
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
Upper Cutoff Frequency – fH
From the previous slide,
Vo
Vsig= −gm (ro ‖ RD ‖ RL)
RG ‖ 1sCeq
Rsig +(
RG ‖ 1sCeq
)= −gm (ro ‖ RD ‖ RL)
1
1 +Rsig
(RG+
1sCeq
)RG
1sCeq
= −gm (ro ‖ RD ‖ RL)1
1 +RsigRG
RG1
sCeq+
RsigRG
= −gm (ro ‖ RD ‖ RL)1
RG+RsigRG
+sCeqRsigRG
RG
= −gm (ro ‖ RD ‖ RL)RG
RG + Rsig
1
1 +sCeqRsigRG
RG+Rsig
. (33)
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
Upper Cutoff Frequency – fH
From the previous slide,
Vo
Vsig= −gm (ro ‖ RD ‖ RL)
RG ‖ 1sCeq
Rsig +(
RG ‖ 1sCeq
)= −gm (ro ‖ RD ‖ RL)
1
1 +Rsig
(RG+
1sCeq
)RG
1sCeq
= −gm (ro ‖ RD ‖ RL)1
1 +RsigRG
RG1
sCeq+
RsigRG
= −gm (ro ‖ RD ‖ RL)1
RG+RsigRG
+sCeqRsigRG
RG
= −gm (ro ‖ RD ‖ RL)RG
RG + Rsig
1
1 +sCeqRsigRG
RG+Rsig
. (33)
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
Upper Cutoff Frequency – fH
From the previous slide,
Vo
Vsig= −gm (ro ‖ RD ‖ RL)
RG ‖ 1sCeq
Rsig +(
RG ‖ 1sCeq
)= −gm (ro ‖ RD ‖ RL)
1
1 +Rsig
(RG+
1sCeq
)RG
1sCeq
= −gm (ro ‖ RD ‖ RL)1
1 +RsigRG
RG1
sCeq+
RsigRG
= −gm (ro ‖ RD ‖ RL)1
RG+RsigRG
+sCeqRsigRG
RG
= −gm (ro ‖ RD ‖ RL)RG
RG + Rsig
1
1 +sCeqRsigRG
RG+Rsig
. (33)
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
Mid-band Analysis
Vo(dB)
Low-frequencyband
ViMidband
All capacitances can be neglected
High-frequency band
Gain falls offdue to the effectof Ci , CSand Co
3 dB
20 log |AM| (dB)
fL fH f (Hz)
Gain falls offdue to the internalcapacitive effectsof the MOSFET
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
Mid-band Analysis
Vo(dB)
Low-frequencyband
ViMidband
All capacitances can be neglected
High-frequency band
Gain falls offdue to the effectof Ci , CSand Co
3 dB
20 log |AM| (dB)
fL fH f (Hz)
Gain falls offdue to the internalcapacitive effectsof the MOSFET
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
Mid-band Gain – AM
From the previous slides where we have derived the expressions for gain in low andhigh frequency regions , mid-band gain is given by
AM = −gm (ro ‖ RD ‖ RL)RG
RG + Rsig. (34)
We don’t even have to derive the above expression ... Simply remove the effect of allthe capacitors (external & internal) then get the gain value, which is nothing but AM.
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
Mid-band Gain – AM
From the previous slides where we have derived the expressions for gain in low andhigh frequency regions , mid-band gain is given by
AM = −gm (ro ‖ RD ‖ RL)RG
RG + Rsig. (34)
We don’t even have to derive the above expression ... Simply remove the effect of allthe capacitors (external & internal) then get the gain value, which is nothing but AM.
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
Outline
1 Small-Signal Model
2 MOSFET Amplifiers
3 High Frequency Modeling
4 Frequency Response of CS Amplifier
5 Summary
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
Definitions – gm & ro
Since in saturation mode
iD =12
kn (vGS −Vt)2 (1 + λvDS) ,
using partial differential equation, we get
∂iD∂vGS
∣∣∣∣vGS=VGS
= kn (VGS −Vt) (1 + λvDS) = gm
and∂iD
∂vDS
∣∣∣∣vDS=VDS
=12
kn (vGS −Vt)2 × λ = r−1
o .
Using the theory of partial differentiation,
∆iD = id =∂iD
∂vGS∆vGS +
∂iD∂vDS
∆vDS =∂iD
∂vGSvgs +
∂iD∂vDS
vds = gmvgs +vdsr0
.
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
Small-Signal Equivalent-Circuit Model
G D
S
rovgs vgsgm
+
-
ig
is
id
ig = 0
id = is = gmvgs +vdsr0
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
Physical Interpretation of gm and ro
Triode Saturation
0
Slope
VOV
=1ro
vDS-VA = 1/
iD
-
vDS vGS –Vtn
vGS
vOV
Vtn
iD
0
0
= gmSlope
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
The T Equivalent-Circuit Model ... Neglecting ro
is
ig = 0
id
vgs
gmvgs
G D
S
is
ig = 0 id
vgs gmvgs
gmvgs
X
G D
S
is
ig = 0
id
vgs
gmvgs
gmvgs
X
G D
S
is
id
vgs gmvgs
1/gm
ig = 0
+
-
+
-
+
-
+
-
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
The T Equivalent-Circuit Model ... Including ro
ro
g
G
S
D
m
1/gm
vgs
vgs
+
-
ro
1 i
G
S
D
i
1/gm
+
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
Using Small-Signal Model for Circuit Analysis
DC Analysis:
First of all, external capacitors are open circuited and inductors are short circuited.
AC voltage sources are replaced by short circuits and AC current sources are replacedby open circuits.
Perform DC analysis on the rest of the circuit to find DC operating point (i.e.,(VGS, VDS, ID)) and calculate gm and ro at that operating point.
AC Analysis:
Once DC analysis is done, DC voltage sources are replaced by short circuits and DCcurrent sources are replaced by open circuits.
All external capacitors are short circuited and inductors are open circuited.
Replace MOSFET with its small-signal circuit model.
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
DC Analysis
VSS
VDD
CC1
CS
Rsig
vsig
RL
CC2
RG
RD
vo
+-
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
AC Analysis
viRo
ii 0
Rin
vgs = vi
vd
(0 V)
VSS
VDD
CC1
CS
Rsig
vsig
RL
CC2
RG
RD
vo
+-
(0 V)
+
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
AC Analysis ... Cont’d
RG
S
Rsig
vsig
ig= 0 Gii
gmvgs
Rin= RG Ro = RD ro
vi vgs ro RD
D
RL
vo = gm vgs (RD RL ro)
+-
+
Rin = RG
Rout = RD‖ro
Gv = − RG
RG + Rsig× gm (RD‖RL‖ro)
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
Basic Configurations (Stripped Down Versions)
Common Source (CS) Common Gate (CG)
Common Drain (CD)
vo
vi
RL
+- +
RDvi
vo+-
+ RD vo
vi +-
+
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
MOSFET Amplifiers – Summary
Type Ri Ro Avo Av Gv
CS ∞ RD −gmRD −gm (RD ‖ RL) −gm (RD ‖ RL)
CG 1/gm RD gmRD gm (RD ‖ RL)RD‖RL
Rsig+1/gm
CD ∞ 1/gm 1 RLRL+1/gm
RLRL+1/gm
CS with Rs ∞ RD − gmRD1+gmRs
− gm(RD‖RL)1+gmRs
− gm(RD‖RL)1+gmRs
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
The SS Circuit Model with Internal Capacitances
Vbs Csb
S B
Cdb
Vbs
Cgd
Cgsgmb
ro
G D
VgsVgsgm
_
+
_
+
CdbVgs
Cgd
Cgs gm ro
G D
Vgs
S
_
+
VgsVgs
Cgd
Cgs gm ro
G D
S
_
+
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
The MOSFET Unity-Gain Frequency (fT)
Ii Vgs Vgs
Cgd sCgd Vgs
Cgs gm ro
Io
_
+
Applying KCL at drain node gives,
IO = gmVgs +Vdsro− sCgdVgd = gmvgs +
Vdsro− sCgdVgs ≈ gmVgs − sCgdVgs ≈ gmVgs.
Since Ii = sCgsVgs + sCgdVgd = sCgsVgs + sCgdVgs,
Io
Ii=
gm
s(Cgs + Cgd
) .
Thus unity-gain frequency, fT , at which |Io/Ii| = 1 is
fT =1
2π
gm
Cgs + Cds.
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
The MOSFET Unity-Gain Frequency (fT) ***
Vgsgm ro
Io
Ii Vgs Cgs_
+
From the above diagram, input voltage Vgs is
Vgs = Ii1
jωCeq= Ii
1jω(Cgs + Cgd
)because gmR′L = 0 (since RL = 0). So,
Io = gmVgs = gmIi1
jω(Cgs + Cgd
) .
Finally, we getIo
Ii=
gm
jω(Cgs + Cgd
) .
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
Frequency Response of CS Amplifier ... fL
i
i
1gm
CS
CC1Rsig
vsig RG+-
vi
RL
CC2
vo
RD
v'o
vo
vsig=
−RL
RL +1
sCc2
[RD ‖
(RL +
1sCc2
)]1
1gm
+ 1sCs
RG
Rsig + RG + 1sCc1
=−gmRLRGRD
(RD + RL)(Rsig + RG
) sCC2 (RD + RL)
1 + sCc2 (RD + RL)
s Csgm
1 + s Csgm
sCC1(Rsig + RG
)1 + sCc1
(Rsig + RG
)5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
Frequency Response of CS Amplifier ... fH
RG
Rsig
vsig +-
VgsVgs Cgs gm ro_
+
RD RL
Vgs = Vsig
RG ‖ 1sCeq
Rsig +(
RG ‖ 1sCeq
)
Vo = −gm (ro ‖ RD ‖ RL)Vgs
Vo
Vsig= −gm (ro ‖ RD ‖ RL)
RG ‖ 1sCeq
Rsig +(
RG ‖ 1sCeq
)
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
Frequency Response of CS Amplifier ... fH
From the previous slide,
Vo
Vsig= −gm (ro ‖ RD ‖ RL)
RG ‖ 1sCeq
Rsig +(
RG ‖ 1sCeq
)= −gm (ro ‖ RD ‖ RL)
1
1 +Rsig
(RG+
1sCeq
)RG
1sCeq
= −gm (ro ‖ RD ‖ RL)1
1 +RsigRG
RG1
sCeq+
RsigRG
= −gm (ro ‖ RD ‖ RL)1
RG+RsigRG
+sCeqRsigRG
RG
= −gm (ro ‖ RD ‖ RL)RG
RG + Rsig
1
1 +sCeqRsigRG
RG+Rsig
.
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Small-Signal Model MOSFET Amplifiers High Frequency Modeling Frequency Response of CS Amplifier Summary
Mid-band Gain – AM
From the previous slides where we have derived the expressions for gain in low andhigh frequency regions , mid-band gain is given by
AM = −gm (ro ‖ RD ‖ RL)RG
RG + Rsig.
We don’t even have to derive the above expression ... Simply remove the effect of allthe capacitors (external & internal) then get the gain value, which is nothing but AM.
5. MOSFET Transistors & Circuits - II ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus