Short Notes: Basic FET Amplifiers- 2

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T ransistor F requency Resp onse
The frequency resp onse of a transistor describ es ho w its gain v aries with the frequency of the input
signal. It is critical in analog circuits for applications lik e amplifiers, where p erformance degrades at high
and lo w frequencies due to parasitic capacitances and other effects.
1. In t ro d uction to F requency Resp onse
T ransistors (BJT s and MOSFET s) exhibit frequency-dep enden t b eha vior due to in trinsic and extrinsic
capacitances. The frequency resp onse is analyzed using:
• Lo w-frequency resp onse : Aff ected b y coupling and b ypass capacitors.
• High-frequency resp onse : Limited b y parasitic capacitances (e.g., C
p
, C
µ
in BJT s; C
gs
, C
gd
in
MOSFET s).
2. K ey P arameters
• Cutoff F requencies : The frequencies (f
L
and f
H
) where the gain drops b y 3 dB (to 1/
v
2 of
midband gain).
• Bandwidth : The range of frequencies (f
H
-f
L
) where the t ransistor op erates effectiv ely .
• Gain-Bandwidth Pro duct : F or a single-stage amplifier, the pro duct of midband gain and band-
width is often constan t.
3. High-F requency Mo del (BJT Example)
The high-frequency h ybrid-p mo del of a BJT includes:
• C
p
: Base-emitter capacitance.
• C
µ
: Base-collector capacitance.
• r
p
: Small-signal input resistance.
• g
m
: T ransconductance.
The small-signal v oltage gain is frequency-dep enden t:
A
v
(s)=
v
out
v
in
=
-g
m
R
L
1+s(C
p
+C
µ
)R
eq
where R
L
is the load resistance , and R
eq
is the equiv alen t resistance seen b y the capacitors.
The high- frequency cutoff ( f
H
) is determined b y the p ole:
f
H
=
1
2p(C
p
+C
µ
)R
eq
4. Lo w-F requency Resp onse
Lo w-frequency resp onse is affected b y coupling capacitors ( C
C
) and b ypass capacitors (C
E
). The transfer
function includes p oles due to these capacitors. F or a coupling capacitor:
f
L
=
1
2pC
C
(R
in
+R
sig
)
where R
in
is the input resistance, and R
sig
is the signal source resistance.
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Page 2


T ransistor F requency Resp onse
The frequency resp onse of a transistor describ es ho w its gain v aries with the frequency of the input
signal. It is critical in analog circuits for applications lik e amplifiers, where p erformance degrades at high
and lo w frequencies due to parasitic capacitances and other effects.
1. In t ro d uction to F requency Resp onse
T ransistors (BJT s and MOSFET s) exhibit frequency-dep enden t b eha vior due to in trinsic and extrinsic
capacitances. The frequency resp onse is analyzed using:
• Lo w-frequency resp onse : Aff ected b y coupling and b ypass capacitors.
• High-frequency resp onse : Limited b y parasitic capacitances (e.g., C
p
, C
µ
in BJT s; C
gs
, C
gd
in
MOSFET s).
2. K ey P arameters
• Cutoff F requencies : The frequencies (f
L
and f
H
) where the gain drops b y 3 dB (to 1/
v
2 of
midband gain).
• Bandwidth : The range of frequencies (f
H
-f
L
) where the t ransistor op erates effectiv ely .
• Gain-Bandwidth Pro duct : F or a single-stage amplifier, the pro duct of midband gain and band-
width is often constan t.
3. High-F requency Mo del (BJT Example)
The high-frequency h ybrid-p mo del of a BJT includes:
• C
p
: Base-emitter capacitance.
• C
µ
: Base-collector capacitance.
• r
p
: Small-signal input resistance.
• g
m
: T ransconductance.
The small-signal v oltage gain is frequency-dep enden t:
A
v
(s)=
v
out
v
in
=
-g
m
R
L
1+s(C
p
+C
µ
)R
eq
where R
L
is the load resistance , and R
eq
is the equiv alen t resistance seen b y the capacitors.
The high- frequency cutoff ( f
H
) is determined b y the p ole:
f
H
=
1
2p(C
p
+C
µ
)R
eq
4. Lo w-F requency Resp onse
Lo w-frequency resp onse is affected b y coupling capacitors ( C
C
) and b ypass capacitors (C
E
). The transfer
function includes p oles due to these capacitors. F or a coupling capacitor:
f
L
=
1
2pC
C
(R
in
+R
sig
)
where R
in
is the input resistance, and R
sig
is the signal source resistance.
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5. MOSFET F requency Resp onse
F or MOSF ET s, the high-frequency mo del includes:
• C
gs
: Gate-source capacitance.
• C
gd
: Gate-drain capacitance.
The gain is:
A
v
(s)=
-g
m
R
D
1+s(C
gs
+C
gd
)R
eq
where R
D
is the drain resistance. The high-f requency cutoff is:
f
H
=
1
2p(C
gs
+C
gd
)R
eq
6. Miller Effect
The Miller effect amplifies the impact of C
µ
(BJT) or C
gd
(MOSFET) due to v oltage gain across the
capacitor. The effectiv e input capacitance is:
C
in
=C
µ
(1+|A
v
|) (for B JT)
C
in
=C
gd
(1+|A
v
|) (for MOSFET)
This increases the total input capacitance, reducing f
H
.
7. F requency Resp onse Analysis
• Bo de Plot : Plots gain (in dB) and phase v ersus frequency to visualize f
L
, f
H
, and bandwidth.
• Unit y-Gain F requency (f
T
) : The frequency where the curren t gain of the transistor drops to 1:
f
T
=
g
m
2p(C
p
+C
µ
)
(for BJT)
f
T
=
g
m
2p(C
gs
+C
gd
)
(for MOSFET)
8. Applications
• Designing amplifiers with desired bandwidth.
• Optimizing high-frequency p erformance in RF circuits.
• Analyzing stabilit y in feedbac k amplifiers.
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