Derivation of
f
T
And
f
MAX
of a MOSFET
Derivation of
f
T
(MOSFETs)
The unity current gain frequency* (aka
cutoff frequency)
Defined under the condition that the output
is loaded with an AC short.
f
T
does not depend on
R
g
and
r
o
Derivation of
f
T
(MOSFETs)
(Continued)
Assume the zero (sCgd) is smaller compared to gm.
f
T
with Parasitic R
S
and R
D
Derivation of
f
T
(MOSFETs)
(Continued)
(R
S
and R
D
are included)
Miller’s
Approximation
Derivation of
f
MAX
(MOSFETs)
f
MAX
* is the frequency at
which the maximum power
gain =1 (*aka maximum
oscillation frequency)
f
MAX
is defined with
its input and output ports
conjugate

matched for
maximum power transfer
So, we need to know the
input and output impedance
to define the input and
output power as well as
achieve the max power
transfer matching condition.
Derivation of
f
MAX
(MOSFETs)
At high frequency (close to
fmax), we can assume that
So, R
g
is independent of R
L
For the matching conditions,
Derivation of
f
MAX
(MOSFETs)
(Continued)
Conjugate match at the
input
:
Conjugate match at the
output
:
Power Gain (Under Conjugate Match)
Using the
definition of
f
T
Derivation of
f
MAX
(MOSFETs)
(Continued)
(R
S
and R
D
are included)
Hence, replace R
g
by R
g
+R
s
For high frequency condition,
C
gs
→ short
w/o (R
S
+R
D
) term
w/ (R
S
+R
D
) term
Derivation of
f
T
And
f
MAX
of a BJT
Derivation of
f
T
(Bipolar)
For Bipolar Transistors,
C
DE
is due to minority
carriers caused by FB
Derivation of
f
T
(Bipolar)
(Continued)
Q
E
= minority holes stored in emitter
Q
B
= minority electrons stored in base
Q
BE
= electrons induced by the current
through the depletion region of BE

junction
Q
BC
= electrons induced by the current
through the depletion region of BC

junction
Derivation of
f
T
(Bipolar)
(Continued)
Width of Neutral Region
Width of
Depletion
Region
if drift current is considered.
is greater than because of reverse

biasing.
Derivation of
f
T
(Bipolar)
(R
S
and R
D
are included)
For bipolar, the result is similar.
The only difference is that the
term must be
included.
Derivation of
f
MAX
(Bipolar)
For bipolar transistors, there is no term.
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