Radio Frequency Integrated Circuit Design - Webs

162 Radio Frequency Integrated Circuit Design
Yc = ic
vc =√2qIC g 2 m
2qIC
g 2 m
Y 2
�
= Y� = j�C�
where it is assumed that r� is not significant. Explicitly,
(6.51)
Gc ≈ 0 (6.52)
Bc = �C�
(6.53)
Thus, the correlation admittance is just equal to the input impedance of the
transistor.
R c , R u , and Gu can also be written down directly.
R c = v 2 c
4kT = 2qIC 4kTg 2 =
m
v T
2IC R u = v 2 u
4kT = 4kTr b
4kT = r b
Gu = i 2 u 2qIB
=
4kT 4kT
= IC
2vT �
(6.54)
(6.55)
(6.56)
Using these equations, an explicit expression for the noise figure can be written
in terms of circuit parameters:
NF = 1 +
IC
2v T � + �G 2
S + (�C� ) 2� v T
2IC
GS
+ G 2
S r b
Here it is assumed that the source resistance has no reactive component.
These equations also lead to expressions for G opt and B opt:
G opt =√
IC
2v T � + r b�− v �2
T
(�C� )
2IC v T
+ r
2I b
C
v T
v T
+ v T
2IC� �C�
2IC
−
v T
2IC (6.57)
�2
(�C� )
+ r b
+ r b
2IC
(6.58)