
301Direct Detection Optical Receivers
where
R
R R
R R
out
d l
d l
=
+
(7.81)
Z
R
sR C
in
g
g d
=
+ 1
(7.82)
Z sL
sC
sL
sC
sC sC
sL
s L L C C
A
in
in
i
= +
⋅ +
+ +
=
1
1
2
1
2
4
1 2 1
1 1
1 1
nn in in
in in
s L C s L C s L C
s L C C s C C
+ + + +
+ +
( )
2
1 1
2
1
2
2
3
2 1 1
1
(7.83)
7.6.2 Noise Theory and Equivalent Input Noise Current
Circuit
diagram
in
Figure
7.20
can
be
represented
with
the
reection
coefcients
shown
in
Figure
7.17.
We
denote
the
reection
coefcient
of
Z Z Z
ph S opt ph S opt
, ,
, ,
,by Γ Γ Γ
which
are
normalized
t
o
Z
0
and dened by
Γ
x
x
x
Z Z
Z Z
=
+
0
0
(7.84)
where
x =
ph,
s,
and
opt.
It
is
useful
to
obtain
the
S
parameters
of
the
third-order
noise-
matching networ ...