
558 Microwave Engineering
Since v
p
is a function of time C(v
p
) is also function of time. Thus,
C t C n t
n p
( ) cos( )=
ω
(13.45)
In Equation 17.45 the coefcient C
n
represents the magnitude of each har-
monic of time-varying C. Also coefcients C
n
are non-linear functions of v
p
.
Since C(t) is non-linear, principle of superposition does not apply for arbi-
trary ac signal amplitudes. The current through C(t) is
i
p
s
= = +
(13.46)
If v
s
≪ v
p
, nonlinear capacitance behaves like a time-varying linear capaci-
tance. The rst term of current i yields a current at f
p
and not related to f
s
. If
v
s
≮ v
p
the Taylors series can be