18-1 Nonlinear elements
1,Nonlinear resistor
A nonlinear resistor is an element whose voltage
and current are related by a nonlinear equation.
i
?? ?
i
?
i
?
If the current can be expressed
as an explicit(单值 ) function of
the voltage.
)(?fi ? ----A voltage-controlled nonlinear resistor.
If the voltage can be expressed
as an explicit function of the
current
)i(h?? ----A current-controlled nonlinear resistor.
2,Nonlinear inductor
A nonlinear inductor is one in which the flux is a
nonlinear function of the current i(t),?)(if??
cet a ni n d u cD y n a m i c
di
d
L
dt
di
L
dt
di
di
d
dt
d
)t(
d
d
???
????
?
??
?
Example,The flux as a function of the current is somewhat like
in shown in Fig,?
i
A
B
C
D
Ai
BiCi
Di DCBA
iiii DCBA
???
???
)(ti
?? )( t?
3,Nonlinear capacitor
A nonlinear capacitor is one whose stored charge is a
nonlinear function of the voltage across it,)(?fq ?
dt
d
C
dt
dk
dt
d
d
dq
dt
dq
ti
kqIf
d
??
?
?
?
?
????
?
?
)
2
()( 2
1
2
1
?? ?
i
2
1
2
?
? ?kC d
Example:If Find i(t),).1(),s i n1( ????? ???? kqtV
)s i n1(
c o s
2c o s
1
2)( tV
tVktVk
dt
d
d
dq
dt
dqti
?
??
?
?
? ?????
)s i n211(c o s2 ttVk ?? ?? )2s i n41( c o s2 ttVk ?? ??
ec a p a c i t a n cd y n a m i c??