Protek Z9216 - Series and Parallel Equivalent Circuits

Series and Parallel Equivalent Circuits
The impedances of Actual resistors, inductors and capacitors are combinations of resistance,
inductance, and capacitance. The simplest models for actual inductors and capacitors are the series
and parallel equivalent circuits shown in Figure 1-1.
For example, the complex impedance of an inductor is
LjRjXRZ
ω
+=+= (series equivalent circuit) (8a)
(
)
()
2
/1
/
pp
pppp
pp
pp
LR
LRjRR
LjR
LjR
ω
ω
ω
ω
+
+
=
+
⋅
=
(parallel equivalent) (8b)
8a - Inductor Series
Equivalent
8b - Inductor Parallel
Equivalent
9a -Capacitor Series
Equivalent
9b - Capacitor Parallel
Equivalent
Figure 1-1 Equivalent circuits for inductors and capacitors.
The complex impedance of a capacitor is
CjRjXRZ
ω
/−=+= (series equivalent circuit) (9a)
(
)
()
2
1
1
1/1
/1
pp
ppp
pp
p
pp
pp
RC
RCjR
RCj
R
CjR
CjR
ω
ω
ωω
ω
+
−
=
+
=
+
⋅
= (parallel equivalent) (9b)
3