31
Fundamentals of Electric Capacitors
1.6.6.2 RLC Circuits Having Other R, L, and C Combinations
There are different RLC circuits with various R, L, and C combinations. Other
RLC circuits include parallel RLC (R/L/C), parallel LC series with R ((L/C)-R),
series CL parallel with R ((C-L)/R), parallel RL series with C ((R/L)-C), series
RL parallel with C ((RL)-C), parallel RC series with L ((R/C)-L), and series RC
parallel with L ((R-C)/L) [3]. The expressions of AC impedance for these RLC
circuits can be obtained and summarized as follows:
Series RLC (R-L-C) circuit:
2
1
Z
2
R L
− −C = R + (ω d L −
)
(1.67)
ω d C
Parallel RLC circuit (R/L/C):
1
1
ω d C −
R
Z
= (
ω
/ /
2
L
R L C
) (
+
d
)
2
(1.68)
1 2
1 2
1 2 2
1
( ) + (ω d C −
)
( ) + (ω
R
ω
d C −
)
2
d L
R
ω d L
Parallel LC series with R ((L/C)-R):
1
2
Z ( /
L C)
)
2
− R = R + (
(1.69)
1 − ω
ω d L
d C
Series CL parallel with R ((C-L)/R):
1
ω d C
R
− − 1
Z
2
ω
2
d CL
2
(C L
− )/ R = (
) (
+
)
(1.70)
1
( )
2
ω
+ (
d C
2
1 2
ω C
2
)
( ) + (
d
)
2
R
ω d CL − 1
R
ω
2
d CL − 1
Parallel RL series with C ((R/L)-C):
ω R L
2
ω R L
2
1
Z
d
2
d
2
( /
R L)− C = (
) + (
−
2
2 2
2
2 2
)
(1.71)
R + ω d L
R + ω d L ω d d C
Series RL parallel with C ((RL)-C):