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3.3.2.2 Theory -- Series and
Parallel Parameters
An impedance that is neither pure reactance nor a
pure resistance can be represented at any specific
frequency by either a series or a parallel combination
of resistance and reactance. The values of resistance
and reactance used in the equivalent circuit depend
on whether a series or parallel combination is used.
Keeping this concept in mind will be valuable in
operation of the instrument and interpreting its
measurements.
Resistance and Inductance
ω
X
L
=
ω
Z
=
Z
=
R
+
j
L
S
S
R
ω
1
θ
Q
=
Q
=
−
=
tan
D
Q
2
L
=
L
L
=
S
p
S
2
1 +
Q
Q
2
1
+
L
=
L
=
L
(
)
P
S
P
Q
2
ω
L
R
=
R
=
S
S
S
Q
1
B
Y
=
G
=
P
ω
L
S
Operation
j
ω
L
R
R
+
j Q
2
P
P
Z
=
P
ω
+
j
L
R
+
j
ω
P
P
P
L
R
S
Q
=
P
R
ω
L
P
S
Q
2
L
p
2
1 +
Q
1 (
+
D
2
)
R
S
1
ω
Q
L
R
=
P
P
G
P
1
−
J
P
ω
C
S
Table 3-5: Equivalent Circuits
The equivalent circuits are shown in Table 3-5, to-
gether with useful equations relating them. Notice
that the Digibridge measures the equivalent series
components Rs, 15, or Cs, if you select SERIES
EQUIVALENT CIRCUIT. It measures the parallel
equivalent components Rp , Lp, or Cp if you select
PARALLEL. D and Q have the same value regard-
less whether series or parallel equivalent circuit is
calculated.
Resistance and Capacitance
1
X
=
−
S
ω
C
S
j
ω
L
Z
=
R
−
P
S
ω
C
L
S
P
1
δ
D
=
−
=
tan
Q
C
=
C
1 (
+
D
2
)
S
P
D
2
R
=
R
S
p
1 +
D
2
D
R
=
S
ω
C
S
B
ω
C
=
P
P
1693 RLC Digibridge
R
D
2
R
Z
=
P
Z
=
P
j
ω
R
C
1
+
P
P
1
D
ω
R
C
=
D
=
S
S
ω
R
p
1
C
C
=
P
S
2
1
+
D
1 +
D
2
R
=
R
S
S
D
2
1
1
R
=
R
=
P
P
ω
C
D
G
P
P
ω
Y
=
G
+
j
C
P
P
ω
+
/ ( 1
j
C
)
P
D
2
1
+
C
p
35
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