Wayne 4310 - Series;Parallel Conversions; Polar Derivations

Theory Reference 8–2
values)C L, R, (series RC
L
R
D
SS
S
S
ω=
ω
=
convention allelseries/par of regardlessconstant is
D
1
Q valueThe :Note =
8.3 Series/Parallel Conversions
( )
2
P
S
Q 1
R
R
+
=
(
)
2
SP
Q 1R R +=
(
)
2
PS
D 1 C C +=
( )
2
S
P
D 1
C
C
+
=








+
=
2
P
S
Q
1
1
L
L








+=
2
SP
Q
1
1L L
Conversions using the above formulae will be valid only at the test frequency.
8.4 Polar Derivations
θ= cos Z R
S
θ= cos Y G
P
θ= sin Z X
S
θ= sin Y B
P
Note that, by convention, +ve angle indicates an inductive impedance or capacitive admittance.
If capacitance is measured as inductance, the L value will be –ve.
If inductance is measured as capacitance, the C value will be –ve.
D = tan δ where δ = (90 – θ)˚ admittance measurement.
δ
=
tan
1
Q
where δ = (90 – θ)˚ impedance measurement.