Raytech CAPO 2.5 - Conversion Series- Parallel-Replacement Circuit Diagram

Preliminary
6.2.3 Conversion series- parallel-replacement circuit diagram
The following formulas are helpful for the conversion of the two models:
where:
Cs serial Capacitance [F] Zs serial Impedance [Ω]
Cp parallel Capacitance [F] Zp parallel Impedance [Ω]
Rs serial Resistance [Ω] Xs serial reactance [Ω]
Rp parallel Resistance [Ω] Xp parallel reactance [Ω]
Z Impedance [Ω] ω angular frequency [s
-1
] ω=2*π*f
90315-1.2 Instruction Manual CAPO
Page 29 of 117
Cs = Cp∗(1+tan
2
δ)
Cp =
Cs
1+tan
2
δ
Cs =
Rp
2
∗ω
2
∗Cp
2
−1
Rp
2
∗ω
2
∗Cp
= Cp∗(1+tan
2
δ)
Cp =
√
Rp−Rs
Rs∗Rp
2
∗ω
2
=
Cs
1+tan
2
δ
Rs =
|
Z
2
|
Rp
=
Rp∗Xp
2
Rp
2
+Xp
2
=
Rp
Rp
2
∗ω
2
∗Cp
2
+1
=
Rp∗tan
2
δ
1+tan
2
δ
=
tan δ
ω∗Cs
Rp =
|
Z
2
|
Rs
=
√
Xp
2
∗Xs
Xp−Xs
=
1
ω∗Cp∗tan δ
= Rs∗(
1+tan
2
δ
tan
2
δ
)
Rp∗Rs =
|
Z
2
|
Z = Xs∗
√
1+tan
2
δ
Zp = Zs = Z
tan δ
serial
= tan δ
parallel
=
1
ω∗Rp∗Cp
= ω∗Rs∗Cs