Specifications

Though series and parallel mode impedance values are identical, the reactance (Xs), is not equal to
reciprocal of parallel susceptance (Bp), except when Rs = 0 and Gp = 0. Also, the series resistance
(Rs), is not equal to parallel resistance (Rp) (or reciprocal of Gp) except when Xs = 0 and Bp = 0.
From the definition of Y = 1/Z, the series and parallel mode parameters, Rs, Gp (1/Rp), Xs, and Bp
are related with each other by the following equations:
Z = Rs + jXs = 1/Y = 1/(Gp + jBp) = Gp/(Gp
2
+ Bp
2
) – jBp/(Gp
2
+ Bp
2
)
Y = Gp + jBp = 1/Z = 1/(Rs + jXs) = Rs/(Rs
2
+ Xs
2
) – jXs/(Rs
2
+ Xs
2
)
Rs = Gp/(Gp
2
+ Bp
2
) ) Rs = RpD
2
/(1 + D
2
)
Gp = Rs/(Rs
2
+ Xs
2
) ) Rp = Rs(1 + 1/D
2
)
Xs = –Bp/(Gp
2
+ Bp
2
) ) Xs = Xp/(1 + D
2
)
Bp = –Xs/(Rs
2
+ Xs
2
) ) Xp = Xs(1 + D
2
)
Table 1-3 shows the relationships between the series and parallel mode values for capacitance,
inductance, and resistance, which are derived from the above equations.
Table 1-3. Relationships between series and parallel mode CLR values
Series Parallel Dissipation factor
(Same value for series and parallel)
Capacitance Cs = Cp(1 + D
2
) Cp = Cs/(1 + D
2
) D = Rs/Xs = wCsRs
D = Gp/Bp = Gp/(wCp) = 1/(wCpRp)
Inductance Ls = Lp/(1 + D
2
) Lp = Ls(1 + D
2
) D = Rs/Xs = Rs/(wLs)
D = Gp/Bp = wLpGp = wLp/Rp
Resistance Rs = RpD
2
/(1 + D
2
) Rp = Rs(1 + 1/D
2
) –––––
Cs, Ls, and Rs values of a series equivalent circuit are different from the Cp, Lp, and Rp values of a
parallel equivalent circuit. For this reason, the selection of the measurement circuit mode can
become a cause of measurement discrepancies. Fortunately, the series and parallel mode measure-
ment values are interrelated by using simple equations that are a function of the dissipation factor
(D.) In a broad sense, the series mode values can be converted into parallel mode values and vice
versa.
Gp
±jBp
Rs
±jXs
1-11