|Z| =
Rs
2
+
Xs
2
Rs = |Zs| cosθ
Xs = |Zs| sinθ
Xs/Rs = tanθ
θ
= tan
-1
(Xs/Rs)
If
θ
> 0, the reactance is inductive. In other words, if
θ
< 0, the reactance is capacitive.
There are two types for reactance. The one is the inductive reactance X
L
and the
other is the capacitive reactance X
C
. They could be defined as: (f = signal frequency)
X
L
= 2πf L (L = Inductance)
X
C
=
1
(C = Capacitance)
2
π
f
C
Measurement mode
The impedance could be measured in series or parallel mode. The impedance
Z
in
parallel mode could be represented as reciprocal of admittance
Y.
The admittance could
be defined as Y = G + jB. The G is the conductance and the B is the susceptance.
Impedance in serial mode
Rs
jXs
Admittance in parallel mode
Rp
Z = Rs + jXs
Rs: Resistance in series mode
Xs: Reactance in series mode
Cs: Capacitance in series mode
Ls: Inductance in series mode
jXp
Rp: Resistance in parallel mode
Xp: Reactance in parallel mode
Cp: Capacitance in parallel mode
Lp: Inductance in parallel mode
Y = 1/Z = 1/Rp + 1/jXp = G + jB
There are two factors to provide the ratio of real part and imaginary part. Usually
the quality factor
Q
is used for inductance measurement and the dissipation factor
D
is
used for capacitance measurement.
D
factor is defined as a reciprocal of
Q
factor.
Q = 1 / D = tanθ
Q = Xs / Rs = 2πf Ls / Rs = 1 / 2πf Cs Rs
Q = B / G = Rp / | Xp | = Rp / 2πf Lp = 2πf Cp Rp
Ver 2.1
3
12/03/01
CYRUSTEK [ Cyrustek corporation ]
