Quality Factors - Protek 9216A User Manual

The complex impedance of a capacitor is


Quality Factors

Originally, the quality factor Q was defined for an inductor as a measure of the efficiency
of energy storage in the inductor when an AC current is passed through it. Mathematical-
ly, the definition is
Since the average power dissipated in the inductor with series resistance R is |I|
the maximum energy stored in the inductor is L|I|
en by
By equating (8a) and (8b), the series equivalent circuit parameters R and L can be ex-
pressed in terms of the parallel parameters R
in equation (10a), we find that the quality factor also is written
While the concept of the quality factor was originally applied to inductors, it may be
extended so that the efficiency of energy storage in a capacitor may be expressed in
terms of the circuit components and frequency. Thus, if the series resistance and capaci-
tance of a capacitor are, respectively, R and C as in Figure 1-1, then (10b) is evaluated to
be
By equating (9a) and (9b), the series equivalent circuit parameters R and C can be ex-
pressed in terms of the parallel parameters R
in equation (12a), we find that the quality factor for a capacitor also is written
1
W. L. Everett and G. E. Anner, Communication Engineering, McGraw-Hill, New York, 1956.
Figure 1-1 Equivalent circuits for inductors and capacitors.


R / 1 j C

p p

 
R / 1 j C 1 j
p p
1
Q  2 (max. energy stored)  (energy dissipated per Hz)
 2 f (max. energy stored)  (average power dissipated)



R R 1 j

p p




C R
1 C
p p
p
2
, the quality factor for an inductor is giv-
Q L / R.
and L
p
Q R / L
.
p p
Q 1 / CR.
and C
p
6
(series equivalent circuit)

C R
p p
 (parallel equivalent)
2
R
p
. When that is done and substituted
p
. When that is done and substituted
p
(9a)
(9b)
(10a)
(10b)
2
R and
(11a)
(11b)
(12a)