Protek Z9216 - Quality Factor

Quality Factor
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. Mathematically, the definition is
1
Q = 2π (max. energy stored) ÷ (energy dissipated per Hz) (10a)
= 2π f (max. energy stored) ÷ (average power dissipated) (10b)
Since the average power dissipated in the inductor with series resistance R is |I|
2
R and the maximum
energy stored in the inductor is L|I|
2
, the quality factor for an inductor is given by
Q = ωL / R. (11a)
By equating (8a) and (8b), the series equivalent circuit parameters R and L can be expressed in terms
of the parallel parameters R
p
and L
p
. When that is done and substituted in equation (10a), we find that
the quality factor also is written
Q = R
p
/ ωL
p
. (11b)
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 capacitance of a capacitor are,
respectively, R and C as in Figure 1-1, then (10b) is evaluated to be
Q = 1 / ωCR. (12a)
By equating (9a) and (9b), the series equivalent circuit parameters R and C can be expressed in terms
of the parallel parameters R
p
and C
p
. When that is done and substituted in equation (12a), we find that
the quality factor for a capacitor also is written
Q = ωC
p
R
p
. (12b)
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1
W. L. Everett and G. E. Anner, Communication Engineering, McGraw-Hill, New York, 1956.