Lecture 15
The analysis of the RLC series resonant circuit is continued.
This lecture covers:
•
The dependence of impedance and current on frequency
•
Concepts of band frequency, cut-off frequency and half
power frequency
•
Expressions for band frequencies
•
Relationship of quality factor with bandwidth
•
Expressions for selectivity
Total impedance (Z
T
) versus frequency
C
R
L
E
s
I
Z
T
Fig. 15-1: Series resonant circuit
We have seen that the total impedance of a series RLC circuit at any
frequency is,
T
L
L
C
Z
R
JX
JX
=
+
−
The magnitude and phase angle of impedance as a function of
frequency can be written as,
2
2
(
)
[
(
)]
[
(
)
(
)]
T
L
C
Z
f
R f
X
f
X
f
=
+
−

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Here, Z
T
(f) means the total impedance as a function of frequency.
The changes of the various terms
R, X
L
, X
C
,
total
X, Z
T
as a function
of frequency are shown in the following figures.
f
0
R(f)
R
Fig. 15-2(a) R as function of frequency
We know the resistance of a circuit does not change with frequency