Page 78 - Circuit Analysis II with MATLAB Applications

Chapter 2 Resonance

or

Z L
0
Q 0S = --------- (2.26)
R
and we observe that (2.26) is the same as (2.9). Similarly,

2 2
e
Maximum Energy Stored 12 I e p 1 Z C f
0
0
Q 0S = 2S------------------------------------------------------------------------------ = 2S------------------------------------------- = 2S--------------
Energy Dissipated per Cycle
2
2
Z RC

e
12 I Rfe
or p 0 0
Z 1
0
Q 0S = ---------------- = -------------- (2.27)
2
Z RC Z RC
0
0
and this is also the same as (2.9).
Following the same procedure for a simple GLC (or RLC ) parallel circuit we can show that:
Z C 1
0
Q 0P = ---------- = -------------- (2.28)
G
Z LG
0
and this is the same as (2.20).
2.7 Half-Power Frequencies - Bandwidth
Parallel resonance is by far more important and practical than series resonance and therefore, the
remaining discussion will be on parallel GLC (or RLC ) circuits.
The plot of Figure 2.12 shows the magnitude of the voltage response versus radian frequency for a
typical parallel RLC circuit.

Bandwidth in Parallel RLC Circuit
V p
Relative Voltage 0.707V p

Z
Z 1 Z 0 Z 2
Figure 2.12. Relative voltage vs.radian frequency in a parallel RLC circuit

2-12 Circuit Analysis II with MATLAB Applications

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