Page 86 - Circuit Analysis II with MATLAB Applications

Chapter 2 Resonance

or

1
3
Y 740 KHz = 5.24 u 10 – 6 2 + § © 2S u 740 u 10 u 77.2 u 10 – 12 – ------------------------------------------------------------------- 3¹ · 2
3
2S u 740 u 10 u 0.5 u 10 –
or
Y 740 KHz = 71.2 P: – 1
and
I
V 740 KHz = --------------------------- (2.40)
71.2 u 10 – 6
Then from (2.39) and (2.40),

V I5.24 ue 10 – 6 71.2 u 10 – 6
810 KHz
------------------------ = --------------------------------- = --------------------------- = 13.6 (2.41)
V 740 KHz I 71.2 ue 10 – 6 5.24 u 10 – 6
that is, the voltage developed across the parallel circuit when it is tuned at f = 810 KHz is 13.6
times larger than the voltage developed at f = 740 KHz .

2.10 Summary

x In a series RLC circuit, the frequency at which the capacitive reactance X = 1 ZC and the
e
C
inductive reactance X = ZL are equal, is called the resonant frequency.
L
f
x The resonant frequency is denoted as Z 0 or where
0
1
Z = -----------
0
LC
and
1
f = ------------------
0
2S LC
x The quality factor Q 0S at series resonance is defined as

Z L 1
0
Q 0S = --------- = --------------
R
Z RC
0
x In a parallel GLC circuit, the frequency at which the inductive susceptance B = 1 ZL and the
e
L
capacitive susceptance B C = ZC are equal is, again, called the resonant frequency and it is also
denoted as Z 0 As in a series RLC circuit, the resonant frequency is

2-20 Circuit Analysis II with MATLAB Applications

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