RESONANT CIRCUIT

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RESONANT CIRCUIT Characteristics of RLC circuits
SEE 1023 Circuit Theory
Dr. Nik Rumzi Nik Idris
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Resonant circuits different from one another
based on their resonant characteristics
Resonant frequency, ?o
Half Power frequencies ?1 ?2
Bandwidth, BW
Quality Factor, Q
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Resonant circuits different from one another
based on their resonant characteristics
Resonant frequency, ?o
Half Power frequencies ?1 ?2
Bandwidth, BW
Quality Factor, Q
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Series RLC
Resonant frequency, ?o
Resonant occurs when imaginary part of impedance
0
0
rad/s
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Resonant frequency, ?o
Half Power frequencies ?1 ?2
Bandwidth, BW
Quality Factor, Q
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Half Power frequencies ?1 ?2
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Half Power frequencies ?1 ?2
Series RLC
If V fixed, I maximum when Z minimum
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Half Power frequencies ?1 ?2
I max
If V fixed, I maximum when Z minimum
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Half Power frequencies ?1 ?2
I max
If V fixed, I maximum when Z minimum
10
Half Power frequencies ?1 ?2
Pmax
P
I max
If V fixed, I maximum when Z minimum
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Half Power frequencies ?1 ?2
Pmax
P
Io
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Half Power frequencies ?1 ?2
Pmax
P
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Half Power frequencies ?1 ?2
Pmax
P
Question At what frequencies will the half of
maximum power occur?
?
?
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Half Power frequencies ?1 ?2
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Half power frequencies ?1 ?2
At half power, Z
?1
?2
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Half power frequencies ?1 ?2
These are the half power frequencies
?1
?2
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Half power frequencies ?1 ?2
?1
?2
?1 and ?2 are NOT symmetrical around ?o
(geometric mean of ?1 and ?2)
However, note that
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Resonant frequency, ?o
Half Power frequencies ?1 ?2
Bandwidth, BW
Quality factor, Q
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Series RLC
Io
Bandwidth, BW
?1
?2
Bandwidth, BW difference between the two
half-power frequencies
BW ?2 ? ?1
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Bandwidth, BW
Series RLC
BW
rad/s
Also known as half-power bandwidth
BW ?2 ? ?1
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Half power frequencies ?1 ?2
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Half power frequencies ?1 ?2
Reduce R by half, i.e. R 2.5?
Double L, i.e. L 0.02H
BW
BW
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Resonant frequency, ?o
Half Power frequencies ?1 ?2
Bandwidth, BW
Quality Factor, Q
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Quality Factor, Q
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Quality Factor, Q
Series RLC
To measure the sharpness of the curve
quantitatively
Peak energy stored in the circuit occur at
resonance
Energy dissipated in one cycle (only due to R)
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Quality Factor, Q
Series RLC
To measure the sharpness of the curve
quantitatively
2??
Q
Peak energy stored in the circuit occur at
resonance
Energy dissipated in one cycle (only due to R)
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Quality Factor, Q
Series RLC
Other form of Q
In terms of BW, Q can be written as
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Quality Factor, Q
Series RLC
It can be shown that for Qgtgt1, (i.e. Q??10) the
half power frequencies are symmetrical around the
resonant frequency
e.g
R10? L 0.01H and C100?F ? Q 1
R0.5? L 0.01H and C100?F ? Q 20
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Quality Factor, Q
Series RLC
Q 1
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Quality Factor, Q
Series RLC
Q 20