RESONANCE

ELE101/102 Dept of E&E,MIT Manipal 2

SERIES RESONANCE - RLC Series Circuit

Is said to be in resonance, when

Current is in phase with voltage

Inductive reactance =Capacitive reactance; XL = XC

Circuit Power factor is unity

Effective Circuit impedance is resistive; Z = R

v(t), variable frequencyC

1XC

)XX(jRZ CL

LXL

ELE101/102 Dept of E&E,MIT Manipal 3

SERIES RESONANCEResonant frequency (f0):

Imaginary part of Zeq = 0

sec/radiansLC

1o

hertz 2

1

LCfo

CL XX

C

1L

00

LC

120

v(t), variable frequency

ELE101/102 Dept of E&E,MIT Manipal 4

Variation of reactance with frequency

ωo

X L=ωL

Z

XC=-1/ωC

R

ωo

ω0 is the resonance frequency.

Series Resonance

ELE101/102 Dept of E&E,MIT Manipal 5

SERIES RESONANCE

ωo ω

I

Imax

valuerms;R

VII maxo

Acceptor circuit

Variation of current

ELE101/102 Dept of E&E,MIT Manipal 6

Series Resonance - Half Power frequencies and Bandwidth

Band Width = ω2- ω1

ω1 = lower half power frequency

ω2 = upper half power frequency

ω1 ωo ω2

i

IO

2

Io

ω

2

II ,ωandωat Therefore, o

21

RI

RIPower o

2

20

22

1

Half Power Frequency =

Frequency at which the power is

half of the power at resonant

frequency

ELE101/102 Dept of E&E,MIT Manipal 7

Half power frequencies and Band Width

R

2

IV

Z and at pedanceImo

o21 2

LC

1

L2

R

L2

R2

1

)(Z1 LC XXjR

R2)XX(R 2LC

2

;RXX LC

RLC

11

1

At ω1:

ELE101/102 Dept of E&E,MIT Manipal 8

L

R 12 Then, 2

012

1 and

LC

)(Z2 CL XXjR

R)XX(R CL 222

;RXX CL

RC

L 2

2

1

LCL

R

L

R 1

22

2

2

At ω2:

Half power frequencies and Band Width

ELE101/102 Dept of E&E,MIT Manipal 9

Series Resonance: - Q-factor

Quality factor- a measure of selectivity

WidthBand

frequencyResonant

ωω

ω

L

R

ω

R

LωQ

12

ooo

;C

L

R

1

CRω

1

R

LωQ

o

o

Cω

1Lω resonanceat - :Note

oo