MECHANICAL DEPARTMENT

Elements of Electrical Engineering

ACTIVE LEARNING ASSIGNMENT

Topic: Resonance in series and parallel circuits

Guided by: Prof. Rahish

Gandhinagar Institute of Technology

Group MembersHardik Panchal (130120119115)Vivek Panchal (130120119122)Parth Panchal (130120119120)

ContentSeries ResonanceParallel ResonanceImportant Parameters

Resonance Frequency, o

Half-power frequencies, 1 and 2

Bandwidth, Quality Factor, Q

Application

IntroductionResonance is a condition in an RLC circuit

in which the capacitive and reactive reactance are equal in magnitude, thereby resulting in a purely resistive impedance.

Resonance circuits are useful for constructing filters and used in many application.

Series Resonance Circuit

At ResonanceAt resonance, the impedance consists only

resistive component R.The value of current will be maximum since

the total impedance is minimum.The voltage and current are in phase.Maximum power occurs at resonance since

the power factor is unity.

Series Resonance

CLTotal jX-jXRZ

R

V

Z

VI m

Total

sm

Total impedance of series RLC Circuit is

At resonance

The impedance now reduce to

CL XX

R ZTotal

)X-j(XRZ CLTotal

The current at resonance

Resonance FrequencyResonance frequency is the frequency where the condition of resonance occur.

Also known as center frequency.

Resonance frequency

rad/sLC

1ωo

HzLC2

1

of

Half-power Frequency

rad/sLC

1

2L

R

2L

Rω

2

2

rad/s

LC

1

2L

R

2L

Rω

2

1

Half-power frequencies is the frequency when the magnitude of the output voltage or current is decrease by the factor of 1 / 2 from its maximum value.

Also known as cutoff frequencies.

Bandwidth,

rad/s)( 12 cc ωωβ

rad/sL

Rβ

Bandwidth, is define as the difference between the two half power frequencies.The width of the response curve is determine by the bandwidth.

Current Response Curve

Voltage Response Curve

Quality Factor (Q-Factor)

The ratio of resonance frequency to the bandwidth

The “sharpness” of response curve could be measured by the quality factor, Q.

R

LQ oo

Q-Factor Vs BandwidthHigher value of Q,

smaller the bandwidth. (Higher the selectivity)

Lower value of Q larger the bandwidth. (Lower the selectivity)

Parallel Resonance

Parallel ResonanceThe total admittance

ωLωC

1

Resonance occur when

)ωω L1/Cj(R

1YTotal

321Total YYYY

C)(-j/

1

L)(j

1

R

1YTotal

CjωL

j-

R

1YTotal ω

At ResonanceAt resonance, the impedance consists only

conductance G.The value of current will be minimum

since the total admittance is minimum.The voltage and current are in phase.

Parameters in Parallel Circuit

rad/sLC

1

2RC

1

2RC

1ω

2

1

Parallel resonant circuit has same parameters as the series resonant circuit.

rad/sLC

1ωo

rad/sLC

1

2RC

1

2RC

1ω

2

2

Resonance frequency

Half-power frequencies

Parameters in Parallel Circuit

RCβ

ωQ o

o

RC

112 ωωβ

Bandwidth

Quality Factor

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