resonance in parallel rlc circuit

Seminar On Basic Electrical Engineering(TEE-201)

Topic:Parallel Resonance

Made By: Shivam Gupta Roll No.-33

Sec.-E

ContentsParallel Resonance •Parallel Resonance

Introduction •Introduction

Parallel RLC Circuit •Parallel RLC Circuit

Resonant Frequency •Resonant Frequency

Parallel Resonant Circuit •Parallel Resonant Circuit

Frequency Curve •Frequency Curve

Impedence Of a Parallel Resonant Circuit •Impedence Of a Parallel Resonant Circuit

Current In Parallel Resonant Circuit •Current In Parallel Resonant Circuit

Susceptance Of a Parallel Resonant Circuit •Susceptance Of a Parallel Resonant Circuit

Bandwidth Of a Parallel Resonant Circuit •Bandwidth Of a Parallel Resonant Circuit

Review •Review

PARALLEL RESONANCE

The resonance that results when circuit elements are connected with their inductance and

capacitance in parallel, so that the impedance of the combination rises to a maximum at the resonant

frequency.

INTRODUCTION

• The resonant electrical circuit must have both inductance and capacitance.

• In addition, resistance will always be present due either to the lack of ideal elements or to the control offered on the shape of the resonance curve.

• When resonance occurs due to the application of the proper frequency ( fr), the energy absorbed by one reactive element is the same as that released by another reactive element within the system.

Resonant Frequency

The frequency at which the inductive and capacitive reactances of a parallel resonant circuit are equal.

The frequency at which the parallel impedance of a parallel resonant circuit is maximum.

The frequency at which the parallel impedance of a parallel resonant circuit has a power factor of unity.

Calculation Of Resonant Frequency

Simple parallel resonant circuit (tank circuit).

Since we know the equations for determining the reactance of each element at a given frequency, and we're looking for that point where the two reactances are equal to each other, we can set the two reactance formulae equal to each other and solve for frequency algebraically.

XL=2πfL

XC=1/2πfC

Resonance occurs when XL = XC

This is a formula to tell us the resonant frequency of a tank circuit, given the values of inductance (L) in Henrys and capacitance (C) in Farads.

Phasor diag. for parallel resonant circuit.

Parallel resonant circuits

• A parallel resonant circuit is resistive at the resonant frequency.At resonance XL=XC, the reactive components cancel. The impedance is maximum at resonance.

• Below the resonant frequency, the parallel resonant circuit looks inductive since the impedance of the inductor is lower, drawing the larger proportion of current.

• Above resonance, the capacitive rectance decreases, drawing the larger current, thus, taking on a capacitive characteristic.

Capacitive

Frequency Curve For Parallel Resonance

Resistive

Inductive

Impedence Of A Parallel Resonant Circuit

Impedance is maximum at resonance in a parallel resonant circuit, but decreases above or below resonance. Voltage is at a peak at resonance since voltage is proportional to impedance (E=IZ).

Impedance peaks at resonance

Current In A Parallel Resonance Circuit

At resonance the current flowing through the circuit is at its minimum as the inductive and capacitive branch currents are equal ( IL = IC ) and are 180o out of phase.

We remember that the total current flowing in a parallel RLC circuit is equal to the vector sum of the individual branch currents and for a given frequency is calculated as:

At resonance, currents IL and IL are equal and cancelling giving a net reactive current equal to zero. Then at resonance the above equation becomes.

Susceptance At Resonance

The inductive susceptance, BL is inversely proportional to the frequency as represented by the hyperbolic curve.

The capacitive susceptance, BC is directly proportional to the frequency and is therefore represented by a straight line.

The final curve shows the plot of total susceptance of the parallel resonance circuit versus the frequency and is the difference between the two susceptances.

At the resonant frequency point were it crosses the horizontal axis the total circuit susceptance is zero.

Bandwidth Of A Parallel Resonant Circuit

BW = Δf = fh-fl = 343-281 = 62

fl = fc - Δf/2 = 312-31 = 281

fh = fc + Δf/2 = 312+31 = 343

Q = fc/BW = (312 Hz)/(62

Hz)=5 The bandwidth of the parallel resonant response curve is measured

between the half power points. This corresponds to the 70.7% voltage points since power is proportional to E2. ((0.707)2=0.50) Since voltage is proportional to impedance, we may use the impedance curve.

Review:

• At resonance parallel RLC circuit acts like an open circuit.• Current at resonance is at it’s minimum.• Impedence of the parallel resonant circuit is maximum and is equal to the

resistance.This resistance is known as dynamic resistance.• Susceptance At resonant frequency is equal to ZERO

THE END

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