Resonant Circuits

UNIT 5

RESONANT CIRCUITS

1. Introduction

A.C Circuits made up of resistors, inductors and capacitors are said to be resonant circuits whenthe current drawn from the supply is in phase with the impressed sinusoidal voltage. Then

1. The resultant reactance or susceptance is zero.

2. The circuit behaves as a resistive circuit.

3. The power factor is unity.

A second order series resonant circuit consists of L,RandC in series. At resonance, voltagesacross Land C are equal and opposite and these voltages are many times greater than the appliedvoltage. They may present a dangerous shock hazard.A second order parallel resonant circuit consists of L,RandC in parallel. At resonance,currents in L andC are circulating currents and they are considerably larger than the input current.Unless proper consideration is given to the magnitude of these currents, they may become verylarge enough to destroy the circuit elements.Resonance is the phenomenon which finds its applications in communication circuits: Theability of a radio or Television receiver

(1) To select a particular frequency or a narrow band offrequencies transmitted by broad casting stations.

(2) To suppress a band of frequencies fromother broad casting stations, is based on resonance.

Thus resonance is desired in tuned circuits, design of filters, signal processing and controlengineering. But it is to be avoided in other circuits. It is to be noted that if R=0 in a seriesRLC circuit, the circuits acts as a short circuit at resonance and if R = ∞in parallel RLCcircuit,the circuit acts as an open circuit at resonance.

2. Transfer Functions

As ω is varied to achieve resonance, electrical quantities are expressed as functions of ω, normallydenoted by F(jω) and are called transfer functions. Accordingly the following notations are used.

If we put jω = s then the above quantities will be Z(s), Y (s), G(s), α(s) respectively. Theseare treated later in this book.

3. Series Resonance

Fig.1 represents a series resonant circuit.Resonance can be achieved by

1. Varying frequency ω

2. Varying the inductance L

3. Varying the capacitance C

The phasor diagram for this condition is shown in Fig.2.The variation of current with frequency is shown in Fig.3.

It is observed that there are two frequencies, one above and the other below the resonantfrequency, ω0 at which current is same. Fig. 4 represents the variations of

From the equation

We see that any constant product of L and C give a particularresonant frequency even if the ratio L/Cis different. The frequency of a constant frequency sourcecan also be a resonant frequency for a number of L and C combinations. Fig.5 shows how thesharpness of tuning is affected by different L/Cratios, but the product LC remaining constant.

For larger L/C ratio, current varies more abruptly in the region of ω0. Many applications call fornarrow band that pass the signal at one frequency and tend to reject signals at other frequencies.