CHAPTER 4 RESONANCE CIRCUIT EET 206 ELECTRICAL CIRCUIT

CHAPTER 4 RESONANCE CIRCUIT EET 206 - ELECTRICAL CIRCUIT II 1

CHAPTER OUTLINE �SERIES RESONANCE �PARALLEL RESONANCE 2

RESONANCE Resonance is a condition in an RLC circuit in which the capacitive and inductive reactance are equal in magnitude, thereby resulting in a purely resistive impedance. Resonance also known as center frequency. The features of resonance: • • The impedance is purely resistive, Z = R; The supply voltage Vs and the current I are in phase, so cos q = 1; The magnitude of the transfer function H(ω) = Z(ω) is minimum; The inductor voltage and capacitor voltage can be much more than the source voltage. EET 206 - ELECTRICAL CIRCUIT II 3

APPLICATION �TV RECEIVER �RADIO RECEIVER �TUNED AMPLIFIER EET 206 - ELECTRICAL CIRCUIT II 4

IMPORTANT PARAMETER IN RESONANCE • • Resonance Frequency, ωo Half-power frequencies, ω1 and ω2 Bandwidth, Quality Factor, Q EET 206 - ELECTRICAL CIRCUIT II 5

SERIES RESONANCE EET 206 - ELECTRICAL CIRCUIT II 6

Resonance results when imaginary part of the transfer function is zero. Value of ω satisfies this condition is called resonant frequency, ω0. EET 206 - ELECTRICAL CIRCUIT II 7

�The frequency response of the circuit’s current magnitude: 8

Average power dissipated by RLC circuit is: Power at resonance: At certain frequency, ω= ω1, ω2, the dissipated power is half the maximum value. Hence ω1 and ω2 are called the half-power frequencies. 9

�Quality factor, Q is ratio of its resonant frequency to its bandwidth. A higher value of Q will result a smaller bandwidth. A lower value of Q will cause a larger bandwith. �Bandwidth, B: 10

SELECTIVITY • • • Selectivity defines how well a resonance circuit response to a certain frequency and reject against all others. A smaller/narrower the bandwidth, the greater selectivity A larger/wider the bandwidth, the least selectivity. 11

A resonant circuit is designed to operate at or near its resonant frequency. It is high-Q circuit when its quality factor is equal to or greater than 10. When , the half-power frequencies are: 12

EXAMPLE In the circuit below, R = 2Ω, L = 1 m. H, and C = 0. 4 μF. a) Find the resonant frequency and the half-power frequencies b) Calculate the quality factor and bandwidth c) Determine the amplitude of the current at ω0, ω1 and ω 2. 13

SOLUTION (a) The resonant frequency is METHOD 1: The lower half-power frequency is Similarly, the upper half-power frequency is 14

(b) The bandwidth is The quality factor is 15

METHOD 2: Alternatively, we could find From Q we find Since Q > 10, this is a high-Q circuit and we can obtain the half-power frequencies as 16

17

PARALLEL RESONANCE 18

�Resonance occurs when the imaginary part of Y is zero; 19

�The current amplitude vs frequency for parallel circuit: 20

�Replace R, L & C in expressions for series circuit with 1/R, C & L. �High-Q circuit 21

PARALLEL RESONANCE If R=8 kΩ, L=0. 2 m. H and C=8 F, calculate n ωo n Q and n ω1 and ω2 n Power dissipated at ωo, ω1 and ω2. 22

PARALLEL RESONANCE Solution : Resonant frequency Bandwidth Quality Factor 23

PARALLEL RESONANCE Since Q ≥ 10 , we can regard this as high-Q circuit. Hence : 24

PARALLEL RESONANCE Power dissipated at ω = ωo Power dissipated at ω = ω1 , ω2 25

Summary of the characteristic of resonant RLC circuits CHARACTERISTIC SERIES CIRCUIT PARALLEL CIRCUIT Resonant frequency, ω0 Quality factor, Q Bandwidth, B Half-power frequency, ω1 ω2 For 26