* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Download Chapter 21: Resonance
Negative resistance wikipedia , lookup
405-line television system wikipedia , lookup
Power MOSFET wikipedia , lookup
Standing wave ratio wikipedia , lookup
Surge protector wikipedia , lookup
Mathematics of radio engineering wikipedia , lookup
Flexible electronics wikipedia , lookup
Resistive opto-isolator wikipedia , lookup
Distributed element filter wikipedia , lookup
Mechanical filter wikipedia , lookup
Radio transmitter design wikipedia , lookup
Rectiverter wikipedia , lookup
Integrated circuit wikipedia , lookup
Wireless power transfer wikipedia , lookup
Crystal radio wikipedia , lookup
Wien bridge oscillator wikipedia , lookup
Switched-mode power supply wikipedia , lookup
Tektronix analog oscilloscopes wikipedia , lookup
Analogue filter wikipedia , lookup
Index of electronics articles wikipedia , lookup
Valve RF amplifier wikipedia , lookup
Regenerative circuit wikipedia , lookup
Chapter 21 Resonance Series Resonance • Simple series resonant circuit – Has an ac source, an inductor, a capacitor, and possibly a resistor • ZT = R + jXL – jXC = R + j(XL – XC) – Resonance occurs when XL = XC – At resonance, ZT = R 2 Series Resonance • Response curves for a series resonant circuit 3 Series Resonance 4 Series Resonance • Since XL = L = 2fL and XC = 1/C = 1/2fC for resonance set XL = XC – Solve for the series resonant frequency fs s fs 1 LC 1 (rad/sec) 2 LC (Hz) 5 Series Resonance • At resonance – Impedance of a series resonant circuit is small and the current is large • I = E/ZT = E/R 6 Series Resonance • At resonance VR = IR VL = IXL VC = IXC 7 Series Resonance • At resonance, average power is P = I2R • Reactive powers dissipated by inductor and capacitor are I2X • Reactive powers are equal and opposite at resonance 8 The Quality Factor,Q • Q = reactive power/average power – Q may be expressed in terms of inductor or capacitor I 2 X L X L L Qs 2 R R I R • For an inductor, Qcoil= XL/Rcoil 9 The Quality Factor,Q • Q is often greater than 1 – Voltages across inductors and capacitors can be larger than source voltage IX V Qs IR E 10 The Quality Factor,Q • This is true even though the sum of the two voltages algebraically is zero 11 Impedance of a Series Resonant Circuit • Impedance of a series resonant circuit varies with frequency Z T R j L j C 2 LC 1 Z R j T C Z T 2 R 2 LC 1 RC 2 LC 1 1 tan RC 2 12 Bandwidth • Bandwidth of a circuit – Difference between frequencies at which circuit delivers half of the maximum power • Frequencies, f1 and f2 – Half-power frequencies or the cutoff frequencies 13 Bandwidth • A circuit with a narrow bandwidth – High selectivity • If the bandwidth is wide – Low selectivity 14 Bandwidth • Cutoff frequencies – Found by evaluating frequencies at which the power dissipated by the circuit is half of the maximum power 15 Bandwidth I hpf I max 2 R R2 1 1 2 f 2 1 2L 4 L LC R R2 1 2 2 f 2 2 2 L 4 L LC 16 Bandwidth • From BW = f2 - f1 • BW = R/L • When expression is multiplied by on top and bottom – BW = s/Q (rad/sec) or BW = fs/Q (Hz) 17 Series-to-Parallel Conversion • For analysis of parallel resonant circuits – Necessary to convert a series inductor and its resistance to a parallel equivalent circuit RS 2 X LS RP RS RS X LS X LS 2 X LP 2 X LS RP Q RS X LP 2 18 Series-to-Parallel Conversion • If Q of a circuit is greater than or equal to 10 – Approximations may be made • Resistance of parallel network is approximately Q2 larger than resistance of series network – RP Q2RS – XLP XLS 19 Parallel Resonance • Parallel resonant circuit – Has XC and equivalents of inductive reactance and its series resistor, XLP and RS • At resonance – XC = XLP 20 Parallel Resonance • Two reactances cancel each other at resonance – Cause an open circuit for that portion • ZT = RP at resonance 21 Parallel Resonance • Response curves for a parallel resonant circuit 22 Parallel Resonance • From XC = XLP – Resonant frequency is found to be R 2C f 1 L 2 LC 1 23 Parallel Resonance • If (L/C) >> R – Term under the radical is approximately equal to 1 • If (L/C) 100R – Resonant frequency becomes f 1 2 LC 24 Parallel Resonance • Because reactances cancel – Voltage is V = IR • Impedance is maximum at resonance – Q = R/XC • If resistance of coil is the only resistance present – Circuit Q will be that of the inductor 25 Parallel Resonance • Circuit currents are V IR R V IL QPI XL V IC QPI XC 26 Parallel Resonance • Magnitudes of currents through the inductor and capacitor – May be much larger than the current source 27 Bandwidth • Cutoff frequencies are 1 1 1 1 2 2 2RC LC 4R C 1 1 1 2 2 2 2RC LC 4R C 28 Bandwidth • BW = 2 - 1 = 1/RC • If Q 10 – Selectivity curve becomes symmetrical around P 29 Bandwidth • Equation of bandwidth becomes X C P BW R BW P QP • Same for both series and parallel circuits 30