Basic Electronics Ninth Edition Basic Electronics Ninth Edition ©2002 The McGraw-Hill Companies Grob Schultz

Basic Electronics Ninth Edition Basic Electronics Ninth Edition ©2003 The McGraw-Hill Companies 26 CHAPTER Resonance

Topics Covered in Chapter 26  The Resonance Effect  Series Resonance  Parallel Resonance  Resonant Frequency  Q Magnification Factor of Resonant Circuit 

Topics Covered in Chapter 26 (continued)  Bandwidth of Resonant Circuit  Tuning and Mistuning  Analysis of Parallel Resonant Circuits  Damping of Parallel Resonant Circuits  Choosing L and C for a Resonant Circuit

Series Resonant Circuit L C where: f r = resonant frequency in Hz L = inductance in henrys C = capacitance in farads

5 A R = 4  20 V 5 kHz For a given coil and capacitor, there is only one f r. At resonance, X L = X C. The reactances are phasor opposites, so they cancel. This leaves only resistance to limit current flow at f r. The current is maximum at resonance. The impedance is minimum at resonance. A Series Resonant Circuit I r = 20/4 = 5 A kHz FmHxLC f r   1 mH 1  F

5 A R = 4  X C = 31  X L = 31  20 V 5 kHz Resonant Rise in V L and V C I r = 20/4 = 5 A V L = I x X L = 155 V V C = I x X C = 155 V Note: The reactive voltages are phasor opposites and they cancel (V X L +V X C = 0).

Frequency in kHz Current in A 4  20 V 1  F 1 mH kHz xxx LC f r     Frequency Response f

Frequency in kHz Current in A 4  20 V 1  F 1 mH Bandwidth  S L r X Q Hz x Q f BW r  Half-power point BW

Frequency in kHz Current in A 4  20 V 1  F 1 mH Increasing the L/C Ratio Raises the Q Half-power point 4  20 V 0.25  F 4 mH Q = 7.8Q = 32

5 A R = 4  L 20 V 5 kHz Resonant Rise in V L and V C 4  0.25  F 4 mH Q = 32 5 A 20 V 5 kHz V L = I x X L = 640 V V C = I x X C = 640 V 32 x 20 V = 640 V V L = I x X L = 155 V V C = I x X C = 155 V 7.8 x 20 V = 155 V Q =  F 1 mH QV S = V X

where: f r = resonant frequency in Hz L = inductance in henrys C = capacitance in farads L C Parallel Resonant Circuit LC f r  2 1  [Ideal; no resistance]

Resonant Frequency The equations for f r for real series and parallel circuits are approximately the same. Series Resonance: Parallel Resonance: Comparison of Series and Parallel Resonance LC f r  2 1  f r  2 1 

20 V 5 kHz R = 1 k  C = 1  F L = 1 mH A Parallel Resonant Circuit At resonance, X L = X C and I L = I C. The reactive currents are phasor opposites, so they cancel. The total current flow is set by the resistive branch. The current is minimum at resonance. The impedance is maximum at resonance. I T = 20 mA I = 20/1000 = 20 mA

Reactance above, at, and below resonance: Series Resonance:  Inductive above f r  Resistive at f r  Capacitive below f r Parallel Resonance:  Capacitive above f r  Resistive at f r  Inductive below f r Comparison of Series and Parallel Resonance

Frequency in kHz I T in A 20 V R = 1 k  C = 1  F L = 1 mH Frequency Response InductiveCapacitive

Current, phase angle, and impedance at resonance: Series Resonance:  I is maximum   is 0°  impedance is minimum Parallel Resonance:  I is minimum   is 0°  Impedance is maximum Comparison of Series and Parallel Resonance

Resonant Rise in I C and I L  L P X R Q 20 V 5.03 kHz R = 1 k  C = 1  F L = 1 mH 632 mA 20 mA I C = QI T = 31.6 x 20 mA = 632 mA I L = QI T = 31.6 x 20 mA = 632 mA mA x R V II S RT 

Q and Bandwidth (BW) at resonance: Series Resonance:  Q = X L /r s or Q = V out / V in  BW =  f = f r / Q Parallel Resonance:  Q = X L /r s or Q = R P /X L or Q = Z max / X L  BW =  f = f r / Q Comparison of Series and Parallel Resonance

Q is often established by coil resistance  S L r X Q 20 V 5.03 kHz C = 1  F L = 1 mH r S = 1 

Time in ms R = 1 k  C = 1  F L = 1 mH 0 Amplitude Damping resistor R = 100 