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RLC Circuits and Resonance

RLC Circuits and Resonance. Analog Circuits I. Series LC Circuit Characteristics. I L = I C V L and V C are 180 ° out of phase V S =V L - V C. Series LC Circuit Characteristics. Voltage Relationships and Phase Angles. Series LC Circuit Characteristics.

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RLC Circuits and Resonance

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  1. RLC Circuits and Resonance Analog Circuits I

  2. Series LC Circuit Characteristics • IL = IC • VLand VC are 180° out of phase • VS =VL - VC

  3. Series LC Circuit Characteristics • Voltage Relationships and Phase Angles

  4. Series LC Circuit Characteristics • Voltage Relationships and Phase Angles (Continued) • Example: VL = 6 V and VC = 2 V • Circuit is inductive • Example: VL= 1 V and VC = 4 V • Circuit is capacitive

  5. Series Reactance (XS) • XS = j(XL – XC)= XL<90 – XC<-90

  6. Putting It All Together • Basic Series LC Circuit Characteristics

  7. Parallel LC Circuit Characteristics • VL = VC • IL and IC are 180° out of phase

  8. Parallel LC Circuit Characteristics • Current Relationships and Phase Angles

  9. Parallel LC Circuit Characteristics • Current Relationships and Phase Angles (Continued) • Example: IL= 5 mA and IC = 8 mA • Circuit is capacitive • Example: IL= 6 mA and IC = 2 mA • Circuit is inductive

  10. Parallel LC Circuit Characteristics • Parallel Reactance (XP)

  11. Putting It All Together • Basic Parallel LC Circuit Characteristics

  12. Resonance • Inductive and Capacitive Reactance • Resonant Frequency: Occurs when XL = XC

  13. Factors Affecting the Value of fr • Stray Inductance • Stray Capacitance • Oscilloscope Input Capacitance

  14. Factors Affecting the Value of fr • Oscilloscope Input Capacitance

  15. Series Resonant LC Circuits • Total reactance of series resonant circuit is 0  • Voltage across series LC circuit is 0 V • Circuit current and voltage are in phase; that is the circuit is resistive in nature

  16. Series Resonant LC Circuits (Continued)

  17. Parallel Resonant LC Circuits • The sum of the currents through the parallel LC circuit is 0 A • The circuit has infinite reactance; that is, it acts as an open

  18. Parallel Resonant LC Circuits (Continued)

  19. Series Versus Parallel Resonance: A Comparison

  20. Series RLC Circuits

  21. Series Circuit Frequency Response • When Fo < Fr • XC>XL • ZT is capacitive • Current IT leads voltage VS • When Fo= Fr (in resonance) • XC=XL • ZT is resistive • Current and voltage in phase • When Fo> Fr • XC < XL • ZT is inductive • Voltage VSleads current IT

  22. Series RLC Circuit • Series Voltages: VLC = VL<90 + VC<-90

  23. Series RLC Circuit • Series Voltages (Continued) where VS = the source voltage VLC = the net reactive voltage VR = the voltage across the resistor

  24. Parallel RLC Circuits

  25. Parallel RLC Circuits

  26. Total Parallel Current where IS = the source current ILC = the net reactive current, ILC = IC - IL IR = the current through the resistor

  27. Parallel RLC CircuitsFrequency Response • When Fo < Fr • IL>IC • ILC is inductive • Current IT lags voltage VS • When Fo= Fr (in resonance) • IL=IC • ILC =0 A • Current and voltage in phase • When Fo> Fr • IL<IC • ILCis Capacitive • Voltage VS lags current IT

  28. Series-Parallel RLC Circuit Analysis

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