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EE 484: Properties and synthesis of L-C networks

EE 484: Properties and synthesis of L-C networks. Ahmed El Moutaouakil. October 18 th 2007. Instructor: Iickho Song. Introduction to LC networks Linear Electric Elements - C, L LC Circuit Impedance Analysis Applications oscillators filters. Introduction to LC networks.

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EE 484: Properties and synthesis of L-C networks

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  1. EE 484: Properties and synthesis of L-C networks Ahmed El Moutaouakil October18th 2007 Instructor: Iickho Song

  2. Introduction to LC networksLinear Electric Elements - C, LLC Circuit Impedance AnalysisApplicationsoscillators filters

  3. Introduction to LC networks • Linear Electric Elements - C, L : • A capacitor consists of two conductive electrodes, or plates, separated by a dielectric. Capacitance (F): Current: Energy: Impedance:

  4. Introduction to LC networks • Linear Electric Elements - C,L : • An inductor is a passive electrical device employed in electrical circuits for its property of inductance. Voltage : L Impedance: Energy:

  5. Introduction to LC networks • Linear Electric Elements - C, L:

  6. LC Circuit: • Impedance: • Series LC: • Parallel LC: L So, IF then

  7. LC Circuit: • Analysis: (Ideal parallel LC) • How do we find the current quantitatively? • Charging Capacitor C: • Or, • And 1 1 2

  8. LC Circuit: • Analysis: (Ideal parallel LC) • How do we find the current quantitatively? • Discharging Capacitor C: • Kirchhoff’s Law: • So, • Or, • Finally : 2 2

  9. LC Circuit: • Analysis: (Ideal parallel LC ) • How do we find the current quantitatively? • We have obtained: • Simple Harmonic Motion : • Where, Q0: Amplitude of Charge Oscillation φ: Phase (time offset)

  10. LC Circuit: • Analysis: (Ideal parallel LC ) • What about the Energy? • Using • Finally: Simulation Total energy is conserved

  11. LC Circuit: • Analysis: • Now, what if we add a resistor? • We have: • Resolved by: • Where Resistor dissipates energy and system rings down over time

  12. Application: • Oscillators: • Colpitts oscillator • Hartley oscillator What is the common point between those oscillator?

  13. Application: • Oscillators: General description: An electronic oscillator is an electronic circuit that produces a repetitive electronic signal, often a sine wave or a square wave.

  14. Application: • Oscillators: Colpitts oscillator In the experiment the LCcircuit is alimented by a voltage source, so it resonates only at f=f0.

  15. Application: • Oscillators: Colpitts oscillator • The ideal frequency of oscillation is given by this equation:

  16. Application: • Oscillators: Hartley oscillator • The ideal frequency of oscillation is given by this equation:

  17. Application: • Filters: • Series/Parallel LC Circuit Pass-Band filter Stop-Band filter

  18. Application: • Filters: • Others configuration Low-Pass filter High-Pass filter

  19. Quiz: ?

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