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EE 484: Properties and synthesis of L-C networks

Learn about LC circuits, impedance analysis, and applications like oscillators and filters in this detailed course by Ahmed El Moutaouakil. Understand linear electric elements, inductance, energy conservation, and circuit analysis principles. Explore various oscillator types and filter configurations.

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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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