1. Ahmed El Moutaouakil EE 484: Properties and synthesis of L-C networks Instructor: Iickho Song October 18 th 2007

2. Introduction to LC networks Linear Electric Elements - C, L LC Circuit Impedance Analysis Applications oscillators filters

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

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

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

6. Impedance: Series LC: LC Circuit: IF thenSo, Parallel LC:

7. Analysis: (Ideal parallel LC) LC Circuit: How do we find the current quantitatively? –Charging Capacitor C: Or, And 12 1

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

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

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

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

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

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

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

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

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

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

19. ? Quiz: