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

Ahmed El Moutaouakil

EE 484: Properties and

synthesis of L-C networks 

Instructor: Iickho Song

October 18th 2007

Introduction to LC networksLinear Electric Elements - C, L

LC Circuit Impedance Analysis

Applicationsoscillatorsfilters

• 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:

C

jZC

Impedance: 2_

I

V

• 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:

Voltage :

jLZL Impedance:2

I

V

• Linear Electric Elements - C, L:

Introduction to LC networks

• Impedance:

Series LC:

LC Circuit:

Lc ZZZ

IF then 12 LC 0Z So,

Parallel LC:

• Analysis: (Ideal parallel LC)

LC Circuit:

How do we find the current quantitatively?– Charging Capacitor C:

Or,

And

C

QVc

dt

dQi

dtiC

Vc .1

cj

Zc

1 2

1

• Analysis: (Ideal parallel LC)

LC Circuit:

How do we find the current quantitatively?– Discharging Capacitor C:Kirchhoff’s Law:

So,

Or,

Finally :

0

0

dt

dIL

C

Q

V LC E

QLCdt

Qd

dt

QdL

C

Q 10

2

2

2

2

dt

dQi

2

2

• Analysis: (Ideal parallel LC )

LC Circuit:

How do we find the current quantitatively?We have obtained:

Simple Harmonic Motion :

Where,

02

2

dt

QdL

C

Q

tQdt

dQtI

tQtQ

00

00

sin)(

cos)(

LC

10

Q0: Amplitude of Charge Oscillation φ: Phase (time offset)

• Analysis: (Ideal parallel LC )

LC Circuit:

What about the Energy?

Using

Finally:

ttC

Q

tLItC

Q

tQLtC

Q

UUU LC

2220

22max2

1220

2202

1220

sincos2

sincos2

sincos2

2max2

120

2LI

C

Q

Total energy is conservedSimulation

• Analysis:

LC Circuit:

Now, what if we add a resistor?We have:

Resolved by:

Where

02

2

dt

QdL

dt

dQR

C

Q

RteQtQ dLRt smallfor cos2

0

2

2

1

L

R

LCd

Resistor dissipates energy and system rings down over time

• Oscillators:

Colpitts oscillator

Hartley oscillator

What is the common point between those oscillator?

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.

Application:

• Oscillators:Colpitts oscillator

Application:

LC

10

21

0111

1

CCL

)arg()arg( 12 cc VV

2

1

1

2

C

C

V

V

c

c

In the experiment the LCcircuit is alimented by a voltage source, so it resonates only at

f=f0.

• Oscillators:Colpitts oscillator

Application:

The ideal frequency of oscillation is given by this equation :

• Oscillators:Hartley oscillator

Application:

The ideal frequency of oscillation is given by this equation :

• Filters:Series/Parallel LC Circuit

Application:

Pass-Band filter

Stop-Band

filter

• Filters:Others configuration

Application:

Low-Pass

filter

High-Pass

filter

?

Quiz: