Lect14

Analysis Methods for Transient Circuits

Dr. Holbert March 17, 2008 EEE 202 1

Impedance, Z

Using Ohm’s Law, impedance (Z) can be defined via: V = I Z Circuit Element Resistor Capacitor Inductor Impedance (ohms) R 1 / (sC) sL Lect14 EEE 202 2

LC Behavior

• Recall some facts on the behavior of LC elements • Inductors (L): – The current in an inductor cannot change abruptly in zero time; an inductor makes itself felt in a circuit only when there is a changing current – An inductor looks like a short circuit to d.c.

• Capacitors (C): – The voltage across a capacitor cannot change discontinuously; a capacitor makes itself felt only when there exists a changing potential (voltage) difference – A capacitor looks like an open circuit to d.c.

Lect14 EEE 202 3

Step-by-Step Approach

1. Assume solution (only dc sources allowed):

x

(

t

) = K 1 + K 2 e

-t/

 2. At

t

=0 – , draw the circuit with

C

or

L

as open circuit as short circuit; find V C (0 – ) or I L (0 – ) 3. At

t

=0 + , redraw circuit and replace

C

or

L

with appropriate source of value obtained in step #2, and find

x

(0)=K 1 +K 2 4. At

t

=  , repeat step #2 to find

x

(  )=K 1 Lect14 EEE 202 4

Step-by Step Approach (cont’d)

5.

6.

Find time constant (  ) Looking across the terminals of the

C

or

L

element, form Thevenin equivalent circuit;  =R Th C or  =L/R Th Finish up Simply put the answer together This is essentially the inspection method except it is expressed in a systematic procedure Lect14 EEE 202 5

Class Examples

• Drill Problems P6-6, P6-7, P6-8, P6-13, P6-14 – We’ll use the inspection (step-by-step) approach for P6-7 and P6-8 Lect14 EEE 202 6