Transcript Analysis Methods for Transient Circuits

Analysis Methods for
Transient Circuits
Dr. Holbert
March 17, 2008
Lect14
EEE 202
1
Impedance, Z
Using Ohm’s
Law, impedance
(Z) can be
defined via:
V=IZ
Lect14
Circuit
Element
Resistor
Capacitor
Inductor
EEE 202
Impedance
(ohms)
R
1 / (sC)
sL
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) = K1 + K2 e-t/
2. At t=0–, draw the circuit with C as open circuit
or L as short circuit; find VC(0–) or IL(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)=K1+K2
4. At t=, repeat step #2 to find x()=K1
Lect14
EEE 202
4
Step-by-Step Approach (cont’d)
5.
Find time constant ()
Looking across the terminals of the C or L element,
form Thevenin equivalent circuit; =RThC or =L/RTh
6.
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