Page 17 - Circuit Analysis II with MATLAB Applications

Response of Series RLC Circuits with DC Excitation

t=0: 0.01: 10; ft=210.*sqrt(2).*(exp( 0.5.*t)).*sin(sqrt(2).*t); plot(t,ft); grid; xlabel('t');...
ylabel('f(t)'); title('Underdamped Response for 210.*sqrt(2).*(exp( 0.5.*t)).*sin(sqrt(2).*t)')

Figure 1.4. Typical underdamped response

1.3 Response of Series RLC Circuits with DC Excitation

Depending on the circuit constants ,RL , and , the total response of a series RLC circuit that is
C
excited by a DC source, may be overdamped, critically damped, or underdamped. In this section we
will derive the total response of series RLC circuits that are excited by DC sources.

Example 1.1

For the circuit of Figure 1.5, i 0 = 5A , v 0 = 2.5 V , and the 0.5 : resistor represents the
L
C
resistance of the inductor. Compute and sketch it for t ! . 0

0.5 :

+ 1mH
it `
15u t V
0
100 6 mF
e
Figure 1.5. Circuit for Example 1.1

Solution:

This circuit can be represented by the integrodifferential equation

1-5 Circuit Analysis II with MATLAB Applications
Orchard Publications