Table 8.3 Equations for analyzing the step response of parallel RLC circuits Characderistic oquation RC LC LC Neper, resonant, and damped frequencies a = = Va - a 2RC VLC Roos of the characteristic equation 51 = -a + Va - wi, 5= -a - Va - o a' > af: overdamped L) = , + Aje + Aje%, 120 0') = 1, + Aj + A; = , di (0") dt < ol: underdamped i0) = | + Be" cos o + Be" sin o4, 120 i(0*) = I, + B} = I, di (0") -aB + w,B; = dt %3D = o: cricaly damped in() = 1, + D'te*" + De, 120 i0) = 1, + D: = 1, di (0*) = Di - aD; = dt (Note that the equations in the last three rows assume that the
Table 8.3 Equations for analyzing the step response of parallel RLC circuits Characderistic oquation RC LC LC Neper, resonant, and damped frequencies a = = Va - a 2RC VLC Roos of the characteristic equation 51 = -a + Va - wi, 5= -a - Va - o a' > af: overdamped L) = , + Aje + Aje%, 120 0') = 1, + Aj + A; = , di (0") dt < ol: underdamped i0) = | + Be" cos o + Be" sin o4, 120 i(0*) = I, + B} = I, di (0") -aB + w,B; = dt %3D = o: cricaly damped in() = 1, + D'te*" + De, 120 i0) = 1, + D: = 1, di (0*) = Di - aD; = dt (Note that the equations in the last three rows assume that the
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
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If the response is overdamped, calculate s1 and s2 using the equations
in Table 8.3;
Transcribed Image Text:Table 8.3 Equations for
analyzing the step response of
parallel RLC circuits
Characderistic oquation
RC
LC LC
Neper, resonant, and damped frequencies a =
= Va - a
2RC
VLC
Roos of the characteristic equation
51 = -a + Va - wi, 5= -a - Va - o
a' > af: overdamped
L) = , + Aje + Aje%, 120
0') = 1, + Aj + A; = ,
di (0")
dt
< ol: underdamped
i0) = | + Be" cos o + Be" sin o4, 120
i(0*) = I, + B} = I,
di (0")
-aB + w,B; =
dt
%3D
= o: cricaly damped
in() = 1, + D'te*" + De, 120
i0) = 1, + D: = 1,
di (0*)
= Di - aD; =
dt
(Note that the equations in the last three rows assume that the
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