Since all the energy starts out the capacitor
684 | C H A P T E R |
|
|
i n | s e c o n d - o r d e r |
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2. Since there is no drive, and since there is a dissipative element in the circuit, the final value of the capacitor voltage is given by
vC(∞) = 0 V.
4. | |||
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α = | 1 | ||
2RC | |||
ωo = | 1 √LC |
|
and the ringing frequency is
5. | ωd = | |||
---|---|---|---|---|
Q =ωo 2α |
The form of vC(t) can now be plotted as shown in Figure 12.59.
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vC(V) | 1.0 | VCM | 2 |
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R1 | C H A P T E R |
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685 | ||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
0.5 | v1 | v2 | ||||||||||
0.0 | ||||||||||||
-0.5 | -VCM | C1 | ||||||||||
R2 | C2 | |||||||||||
-1.0 | 3 | 4 | ||||||||||
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t (ms) |
FIGURE 12.59 Sketching the form of vC for a parallel RLC circuit driven by an impulse current input.
C | dv1(t) | 1 | v(t)1 |
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|
---|---|---|---|---|---|
1 | dt | + R1 |
|
C | dv2(t) | 1 | v(t)1 | ||
---|---|---|---|---|---|
2 | dt | + R2 |
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|
v2(t) = R3C1 | dv1(t) | + | �1R3 | � | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
dt | + R1 | � | ||||||||||||
|
1 | + | 1 |
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||||||||||
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+ | R2C2 | R3C1 | |||||||||||
1 | + | |||||||||||||
+ | R1R3C1C2 |