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 |
|---|
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. | |||
|---|---|---|---|
| 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.
|
|---|
| vC(V) | 1.0 | VCM | 2 |
|
R1 | C H A P T E R |
|
685 | ||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 0.5 | v1 | v2 | ||||||||||
| 0.0 | ||||||||||||
| -0.5 | -VCM | C1 | ||||||||||
| R2 | C2 | |||||||||||
| -1.0 | 3 | 4 | ||||||||||
|
||||||||||||
| 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 |
|
|
|---|---|---|---|---|---|
| 1 | dt | + R1 |
|
| C | dv2(t) | 1 | v(t)1 | ||
|---|---|---|---|---|---|
| 2 | dt | + R2 |
|
|
| v2(t) = R3C1 | dv1(t) | + | �1R3 | � | ||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| dt | + R1 | � | ||||||||||||
|
1 | + | 1 |
|
||||||||||
|
+ | R2C2 | R3C1 | |||||||||||
| 1 | + | |||||||||||||
| + | R1R3C1C2 | |||||||||||||
