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Hi there!
Please refer to the circuit. I would like to derive a formula for the capacitor waveforms' peaks.
The scenario is that when S1 is closed circuit, S2's contact is at its lower position, and vice versa.
Let the circuit run like this for a very long time, until it reaches its equilibrium points: vc1 and vc2 becomes periodic, having period of T.
Then, we observe the waveforms from time tA to tA+T
Supposed that Vcc, R1, R2, C1, C2, tA, tB, and T are all given. Please derive a formula for vc1(tA), vc1(tB), vc2(tA), and vc2(tB).
PS. Actually, I have derived the transient response of C1 and C2 for both two cases of switching (see the other attachment).
However, when I tried to solve for vc1(tA), vc1(tB), vc2(tA), and vc2(tB), I substituted t=tA and t=tB into these equations, and got four solvable equations. THEY ARE VERY UGLY!!
Do you have any tips for this?? Is there any easier way to deal with this problem???
Best Regards,
BlackMelon
Please refer to the circuit. I would like to derive a formula for the capacitor waveforms' peaks.
The scenario is that when S1 is closed circuit, S2's contact is at its lower position, and vice versa.
Let the circuit run like this for a very long time, until it reaches its equilibrium points: vc1 and vc2 becomes periodic, having period of T.
Then, we observe the waveforms from time tA to tA+T
Supposed that Vcc, R1, R2, C1, C2, tA, tB, and T are all given. Please derive a formula for vc1(tA), vc1(tB), vc2(tA), and vc2(tB).
PS. Actually, I have derived the transient response of C1 and C2 for both two cases of switching (see the other attachment).
However, when I tried to solve for vc1(tA), vc1(tB), vc2(tA), and vc2(tB), I substituted t=tA and t=tB into these equations, and got four solvable equations. THEY ARE VERY UGLY!!
Do you have any tips for this?? Is there any easier way to deal with this problem???
Best Regards,
BlackMelon
