Capacitor with initial values

[venn_ng]

Hi,

I have attached a circuit below.

Do you know what would be the closed form expression of vout (t) assuming that C1 is charged to VDD at t=0 and C2 is at 0V at t=0?
The switch turns ON at t=t1

I tried to think about it but I am not able to get a closed form expression after t=t1, as the C1 is charged to VDD (initial value). I feel like this circuit is not linear and doesn't obey superposition because of initial value of C1. What do you think?

 

[d123]

Hi,

Looks complicated...

Wouldn't Vout equal whatever tau is reached by each capacitor respectively at t1?

C1 would discharge to x% and so to x voltage and C2 would charge to x% and so to x voltage and Vout would be C2 state of charge? Looks awfully complicated to calculate as both are dynamic values until t1 and in opposing directions?

 

[FvM]

The solution is the superposition of two exponential functions, but the waveform can be quite different depending on the actual RC values.

 

[venn_ng]

The solution is the superposition of two exponential functions, but the waveform can be quite different depending on the actual RC values.

Exactly, is there a closed form expression after t=t1, based on initial conditions?

--- Updated Jul 22, 2020 ---

Hi,

Looks complicated...

Wouldn't Vout equal whatever tau is reached by each capacitor respectively at t1?

C1 would discharge to x% and so to x voltage and C2 would charge to x% and so to x voltage and Vout would be C2 state of charge? Looks awfully complicated to calculate as both are dynamic values until t1 and in opposing directions?

lol yeah. I was breaking my head too on this

 

[FvM]

I suppose there's a closed form solution, but I need to consult my text books or have large sheet of paper to calculate it.

 

[Dominik Przyborowski]

After commutation you have 2 nodes circuit with additional voltage source in series with C1. There is nothing more than simple 2x2 matrix for nodal analysis.