How to Derive the ODE for a Series RC Circuit with a Current Source?

[ntmkd]

Dear all,

I have problem to find the differential equation for my circuit shown in the attached picture.

For input I have a current source, and the output is the voltage U (the voltage between the first and the ground node). I need the ODE to find the mathematical response of the system.

Thank you very much for all answers.


Cheers,
Nikola

 

[HallsofIvy]

Part of your picture has been cut off so we cannot see some of the data. Thus will actually be a sytem of equations, or a matrix equation, not a single equation, with a different equation (or line of the matrix) for each "side" of the circuit. I believe I count 6 such equations.

 

[ntmkd]

Hi Hallsoflvy,

thank you very much for your reply.

Yes, I know that the picture is cut off, just because the data is not important. Actually, I am not interested in any numerical values, the component values on the picture is only for some simulation to check the correctness of the formula that I will get, but unfortunately so far I didn't get the formula that I need.

Also, I know that there will be more equations to solve the circuit. But at the end, I am interested i only one equation that will give me the answer of the system (the output voltage), according the input of the system (applied current). If I describe the system with this kind of ODE, I can get the system's response for any different input current. That is what I need, but I have some problems to construct this ODE :) Hope someone can help me :)

Thanks a lot,
Nikola