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

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SUMMARY

The discussion focuses on deriving the ordinary differential equation (ODE) for a series RC circuit with a current source, specifically to determine the output voltage (U) in response to varying input currents. Nikola, the original poster, seeks a single ODE that encapsulates the system's behavior despite acknowledging the need for multiple equations due to the circuit's complexity. The conversation highlights the necessity of understanding circuit dynamics and the relationship between current and voltage in electrical engineering.

PREREQUISITES
  • Understanding of series RC circuits and their components
  • Familiarity with ordinary differential equations (ODEs)
  • Knowledge of circuit analysis techniques, including Kirchhoff's laws
  • Basic skills in mathematical modeling of electrical systems
NEXT STEPS
  • Study the derivation of ODEs for series RC circuits with current sources
  • Learn about Laplace transforms for solving circuit differential equations
  • Explore simulation tools like SPICE for validating circuit responses
  • Research matrix equations in circuit analysis for complex systems
USEFUL FOR

Electrical engineers, students studying circuit theory, and anyone involved in modeling and analyzing the behavior of RC circuits under varying current inputs.

ntmkd
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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
 

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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.
 
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
 

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