As far as I know most simulation tools use numerical methods to solve a system of equations ( differential ,non linear etc) as a result, even if there existed a closed form equation for the results of a simulation (which is not very likely in real life problems), no such equation is actually calculated by the software; instead a set of discrete points are calculated and the "estimated" waveform ( or any other function or relation for that matter) is given as the output. This is specially the case with PSPICE. You can easily see the real data points by clicking on the corresponding button in the toolbar. This approach may create unrealistic waveforms since such estimations may not by thoroughly correct (for instance ,try increasing the step size in PSPICE and see what happens)

But all hope is not lost! since there are a set of thoroughly investigated methods for providing better and better approximation functions for a set of discrete data points.(known as Curve Fitting) Some of these methods are masterfully implemented in the "Curve Fitting" Toolbox of MATLAB.

I hope this helps.

Hello Suman,

As Mohammad said, you can try using Matlab's curve fitting options. They work really nice and should be able to give you good approximations to your calculated data. Matlab has a lot of different curve fitting options so I think it is a good option to try out. Besides, you can find a lot of good references on the Internet by simply searching something like curve fitting on Matlab. Sometimes, the curve fitting option will not give you a perfect match to your calculated data but you could play a little bit with the options and it will get pretty close.

I hope this helps.

Best regards,

Christian

Suman - please, can you further explain your problem?

Are you really asking for a way to express " the output waveform with mathematical equation."?

Output waveform or transfer properties (gain)?

Example: As you know - in reality there is no squarewave form at all.

What do you want? To find a mathematical expression for a pseudo-squarewave with finite rise and fall times? Or for a distorted sinewave?

I can`t imagine.

Respected sir @Lutz von Wangenheim

In simulink model we connect R, L, C in series or parallel, simulate the circuit and we get output. If the circuit is simple (having less RLC) then it is very easy to find the mathematical expression theoritically. But it becomes very difficult to give mathematical expression when the circuit become complex. The whole simulation circuit is working on mathematical equation (internally). I need to know is there any tool (simulation/programming) to give the mathematical expression so that we can use those mathematical formula in special use (in optimization ..etc).

@ Suman Debnath:

You only speak of "mathematical expressions".

But you did ot answer my question:

Expression FOR WHAT? For which QUANTITY?

For the output VOLTAGE or for the TRANSFER FUNCTION?

(I ask this question because the title of this thread contains the term "output")

Respected sir @Lutz von Wangenheim

Output voltage

(Is it possible to get Transfer function also?)

There are symbolic simulation programs which are able to calculate (linear) transfer functions (symbolic formulas) for electronic circuits.

But what do you expect as "output voltage"? This voltage, of course, depends on the particular input signal. In case you want a techcnial expression (formula) for the output voltage you can use the Fourier transform to get such an expression.

Or what is your desire?

Dear Suman,

It is possible to find a mathematical function for an output signal. What you need is appying linear regression to your output signals. Find the description on linear regression from Mathworks http://www.mathworks.de/de/help/matlab/data_analysis/linear-regression.html.

But the found coefficients map to physical parameters like RLC of a physical curcuit. linear regression mix those parameters.

Howerver If you only need the function for your out put linear regressions will work.

Dear Suman

There is an amazing evolutionary computing program called Eureqa(which was, and still is, I think, free), which uses genetic algorithms and  which accepts a time-voltage series applied to an Excel-type spreadsheet, to find an expression for the inputted series. For example, I have exported from PSpice Probe, the output signals, x, y,z,  from a circuit which implemented the famous Lorenz equations. After copying the various signals from the bottom of the Probe output, and pasting the signals into Eureqa, Eureqa churned away for a while and you could see the progress as it processed several million equations 'tries' per second. Eventually, it reached an acceptable facsimile of the famous butterfly algorithm.

It's quite uncanny to see it in operation

Hope this is what you require.

Paul