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# Inverse engineering : from a transfer function to an electronic circuit systems !

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#### hananeel

##### Newbie level 3
Design control systems in matlab and other software today its very easy, get for example the transfer function of a circuit , then optimize it,... its kinda easy these days,...

what I'm looking for,... its a easy way , once I have my electronic system, mathematically speaking - get the design of the real circuit with its devices like loads, capacitors, diode, transistor, etc etc ,...

so, I can Begin from the equations/ and my system responses, and then develop the actually electronic system,..

well,...
thanks for any idea,..

Yeah, you can. That's something they show you in sophomore/junior EE classes (s domain).

Take a look at circuit equations for RLC circuits when taking their Laplace transforms. It will give you elements like R, Ls and 1/sC. This should like vaguely familiar to transfer functions, which are functions of s, i.e. H(s). When you substitute s = jω, you can plot the response of the circuit versus frequency (Bode plots), which is handy in designing/analyzing filters. That filtering is what causes you to speed up or slow down control loops, depending on the type of filter/circuit you implement in the feedback path of your loop.

Yeah, you can. That's something they show you in sophomore/junior EE classes (s domain).

Take a look at circuit equations for RLC circuits when taking their Laplace transforms. It will give you elements like R, Ls and 1/sC. This should like vaguely familiar to transfer functions, which are functions of s, i.e. H(s). When you substitute s = jω, you can plot the response of the circuit versus frequency (Bode plots), which is handy in designing/analyzing filters. That filtering is what causes you to speed up or slow down control loops, depending on the type of filter/circuit you implement in the feedback path of your loop.

suppose I have f(s) = (s^2 + 5s^4 ) / (2s^4 + 3s^2 +9s) for example,... now,... i want to develop the electronic circuit
how you would do it ?,...

PS: thanks for the pdf link,.. !!

In filter design the traditional way is to use a ladder topology, as in File:Cauer lowpass.svg - Wikipedia, the free encyclopedia.

If you sit down and work out the impedence at the input, it turns out to be:
$\frac{1}{sC_1 + \frac{1}{sL_2 + \frac{1}{sC_3 + \cdots}}}$

So, by finding the impedence of the network that implements the transfer function (I cannot recall how exactly to do this, or I would give some more details; it involves two-port networks), and representing it as a continued fraction, you can read off the component values.

The nature of the transfer function obviously has an effect on the networks that you can use; looking at the schematic above it should be clear that the filter is by nature low-pass.

Long story short: If you want to produce an analogue implementation, grab a book on analogue filter design and you will find information on the synthesis of arbitrary transfer functions. Or failing that use a digital controller and just read off the z-coefficients to get your filter.

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