(I hope I have posted this in the appropriate forum. I have consulted the posting guidelines and this seems to be OK. The subject of my post certainly isn’t homework or academic coursework, rather it is self-study for its own sake. If this is the wrong place – apologies, and maybe an admin could move it to a better place).(adsbygoogle = window.adsbygoogle || []).push({});

For some weeks now I have been studying what happens to RLC circuits when they are subject to a step change in applied voltage. The real-life applications for this include, for instance, DC-DC converters and full-bridge motor drive circuits, where a network composed of inductive, resistive and capacitive elements can experience a rapid change in voltage when one of the switching components changes state. My goal has been to find general equations describing current “i”, and from this equations describing the voltages appearing across the various circuit elements. It is specifically the transient behaviour of the circuits that I am interested in.

So far I have had success with the series-RLC configuration, and one where R and C are in parallel, and that combination in series with L. In both cases I was able to use Laplace transforms to analyse the circuits and find general equations describing the currents and voltages. Also in both cases, the solutions involved transforming a second-order DE from the s-domain to the time domain. The results were found to be identical to those produced by Spice simulations of the same circuits.

I have now moved on to a four-component configuration (RLCC), and have run straight into a brick wall. After several attempts I am stuck at the same point, and I do not know how to proceed. I have laid out my working in the attached pdf, as it is rather long and I have no idea where any errors may have slipped in. The general approach I have adopted is identical to that used for the simpler (three-component) cases, but I keep getting stuck at the point where I have to transform a third-order DE.

Any pointers which anyone could offer would be gratefully received. Finally, I should also apologise for any inadvertent misuse of mathematical terminology. These aren’t the kind of discussions in which I normally become involved!

Thanks and regards,

MR.

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# Laplace analysis of RLC and RLCC circuits

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