Quote:
Originally Posted by G8HQP Dave
There is a formula for solving cubics but it is very complicated and probably rarely used.
You might be better doing complex algebra and get a complex formula for each impedance (unknown) in the network in terms of source and load (knowns). Then simply do complex arithmetic.
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Which is exactly what I did. And the aforesaid cubics were the result.
As far as solving cubic equations, I do have the standard solution stored on this PC which runs under Excel. It's fine for 'simple' cubics with real number co-efficients, of course, but when those co-efficients are themselves algebraic expressions (especially cumbersome ones), i.e. the 'general case' for a given attenuator, obviously it isn't any use.
Upon reflection, though, these cubic equations might be amenable to an analysis to see if logical simplifications can be obtained on the basis that there
might only be
one real-valued solution (the other pair being a complex conjugate pair), as opposed to three!
But that's very much a 'maybe, one day' notion. Right now, I'm quite busy on a host of other tasks, not necessarily electrically-related.
Al.