Re: [Maxima-discuss] linear circuit analysis example?

[Henry B. <hb...@pi...>]

Thanks, Sidney!

Yes, what you are describing is what I have since learned is called "stamping" (?!?).

I.e., the pattern:

g      -g


-g     g

is the "stamp" for this element.

Unfortunately, explaining stamping is too complicated and diverts attention from the main point; since I'm more interested in pedagogy than efficiency, I wanted a 1-1 correspondence between the trivial circuit and the matrix.  I believe that this used to be called "nodal analysis".

At 04:27 PM 1/21/2018, Sidney Marshall wrote:
>Henry Baker,
>
>There are many ways to do this.  The simplest is nodal analysis and assumes that the circuit consists of current sources and conductances (G = 1/R).  Ohm's law is GE = I where G is the conductance, E is the voltage, and I is the current.
>
>Construct an n x n matrix for G, an n x 1 column vector E, and an n x 1 column vector I.  If there is a conductance between node j and k add to the G matrix the pattern
>
>g      -g
>
>
>-g     g
>
>for the jth and kth rows and columns.  If there is a current source between nodes j and k add to the I column vector the pattern
>
>i
>
>
>-i
>
>Now delete the last row and column from the G matrix and the last entry from the E and I vectors (otherwise the matrix G is singular) and call this (deleted) node the ground node.  Solve the matrix equation GE = I for E.  E is then the node voltages.
>
>Note that the pattern for each row calculates the voltage difference between nodes j and k and when multiplied by the conductance gives the current through the conductance.  This is set equal to the current specified by the I vector.
>
>If you use complex admittance and complex currents (to specify phase) you can add capacitors and inductors. Capacitors are 2[pi]fiC and inductors are 1/2[pi]iL.
>
>Laplace transforms can be done by using g, sC, and 1/sL in the matrix - the right-hand side is then the Laplace Transform of the current source.
>
>You can also add voltage sources, inductors, transformers etc. by using different patterns.
>
>There is also loop analysis and hybrid analysis systems.
>
>Ask if you need more information.
>
>References:
>
>J. Vlach and K. Singhal, "Computer Methods for Circuit Analysis and Design", Applied Mathematical Sciences, Van Nostrand, New York (1984) - a really good book for this sort of thing
>
>Laurence W. Nagel, "SPICE2: A Computer Program to Simulate Semiconductor Circuits", Memorandum No. ERL-M520, Electronics Research Laboratory, College of Engineering, University of California, Berkeley 94720 (9 May 1975) - describes the inner workings of SPICE
>
>--Sidney Marshall
>-----------------------------------------
>On Fri, 19 Jan 2018, Henry Baker wrote:
>
>>Hi:
>>
>>I was looking for a trivial linear circuit analysis example for Maxima.
>>
>>I want to show how the circuit of R's, L's, and C's maps into a matrix.
>>
>>In particular, the matrix should "mirror" the topology of the circuit.
>>
>>Thanks in advance for any pointers.
>>
>>Henry Baker