Re: Parallel and Series LCR Circuit Qs

[ghub005-at-xtra.co.nz (by way of Terry Fritz <twftesla-at-uswest-dot-net>)]

Sorry I wasn't more clear. What I meant was that in the Norton 
equivalent, a zero output-impedance (in parallel with the ideal 
current source) intuitivly results in a zero-output voltage.


Speaking of equivalent circuits (Thevenin, Norton etc). I have been 
doing some simple circuit analysis for fun (I'm making some simple 
numerical models for a classical TC in Matlab). Here is a useful 
result that I derived about a week ago - it is a simple transformation 
for a two terminal, two element linear network that lets me 
progressively collapse and absorb the elements in a network 
(reducing the number of numerical parameters by 1 each time).

This transformation probably has a name - has someone on the list 
has come across it before? 

fixed width (courier) font etc:

o---WWW---+
     r    |
          E   
          E Xs
          E
          |
o---------+

o---+------+
    |      |
    W      E
    W R    E Wp
    W      E
    |      |
o---+------+

To transform in either direction use

R = r(1 + Q^2)
Xp = Ws (1 + INV[Q^2])

where Q = Xs/r = R/Xp as usual

Note that Q will be negative for capacitive reactances, but since the 
equations use Q^2 this isn't a problem.

Example:

Consider the following circuit:

    3j    3j 
o--www-+-www-+
       |     |
       c     R
   -3j c     R 10
       c     R
       |     |
o------+-----+

In this example, applying the transformation one element at a time 
results in a purely resistive circuit (1 ohm) - which is not 
immediately apparent at first sight.

Best regards,

Gavin Hubbard

P.S. I realise that my second paragraph in that previous post was 
incorrect also - of course a zero-impedance output impedance in 
parallel with a ideal current source won't give an infinite loop current! 
I have to stop writing these emails so late at night :-o 


On 22 Aug 2000, at 19:24, Tesla list wrote:

> Original poster: "Antonio Carlos M. de Queiroz"
> <acmq-at-compuland-dot-com.br> 
> 
> Tesla list wrote:
> > 
> > Original poster: ghub005-at-xtra.co.nz
> 
> > I almost always instinctively think of a power source as being an
> > ideal current source in parallel with an internal impedance (the
> > Norton equivalent?). With that model, a zero-impedance intuitively
> > results in a zero-output voltage.
> 
> The Norton equivalent has a -current- source (V/Z) in parallel
> with the output impedance Z. The short-circuit current is just
> V/Z.
> 
> Antonio Carlos M. de Queiroz