Expressing impedence in series/parallel combinatio

[mark_neil2]

Hi,
I want to figure out the connection of a two-terminal circuit knowing impedance formula across the two terminals. I have the impedence of the circuit in terms of circuit parameters in symbolic form. If I can express it in the form of "continued fraction expansion", then I can figure out the connection between the components. Please see the attached file for an example. I wonder if this can be done in Mathcad.

Thanks.

[ptc-1368288]

On 2/20/2009 6:45:53 PM, mark_neil wrote:
...>
>jmG,
>I have seen your Mathcad file but found
>it irrelevant to my question (maybe I
>didn't understand it). Your file uses
>the A0, numer(s) and denom(s) as given
>by the textbook. Just keep in mind that
>I don't have them as nicely arranged
>with series/parallel combinations of the
>circuit components but instead fully
>expanded out. I am trying to transform
>my transfer function into the form in
>your Mathcad file (as arranged my
>series/parallel combinations). You have
>assumed some numeric values and did more
>stuff. Assigning numeric values is the
>last thing to do it is no challenge.
>Just to let you know, I use MC14. Some
>lines on your files do not execute on my
>MC14; I think due to the differences
>between MC11 and MC14.
>
>Mark.
_____________________________________

Before this project goes on ice and if you think the attached is irrelevant, please don't even download. Yes, my work sheet uses the Ao, num, denom as per your book and if your book is in error ? You don't have to arrange them, I did. I have assigned numerical values to illustrate the global solution ... if you want to see it differently, get inspired by the last example. And all that might be useless if your version 14 does not digest CF . But you have to do something: make an *.gif of the part(s) red. Never know about alternate solution.

I distracted myself, spending 1 hour visiting the web and got fed up reading nothing except for the two sites linked. Two more things:

1. your gm, it threw it in the garbage. It does have a unit default value. OK symbolic does not care but that has created lot of problems in the past. C is OK because it defaults to 1. Your gm is now 'q'.

2. Before the Given/Find the result is XXXX + AAAA/[x+BBBB] ... in 'q' substitute a wild name like 'Q' for instance, that will expand a bit wider as well as isolate 'q'. Just a trick of practice.

Please don't hesitate to post your progress.

jmG

[LouP]

I don't know how to ask MCD to "look for Rs*Rb/(Rs+Rb) or 1/(1/Rs+1/Rb)," but there is an equivalent way that does work (at least on Tom's simple example of (R1*R3+R1*R4+R2*R3+R2*R4)/(R1+R2+R3+R4)). Let's assume you have the circuit and know the element combos in the system function. If R1 and R2 are in series, then perform the symbolic substitutions R1 = (Ra+Rb)/2, R2 = (Ra-Rb)/2. In terms of R1 and R2, we have Ra = (R1+R2), Rb = R1-R2. If the symbolic function depends only on the sum R1 and R2, then using the substitutions for R1 and R2 as given, the result will depend only on Ra, with no dependence on Rb (some manipulation and/or simplification may be necessary). Thus, one variable has been eliminated, and the new result only has a dependence on Ra (=R1+R2). Similar transformations of any number of variables (2-2, 3-3, etc) for other circuit combos can be done; the object is that only one of the new variables - the one encoding the expected combined form - should appear in the result.

This works if you know where you need to go, and want MCD to do the manipulation for you. It's not a continued fraction expansion, but I don't think that would lead to anything useful in the general case.

Hope this helps.

Lou

[mark_neil2]

On 3/4/2009 3:24:48 PM, lpoulo wrote:
>I don't know how to ask MCD to
>"look for Rs*Rb/(Rs+Rb) or
>1/(1/Rs+1/Rb)," but there is
>an equivalent way that does
>work (at least on Tom's simple
>example of
>(R1*R3+R1*R4+R2*R3+R2*R4)/(R1+
>R2+R3+R4)). Let's assume you
>have the circuit and know the
>element combos in the system
>function. If R1 and R2 are in
>series, then perform the
>symbolic substitutions R1 =
>(Ra+Rb)/2, R2 = (Ra-Rb)/2. In
>terms of R1 and R2, we have Ra
>= (R1+R2), Rb = R1-R2. If the
>symbolic function depends only
>on the sum R1 and R2, then
>using the substitutions for R1
>and R2 as given, the result
>will depend only on Ra, with
>no dependence on Rb (some
>manipulation and/or
>simplification may be
>necessary). Thus, one variable
>has been eliminated, and the
>new result only has a
>dependence on Ra (=R1+R2).
>Similar transformations of any
>number of variables (2-2, 3-3,
>etc) for other circuit combos
>can be done; the object is
>that only one of the new
>variables - the one encoding
>the expected combined form -
>should appear in the result.
>
>This works if you know where
>you need to go, and want MCD
>to do the manipulation for
>you. It's not a continued
>fraction expansion, but I
>don't think that would lead to
>anything useful in the general
>case.
>
>Hope this helps.
>
>Lou
>

Lou,
I will apply this to the transfer function of the emitter follower circuit and see if it works efficiently. Thanks for your suggestion.

Mark.