All EE's; Need help solving circuit equations for L-net, Pi-net and T-net
 

ANy EE's out there that remember their circuit design course work. I
need the general solutions for L-net, Pi-net and T-net, including
reactive loads.
I have cobbled together solutions for these but am not happy with
what I have.

General forms in Z would be nice then Fortran can solve them.

A vexing problem. Any inductor in the soultion will have a series R
term.
This R needs to be subtracted off the Source or Load and then the
calculations run again!. Anyone figured this out ?? Precision is a
requirement.

Pat W

In article ,
(PatW) writes:

ANy EE's out there that remember their circuit design course work. I
need the general solutions for L-net, Pi-net and T-net, including
reactive loads.
I have cobbled together solutions for these but am not happy with
what I have.

[why do I sense a student needing help on an assignment? :-) ]

General forms in Z would be nice then Fortran can solve them.

I have them handy for the two-element L-C matching network,
including the range of values possible with the two basic
configurations of R-load higher-than or lower-than R-source.
Reactance of the load can be cancelled out via the match
network opposite reactance...one type may require an Z to Y
(and vice-versa) transform in order to "see" that.

Before going into all of that, the load impedance (or admittance)
has to considered and known approximately. Loads, whether
of an antenna or a following stage, all have great variations,
especially in reactance values. The choice of network will be
governed by the necessary bandwidth as well as range of R and X.

Reg Edwards ought to have a program on his website that does
the solution for all those networks. He has a lot of good, useful
little programs that don't take up much space in the computer
and have good accuracy.

A vexing problem.

Not if you know complex arithmetic rules. It's just a lot of work
in solving equations with complex quantities.

Any inductor in the soultion will have a series R term.

Not necessarily. Only if there is an inductor with very low Q in the
circuit. For most impedance magnitudes of 500 Ohms or less, the
inductive loss can essentially be neglected. Once the approximate
values are found, the matching network losses can be examined in
detail to determine heating and/or efficiency.

This R needs to be subtracted off the Source or Load and then the
calculations run again!

No. The solutions can be done simultaneously in the computer...
or reduced to two equations for calculation on a scientific calculator.

Anyone figured this out ?? Precision is a requirement.

Okay...that sounds even more suspicously like an assignment... :-)

Yes, I "figured it out" some while ago and can do precision via my
FORTRAN compiler program to 14 digits. My H-P 32 S II does
things to 10 decimal digits. Couldn't even come close to that kind
of accuracy in real, practical parts. :-)

If you were actually building something (that's why this is called a
"homebrew" forum), I'd supply the formulas. Those aren't rocket
science. Working out the solutions via complex quantities is good
learning for students (whether they like it or not); that CAN find a
need later in life when stuck with real design problems.

Len Anderson
retired (from regular hours) electronic engineer person