# RE: [SI-LIST] : Transmission Line Conductors

Brian C. Wadell ([email protected])
Sun, 21 Sep 1997 18:08:45 -0400

On Thursday, September 18, 1997 6:19 PM, Alastair =
Hardie[SMTP:[email protected]] wrote:
> All the transmission line impedance formulae that I can find do not =
take
> into account the
> conductor's properties such as conductivity and frequency dependant
> permeability (mu).
> Alastair Hardie.
>=20

Alastair,

Formulas for Z0 have an implicit or explicit term of eta0 (aka Z0 of =
free space, 377 ohms). This is the Sqrt[(mu0 * murel)/(epsilon0 * =
epsilonrel)]. The mus are permeability and the epsilons are =
permittivities, the subscript 0 means "of free space".

Similarly, the propagation constant is more generally calculable as =
Sqrt[j omega mu (sigma + j omega epsilon)] (2.2.27 in TLDH) which =
includes all the terms you requested. Usually this is just reduced to =
the imaginary part because the losses are small. Remember seeing all =
those 1/sqrt(eeff)'s?

These formulas can be modified for other mus and epsilons by plugging in =
the appropriate epsilon-rel-effective (er,eff) or mu-rel-effective =
(ur,eff). That is the reason I tried to make the eta0 (h0) explicit =
where ever I could in my book (for those of you who were wondering!).

Getting the values of mur,eff and er, eff for non-homogeneous =
dielectrics (like microstrip line) is the big trick. Also, if you stray =
too far you open issues regarding the mode's propagation.

> Does anyone know how a change in transmission line material part of =
the way
> along it's length
> affects the transmission line's performance?
>=20

"Changing the material along its length" creates a different =
transmission line. Model it as a new line in series along with the =
associated discontinuities.

BTW, in a related vein the value of tan delta you use is an "effective" =
value for the total dielectric structure. So tan delta,effective for =
stripline is the same as tan delta of the dielectric. However, tan =
delta,effective for microstrip line (partly air dielectric) is lower =
than the actual tan delta of the dielectric.

Regards,

BCW