William E. Sabin wrote:
Dan wrote:

Now that the various typo mistakes have been corrected, and putting
aside for the moment the name calling and ad hominem arguments, could
it be that _both_ sides in this discussion are correct? Camp 'A' says
that the reflection coefficient is computed the classical way, without
using Zo conjugate, and offers various mathematical proofs and
discussions of infinitely long lines. Camp 'B' says the reflection
coefficient is computed with Zo* (Zo conjugate) in the numerator, and
offers explanations dealing with the conservation of energy and
maximum transfer of power.

Both sides may be correct since they are talking about _two different_
meanings for the term "reflection coefficient." One has to do with
voltage (or current) traveling waves and the other has to do with
power.


If a lossy line is terminated with the complex Z0, there is no
reflection from the load, but the maximum possible power is not
delivered. If the *load* is made equal to the complex conjugate of Z0
the maximum *forward power* is delivered but there is a reflected power
(VSWR is not 1:1).

It is difficult to say that the maximum *power* is delivered without
knowing the generator impedance, since it is involved in any so-called
"conjugate match". For a lossy line, the idea of conjugate match is, at
best, very approximate anyway. And generator impedance is a mystery in
most, but not all, transmitter PA situations. One possible exception: a
large amount of negative feedback helps to determine, to some extent,
output impedance, for a signal with time-varying amplitude (e.g. SSB).

It seems to me to be clear that the use of Z0* in the reflection
coefficient equation has not been corroborated (see Roy's post), but the
use of ZL=ZO* has been. The two ideas are not equivalent.

After looking at some examples, using the exact complex hyperbolic
equations with Mathcad, it is obvious that a line must be very lossy to
make a significant difference whether ZL or ZL*

Correction: Z0 or Z0*

is used to terminate the
line. Still, it is important to understand the basic principles
involved, so this exercise is not foolishness at all.

A word about "credentials". We all respect established and competent
authors. But I have noticed on several occasions that blind faith has
some exceptions. As an experienced author, I am personally familiar with
this problem.

G. Gonzalez (highly respected) "Microwave Transistor Amplifiers" second
edition, has a good discussion of Power Waves, based on Kurokawa (I also
have his article). There are no transmission lines, and the term ZS*
(ZS=generator impedance) is used. In particular, a power wave reflection
coefficient is defined:

Gp = (ZL-ZS*)/(ZL+ZS)

which looks quite familiar, with ZS replacing Z0. Also, a voltage
reflection coefficient:

Gv = [Zs/Zs*] x [(ZL-ZS*)/(ZL+ZS)]

and a current reflection coefficient

Gv = Gp.

Correction: Gi = Gp


The author also defines two-port scattering parameters in terms of power
waves, in which ZS* and ZL* appear.

For the purposes of the present topic, involving transmission lines, it
seems best to stay away from power waves, without a lot more studying.

Bill W0IYH