RadioBanter - View Single Post - A Subtle Detail of Reflection Coefficients (but important to know)

August 24th 03, 07:25 PM

(Dan) wrote in message . com...

From Kurokawa, "Power Waves and the Scattering Matrix," IEEE
Transactions on Microwave Theory and Techniques, March 1965:

Section 2, explanation of and mathematical definition of the concept
of "power waves," explicitly noted by the author to be distinct from
the more commonly discussed voltage and current traveling waves.

Section 3, definition of the reflection coefficient [for power waves]:
s = (ZL - Zo*) / (ZL + Zo)
with a footnote "[Only w]hen Zo is real and positive this is the
voltage wave reflection coefficient." Kurokawa takes pains to make it
clear that his "s" power wave reflection coefficient is not the same
as the (usually rho or Gamma) voltage wave reflection coefficient.

I've got the same paper. It's a bit confusing, because then he
calls

[s]**2 = [(ZL - Zo*) / (ZL + Zo)]**2 the "power reflection
coefficent".

Where if you take the square root to the power reflection
coefficient, you should get the voltage r. c.

So perhaps s = (ZL - Zo*) / (ZL + Zo) really IS the voltage R.
C., even in this paper!

Section 9, comparison with [voltage and current] traveling waves:
"... since the [voltage or current] traveling wave reflection
coefficient is given by (ZL - Zo) / (ZL + Zo) [note no conjugate] and
the maximum power transfer takes place when ZL=Zo*, ... it is only
when there is a certain reflection in terms of [voltage or current]
traveling waves that the maximum power is transferred from the line to
the load."

Perhaps he is confused on this point, because he previously
stated:

"When the matching condition (4) is satisfied , the power
reflection
coefficient becomes zero, as expected."

Condition (4) is the Zl=Zo*, which is also called the conjugate
matched condition for maximum power delivered to the load.

It's only when you have a simultaneous conjugate match with a
transistor, that you get the max gain.

So Kurokawa agrees with Chipman concerning the condition for maximum
power transfer. Kurokawa also defines two different reflection
coefficients, both in the same paper.

Again, you failed to mention that he defined:

[s]**2 = [(ZL - Zo*) / (ZL + Zo)]**2 the "power reflection
coefficent".

Note the squares.

Copy of the Kurokawa paper, in pdf format, available on request
via
private email.

Slick