On 06/15/2011 10:57 AM, walt wrote:

As I'm sure you know, reflection degrees equals two electrical
degrees. Therefore, the normalized impedance 1.0 -j1.1547 ohms occurs
at 30° rearward of the load. That OK?


Well, I'm not clear what you mean by "rearward of the load". At 60
degrees toward the generator the normalized impedance looking into the
line is 1.0 - j1.1547 ohms and that corresponds to a reflection
coefficient of -j1.1547/(2-j1.1547) or alternatively, 0.5 @ -60 degrees
(sorry my char set doesn't do Steinmetz notation). So I think we're in
agreement here. What more needs to be said? Now put in a shorted stub
(of appropriate length at the desired frequency) in series to tune out
(cancel) the reactive part of the line impedance. The combination of
the series stub and the line will appear as 1.0 + j0 to the
generator/source and the reflection coefficient is now 0. How could it
be anything else (at the desired frequency) in this scenario? You don't
need a discussion of travelling waves to arrive at the correct answer.
The reflection coefficient corresponding to a normalized (say to 50
ohms) impedance zx = Zx/50 is rho = (zx - 1)/(zx +1). Clearly a values
of rho = 1 + j0 or -1 + j0 correspond to a zx values of infinity (open
circuit) or zero (short circuit), respectively.


You might want to think of the shorted line stub as inside one box and
the transmission line + 150 ohm load in another black box. Let's assume
someone hands you these two boxes and you have no idea what's inside but
you do have access to set of terminals (input port) on each box from
which you can measure steady-state impedance of each. At some frequency
you find the normalized input impedance on one box is +j1.1547 ohms and
on the other box at that same frequency it is 1.0 - j1.1547 ohms. Now
you connect the boxes is series and measure the impedance of the series
combination again at that frequency. The point I'm making here is that
at the terminals of either of the boxes you measured the impedance at
some frequency - it doesn't matter what's inside the box. (Of course
the impedance behavior over a range of frequencies certainly is
dependent on the circuit topology within the box.) Sincerely,

--
J. B. Wood e-mail: