On Dec 10, 8:33 am, Cecil Moore wrote:
Keith Dysart wrote:
It seems to me that if connecting a -j567 impedance
produces a certain response, it should not matter how
that -j567 impedance is produced. Consider the following
cases:

(1) - produce the -j567 with a lumped capacitor
(2) - produce the -j567 with 10 degrees of 100 ohm line
(3) - produce the -j567 with 46.6 degrees of 600 ohm line

The claim appears to be that despite the 43.4 degrees
of 600 ohm line being terminated in the exact same
-j567 impedance in all cases, the phase shift
experienced at the interface is different in each
case.

They are terminated in the same value of impedance
but they are not terminated in identical impedances.
Please see the IEEE Dictionary for the three different
definitions of impedance. Each case involves a different
reflection coefficient at the -j567 point.
(I added a number to each case above.)

(1) involves an *impedor* with a reflection coefficient
of 1.0 at -93.2 degrees when connected to the 600
ohm line. The reflected wave at the feedpoint lags
the forward wave by 43.4 + 93.2 + 43.4 = 180 degrees.
The impedance is a real impedor, not a virtual impedance.

(2) involves an impedance discontinuity with a
reflection coefficient of -0.7143. With 10 degrees
of 100 ohm line, the reflected wave lags the forward
wave by 2(43.4 + 36.6 + 10) = 180 degrees. The phase
shift at the discontinuity is 36.6 degrees each way.
The impedance is caused by superposition of component
waves at the impedance discontinuity.

(3) with 46.6 degrees of 600 ohm line, the reflected
wave lags the forward wave by 2(43.4 + 0 + 46.6) = 180
degrees. The phase shift at the 600 to 600 ohm junction
is zero. The reflection coefficient at the 600 to 600
ohm junction is 0, different from (1) and (2) above.
The impedance is completely virtual and thus cannot
cause anything.

I see how you have done the arithmetic, and if I
understand correctly, you would claim these are
all systems with 90 "electical degrees".

What about the following...

Open circuit 46.6 degrees of 600 ohm line attached
to 80 degrees of 100 ohm line. The drive point impedance
will be 0 ohms. And the impedance at the junction will
be the same -j567. Using your arithmetic, there is
90-46.6-80 - -36.6 degrees of phase shift at the
junction. The physical length is 126.6 degrees
while the system is 90 "electrical degrees".

Is the definition of a system with 90 "electrical degrees"
becoming any system where the drive point impedance
has no reactive component?

....Keith