[TowerTalk] Jim Reid's (KH7M) Comments (1)

[Steven Best]

In an earlier post to TowerTalk, Jim Reid (KH7M) made a few comments
regarding my work that I would like to respond to in an effort to clarify my
position.

One of Jim's comments was:

"but he failed, at least in the early papers and e-mail discussions I have
seen about his work, to account for propagation time in the transmission
line. ..."

Jim's statement that my analysis does not correctly account for the
propagation time in the transmission line is not correct.  Given the recent
e-mail exchange that occurred on rec.radio.amateur.antenna regarding this
topic, I can see how Jim would have reached this conclusion.

I made a statement to the rec. newsgroup that basically said that phase
change in the transmission line system occurring as a function of time was
irrelevant.  In the exchange that followed, the participants (especially
myself) never really explained their position in sufficient depth and the
technical aspects of the discussion were lost in the newsgroup rhetoric.

My statement regarding phase change as it relates to time is based upon the
following scenario.

At t=0, a transmitter delivers a forward driving voltage and current to the
input of a lossless transmission line of length d=L.  The time point of
reference in this system is t=0 and the position point of reference in the
system is the transmission line input, d=0.  If we follow the forward
traveling voltage as it propagates, it travels the length of the
transmission line, it is partially reflected at the antenna (Za is not equal
to Zo) and the resulting reflected voltage travels rearward towards the
transmitter arriving back at the transmission line input at some time t=t+.

In the time t=t+, the forward driving voltage measured at the fixed point
d=0 will have undergone a phase change wrt the forward driving voltage
measured at d=0 and t=0.  The reflected voltage arriving back at d=0 at a
time t=t+ will not have undergone a phase change wrt the forward driving
voltage at d=0 and t=0 (except for the phase change occurring due to the
partial reflection at the antenna).  Therefore, at time t=t+, the forward
driving voltage at d=0 and the reflected voltage at d=0 will be out of phase
wrt one another.

However, if we simultaneously measure the phase of the forward driving
voltage and the reflected voltage at a fixed point d=0, the relative phase
difference between the two as a function of time will be constant.  The
relative phase difference between the two voltages will not change from the
value measured at t=t+ because both are measured at a fixed point in the
transmission line.  At any fixed point in the transmission line, the phase
change for all voltages as a function of time is identical.  From this
perspective, the phase change as a function of time is irrelevant.

Since the relative phase of both voltages wrt to one another at a fixed
point d=0 is constant wrt to time change, we can remove time from the
analysis.  The relative phase of each voltage wrt to one another at d=0 at
the time t=t+ is more important to the analysis than the relative or
absolute phase change of each wrt to t=0.  Since our position reference
point in the transmission line system is d=0, we define the forward driving
voltage at d=0 as the reference voltage (0 degrees phase) and determine the
relative phase change of the reflected voltage as a function of the distance
the reflected voltage traveled wrt d=0.  For this reason, the relative phase
change of the reflected voltage at d=0 wrt the forward driving voltage at
d=0 at any time t=t' is given by e^(-j 2 beta L).  The phase change
occurring due to the reflection at the antenna must also be included to
complete the analysis.

In the analysis presented in my Comm Quart articles, I simply used distance
traveled to determine the relative phase of all voltages at any fixed point
within the system.  This approach is consistent with general transmission
line theory.

73,
Steve, VE9SRB


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