Tom Donaly, KA6RUH wrote:
""---first you have to find out what phase means in a standing wave
transmission line."

Cecil knows very well what phase means in a transmission line. Terman
describes it best for me, but it would be best to have his book with all
his diagrams which makes his explanation of how standing waves are
established simple indeed.

Terman writes on page 89 of his 1955 edition:
"Transmission line with Open-Circuited Load."
(This is related to the standing-wave antenna which also ends up with an
open-circuit load.)
"When the load impedance is infinite, Eq.(4-14)
(This gives the reflection coefficient rho as the vector ratio of the
reflected wave to the incident wave at the load) shows that the
coefficient of reflecftion will be 1 on an angle of zero. Under these
conditions the incident and reflected waves (voltages) will have the
same phase. As a result, the voltages of the two waves add
arithmetically so that at the load E1 = E2 = EL/2. (Voltage doubles at
the open circuit.)

Under these conditions it follows from Eqs. (4-8)
(Eforward/Iforward=Zo) and (4-11)
(Ereflected / Ireflected=-Zo) that the currents of the two waves are
equal in magnitude but opposite in phase; they thus add up to zero load
current, as must be the case if the load is open-circuited.

Consider now how these two waves behave as the distance l from the load
increases. The incident wave advances in phase beta radians per unit
length, while the reflected wave lags correspondingly; at the same time
magnitudes do not change greatly when the attenuation-constant alpha is
small. The vector sum of the voltages of the two waves is less than the
arithmetic sum, as illustrated in Fig. 4-3a, for l=lambda/8. This
tendency continues until the distance to the load becomes exactly a
quarter wavelength, i.e.,until beta l = pi/2. The incident wave has then
advanced 90-degrees from its phase position at the load, while the
reflected wave has dropped back a similar amount. The line voltage at
this point is thus the arithmertic difference of the voltages of the two
waves, as shown in Fig. 4-3a, for l=lambda/4 and it will be quite small
if the attenuation is small. The resultant voltage will not be zero,
however, because some attenuation will always be present, and this
causes the incident wave to be larger and the reflected wave to be
smaller at the quarter-wave length point than at the load, where the
amplitudes are exactly the same."

This is enough of Terman`s desctiption to establish the pattern of SWR.
He describes simply but not too simply. Almost anything anyone would
want to know is in the book. The illustrations are worth thousands of
words.
Anytime I have any doubt about radio, Terman can straighten me out.

Best regards, Richard Harrison, KB5WZI