On Mon, 7 Jan 2008 20:13:32 -0500
"AI4QJ" wrote:


"Roger Sparks" wrote in message
...
On Mon, 07 Jan 2008 12:34:03 -0600

After considerable thought and time, I realized that the origin of "x"
was not at the input point, but was at the reflection point. Then the
notation made perfect sense.

Forward wave-
input-_____________________________________|Reflectio n point
++x - increasing x - Reflected wave 0

Scale both the sine wave and physical line in degrees. The wave will
repeat every 360 degrees (2pi radians). The x scale can be as long (in
degrees or radians) as desired

Think of the sine wave as an curve traced on a MOVING sheet of paper. The
paper/curve moves in the direction of the forward wave.

Try this:

Pick a distance x = pi/3. Now take the sheet of paper perpendicular to the
dipole wire. Move it at a constant velocity in the perpendicular direction
with a pen recorder tracing the magnitude of the voltage on the antenna to
the paper as it moves. There will be a cosine function drawn on the paper.

Given: I = Io*cos(kx)*cos(wt)

Thanks for the examples. You use the term "I" which is usually the current, but the math makes sense for voltage.

To find the distance x = pi/3, I assume you mean from one end of the dipole, back toward the dipole center?


At pi/3 radians, cos(pi/3) = 0.5

The cosine function drawn on the paper moving at right angles to the antenna
will be:

I = 0.5*Io*cos(kt).

Now move the paper to x = pi/2.

cos(pi/2) = 0

The function drawn on the paper will be I = 0.

Now move the paper to x = pi

cos(pi) = -1

The function drawn on the paper, at RIGHT ANGLES tio the antenna will be:

I = -Io*cos(wt)

As cos(wt) rotates between 0 and 2pi, cos(wt) moves between +1 and -1. The voltage will always be the negative of the initial voltage times the cosine of the instantaneous angle wt.

That is how a standing wave operates.

OK, I think I understand.

Thanks for sending the examples.


73, Roger W7WKB