Cecil Moore wrote:
Roger wrote:
Cecil Moore wrote:
Are there any reflections at point '+'?

If not, how is energy stored in the stub?

If so, what causes those reflections?

I am not sufficiently familiar with circulators to respond.

If the circulator is bothering you, forget it and assume the
following lossless conditions:

Ifor = 1 amp --
------------------------------+
-- Iref = 1 amp | 1/4
| WL
All Z0 = 50 ohms | shorted
| stub

Please think about it and answer the questions above.
The main point to remember is that there is no physical
impedance discontinuity at '+'.

OK. Let's begin by recognizing that this circuit is identical to a
straight transmission line. The purpose of identifying the stub is to
clearly locate the point 1/4 wavelength from the end of the line. The
line is shorted at the end.

We further assume that the peak current is 1 amp.

Are there reflections at point "+"? Traveling waves going in opposite
directions must pass here, therefore they must either pass through one
another, or reflect off one another.

Is it important to decide this issue? Yes, if it will affect the answer
to questions such as what is the voltage or current at this point.

Will it affect the answers? No. Under the conditions described, the
waves passing in opposite directions will have equal voltages and
opposite currents. If they pass through one another, the voltages will
add, but the currents will subtract. If they reflect, the voltage of
each component (Vf and Vr) will add on itself, and the individual
currents will reverse on themselves and therefore subtract. Either way,
the total voltage will double, and total measured current would be zero.
There is no reason to decide the issue.

How is energy stored in the stub? We have defined current as entering
an leaving the stub. Current is thought of as movement of charged
particles, but not as a concentration of particles. A concentration of
charged particles exhibits voltage. Energy is present when EITHER
current or voltage are shown to be present. Here, current is defined as
one amp so energy must be present some place on the line. The stub is
1/4 wavelength long physically, but it is 1/2 wavelength long
electrically, so that if we have energy present in the time-distance
shape of a sine wave, we would have an entire 1/2 wave's worth of energy
present on the stub at all times. The location of peak voltage (or peak
current) will depend upon the time-distance reference used to describe
the moving wave. (We would have equal voltage(but opposite polarity)
peaks located at the point {+} if we assumed the center of the forward
and reflected wave each to located 90 degrees from the shorted end.)

The circuit shows forward current Ifor and reflected current Iref as if
each were only one current. When we consider traveling waves, we need
to remember that Ifor and Iref can be measured on either of the two
wires composing a transmission line. The forward wave exists on both
wires, but the sides display opposite polatity and direction of current
despite both moving in the same direction. It is best to consider the
forward traveling wave as two waves, each carrying half the power, with
one wave per wire.

Does this match your own concept of the traveling waves acting at the
{+} point Cecil? If not, where do we differ?

73, Roger, W7WKB

Is this the kind of answer you were looking for? The answer could be
given mathematically but that might be even more confusing.