## Standing Waves

As we go into the area of standing waves we will continue our discussion on the instantaneous values of incident and reflected waves on an open-ended line from the previous tutorial.

Refer to the illustration below once again. Instantaneous values of incident and reflected waves on an open-ended line.

In waveform (4), the incident wave is at a maximum negative value at the end of the line. The wave has moved another 45 degrees to the right from the wave in the preceding illustration. The reflected wave has also moved 45 degrees, but to the left. The reflected wave is in phase with the incident wave. The resultant of these two waves, shown by the dark line, again has a negative maximum at the end of the line and a positive maximum 1/2 wavelength from the end of the line. Notice that these maxima have a greater amplitude than those in waveform (3).

In waveform (5), the incident wave has moved another 45 degrees to the right and the reflected wave 45 degrees to the left.The resultant again is maximum negative at the end and positive maximum 1/2 wavelength from the end. The maxima are lower than those in waveform (4). In waveform (6), the incident and reflected wave have moved another 1/8 wavelength.

The two waves again are 180 degrees out of phase, giving a resultant wave with no amplitude. The incident and reflected waves continue moving in opposite directions, adding to produce the resultant waveshapes shown in waveforms (7) and (8). Notice that the maximum voltage in each resultant wave is at the end and 1/2 wavelength from the end.

Study each part of the figure above carefully and you will get a clear picture of how the resultant waveforms of voltage are produced. You will also see that the resultant voltage wave on an open-ended line is always zero at 1/4 wavelength and 3/4 wavelength from the end of the transmission line. Since the zero and maximum points are always in the same place, the resultant of the incident and the reflected wave are called STANDING WAVES of voltage.

The right-hand column in the figure above shows the "current" waveshapes on the open-ended line. Since the current is reflected out of phase at an open end, the resultant waveshapes differ from those for voltage. The two out-of-phase componnts cancel at the end of the transmission line, so the resultant is always zero at that point. If you check all the resultant waveshapes shown in the right-hand column of figure, you will see that a zero point always occurs at the end and at a point 1/2 wavelength from the end. Maximum voltages occur at 1/4 and 3/4 wavelengths from the end.

When an ac meter is used to measure the voltages and currents along a line, the polarity is not indicated. If you plot all the current and voltage readings along the length of the line, you will get curves like the ones shown in the next figure below. Notice that all are positive. These curves are the conventional methodof showing current and voltage standing waves on rf lines. Conventional picture of standing waves.

When an rf line is terminated in a short circuit, reflection is complete, but the effect on voltage and current differs from that in an open-ended line. Voltage is reflected in opposite phase, while current is reflected in phase. Again refer to the series of pictures shown in the first figure above. However, this time the left column represents current, since it shows reflection in phase; and the right column of pictures now represents the voltage changes on the shorted line, since it shows reflection out of phase.

The composite diagram in the figure below shows all resultant curves on a full-wavelength section of line over a complete cycle. Notice that the amplitude of the voltage varies between zero and maximum in both directions at the center and at both ends as well but, one-fourth of the distance from each end the voltage is always zero. The resultant waveshape is referred to as a standing wave of voltage. Standing waves, then, are caused by reflections, which occur only when the line is not terminated in its characteristic impedance. Composite results of instantaneous waves.

The voltage at the center and the ends varies at a sinusoidal rate between the limits shown. At the one-fourth the three-fourths points, the voltage is always zero. A continuous series of diagrams such as these is difficult to see with conventional test equipment, which reads the effective or average voltageover several cycles. The curve of amplitude over the length of line for several cycles is shown in the figure above, view B. A meter will read zero at the points shown and will show a maximum voltage at the center, no matter how many cycles pass.

As shown in view D, the amplitude varies along the length of the line. In this case it is zero at the end and center but maximum at the one-fourth and three-fourths points. The entire diagram of the openended line conditions is shown in view E. The standing waves of voltage and current appear together.Observe that one is maximum when the other is minimum. The current and voltage standing waves are one-quarter cycle, or 90 degrees, out of phase with one another.

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