Standing Waves

Whenever there is a mismatch of impedance between transmission line and load, reflections will occur. If the incident signal is a continuous AC waveform, these reflections will mix with more of the oncoming incident waveform to produce stationary waveforms called standing waves. The following illustration shows how a triangle-shaped incident waveform turns into a mirror image reflection upon reaching the line's unterminated end. The transmission line in this illustrative sequence is shown as a single, thick line rather than a pair of wires, for simplicity's sake. The incident wave is shown traveling from left to right, while the reflected wave travels from right to left: (Figure 18.1) If we add the two waveforms together, we find that a third, stationary waveform is created along the line's length: (Figure 18.2)

Figure 18.1: Incident wave reflects off end of unterminated transmission line.

This voltage standing wave ratio, "standing" wave, in fact, represents the only voltage along the line, being the representative sum of incident and reflected voltage waves. It oscillates in instantaneous magnitude, but does not propagate down the cable's length like the incident or reflected waveforms causing it. Note the dots along the line length marking the "zero" points of the standing wave (where the incident and reflected waves cancel each other), and how those points never change position: (Figure 18.3)

Figure 18.2: The sum of the incident and reflected waves is a stationary wave.

Figure 18.3: The standing wave does not propagate along the transmission line.

One way of expressing the severity of standing waves is as a ratio of maximum amplitude (antinode) to minimum amplitude (node), for voltage or for current. When a line is terminated by an open or a short, this standing wave ratio, or SWR is valued at infinity, since the minimum amplitude will be zero, and any finite value divided by zero results in an infinite (actually, "undefined") quotient. In this example, with a 75 line terminated by a 100 impedance, the SWR will be finite: 1.333, calculated by taking the maximum line voltage at either 250 kHz or 750 kHz (0.5714 volts) and dividing by the minimum line voltage (0.4286 volts). Standing wave ratio may also be calculated by taking the line's terminating impedance and the line's characteristic impedance, and dividing the larger of the two values by the smaller. In this example, the terminating impedance of 100 divided by the characteristic impedance of 75 yields a quotient of exactly 1.333, matching the previous calculation very closely. Standing wave ratio are as given

A perfectly terminated transmission line will have an SWR of 1, since voltage at any location along the line's length will be the same, and likewise for current. Again, this is usually considered ideal, not only because reflected waves constitute energy not delivered to the load, but because the high values of voltage and current created by the antinodes of standing waves may over-stress the transmission line's insulation (high voltage) and conductors (high current), respectively.

ELABORADO POR:

NERWIN ANTONIO MORA REINOSO

C.I: 17.557.095

CAF