Standing Waves Part ll


In ‘Standing Waves Part l’ we looked at a number of features of standing waves including:-
a) the peculiar shape of standing waves, (i.e. they are not sine waves),
b) the fact that their crests or their minima are spaced half a wavelength apart, (for an air filled transmission line),
c) that more power may be dissipated in the line when standing waves are present than that calculated from the quoted loss of the line per given length,
d) that the ratio of the maximum amplitude, (voltage or current), to the minimum amplitude, is known as the Standing Wave Ratio, (SWR), and that this is used as a measure of the magnitude of the mismatch between the load, (often an aerial) and the characteristic impedance of the transmission line. This important ratio is used even though the width of the maximum is broad and that of the minimum is often very much less.

The Standing Wave Ratio of an Aerial.
One of the most frequently made measurements of SWR is in connection with the performance of an aerial, and this will be used as an example in the following discussion. However, when making the measurement on an aerial, it is often inconvenient to break into the aerial system and insert an SWR meter between the far end of the transmission line, (or feeder), and the aerial. The reason that it may be inconvenient is that often this would require climbing on a roof or up onto a chimney or tower. What is often done is to insert the SWR meter between the transceiver and the near end of the line and measure the SWR of the aerial plus the transmission line. It is sometimes said that it doesn’t matter where in the transmission line the meter is placed, the SWR is the same everywhere as long as there is no current on the outside of the line. In general, this statement is not true unless the line is lossless. The true SWR of the aerial at the end of the line is “softened” by the loss in the transmission line making a bad aerial SWR look better than it really is. An indication of this is shown in the log-log graph of figure 1. Here the SWR measured at the generator, (transceiver), end of the line is plotted against the true SWR of the load for five different representative amounts of loss in the transmission line. It can be seen for example, that even a modest line loss of 2dB can convert a true SWR of 5:1 of the aerial, into about 3:1 as measured at the transceiver.

Multiple Reflections.
What happens to the RF power that is reflected by the mismatched load? In the following, the generator and load will be assumed to be a transceiver and an aerial respectively. Any RF power that is not used by the aerial travels back, suffering line attenuation on the way, to the transmitter. Here various things can happen. Some books assume it is absorbed, i.e. the transmitter looks like a matched load. Others assume that it is totally reflected, and some that it is partially reflected. Transmitters have an effective impedance just as aerials or other systems have, and this causes reflections to lie somewhere between the two extremes of total and no reflection.

In designing a transmitter, the outtput impedance is chosen to be a compromisee between the maximum possible power output which could be obtained from the circuit and components, and an acceptable efficiency. If the output impedance oof the transmitter were made equal to the line impedance, the maximum efficiency, (in CW mode or on SSB ppeaks), would be only 50% and half the DC innput power to the PA would be dissipated in it. This figure is often considered too low, and an efficiency nearer 75% is usually considered more acceptable. This requires the PA to be designed to have an outpuut impedance of 16 2/3 ohms when working into a 50 ohm load or trannsmision line. Assuming the transmitter output impedance is purely resistive, the returning wave reflectedd by the aerial sees this rather low impedance and therefore produces an SWR of 3:1. This means that 25% off this returning power is reflected back towards the aerial. Whether it is in phase or not when it gets there determines whether a portion of it adds to or subtracts from the radiated power. Hence the discrepancy between the accounts. (This is an over-simplification for simplicity).

What happens if we include an ATU between the transmitter and the feeder line to the aerial? We have already discussed the fact that this is not the ideal place for it, but it is easier to tune it here than if it were at the aerial end of the line. Placing the ATU adjacent to the transmitter will at least ensure that the transmitter sees its optimum load. The purpose of an ATU is to produce its own “mismatch” which is said to be the “complex conjugate” of the aerial missmatch. That is to say, it produces a similar mismatch but of the opposite phase, thus cancelling the aerial mismatch as far as the transmitter is concerned. Now a mismatch is the same mismatch from whichever side the wave approaches. So the reflected wave returning from the aerial encounters the same mismatch at the ATU as it did at the aerial, and the samme proportion of the power is again reflected back towards the aerial. Due to the workings of a complex conjugate match, (a description of which is beyond the scope of this article), the phase of this reflection is such that when it arrives back at the aerial it is in phase with the original signal and so adds constructively to it. A portion is again reflected by the aerial mismatch, and so on and so on. In theory, this process continues until all the power except that lost in the transmission line is absorbed by the aerial.

Measuring transmission Line Loss.
A gross mismatch can be used to advantage. By measuring the SWR at one end of a transmission line which is open or short circuited at the other, a good estimate of the loss of the line can be obtained.
Unfortunately, one has to get at the far end of the line to disconnect the aerial, and this is often inconvenient for the reasons mentioned above. The method recommended in at least one edition of the RSGB Communications Handbook, is that you make the measurement at an inappropriate frequency for the aerial.
This is not really valid. The reason is that an aerial designed for one frequency very seldom looks like either a good open or a short circuit at an “out of band” frequency, and this can lead to significant errors.

Unfortunately, there is no substitute for disconnecting the aerial. For best accuracy with transmission lines of moderate loss, (say up to a few dBs), it is better to make the measurement of line loss at the highest frequency which one’s transceiver is capable of, (say 30MHz). If you want to know what the loss is at some lower frequency it is usually easier and more accurate to interpolate using the usual square root rule between loss and frequency. Unfortunately, even making the measurement with a good open or short circuit at the far end introduces a small error if a frequency even a few MHz away from the measurement frequency is used. This is because the number of lossy quarter wavelengths of high current along the line will have changed.



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