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Restricted Space Antennas

by Walt Fair, Jr., W5ALT

What is SWR?

SWR or Standing Wave Ratio is one of the most misunderstood terms in amateur radio. Even though every antenna and transmission line book that I have seen is quick to point that out, it still is the source of many misconceptions. To most hams with an SWR meter, SWR is whatever the meter reads and if the meter says there's no problem, then all is well. That simply isn't true. In this section, we'll try once again to explain what exactly SWR is and isn't. There are enough problems in antenna design and construction without adding another source of confusion! Especially when dealing with compromise antennas, we need to make sure we undertand exactly what SWR means, since we generally will have short, low impedance antennas and SWR can be a major source of inefficiencies.

Back to Transmission Lines. In the previous section the subject of matching an antenna to a transmission line was discussed and it was pointed out that matching the antenna to the transmission line is very different than matching the transmitter to the line. It was also mentioned that every transmission line has a characteristic impedance, which is normally 50, 75, 300 or 450 ohms, depending totally on the construction of the line.

In the best circumstances, we would use a 50 ohm transmission line to connect a 50 ohm impedance antenna to a transmitter rated at 50 ohms output impedance. In that case everything is matched and as long as we make sure there are no currents flowing on the coax shield, everything should work great. Since all parts of the system are matched, transmission line losses are minimized, the transmitter can operate at its designed efficiency and almost all of the power output by the transmitter will get to the antenna and be radiated.

But what happens when we connect a 50 ohm transmission line to an antenna with a feed point impedance that is not 50 ohms? Let's say, for example, that the antenna has an input impedance of 10 ohms resistive, which is not too uncommon in short antennas. Notice that the transmission line is 50 ohms and is matched to the 50 ohm transmitter output. However, the impedance mismatch between the 50 ohm transmission line and the 10 ohm antenna causes an SWR of 50/10 = 5:1 and a substantial amount of power is reflected from the antenna back down the transmission line. More than likely the protective circuits in the transmitter will cause it to reduce power.

Standing Waves. Consider what is happening in the transmission line. The transmitter is feeding power (current and voltage) at a certain frequency or wavelength into the line. At the antenna or load end, some of the power is absorbed by the load or radiated. The rest of the power is reflected back along the line towards the transmitter. All along the transmission line the forward and the reflected current and voltages combine to give the total current and voltage anywhere along the line. As long as the load impedance, line length and frequency do not change, a stable pattern of voltage and current peaks and valleys will appear on the line. That is called a "standing wave," since it doesn't change. The ratio of the maximum voltage to the minimum voltage is a measure of the mismatch and is called the "Voltage Standing Wave Ratio" or VSWR.

In the same way, the ratio of the maximum to minimum current is called the "Current Standing Wave Ratio" or ISWR, where the I stands for current. It can be shown that the ISWR is the same as the VSWR, but VSWR is normally easier to measure. Normally we just say SWR, implying VSWR. But don't forget that what is being described is the voltage distribution along the transmission line caused by the mismatch between the transmission line and the load or antenna.

In our example, the SWR on the transmission line is 5:1. This is equal to the ratio of the antenna impedance (10 ohms) to the transmission line characteristic impedance (50 ohms). Thus, without knowing anything else, we know that the maximum voltage along the line is 5 times the minimum voltage. And we also know that the maximum current on the transmission line is 5 times the minimum current on the line. Since resistive losses depend on the current squared (I2), we also know that whatever losses there are on the line are larger than if the current were smaller.

Impedance. What about the impedance? We know that at the antenna the impedance is 10 ohms. We also know that impedance is the ratio of voltage to current and both voltage and current are changing along the line, since we have standing waves. In fact they both change by a factor of 5, in the example. Let's assume that the current is minimum and the voltage maximum at the antenna. Then 1/4 wavelength away from the antenna the current is maximum and the voltage is minimum. It can be shown that at that point the voltage is 5 times greater than at the antenna and the current will be 5 times less, so the impedance will be 25 times greater. Instead of 10 ohms, it will be 250 ohms. Notice that 250/50 = 50/10 = 5, which is the SWR.

Now, since in our example, there is a point on the transmission line (at the antenna) where the impedance is 10 ohms and there is also another point on the line (1/4 wavelength away) where the impedance is 250 ohms, it stands to reason that there is some point on the line in between where the impedance is exactly 50 ohms. In fact, that is correct. If we found that point and connected the transmitter exactly at the 50 ohm impedance point, the transmitter would be satisfied and transmit at full efficiency. But, the current and voltage distribution along the line is still the same! There are still standing waves, there is still higher current than necessary, and there are still excess losses in the transmission line because of the standing waves.

So, let's see what happens with our SWR meter. If we connect the transmitter directly to the antenna and measure the SWR there, the meter will read an SWR of 5:1, just as expected. If we connect the transmitter exactly at the 50 ohm impedance point, the meter will read an SWR of 1:1. If we connect the transmitter at the 1/4 wavelength point, where the impedance is 250 ohms, the meter will again read 5:1, since 250/50 = 5.

How can that be? The SWR isn't changing, because the standing waves still exist due to the impedance mismatch between the 50 ohm transmission line and the 10 ohm antenna. Yet the meter reads anywhere from 5:1 down to 1:1 and back to 5:1, depending on where the transmitter and meter are connected. What the heck is going on!?

SWR Meters. To understand this phenomenon we need to know exactly what a typical SWR meter is measuring. Notice that it is not measuring the maximum and minimum voltages (or currents) along the transmission line. Obviously it can't do that because it is only at one place on the transmission line. That means that it is not measuring the transmission line SWR, even though it is called an "SWR Meter." So just what is it measuring?

The ARRL Antenna Book and other textbooks that describe SWR meters generally talk about bridge circuits and directional couplers. In these circuits the transmitted signal is fed across a bridge consisting of resistors that equal the transmission line characteristic impedance of 50 ohms. (Note that some professional meters may use other impedances, but they are generally expensive and not used for amateur purposes.) The meter is essentially measuring the ratio of the impedance at the point it is inserted to 50 ohms. Thus, in the example, it will read anywhere from 50/10 = 5 to 50/50 = 1 back to 250/50 = 5, depending on where in the line it is inserted.

In other words, the common SWR meter measures the ratio of impedance to 50 ohms. It does not measure the transmission line "standing wave ratio."

It is apparent that we need to keep the SWR as close to 1:1 as possible to reduce feed line losses. However, our meter cannot read the actual SWR on the transmission line and just because it indicates 1:1 does not mean that the transmission line and antenna are matched with no standing waves on the transmission line. What are we to do?

At this point, it would behoove anyone interested in optimizing their antenna to grab a book on transmission lines and study the distribution of impedance along a line. The example used here showed a purely resistive load. While things are more complicated when the antenna shows a resistive and reactive load, the concepts are the same. There is one place along the transmission line where we can always guarantee that we can read the actual SWR with respect to a 50 ohm line. That is exactly at the antenna. In other words, if you want to know what the SWR is for line losses, then read the SWR using 50 ohm coax at the antenna, not at the transmitter.