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Restricted Space Antennas

by Walt Fair, Jr., W5ALT

Impedance Matching

Impedance matching is another subject which often causes confusion. In this section we'll take a look at why we should worry about impedance matching in antenna systems and what effect may be due to a matched or unmatched condition. It will be seen that impedance matching is important in two separate instances for very different reasons: the transmitter to transmission line match and the transmission line to antenna match.

Transmitter Power. We've all heard that our transmitters have an output impedance of 50 ohms. (No, you can't measure that with an ohm meter - I tried.) Or perhaps in the transmitter specifications it says that the transmitter will deliver 100 watts, for example, into a 50 ohm load, which is the same thing. What does that mean? What is the significance of 50 ohms?

First, remember that power is voltage times current: P = E I. Also from Ohm's Law voltage is current times resistance: E = I R. Therefore, we can calculate the needed voltage and current from power and resistance using I = SQRT(P / R) and V = SQRT(P R).

Let's say we have a transmitter output of 100 watts. If the transmitter is connected to a 50 ohm dummy load, then we can calculate that the current is 1.414 amps and the voltage is 70.721 volts, forgetting about whether that is peak, average, RMS or whatever. (You can check that 1.414 x 70.721 = 100) This means that the manufacturer (or circuit designer, if it's homebrew) is willing to guarantee that the transmitter will generate 1.414 amps at 70.721 volts, which is what is needed to output 100 watts into a 50 ohm load. And that's all it means.

What happens if we want to put 100 watts into a different load, say 25 ohms or 100 ohms? In the same way, from Ohm's Law we can calculate that the current and voltage for 100 watts into a 25 ohm load are 2 amps and 50 volts, while for a 100 ohm load the current is 1 amp at a voltage of 100 volts. Notice that in the first case the current is higher (2 amps instead of 1.414 amps), while in the second case the voltage is higher (100 volts, instead of 70.721 volts). Now perhaps the transmitter will handle that, but the manufacturer isn't willing to guarantee it.

Likewise, we can calculate the current and voltage required to generate 100 watts into any type of load. We will see that in all cases, either the current will be higher than 1.414 amps or the voltage required will be higher 70.721 volts. Sooner or later we will arrive at a current or voltage that exceeds the design specifications of the transmitter circuits. In that case, most modern transmitters contain additional circuitry to limit the current or voltage, hence reducing the output power. Of course the alternative is to exceed the ratings of the internal circuitry and burn up the transmitter.

So, in order to get the most power out of the transmitter, it is neccesary to ensure that the transmitter is connected to a 50 ohm load. If the load impedance is different, then the transmitter will require either more current or more voltage, and the manufacturer isn't willing to guarantee that it will deliver. That's why we want to match the load impedance at the transmitter output to 50 ohms. It has nothing to do with the function or efficiency of the antenna. We can do that in several ways, including the use of an antenna tuner at the transmitter output. We are simply making sure that the transmitter is operating within its specifications. Nothing more.

When should we be worried about matching the transmitter to the transmission line? If the transmitter is generating full power into the line, then there is no more power available. Spending time and effort improving the match will not increase the power output of the transmitter, since it's already at maximum. If the transmitter is generating less than maximum power, however, improving the match will allow it to generate more. In that case the effort may be worthwhile.

Transmission Lines. The subject of transmission lines is an entire field of study in and of itself, so we won't cover very much here. However, at least a basic understanding of transmission line theory is essential to understanding antenna systems. After all, the transmission line is what delivers power from the transmitter to the antenna, or from the antenna to a receiver. We certainly want to make sure that all the power gets where we want it to go. The ARRL Handbook, the ARRL Antenna Book, or most any textbook on antennas has a more detailed description and discussion of transmission lines.

It is well known that every common type of transmission line has a characteristic impedance. When you hear of 50 ohm coax or 75 ohm cable or 300 ohm twin lead, the 50, 75 and 300 ohm numbers refer to the characteristic impedance of the particular transmission line. It can also be shown that when a transmission line is terminated in a load that matches its characteristic impedance, the power is totally absorbed in the load, which is what we want from our antenna systems. However, if the line is terminated in an impedance that is not the same as its characteristic impedance, then the power is not totally absorbed and some of it is reflected back down the line toward the tranmitter. When it reaches the transmitter, it again is reflected back towards the load. After all, we hope that the transmitter is generating power, not absorbing it!

This process of reflecting power back and forth between the transmitter and load eventually leads to a steady state condition where a distribution of current exists on the transmission line. The power all eventually gets absorbed by the load, but in the meantime there is a higher current on the transmission line than need be. Since a higher current means more losses within the transmission line, due to wire resistance and other effects, when the load is not matched to the transmission line, there will be more losses in the line. Remember that power losses are represented by I2 R, so doubling the current will cause 22 = 4 times more losses.

In addition, the current reflected back and forth creates standing waves on the transmission line. That means that the voltage and the current vary along the line when the load is not equal to the characteristic impedance of the line. We can use an SWR (Standing Wave Ratio) meter to measure the magnitude of these waves. The SWR meter gives the ratio of the highest and lowest voltage along the line, which is the same as the ratio of the highest to lowest currents on the line. A perfect match is a standing wave ratio of 1:1, meaning that the highest and lowest voltages and currents are equal; in other words, there is no variation along the line.

When should we be worried about matching our antenna, which is the load, to the transmission line? As shown in most books about antennas and transmission lines, the power losses on the line depend on the line length, the type of transmission line, the frequency and the SWR on the line. So, in order to determine whether the losses due to mismatch are important, it is neccesary to determine the feedline losses.

Parallel lines normally have a relatively low loss and are not severely affected by high SWR or mismatch. Generally speaking, rarely will there be a major benefit from improving the match to parallel lines, unless the frequency is very high or the line is very long. At normal HF frequencies and lines less than 100 feet long, the improvement will not usually be noticable.

Coaxial cables, however, generally have a higher loss and are more dramatically affected by high SWR and mismatch. Especially for longer lines and higher frequencies, improving the match between the antenna and the feed line may well yield a significant improvement in antenna performance by reducing transmission line losses. For both parallel and coaxial transmission lines, refer to the charts in most textbooks to determine the magnitude of the losses.

Another of the concepts related to transmission lines was discussed in the previous section on antenna balance. It must be noted that the consequence of a mismatch is entirely different from the concept of balance. They have absolutely nothing to do with each other. It is possible to have a matched system with a SWR of 1:1 and still have an unbalanced feed line. Likewise, it is quite easy to have a balanced feedline and have a terrible SWR and high transmission line losses.

Finally, we noted that matching the transmitter to the transmission line and matching the transmission line to the antenna serve 2 very different purposes. Note that matching the transmission line to the antenna may well ensure that all power is absorbed by the antenna and therefore radiated, but it will not ensure that the transmitter is operating at maximum efficiency. Likewise, matching the transmitter to the transmission line will not affect the transmission line losses, since those are determined only by the match between the transmission line and antenna.

Next - SWR