Consider how electricity gets to your home. Generators produce large voltages and currents at a power plant. The problem: getting the electricity from the plant to the homes, businesses, and other facilities that need it. This process involves the use of long wire transmission lines.Transformers are also required to step the voltages up or down. As another example, consider a radio broadcast or communications station. The transmitter produces high frequency ac. The problem is getting the power to be radiated by the antenna, located some distance from the transmitter. This involves the use of an RF transmission line. The most common type is coaxial cable. Two wire line is also sometimes used. At ultrahigh and microwave frequencies, another kind of transmission line, known as a waveguide, is often employed.
Loss: The Less, The Better!
The overriding concern in any power transmission system is minimizing the loss. Power wastage occurs almost entirely as heat in the transmission line conductors and dielectric, and in objects near the line. Some loss can take the form of unwanted electromagnetic radiation from the line. Loss also occurs in transformers. Power loss in an electrical system is analogous to the loss of usable work produced by friction in a mechanical system. The less of it, the better! In an ideal power transmission system, all of the power is VA power; that is, it is in the form of ac in the conductors and an alternating voltage between them. It is undesirable to have power in a transmission line or transformer exist in the form of true power, because that translates into either heat loss, or radiation loss, or both. The place for true power dissipation or radiation is in the load, such as electrical appliances or radio antennas.
Power Measurement in a Transmission Line
Power measurement in a transmission line. Ideally, the voltage and the current should be measured at the same physical point on the line.
In an ac transmission line, power is measured by placing an ac voltmeter between the conductors, and an ac ammeter in series with one of the conductors (above figure). Then the power P (in watts) is equal to the product of the rms voltage E (in volts) and the rms current I (in amperes). This technique can be used in any transmission line. But this is not necessarily an indication of the true power dissipated by the load at the end of the line.
Recall that any transmission line has a characteristic impedance. This value, Zo, depends on the diameters of the line conductors, the spacing between the conductors, and the type of dielectric material that separates the conductors. If the load is a pure resistance R containing no reactance, and if R = Zo, then the power indicated by the voltmeter/ammeter scheme will be the same as the true power dissipated by the load—provided that the voltmeter and ammeter are placed at the load end of the transmission line.
Power measurement in a transmission line. Ideally, the voltage and the current should be measured at the same physical point on the line. If the load is a pure resistance but it differs from the characteristic impedance of the line, then the voltmeter and ammeter will not give an indication of the true power. Also, if there is any reactance in the load, the voltmeter/ammeter method will not be accurate, even if the resistive component happens to be the same as the characteristic impedance of the line. The physics of this is rather complicated, and we won’t get into the details here. But you should remember that it is optimum for the impedance of a load to be a pure resistance R, such that R = Zo. When this is not the case, an impedance mismatch is said to exist.
Small impedance mismatches can often be tolerated in power transmission systems. But this is not always the case. In very high frequency (VHF), ultrahigh frequency (UHF), and microwave radio transmitting systems, even a small impedance mismatch between the load and the line can cause excessive power losses in the line. An impedance mismatch can usually be corrected by means of a matching transformer between a transmission line and the load, and/or the deliberate addition of reactance at the load end of the line to cancel out any existing load reactance.
Loss in a Mismatched Line
In a matched line, the ratio of the voltage to the current (E/I ) is constant everywhere along the line, although the actual values of E and I decrease with increasing distance from the source.
When a transmission line is terminated in a resistance R = Zo, then the current and the voltage are constant all along the line, provided the line has no loss. The ratio of the voltage to the current, E/I, is equal to R and also equal to Zo. But this is an idealized case. No line is completely lossless. In a real world transmission line, the current and voltage gradually decrease as a signal makes its way from the source to the load. But if the load is a pure resistance equal to the characteristic impedance of the line, the current and voltage remain in the same ratio at all points along the line (above figure).
If the load is not perfectly matched to the line, the current and voltage vary in a complicated way along the length of the line. In some places, the current is high; in other places it is low. The maxima and minima are called loops and nodes, respectively. At a current loop, the voltage is minimum (a voltage node), and at a current node, the voltage is maximum (a voltage loop). The current and voltage loops and nodes along a mismatched transmission line, if graphed as functions of the position on the line, form wavelike patterns that remain fixed over time. They just stand there. For this reason, they are called standing waves.
Standing Wave Loss
At current loops, the loss in line conductors reaches a maximum. At voltage loops, the loss in the dielectric reaches a maximum. At current nodes, the loss in the conductors reaches a minimum. At voltage nodes, the loss in the dielectric reaches a minimum. It is tempting to suppose that everything would average out here, but it doesn’t work that way! Overall, in a mismatched line, the line losses are greater than they are in a perfectly matched line. This extra line loss increases as the mismatch gets worse.
Transmission line mismatch loss, also called standing wave loss, occurs in the form of heat dissipation. It is true power. Any true power that goes into heating up a transmission line is wasted, because it cannot be dissipated in the load.
The greater the mismatch, the more severe the standing wave loss becomes. The more loss a line has to begin with (that is, when it is perfectly matched), the more loss is caused by a given amount of mismatch. Standing wave loss also increases as the frequency increases, if all other factors are held constant. This loss is the most significant, and the most harmful, in long lengths of transmission line, especially in RF practice at VHF, UHF, and microwave frequencies.
A severe mismatch between the load and the transmission line can cause another problem: physical damage to, or destruction of, the line! A feed line might be able to handle a kilowatt (1 kW) of power when it is perfectly matched. But if a severe mismatch exists and you try to feed 1 kW into the line, the extra current at the current loops can heat the conductors to the point where the dielectric material melts and the line shorts out. It is also possible for the voltage at the voltage loops to cause arcing between the line conductors. This perforates and/or burns the dielectric, ruining the line.
When an RF transmission line must be used with a mismatch, derating functions are required to determine how much power the line can safely handle. Manufacturers of prefabricated lines such as coaxial cable can supply you with this information.