A losing proposition

Dec 1, 2007 12:00 PM, By Harold Kinley

In the first example, there was no line loss, so the transmitted power is simply equal to the difference between the forward power and the reflected power at point A. In the second example, the forward power at the antenna (point C) was 50 W and the reflected power was 10 W; accordingly, the net power is 40 W. At the input side of the line at point A, the difference between the forward and reflected power results in net power of 95 W. By comparing the net input power with the net output power we can determine the net line loss. In this example, the net line loss in decibels is shown in Equation 1.

In the third example the antenna was matched to the 50-ohm system impedance, so there is no reflected power and the radiated power is 50 W. Thus, the line loss is 3 dB. Compare this with the line loss in the second example, where there was a mismatch at the antenna. The additional loss caused by such a mismatch is equal to 0.76 dB (3.76 dB - 3 dB). This extra line loss (above the normal matched line loss) increases with normal transmission line loss; it also increases with higher VSWR at the antenna. Remember, in the first example there was a mismatch at the antenna but no line loss, and the net input power at point A was equal to the net output power at point C, the antenna. In the second example, the VSWR at the antenna was 2.62:1 while the directional wattmeter readings indicated that the VSWR at the input side of the line was only 1.58:1.

It is important to note that the line loss actually masked the VSWR that existed at the antenna. This is quite misleading; the line loss must be taken into consideration when trying to determine the VSWR at the input side of the transmission line. This discussion assumes that the reflection is a single-point reflection occurring at the antenna (point C).

The VSWR can be calculated from the forward and reflected power. In the first example the forward power at point A on the line was 100 W and the reflected power was 20 W. From this, assuming a 50-ohm line, we can calculate the voltage in the forward and reflected waves. The calculation is shown in Equation 2. In this equation, Ef represents voltage in the forward wave, P represents power in the forward wave and Z represents the system impedance. The voltage in the reflected wave is calculated as shown in Equation 3, where Er represents voltage in the reflected wave.

Now that we know the voltages in the forward and reflected waves, we can calculate the VSWR as shown in Equation 4. In most cases, the RF attenuation of the transmission line is undesirable and causes a waste of RF power. In planning a base station and the desired coverage area, software usually is used to determine the antenna height and power required to provide adequate coverage of the desired area. Suppose the system required a minimum of 300 W of effective radiated power (ERP) at a given location and antenna height. Further suppose that the transmitter power is limited to 100 W and the antenna gain is 6 dBd. If the line loss were 0 dB, then the ERP would be 400 W. The loss of the required transmission line should not exceed 1.25 dB. (See Equation 5.)

From this, it is obvious that a transmission line with a loss no greater than 1.25 dB at the operating frequency must be used. Consult manufacturers' catalogs to find the cable that offers RF attenuation (at the required length) of no more than 1.25 dB. Attenuation values are usually specified in terms of dB/100 feet. If the required cable length is 200 feet, the attenuation should be no more than 1.25 dB/2, or 0.625 dB/100 feet.

Many amateur radio operators and experimenters choose to use an open-wire feeder, sometimes called a ladder line or window line. (Technically speaking, however, ladder lines and window lines are not the same.) These are very low-loss transmission lines that can handle high VSWR without causing any significant additional line loss. Typically, these types of transmission lines are not suitable for use in commercial land mobile radio applications.

It should be noted that a high VSWR seen at the transmitter output could trigger the protective foldback circuit, which causes a reduction of transmitter output power. This protective circuit prevents blowing RF output transistors. The power reduction caused by the triggering of this protective circuitry is as significant as the additional line loss caused by a high VSWR.

This discussion has centered around the effects of line loss on the transmitted signal. In a future issue we will look at the effects of line loss on the received signal.

Until next time, stay tuned!