A losing proposition

Imagine an RF transmission line without any RF attenuation. All the power from the transmitter would be delivered to the antenna. Conversely, all the signal from the antenna would be delivered, unattenuated, to the receiver input.

To understand the effects of transmission line attenuation on the transmitter signal, we will examine three basic examples: one with a theoretically lossless transmission line and a mismatched load, one with a lossy transmission line with a mismatched load and one with a lossy transmission line with a matched load. In this discussion it is assumed that a single point of reflection exists on the line, and that is at the load or antenna.

Let's look at the effect of RF attenuation on a transmission line that connects a radio transceiver to the antenna through a lossless line. A typical base station setup used with land mobile radios is shown in Figure 1. A transmitter is connected to an antenna through a length of transmission line, which is represented by A-C. Let's analyze this setup based on the traveling wave concept. Assume, for this discussion, that the antenna mismatch is such that the directional wattmeter, at position A, indicates 100 W in the forward direction and 20 W in the reverse direction. In a lossless transmission line, the power or voltage in the forward wave will be at the same level at any point on the transmission line. Similarly, the voltage or power in the reflected wave will be at the same level at any point on the transmission line.

Because the power (either forward or reflected) is the same at any point along the line, the voltage standing wave ratio (VSWR) also will be the same at any point along the line. In addition, the power delivered to the antenna will be equal to the difference between the measured forward power and the measured reflected power (100 W – 20 W = 80 W). This means that there is 20% reflected power. According to Table 1, this represents a VSWR of 2.62:1. Note that this VSWR will be the same at any point on the line because the line is lossless.

Now, let's assume that the transmission line in Figure 1 has an end-to-end loss, or RF attenuation, of 3 dB at the operating frequency. This changes things quite a bit. Let's examine the situation more closely. Assuming that we are using the same antenna, the percentage of power reflected from the antenna will be the same. However, the actual amount of RF power reflected will not be the same. This is because the line loss of 3 dB causes a 50% loss of power between the wattmeter and the antenna.

Again, suppose that the wattmeter indicates a forward power of 100 W at point A. A line loss of 3 dB means that only 50 W is reaching the antenna at point C. Using the same antenna means that 20% of this power will be reflected, so the reflected power is equal to 10 W. As a result, the power in the reflected wave at point C is 10 W. However, in traveling back down the line toward the transmitter, the line loss diminishes this reflected power to 5 W at point A. Moreover, the power at point A in the forward wave is 100 W, while the power in the reflected wave is 5 W. Thus, the percentage of reflected power has changed from 20% to 5%. Accordingly, the VSWR has changed from 2.62:1 to 1.58:1 between points C and A on the line. (See Table 1.) At point B, the VSWR would be less than at point C, but more than at point A.

The power radiated by the antenna is equal to the net power, or the difference between the forward and reflected power at the antenna. In this case, the radiated power is equal to 50 W – 10 W = 40 W. Yet the net power delivered to the line at point A is 100 W – 5 W = 95 W.

Let's assume that a new antenna is installed that properly matches the system impedance (50 ohms). Using the line with 3 dB loss, the forward power at the antenna is 50 W and the reflected power is 0 W. Thus, the VSWR at the antenna is 1:1. This means that all the forward power (50 W) is radiated. Thus, the amount of power wasted in the line is 50 W because the forward power at point A is 100 W. In each example, we will compare the net power radiated by the antenna to the net power at point A to determine the actual line loss in decibels.

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!

Equation 1

L = 10log (40/95) = 3.76 dB

Equation 2

E_f = √PZ = √100 × 50 = √5000 =70.7 V

Equation 3

E_r = √PZ = √20 × 50 = √1000 =31.6 V

Equation 4

VSWR= E_f + E_r/E_f – E_r 70.7 + 31.6/70.7 – 31.6 = 102.3/39.1 = 2.62:1

Equation 5

L = 10log P₁/P₂ = 10log 300/400 = 10log (0.75) = 1.25 dB