A losing proposition

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

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.