3.1 Bandwidth and Quality Factor, Q

In the early days of electronic radio, the ability of a receiver to select just one station out of the many with sufficient strength to be detected was determined by the quality of a coil. Figure 3.1 shows a simplified schematic of an RF amplifier. To begin, we assume that the following stage has a very high input impedance so that the load on the active device (a vacuum tube in those days) is just the elements shown. Here r _c is the resistance inherent in the coil wire. An ideal (perfect) coil would have no loss resistance. The voltage out of the stage is:

Figure 3.1: Simplified schematic of a radio receiver amplifier stage.

We may further assume that the power into a load further into the receiver is proportional to the square of the output voltage of our stage. This output power is:

where G is a constant representing the power gain of the following stages. Let P _m be the maximum power as a function of frequency, and Z _m be the maximum magnitude of Z( j ?). Then the normalized power is:

This normalized power is similar in concept to a gain known as transducer power gain (TPG).

When we talk about antenna bandwidth and bandwidth of an antenna-matching network combination, it is with respect to this gain.

Ordinarily we think that the maximum impedance of a parallel-resonant circuit is at the frequency...