Читать книгу Antenna and EM Modeling with MATLAB Antenna Toolbox - Sergey N. Makarov - Страница 16

One question you have to ask yourself is this: for a fixed resistance R_g, can the electric power delivered to the antenna be maximized, and at which value of R_a does the maximum occur? In other words, we would like to know what parameters the antenna should have in order to acquire and radiate maximum electric power from the given RF generator (an RF amplifier). In an electric circuit, the passive load – the antenna – may have only one such parameter – the antenna resistance. All other antenna parameters (geometrical, material, etc.) are implicitly included into antenna's resistance.

The answer is given by the maximum power transfer theorem and found by solving the circuit in Figure 1.1. We assume that voltages and current are all functions of time and solve the circuit for an arbitrary time moment. First, the current is determined from the given voltage source υ_g(t) and the total resistance using the series equivalent,

(1.5a)

This allows us to compute the (instantaneous) power delivered to the antenna based on

(1.5b)

For a generator with fixed resistance R_g, the load resistance determines the power P_a(t) at any time instant. Eq. (1.5b) is identical to the corresponding result at DC.