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The second flux, through S, is precisely P^rad

Since all terms in Equation (50) depend on the presence of the antenna, it is difficult to pinpoint the “scattered power”, since it does not exist as a separate entity, and the observable is actually the total radiated power. In some cases (see the example mentioned in Section 4) the interaction term vanishes, and one may be inclined, in that case, to call P^rad the scattered power (more precisely, the power due to loading with Y_L).

6. A Simple Application

Consider again the two dipoles shown in Figure 6b, and assume that P_el is a given, active element (the source), and the P_el is a dipole moment induced in the passive, parasitic element 2. That element is in the form ofa short linear antenna, with terminals AB (Figure 7a). We shall evaluate the “s” and “a” fields for that simple configuration. The “s” fields are obtained by short-circuiting AB. At sufficiently large distances l, the induced P_e2 is proportional to P_el, and we may write

Формула

Where Ke^ja is an casily determined factor. The far field of dipole P_el is a given in Equation(36), and similar relationships can be invoked for P_e2. A few simple steps lead to a far field

Формула

If we open the terminals AB, and load them by an impedance Z_l, we create a configuration similar to that a Figure 1, where cross section S_g is now replaced by the terminals AB. The field E_s in Equation (8) in now Equation (54), and the radiated field contributed by loading the antenna with Z_L can be determined by means of either the Thevenin or the Norton equivalent circuits of the receiving antenna (Figure 7b). The resulting dipole P_e2 can be written as Ce^jyP_el. It radiates a field

Формула

The total field E=E_S+E_a is equation (54), with Ke^ja replaced by (Ke^ja+Ce^eb). It isow a simple matter to derive the radiated power, an to identify the interaction terms. For example, the term P^rad in Equation (52) takes the form

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The interacting sources are P_el and the “shorted” P_e2 given in Equation (53). The integration over can be performed, if needed by means of the relationship

Формула