Читать книгу Antenna and EM Modeling with MATLAB Antenna Toolbox - Sergey N. Makarov - Страница 23

In order to become familiar with the problem of antenna matching, we now need a practical antenna example and a practical antenna impedance behavior. This example will also help us to define the antenna impedance bandwidth in future. To do so, we consider a cylindrical metal dipole antenna shown in Figure 1.4.

The antenna includes two dipole wings fed by a generator. In Figure 1.4, l_A is the total dipole length, a is the dipole radius.

During the last 70 or so years, a lot of efforts have been made to develop a good analytical terminal dipole model. As a result, one can use the following proven semi‐analytical expression for the input dipole impedance [2]:

(1.14)

Figure 1.4 Dipole antenna for the evaluation of the reflection coefficient.

In Eq. (1.14), l_A is the total dipole length, a is the dipole radius, z = kl_A/2, and is the wavenumber with c₀ being the speed of light in vacuum.

If a strip or blade dipole of width t is considered, then a_eq = t/4 [3] (providing the same equivalent capacitance of a dipole wing per unit length). We note here that a is the radius of a cylindrical dipole, while a_eq is the equivalent radius of a wire approximation to the strip dipole. Eq. (1.14) holds for relatively short nonresonant dipoles and for half‐wave dipoles, i.e. in the frequency domain approximately given by

(1.15)

where f_res ≡ c₀/(2l_A) is the resonant frequency of an idealized dipole having exactly a half‐wave resonance (c₀ is again the speed of light) and f_C is the center frequency of the band. This means that the ideal dipole resonates when its length is the half wavelength. When a monopole over an infinite ground plane is studied, the impedance in Eq. (1.14) halves.