[10] In this section we will investigate the impact of an azimuthal slot on the surface current distribution and will demonstrate that the slot plays a role of complex load. The current on antenna flairs mainly flows in azimuthal direction from the feeding point to the flair termination. A slot in the flair introduces a discontinuity in the antenna and distorts the electromagnetic field around it. Let us call this distortion scattered field *E*^{SC}. According to simulations, the scattered field is concentrated around the slot (Figure 2), and this concentration becomes more pronounced with frequency increase. Numerical analysis also shows that the electric field is reasonably constant through the slot if Δ ≪ λ (Figure 3a). Frequency increase causes both increase of the absolute value of the scattered field in the slot and inhomogeneity of the field distribution over the slot (Figure 3b).

[11] There is no surface current in the slot. However, there is a displacement current , which is equal to the time derivative of the electric displacement in the slot [*Collin*, 1991]. The total flux of the displacement current through the slot can be found by the following expression:

where *E*_{ρ} is the radial component of the scattered field in the cylindrical coordinates introduced in Figure 1, and integration on azimuthal angle ϕ is performed over all angles Φ corresponding to the antenna flair. In equation (1) we assume that the scattered field at ϕ ∉ Φ is negligible. Assuming further a cylindrical symmetry for the scattered field at ϕ ∈ Φ and time dependence exp (*j*ω*t*), one can derive from equation (1)

On the other hand, the displacement current can be written as

where *Y* is the complex-valued (*Y* = *Y*′ + *jY*″) admittance of the slot, and *U* is the voltage across the slot

Comparing equations (2) and (3), one can conclude that the slot has the same impact on the surface current as RC loading (parallel connection of resistor and capacitor), where the slot equivalent resistance *R* ≡ 1/*Y*′ equals

The resistance of the slot is physically caused by radiation of electromagnetic energy from the slot. The imaginary part of the slot admittance can be represented as *Y*″ = ω*C*, where the equivalent capacitance of the slot is given by

Variation of the electric field over the slot causes minor influence (less than 10%) on the values of the equivalent parameters of the slot. For example, for a frequency of 5 GHz and values of geometrical parameters *l*_{0} = 8 mm, *l*_{1} = 10 mm, and Δ = 1 mm, by using equations (5) and (6), we obtain *R* = 416.63 ohms and *C* = 0.4048 pF. If we neglect a variation of the electric field in the slot by using instead of equation (4) an approximate expression for the voltage across the slot *U*,

we arrive at the approximate values of the slot equivalent resistance and equivalent capacitance *R* = 383.5 ohms and *C* = 0.450 pF. Since the approximate values differ less than 10% from the values calculated by using equations (5) and (6), we shall use the approximation (7) for computing the voltage across the slot below.

[12] The dependence of the equivalent parameters of the slot (with a width of 1.1 mm) on the frequency is shown in Figure 4a. The equivalent resistance decreases with the frequency. Within the frequency band from 3 to 6 GHz, the resistance is inversely proportional to frequency squared. Taking into account that for the above-mentioned frequencies the slot width remains small compared to the wavelength, the observed frequency dependency can be explained by the linear increase of both the total electrical length and the electrical width of the slot with frequency. The equivalent capacitance remains almost constant over the frequency band because the increase of the capacitance due to the linear increase of the electrical length of the slot with frequency is compensated by the decrease of the capacitance due to the linear increase of the electrical width of the slot.

[13] The equivalent resistance of the slot linearly increases with its width (Figure 4b). The equivalent capacitance decreases while the slot gets wider (similar to conventional capacitors). The equivalent resistance of the slot depends only slightly on the distance *l*_{0} between the feeding point and the slot, while the equivalent capacitance linearly increases with *l*_{0}. The latter phenomenon reflects a decrease of the slot curvature and an increase of the slot length. Finally, the equivalent capacitance is almost independent of the strip width *l*_{1}.

[14] The impact of the azimuthal slot on the input antenna impedance is shown in Figure 5. It can be seen that the slot substantially flattens both the real and imaginary parts of the input impedance and transforms them into monotonically increasing functions of the frequency. Furthermore, in the frequency band from 3 to 9.5 GHz, the slot decreases the input impedance of the antenna, which results in better matching of the antenna to a pulse generator.