Mutual Coupling between Active and Loaded Parasitic Elements 66

impedance matrix Z is calculated with the induced EMF method as discussed in section 2.8.

3.3.2 Mutual Coupling between Active and Loaded Parasitic Elements

Since the introduction of Yagi-Uda antennas, the use of parasitic elements is common in directive antennas that provide high gain. Based on the fundamental principle of electromagnetic mutual coupling, the directivity property of the antennas can be exploited. The use of parasitic elements offers advantages in terms of bandwidth and gain. These elements also combat the negative effect of mutual coupling by decorre-lating the antenna signals. Thus, parasitic elements convert the curse of the mutual coupling effect to a benefit for antenna arrays. The characteristics of the antenna array in terms of the radiation pattern can be modified by altering the properties of the parasitic elements.

The mutual coupling between antenna elements can be altered by changing these three factor: length, width and the relative positioning between the antenna elements.

In classical Yagi-Uda antennas, the length of the antenna elements is mechanically fixed. The length of the parasitic elements can be changed electronically by using RF switches. The terminated loads on the parasitic elements alter the impedance load values with these switches. The electromagnetic interaction between the active and parasitic elements can be affected by the length variation and the relative distance between the antenna elements. It has been mentioned in [116] [117] that the mutual

coupling between two printed antennas is reduced around 40 dB by using printed parasitic elements.

The effect of mutual coupling between antenna elements is explained with the simple structure of one active dipole (ad) element and one parasitic dipole (pd) element as shown in Figure.3.5. The active dipole has a length of (l_ad), the parasitic dipole length is (l_pd), and the distance between the two dipoles is represented as (d_ap).

Figure 3.5: Active dipole and parasitic dipole.

• when the length of the parasitic dipole (l_pd) is slightly longer than the length of active dipole (l_ad), it is known as a reflector. The reflector with a length longer than the resonant length makes the dipole inductive in nature. Hence, the current lags the voltage and this causes the RF antenna to radiate more power away from the parasitic element.

• when the parasitic dipole (l_pd) has the same length as the active dipole (l_ad), the radiation pattern shape is almost symmetrical.

• when the parasitic dipole (l_pd) is slightly shorter than the active dipole (l_ad), it is known as a director. The director with a length shorter than resonant length makes the dipole capacitive in nature. Hence, the current leads the voltage and this causes the RF antenna to radiate more power in the direction of the parasitic element.

The total field produced by the active dipole and the parasitic dipole at point P, as shown in Figure 3.5 can be represented with Thevenin’s-equivalent circuit equations as:

V_1a^ad = Z₁₁^adI_a+ Z₁₂^pdI_p 0 = Z₂₁^pdIa+ Z₂₂^pdIp

(3.13)

where

I_a represents the current through the active dipole,

I_p represents the induced current of the parasitic element by the active dipole, V_1a^ad is the voltage at the active dipole that is connected with the voltage source and V_1p^pd is the voltage across the parasitic element, with V_1p^pd = 0 because it is not con-nected to any voltage source. The induced current at the parasitic dipole can be obtained as [118]:

I_p = −Z₂₁^pd Z₂₂^pd I_a Z_in^ad = Z₁₁^ad+ Z₂₂^pdI_p

I_a

(3.14)

The voltage across the parasitic dipole element due to the induced current of active element can be defined as:

V_1p^pd = −Z_L2I_p (3.15)

one active dipole is connected to the ideal generator then Z₁₁^ad = 0 and V₁ = V_1a^ad. The parasitic element is terminated with some load Z₂₂^pd = Z_L2. The network equations of (3.13) become:

However, the current convention in (3.16) can be extended to an N-port system with all parasitic port voltages replaced by the negative product of their current and load impedance as in (3.15). The antenna array with only a single active element and N parasitic elements in (3.10) becomes:



where the diagonal matrix:

Z_L=

contains the load impedances terminated at each parasitic element.

Equation (3.18) has been well analyzed in parasitic arrays by Harrington [96], Mautz and Harrington [119], and later by Dinger [120]. Any change in the loading configura-tion of the parasitic elements only affect the load impedance matrix. Hence, ZL can be calculated independently without making any amendments in the antenna array design. According to (3.17), the values of self-impedances Z₁₁^ad and mutual-impedances Z_NN^pd need to be calculated by considering the mutual coupling effect.

As already discussed in chapter 2 (section 2.8) of this thesis, the values of mutual impedance between the active and parasitic elements and self-impedance of an an-tenna can be calculated by using (2.28) and (2.31) and respectively. The MATLAB simulation code function ‘impedmat’ is used for solving these impedances of the par-asitic arrays is presented in the Appendix-B.

3.4 SPA System Description

In this thesis, a low-cost beam steering SPA is used to consider the radiation patterns in the azimuth plane with an operating frequency of 2.4 GHz in the industrial, scien-tific, and medical radio (ISM) band. The parasitic elements are terminated with load impedance with the use of ideal RF switches. The switching between on/off states, results in fixed radiation patterns in different directions.

When the RF switch is in the on state, the parasitic element is short-circuited and acts as a reflector with an assumed theoretical value of the load impedance ≈ 10000 Ω.

When the RF switch is in the off state, parasitic element is open-circuited and act as director and assumed with theoretical value of the impedance load ≈ 0Ω. As the RF switches are assumed ideal, no insertion losses are considered in the calculation of the impedance matrices.

The number of radiation patterns can be determined by the number of parasitic elements and the switching load configurations of the parasitic elements. The perfor-mance and functionality of using SPA depends on the basic principle of electromag-netic mutual coupling. The design procedure of MIMO-SPA requires the structural parameters of the antenna elements and the load configuration parameters terminated on the parasitic elements [121]. The structural parameters of the antenna elements include :

• Total number of elements (T =A+P), where T is the total number of the ele-ments in the antenna array, A is the number of active eleele-ments and P is the number of parasitic elements.

• The length of the active elements (lad);

• The length of the parasitic elements (l_pd);

• The width of the elements, (W ); and

• The distance of the parasitic elements from the active elements, (d).

The load configuration parameters can be set as reactive loads or resistive loads.

The reactive loads with varactor diodes provide the tuning between the loads over an infinite number of levels. The resistive loads can provide switching in fixed or pre-defined levels.

In this thesis, the parasitic elements are terminated with impedance loads. The length of the parasitic elements is the same in order to achieve omni-directional patterns [122].

An even number of parasitic elements is used to attain the antenna symmetry property [121] [123]. However, the structural and load configurations can be optimized for the better system performance. In the literature, most researchers have used optimization algorithms and numerical analysis for the optimization purpose [124]. In this work,

the structural parameters are assumed based on the array theory and the geometry used for the array design is presented as by Varlamos et al. [125].