A simple closed‐form formula for the mutual impedance of dipoles

Abstract

facturing process may not seriously impair the deliverable bandwidth.The Bragg regime vanishes if c ϭ d even though a b c , as per Eq. (6). This condition denotes the pseudo-isotropic point, when the axially excited chiral STF effectively responds as an isotropic and homogeneous material (despite being anisotropic and unidirectionally nonhomogeneous), and does not distinguish between incident left and right circularly polarized light: R LL ϭ R RR , R LR ϭ R RL , T LL ϭ T RR and T LR ϭ T RL . Table 3 provides values of v and the consequent values of and a,b,c calculated for chiral STFs of the same three materials as in Table 1. Figure 4 presents contour plots of the differences ͉R RR Ϫ R LL ͉ and ͉T RR Ϫ T LL ͉ as functions of v and 0 for chiral STFs made of titanium oxide. In both contour plots, the cross marks the location of the center wavelength of the Bragg regime that is missing because v is at the pseudo-isotropic point. These plots show clearly the singularity of the pseudo-isotropic point, highlighting the potential for its disturbance by some perturbation, as mentioned earlier.As the requirements of maximum and null bandwidths are mutually exclusive, the same value of v cannot deliver both, according to Eq. (6). Significantly, as the maximum bandwidth and the pseudo-isotropic points turn out to be widely separated on the v axis, device designers with different objectives cannot confuse between the two. Furthermore, both points are realizable because the corresponding values of substantially exceed the lowest values of reported till date. The deliverable value of 0Br , for either of the two points, will require the selection of ⍀ during deposition; with postdeposition tuning possible perhaps with piezolelectric actuators [17]. INTRODUCTIONIn the design of antenna arrays or in the electromagnetic compatibility domain, coupling effects are very important phenomena. To have a good knowledge of coupling effects, it is necessary to use a full-wave method, but for an array with many radiating sources, or for a complex EMC environment, full-wave modeling leads to complex and lengthy numerical simulation. The idea is to achieve a simple and compact analytical formula for taking into account the coupling effects, to have real information quickly. As the basic radiator elements, linear dipoles could be used to investigate any complex form of antenna. For this reason and their simple physics, dipole antennas are largely studied and used [1]. Usually for calculating the self-impedance and mutual impedance of dipoles, one supposes one-term [2] sinusoidal current density or a combination of a few sinusoidal functions [3] along the dipole, making it possible to determine the impedances analytically in the form of S i or C i integrals. Using this well-known method permits having the mutual impedances of the dipoles in the near-or far-field region of each other. But the complexity of C i and S i integrals is a serious obstacle for considering this method to be useful one for the quick and simple expression of impedances...

Dipole model of rectangular patch antenna, application to self, and mutual impedance analysis

“…The printed dipole itself can be studied analytically to evaluate the self and mutual impedances. These impedances are presented by using the “image theory” and supposing normal dipoles in near‐field region [2, 5, 6]: The input impedance of the patch antenna can be therefore evaluated by the equivalent ( Z 11 + Z 12 ) of two printed dipoles. The initial value of ( Z 11 + Z 12 ) in formulas (1, 2) is calculated at the central point of each dipole (at the edges of the patch).…”

Analytical study of printed dipoles with closed‐form impedance formulas

“…Integration of cellular and WLAN communication networks can provide users with ubiquitous or seamless data services [1]. For such an integrated cellular/WLAN network application, many dual-mode or dual-network wireless devices (such as PDA phones) are expected to emerge in the market in the near future.…”

“…The self and mutual impedances of normal dipoles can be described by closed-form formulas [1]. However, the analytical formulations are for printed dipoles almost as complicated [2,3].…”