Vector Hankel transform analysis of a tunable circular microstrip patch

Abstract

SUMMARYIn this paper, a rigorous analysis of the tunable circular microstrip patch is performed using a dyadic Green's function formulation. To make the theoretical formulation more general and hence valid for various antennas structures (not only limited to tunable microstrip patch); the dyadic Green's function is derived when the patch is assumed to be embedded in a multilayered dielectric substrate. A very e cient technique to derive the dyadic Green's function in the vector Hankel transform domain is proposed. Using the vector Hankel transform, the mixed boundary value problem is reduced to a set of vector dual integral equations. Galerkin's method is then applied to solve the integral equation where two sets of disk current expansions are used. One set is based on the complete set of orthogonal modes of the magnetic cavity, and the other consists of combinations of Chebyshev polynomials with weighting factors to incorporate the edge condition. Convergent results for these two sets of disk current expansions are obtained with a small number of basis functions. The calculated resonant frequencies and quality factors are compared with experimental data and shown to be in good agreement. Finally, numerical results for the air gap tuning e ect on the resonant frequency and half-power bandwidth are also presented.

Full-Wave Analysis of Anisotropic Circular Microstrip Antenna With Air Gap Layer

“…The transverse fields inside the dielectric layer can be obtained via the inverse vector Hankel transforms as [2,17] …”

“…(7),H n (ρk ρ ) is the kernel of the vector Hankel transform (VHT) [2,17], J n (.) is the Bessel function of the first kind of order n, and the prime denotes differentiation with respect to the argument.…”

“…The tangential electric field is null on the conducting patch, which leads to an integral equation. To solve the integral equation, we apply the procedure of Galerkin which consists in developing the unknown distribution of the current on the circular patch is expanded into a series of basis functions [2,17]. The basis functions chosen in this article for approximating the current density on the circular patch are obtained from the model of the cavity.…”

“…. , Q), and while integrating from 0 to a, and using the Parseval's theorem for vector Hankel transform [2], we obtain a system of linear P + Q algebraic equations for each mode n which can be written in the matrix form:…”

“…Such advantages include small size, light weight, low production cost, conformal nature, and good aerodynamic characteristics [2]. Since the bandwidth of microstrip patch resonators and antennas around their operating frequencies is known to be very narrow, it is important to develop accurate algorithm for the computations of those resonant frequencies [3].…”