circular microstrip

CIRCULAR PATCH

Circular Patch

• The modes supported by the circular patch antenna can be found by treating the patch, ground plane, and the material between the two as a circular cavity. substrate height is small (hλ) are where z is taken perpendicular to the patch

• The circular patch there is only one degree of freedom to control (radius of the patch). Doing this does not change the order of the modes; however, it does change the absolute value of the resonant frequency of each

• The cavity is composed of two perfect electric conductors at the top and bottom to

represent the patch and the ground plane, and by a cylindrical perfect magnetic

conductor around the circular periphery of the cavity. The dielectric material of the

substrate is assumed to be truncated beyond the extent of the patch

• The circular patch antenna can only be analyzed conveniently using the cavity mode

Electric and Magnetic Fields-• To find the fields within the cavity, we use the vector potential approach. For we need to

first find the magnetic vector potential , which must satisfy, in cylindrical coordinates, the homogeneous wave equation of

• The electric and magnetic fields are related to the vector potential by

• subject to the boundary conditions of

• The primed cylindrical coordinates are used to represent the fields within the cavity while Jm(x) is the Bessel function of the first kind of order m, and

• represents the zeroes of the derivative of the Bessel function Jm(x), and they determine the order of the resonant frequencies.

Resonant Frequencies

• the substrate height h is very small (typically h<0.05λ0), the fields along z are essentially constant and are presented in by p = 0 and in by kz = 0. Therefore the resonant frequencies for the modes can be written using

• fringing makes the patch look electrically larger and it was taken into account by introducing a length correction factor given. Similarly for the circular patch a correction is introduced by using an effective radius

• The dominant mode is the whose resonant frequency is

Design

Equivalent Current Densities and Fields Radiated

• The fields radiated by the circular patch can be found by using the Equivalence Principle whereby the circumferential wall of the cavity is replaced by an equivalent magnetic current density

• The normalized electric and magnetic fields within the cavity for the cosine azimuthal variations can be written as

• The electrical equivalent edge of the disk (), the magnetic current density of can be written as

• The filamentary magnetic current of

• the microstrip antenna can be treated as a circular loop