Circular microstrip
- 2. 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 (h≪λ) are 𝑇𝑀 𝑧 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
- 3. • 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
- 4. Electric and Magnetic Fields-𝑻𝑴 𝒎𝒏𝒑 𝒛 • To find the fields within the cavity, we use the vector potential approach. For 𝑇𝑀 𝑧 we need to first find the magnetic vector potential 𝐴 𝑧, which must satisfy, in cylindrical coordinates, the homogeneous wave equation of • The electric and magnetic fields are related to the vector potential 𝐴 𝑧 by • subject to the boundary conditions of
- 5. • The primed cylindrical coordinates 𝜌′, ∅′, 𝑧′are used to represent the fields within the cavity while Jm(x) is the Bessel function of the first kind of order m, and
- 6. • 𝑥 𝑚𝑛 ′ represents the zeroes of the derivative of the Bessel function Jm(x), and they determine the order of the resonant frequencies.
- 7. 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 𝑇𝑀 𝑚𝑛0 𝑧 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 𝑎 𝑒 • The dominant mode is the𝑇𝑀110 𝑧 whose resonant frequency is
- 8. Design
- 9. 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
- 10. • The electrical equivalent edge of the disk (𝜌′ = 𝑎 𝑒), the magnetic current density of can be written as • The filamentary magnetic current of
- 11. • the microstrip antenna can be treated as a circular loop