good information about circular patch

1. CIRCULAR PATCH

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