The Electric and Magnetic Field variations within a patch are sometimes a bit confusing and difficult to visualize. The figure below shows the E and H Field variations within a rectangular patch of length L and width W.
E and H Field of a Patch
As can be seen the E-field varies along the length of the patch with minimum at the centre and maximum at the edges (maximum positive and maximum negative). The H-field also varies along the length is in a direction perpendicular to the E-field. The H-field is maximum at the center and minimum at the edges. Thus the impedance is zero at the center of the patch (using Z=V/I).
Another point to note is that the E-field does not completely terminate at the edges along the length of the antenna rather it extends at the outer periphery. These field extensions are known as fringing fields and cause the patch to radiate .
A Microstrip Patch Antenna or simply a Patch Antenna is a very common antenna type used in cell phones and many other electronic devices. It basically consists of two metallic plates separated by a dielectric layer. The metallic plates are usually made of copper or some other highly conductive material. Another important feature of this antenna is the feeding mechanism, which is also made of a highly conductive material. A Microstrip Patch Antenna fed by a 50 ohm transmission line and a quarterwave transformer is shown below.
The E-field and H-field generated by the Patch Antenna can be calculated by using a simulation tool such as CST Microwave Studio. It is dependent on the length ‘L’ and width ‘W’ of the patch as well as on the wavelength ‘λ’ and the feeding mechanism. Other important parameters are the width of the substrate and the permittivity of the substrate. The E-field can be approximated as.
Part of the above equations is a sinc function which can be calculated by the MATLAB sinc function.
Antenna Pattern or Radiation Pattern is a three dimensional description of how the antenna radiates energy in to the space around it. All practical antennas are directional i.e. they radiate more energy in certain directions and lesser energy in other directions. Although the Radiation Pattern is a three dimensional quantity it can be described in two perpendicular planes known as the principal planes. Usually one of these planes is horizontal (azimuth plane) and the other is vertical (elevation plane).
As discussed previously antennas do not radiate uniformly in all directions. Antenna Gain is the ratio of the power transmitted in a certain direction to the power transmitted in that direction by an isotropic source. An isotropic source is an imaginary source which radiates power uniformly in all directions. The Antenna Gain is usually given in units of decibels and is given as dBi (dB above an isotropic source). The Antenna Gain may also be given with reference to a Dipole Antenna and this is labelled as dBd. When no direction is specified Antenna Gain refers to the maximum Gain.
The 3-dB Beamwidth is the angle between two points on the main lobe of the antenna that are 3dB down from the maximum value. A smaller Beamwidth means that an antenna is more directional and a higher Beamwidth means that the antenna is less directional. The 3-dB Beamwidth is usually defined in the two principal planes i.e. the azimuth plane and elevation plane.
The front to back ration (F/B) is the ratio of the Gain in the forward direction to the Gain in the backward direction within a principal plane (azimuth or elevation). It is an important metric in certain scenarios where radiation towards the back of the antenna is undesirable e.g. as in 120 degree sectored antennas used in cellular networks. The ratio is usually given on a logarithmic scale and labelled as dB.
The polarization of an antenna is a somewhat difficult concept to comprehend. The polarization of an antenna describes the orientation of the E-field that is generated by the antenna. Usually the orientation is horizontal or vertical but it could also be circular for the case where the E-field rotates (clockwise or counter clockwise) as it travels. If a transmit antenna is vertically polarized then the receive antenna should also be vertically polarized to achieve maximum power transfer through the medium.
The voltage standing wave ratio (VSWR) is defined as the ratio of the maximum voltage to the minimum voltage in a standing wave pattern. A ratio of 1:1 means that all power was transferred to the antenna and there are no reflections. Typically RF components have 50 or 75 ohms impedance and antennas must have the same impedance to achieve maximum power transfer.
The VSWR bandwidth is defined as the frequency range over which an antenna has a specified VSWR. Often, the 2:1 VSWR bandwidth is specified, but 1.5:1 is also common.
An omnidirectional antenna is an antenna that has a non-directional pattern (circular pattern) in a given plane with a directional pattern in any orthogonal plane. Examples of omnidirectional antennas are dipoles and collinear antennas.
 Cisco Aironet Antennas and Accessories, Antenna Patterns and Their Meaning.
A Radiation Pattern is a 3 dimensional description of how an antenna radiates power in the surrounding space. This pattern is usually measured at a sufficient distance from the antenna known as the far-field. In simple words it is the power radiated in a certain direction with reference to an omni-directional antenna (a theoretical antenna that radiates equally in all the directions). Given below are the radiation patterns for some common antenna types.
Dipole Antenna 3D Radiation Pattern
Yagi Antenna 3D Radiation Pattern
Sector Antenna 3D Radiation Pattern
Although the Radiation Pattern is a 3 dimensional quantity it is usually sufficient to describe it in two orthogonal planes (one horizontal and one vertical) as shown in the figures above.
 Cisco Aironet Antennas and Accessories: Antenna Patterns and Their Meaning