Microstrip Antenna  Design Parameters and Tradeoffs
All of the parameters in a rectangular patch antenna design (L, W, h, permittivity)
control the properties of the antenna. As such, this page gives a general idea of how the parameters
affect performance, in order to understand the design process. First, the length of the patch L controls the resonant frequency as seen here. This is true in general, even for more complicated microstrip antennas that weave around  the length of the longest path on the microstrip controls the lowest frequency of operation. Equation (1) below gives the relationship between the resonant frequency and the patch length:
Second, the width W controls the input impedance and the radiation pattern (see the radiation equations here). The wider the patch becomes the lower the input impedance is. The permittivity of the substrate controls the fringing fields  lower permittivities have wider fringes and therefore better radiation. Decreasing the permittivity also increases the antenna's bandwidth. The efficiency is also increased with a lower value for the permittivity. The impedance of the antenna increases with higher permittivities. Higher values of permittivity allow a "shrinking" of the patch antenna. Particularly in cell phones, the designers are given very little space and want the antenna to be a halfwavelength long. One technique is to use a substrate with a very high permittivity. Equation (1) above can be solved for L to illustrate this:
Hence, if the permittivity is increased by a factor of 4, the length required decreases by a factor of 2. Using higher values for permittivity is frequently exploited in antenna miniaturization. The height of the substrate h also controls the bandwidth  increasing the height increases the bandwidth. The fact that increasing the height of a patch antenna increases its bandwidth can be understood by recalling the general rule that "an antenna occupying more space in a spherical volume will have a wider bandwidth". This is the same principle that applies when noting that increasing the thickness of a dipole antenna increases its bandwidth. Increasing the height also increases the efficiency of the antenna. Increasing the height does induce surface waves that travel within the substrate (which is undesired radiation and may couple to other components). The following equation roughly describes how the bandwidth scales with these parameters:
