A novel multi band patch antenna based on plotting exponential partial sums in the complex plane

This document presents the design, simulation and measurement of a new multi-resonant patch antenna, whose shape is based on the graph obtained from the traces of a partial exponential sum in the complex plane. The shapes obtained from these equations are similar to the fractal geometry shapes, that applying to the design of antennas, drift in both Ultra Bandwidth (UWB) and multi-resonance features. In this work we try to verify that the images derived from the exponential sums can have a real application. Using a specific form, the simulation process is detailed to obtain the ideal structure of an antenna that works in the S band (2 - 4 GHz), leaving open the possibility of experimenting with new forms coming from different equations. For the construction and measurement of the antenna, a FR4 substrate with a dielectric constant {varepsilon {r}}=4.4 a thickness boldsymbol{h}=1.5boldsymbol{mm}, and a tangent of losses of {delta}=0.02 is used. The obtained antenna has an omnidirectional radiation pattern with small variations, an impedance that allows the coupling to 50{Omega} and losses by return below the -10dB. This model has two resonance frequencies within the S Band in 2,4GHz and 3,6GHz with bandwidth of 200MHz and 500Mhz respectively.