In this paper the way of modeling phenomena occurring during the voltage and current waves passing through a point connection of two lines, with different wave impedance operators, is presented. This connection point is called „the wave transformer”. The analyzes and the resulting formulas concern not the frequency domain, but the time domain. The appropriate transition matrices of waves through the wave transformer are defined. This matrices are the convolution integral-derivative operators of fractional order (the digital filters). For a lossless line the wave transition matrices through the wave transformer become number type instead of operator type. All matrix multiplications occurring in the formulas should be understood in convolution way.

This Article presented the study of a single pacth antenna and array patch antenna. We will focus on the design based on a small size at a resonant frequency of 30GHz. using the software CST Microwave Studio (FEM method) and ADS software (Moments method) to find internal parameters (S... parameters, bandwidth ,VSWR) and external characteristics (gain, directivity and radiation pattern, efficiencies) . To increase the total gain of the antenna and to have a wider bandwidth band width and taking advantage of the functionality of the radiation overlap of several elements radiating in the same direction, we suggest the second and most important step to design a most important step to design an antenna array grouping patches identical to our first patch antenna proposed in first patch antenna proposed in the first step