Design of a UWB (Ultra Wideband) microstrip patch antenna to operate in the first channel of the UWB standard and a bandpass (BP) UE (Unit Element) microstrip filter (BPUEF) for this antenna are studied and presented with promising experimental results. A typical UE BP filter is a lossless 2-port network which is formed with certain number of cascade connected commensurate transmission lines. Based on the simplified real frequency technique (SRFT) in Richards domain, driving point Darlington impedance function of the BPUEF is obtained via optimization such that optimum power transfer would be possible between a PA (power amplifier) and the antenna. Using the UE synthesis, characteristic impedance values of each UE is extracted from the input impedance function. Theoretical design (Matlab), simulation (ADS, Agilent Inc.) and the measurements are shown to be in a high degree of agreement.