Fast simplified real frequency technique (FSRFT) is a numerical solver used to solve microwave broadband doublematching (DM) circuit design problems in a much faster and effective manner. Recently, it has been reported that an FSRFT based Matlab code can complete the design of a order lowpass lumped element double matching network to match a given generator and load impedance within an optimization time of only 0.6 seconds, a 47 fold less time than that of the same design done using the classical simplified real frequency technique (SRFT). FSRFT owes this superior speed performance to the fact that it tracks only (system unknowns plus 1) number of passband extremum points selected from among the number of gain data (). This work introduces a simple numerical technique called PED (passband extremums determination technique) to be used in determination of these passband extremum points (PEs). An exemplary order microwave bandpass DM circuit design using FSRFT based Matlab (of Mathworks Inc.) code and the simulation of this design via MWO (of AWR Corp.) has yielded the same circuit performance with an exact agreement. Thus, FSRFT, equipped with the PED, newly proposed hereby, might be used as a powerful solver in designing broadband circuits in many fields such as RF/microwave, radar, and communications.