Study of Rauch Low-Pass Filters using Pascal's Triangle

This paper explores the use of the Pascal's triangle to study the operating regions and compute the phase margins of second-order Rauch low-pass filters. Inspection of the Pascal's triangle allows the determination of the exact values of the phase margin at unity gain of the self-loop function in a transfer function. The phase margin on Nichols chart allows the prediction of the ringing that drives the system unstable. Several illustrative examples of high-order linear systems are provided. Experimental measurement results of the implemented circuit show that the proposed method is quite effective.