Ringing Test for Second-Order Sallen-Key Low-Pass Filters

This paper presents a ringing test for 2nd-order Sallen-Key low-pass filters. A comparison measurement is constructed, which takes into account the measurement of a self-loop function in a transfer function. Based on the phase margin at unity of the self-loop function, a general stability criterion for second-order linear systems is proposed in terms of operating regions. In case of under-damping region, the ringing occurs and makes the system unstable. The advantage of the proposed criterion lies in its simplicity than some of the existing results. The new stability criterion is applied to the network based negative feedback issues. Experimental results show that the proposed method is quite effective.