Ringing Test for Tow-Thomas Low-Pass Filters

This paper presents a ringing test for 2
^nd
-order Tow-Thomas low-pass filters. A new concept of self-loop function in a transfer function for a class of linear negative feedback systems is introduced. The introduction of the self-loop function allows the extension to the stability test for high-order linear systems. Based on the proposed comparison measurement technique, the self-loop function is derived directly from the measurement results of the transfer function without breaking the feedback loop. The phase margin at unity of the self-loop function on the Nichols chart determines the operating region of a linear system. As a high-order system operates on the under-damping region, the damped oscillation noise causes ringing and makes the network unstable. In case of the second-order system, if the phase margin is smaller than 76.3 degrees, the ringing occurs and makes the system unstable. The measurement results of the magnitude of the transfer function in the implemented circuit at around the cutoff frequency 25 kHz are -10 dB (over-damping region), 0 dB (critical damping region), and 15 dB (under-damping region). The measurement results of the phase margin are 95 degrees (over-damping region), 77 degrees (critical damping region), and 40 degrees (under-damping region). Experimental results show that the proposed method is quite effective on the ringing test for high-order linear negative feedback systems.