TMSE Optimization of Bandwidth of Tuned Electronic Circuits

Abstract

As transfer functions of realizable electronic devices differ from the ideal п-shaped one, at the design stage an optimal choice of bandwidth is required. Total mean square error (TMSE) criterion allows balancing linear distortions of the signal and remaining noise at the device’s output. It is shown that the former term should be determined based on an easily calculated constant level but not necessarily 1 as used by the TMSE. Relative TMSE criterion was derived to address the above and some other shortcomings. It is shown by examples (bandpass RLC circuit, low pass Butterworth filter) that using relative criterion could lead to substantially lower output error spectra comparing to the TMSE.