
Upper and lower bounds on a system's bandwidth based on its zero‐value time constants
Author(s) -
Hong B.,
Hajimiri A.
Publication year - 2016
Publication title -
electronics letters
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.375
H-Index - 146
eISSN - 1350-911X
pISSN - 0013-5194
DOI - 10.1049/el.2016.1724
Subject(s) - upper and lower bounds , cutoff , mathematics , zero (linguistics) , bandwidth (computing) , cutoff frequency , constant (computer programming) , pole–zero plot , mathematical analysis , time constant , control theory (sociology) , value (mathematics) , physics , telecommunications , statistics , quantum mechanics , computer science , transfer function , optics , engineering , linguistics , philosophy , electrical engineering , control (management) , artificial intelligence , programming language
It is shown that for systems with no zeros and no complex poles, the classical estimate of the 3 dB cutoff frequency based on the sum of the zero‐value time constants (ZVTs) is always conservative. A non‐trivial upper bound on the cutoff frequency which depends only on the sum of the ZVTs and the system's order is also derived. It is demonstrated that both bounds are tight – specifically, the lower bound is approached by making one of the system's poles increasingly dominant, whereas the best possible bandwidth is achieved when all of the system's poles overlap. The impact of complex poles on the results is also discussed.