Upper and Lower Bounds on a System’s Bandwidth Based on its Zero-Value Time Constants

B. Hong and A. Hajimiri

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. The opposite problem is also solved, whereby a non-trivial upper bound on the cutoff frequency which depends only on the sum of the ZVTs and the system’s order is 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.