Generalized Time- and Transfer-Constant Circuit Analysis

Abstract

Abstract-The generalized method of time and transfer constants is introduced. It can be used to determine the transfer function to the desired level of accuracy in terms of time and transfer constants of first-order systems using exclusively low frequency calculations. This method can be used to determine the poles and zeros of circuits with both inductors and capacitors. An inductive proof of this generalized method is given which subsumes special cases, such as methods of zero-and infinite-value time constants. Several important and useful corollaries of this method are discussed and several examples are analyzed.Index Terms-Bandwidth enhancement techniques, circuit Analysis, Cochran-Grabel method, determination of poles and zeros, infinite-value time constants (IVT), method of time and transfer constants (TTC), zero-value time constants (ZVT) .

Upper and lower bounds on a system's bandwidth based on its zero‐value time constants

“…from which the ZVT bandwidth estimate of ωc ≈ 1/b 1 follows [1,3]. In this Letter, we prove that for a system whose poles are all real, this ZVT estimate of the bandwidth is always a lower bound on the system's actual bandwidth ωc.…”

“…, n are the time constants associated with the system's n poles. (Note that the τ i 's are equal to the system's ZVTs only if the poles are decoupled from one another [3]. In general, this is not the case.…”

“…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.Introduction: The estimate of a low-pass circuit's 3 dB bandwidth via the method of zero-value time constants (ZVTs) is well-known [1][2][3]. This procedure entails computing the time constant of each reactive element in a circuit based on the resistance it sees when all other reactive elements are zero-valued (capacitors opened, inductors shorted).…”

“…Introduction: The estimate of a low-pass circuit's 3 dB bandwidth via the method of zero-value time constants (ZVTs) is well-known [1][2][3]. This procedure entails computing the time constant of each reactive element in a circuit based on the resistance it sees when all other reactive elements are zero-valued (capacitors opened, inductors shorted).…”

“…it can be shown [1][2][3] that the sum of the ZVTs is equal to b 1 . For now, we will consider systems with no zeros (a 1 = a 2 = · · · = am = 0), which serve as a good model for circuits where the zeros occur at very high frequencies beyond the passband and are hence unimportant.…”