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The linear time-varying approach applied to a first-order dynamic translinear filter

Dynamic translinear (DTL) circuits use the exponential input-output relation of the transistor as a primitive for the synthesis of electronic circuits. As a consequence the analysis of the dynamic behaviour of this type of circuit in the presence of parasitics results in analyzing dynamic nonlinear circuits. There are three different approaches that can be applied: the linear time-invariant (LTI) approach, the quasi-static (QS) approach and the linear time-varying (LTV) approach. The LTI approach is limited to circuits in which the bias points are fixed. The QS approach can be applied to circuits with time-varying bias points, but these time-variations must be relatively slow. The LTV approach has none of these restrictions and opens the way to a general and structured design method for dynamic nonlinear circuits. We apply the linear time-varying approach to a first-order dynamic translinear filter. Its dynamic eigenvalue is calculated and stability is determined by means of the corresponding Floquet exponent. We also apply the quasi-static approach to the same DTL filter. Comparisons between the linear time-varying approach and the quasi-static approach show the limitations of the quasi-static approach and the usefulness of the linear time-varying approach in the design of DTL circuits.