An accurate rational 2‐port model of a class of tapered lossless and RC lines

Abstract

SUMMARYA rational 2-port model of a class of tapered z a n d =lines which includeae e x p o m i a l , hyperbolic, trigonometric and square, or INTRODUCIIONNonuniform distributed parameter structures-LC as well as RC (henceforth referred to as and RC lines)-possess extremely valuable properties, and find numerous applications in electronic circuits, by virtue of the enhancement in desired characteristics resulting from tapering. For an arbitrary variation of the line parameters, there is no general closed-form solution to the telegrapher's equations. The closedform analytical expressions are available for only a few particular geometries; they involve complex transcendental, Bessel or certain special functions.' These are not suitable for handling by conventional network analysis and synthesis techniques, since they give rise to an infinite number of singularities. As such, to deal with the exact characteristics of these lines is extremely complicated, and necessitates prohibitive computational labour, which is incompatible with the demands of flexible circuit design. In view of the considerable importance and utility of these lines, it seems useful to develop simple, rational and accurate models for them.2-port modelling of nonuniform lines has received only little attention so far. A finite ladder consisting of a cascade of T and T sections has been employed in most cases to replace the general --infinite-ladder The simplest of these is the Gupta model9 for the exponentially tapered RC (ERG case shown in Figure 1. A salient disadvantage of this single r-section m a t h e m a 9 model is the need to adjust the coefficients of the capacitances for each particular application of the ERC line.