Abstract :
Reactively constrained two-terminal immittances having a prescribed magnitude over a frequency band of maximum width are useful for the equilization of parasitic reactance in ordinary linear circuits, and for the broad-band matching of frequency converting devices such as parametric amplifiers. Two methods are illustrated for deriving optimum immittances having tapered magnitudes over a passband for networks that are constrained to begin with a single reactive element, i.e., either a series or shunt capacitance or inductance. It is shown that for simple tapers, the optimum immittances can be represented as constant magnitude immittances after extraction of a single tuned branch containing the constraining element. Six simple tapers are derived for each of the four types of reactive constraints, and the relationship between the bandwidth, the magnitude of the immittance, and the value of the constraining element are shown for each. All of the optimum immittances are irrational and can be exactly synthesized only with an infinite number of elements. Approximate methods of synthesis using a finite number of elements are discussed. Several branch-point integrals that have not been derived previously are listed in the Appendix.
