Some synthesis methods for adjustable networks using multivariable techniques

The synthesis of the class of adjustable networks that respond or adapt to an independent (with respect to frequency) real variable, or several such independent real variables, and that respond as linear time-invariant networks for fixed values of these variables, is considered. Thus, for general networks in this class, the network functions (possibly after some frequency transformations) are real and rational in (possibly) several frequency variables, and the coefficients of the numerator and denominator polynomials in the several frequency variables are real functions of the real independent variables. An objection to most synthesis procedures for adjustable networks is that the adjustable elements used, whether passive or active, have had to be assumed to be highly versatile in their functional form. Practically, however, such adjustable elements may not exist. Also, synthesis procedures that use more than one type of adjustable elements for each independent real variable may result in a serious tracking problem. The synthesis methods developed here allow the designer 1) to choose a single type of adjustable building block for each independent real variable; 2) to maintain control of the functional complexity of these adjustable blocks; and 3) to use, in the single real variable case, only the absolute minimum number of such adjustable blocks.