Abstract
The necessary and sufficient condition for the positiverealness of a general biquadratic function <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Z(s)</tex> is presented. It is shown that for each given pair of conjugate-complex poles of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Z(s)</tex> with negative-real parts, the zeros of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Z(s)</tex> are graphically restricted in a realizability region, which is an open region bounded by two curves. One of these curves is the locus of the zeros for which <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Z(s)</tex> is a minimum positive-real function. A theorem is given stating the realizability conditions for <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Z(s)</tex> as a driving-point immittance with passive elements.
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