Scattering Matrix of a Reciprocal, Lossless, and Symmetrical Three-Port Power Divider

Abstract

This letter provides the analytical expression of the scattering matrix of an arbitrary loss-less reciprocal three-port junction with a plane of symmetry. The 3 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\times $ </tex-math></inline-formula> 3 matrix is given in terms of two arbitrary real angles, <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\vartheta $ </tex-math></inline-formula> and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\varphi $ </tex-math></inline-formula> . Experimental evidence of this fact is also included.