Generalized Theory of the Thru-Reflect-Match Calibration Technique

Abstract

The thru-reflect-match (TRM) calibration technique uses as standards a through connection of ports 1 and 2 of the vector network analyzer, two symmetrical highly reflecting loads, and two broadband loads (match) of impedance close to the measuring system impedance ( <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$ { Z} _{0}$</tex></formula> ). The classical theory of the TRM calibration refers the calibration to the impedance of the load used as the match standard ( <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">${ Z} _{M}$</tex></formula> ), which is assumed as symmetrical. In practice, <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">${ Z} _{M}$</tex></formula> may be frequency dependent. Moreover, as the frequency increases, the symmetry condition of the load used as match standard may become difficult to preserve, thus affecting the reference impedance definition and reducing the accuracy of the calibration. In this paper, the <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">${ ABCD}$</tex></formula> -parameters matrix formalism is used to introduce for the first time a generalized TRM calibration theory, allowing the use of either symmetrical or nonsymmetrical loads of arbitrary impedance as the match standard.