Automatic root selection for the unknown thru algorithm

This paper presents a method for automatic root selection in the unknown thru algorithm. The described method can be used for any thru standard that has a simple phase expression. Examples for coaxial, waveguide and waveguide to coaxial adapters are discussed. The paper also includes equations for converting the resulting 7-term error model to the 12-term model commonly used in network analyzers. And also how to combine these steps into a simple algorithm that utilizes as much as possible of the VNA firmware for computations.