A Hybrid De-Embedding Method for Low Loss and Reciprocal PCB Fixtures
Bo-Wen Liu, Xing‐Chang Wei, Chong-Xin Xv
Abstract
This article presents a hybrid de-embedding method by combining the unitary condition of lossless networks and the impulse response curve truncation. A magnitude-symmetry formula is derived for reciprocal and low loss printed circuit board (PCB) fixtures. It gives the analytical relationship between <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$S_{11}$ </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">$S_{22}$ </tex-math></inline-formula> for asymmetric PCB fixtures. At the same time, the impulse response curve truncation is used to solve <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$S_{11}$ </tex-math></inline-formula> . Based on above two methods, the number of fixture’s unknown <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$S$ </tex-math></inline-formula> -parameters is reduced. The reasonableness of the magnitude-symmetry formula is verified by simulated fixtures, which are commonly used in radio frequency and microwave engineering measurements. The accuracy and feasibility of the proposed hybrid de-embedding method are also numerically and experimentally verified. Good <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$S$ </tex-math></inline-formula> -parameters correlations of fixtures and devices under test (DUT) can be observed in all examples.