S-Parameter Model of Three Parallel Interconnect Lines Generating Negative Group-Delay Effect

Abstract

This paper develops a negative group-delay (NGD) microwave circuit theory regarding topology consists of three parallel interconnect lines (3-PILs). The NGD topology under study is built using completely distributed microstrip lines. The 3-PIL NGD theory is established from the S-parameters which are determined from the general admittance matrix of the 3-PILs. The analytical expressions of reflection coefficient (S <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">11</sub> ), transmission coefficient (S <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">21</sub> ) and group-delay (τ) which behave as periodical functions are presented. The frequency period proper to the 3-PIL topology is established. Then, S <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">11</sub> , S <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">21</sub> and τ illustrating the possibility to generate bandpass NGD function are formulated in function of the PIL parameter physical lengths and attenuation loss. Then, the NGD characterization of the 3-PIL topology is presented. The relevance of the NGD theory is verified with simulations and experimentations around the NGD center frequency of about 2.3 GHz. To do this, a 3-PIL microstrip circuit is designed and fabricated as proof-of-concept. It is shown that the simulated and measured group-delays are well-correlated. As expected theoretically, the demonstrator with identical characteristic impedance enables to generate an NGD level of approximately -2 ns at 2.3 GHz. In the future, the NGD function can be potentially used for the microwave signal integrity improvement.