Approximating the Impedance Profile of Multilayer Reference Plane Cut-Out Compensation up to Ka-Band

Abstract

This paper addresses and solves a problem finding the reference plane impedance compensation impedance profile using a modified logistic function approximation and avoiding both the search for complex fringe capacitance equations, when the reference plane impedance compensation cut-out is larger than the cut-out, and solving Maxwell’s equations using finite element methods. The proposed approximation method allows designers and researchers to estimate the optimal width of the cut-out for each specific PCB stack-up and layout density case without the need of heavy computational power and specific CAD software tools. The proposed method is applicable to multiple-layer cut-out compensation with different dielectric height ratios. A full mathematical description along with multiple examples is provided, including practical measurements up to the Ka-band. The goodness of fit between the calculated and the approximated impedance value plots is R $^{2} = 0.975$ , while the measured discontinuity impedance values are within and less than 5% tolerance. The measured reference plane cut-out compensation improved the impedance of the discontinuities by up to $30~\Omega $ .

Keywords

• Approximation
• compensation
• cut-out
• discontinuity
• impedance
• reference