Bi-Cubic Spline Based Temperature Measurement in the Thermal Field for Navigation and Time System

Abstract

This paper highlights the use of Bi-cubic splines sets for measuring the temperatures at any point (x, y) on printed circuit boards (PCB). This has accomplished by approximating the system of bi-cubic splines of sets of temperatures measured at points on the PCB in a graphical view. The proposed approximation method is using Bi-cubic splines of modeling the temperature field T (x, y) and replace the continuous two variable function by a combination of single variable functions. While developing designs for the navigation and time system (NTS), there is a need for calculating and analyzing the heat generation processes in units in the NTS equipment, which is a factor in choosing design solutions for systems. The boards currently used can conduct full-fledged 3D simulations of heat transfers to PCB which are about 10 percent accurate compared to full-scale tests. It is always difficult to determine the temperatures at specific points on the PCB. Therefore the accurate numbers are only available at the boundaries of temperature zones.