The damped dynamics of printed circuit board and analysis of distorted and deformed half-sine excitation

The JEDEC test standard JESD22-B111 that introduced a half-sine pulse excitation to the supports of the printed circuit board (PCB) is known to suffer from poor reproducibility. Closed formed solutions for the damped dynamic responses of the test board are developed to gain in-depth understanding of the physics. The ratio of the resonant frequency of the test board to the frequency of the half-sine excitation has been found to be the single most important parameter that governs the response of the test board. The magnitude of response increases almost linearly with frequency ratio up to the ratio of 0.7 then increases non-linearly before decreases towards a quasi-static response. In case of no damping, the test board would vibrate perpetually, except for the frequency ratios of 3, 5, 7, etc. for which the test board will cease to vibrate immediately upon the ending of the half-sine excitation. For the specific frequency ratio of 3, the test board exhibits an ideal bell shape response within the duration of the half-sine excitation. Using the closed formed solutions, simple expressions for the maximum fibre strain on the test board and the maximum stresses in the solder joints have been developed. The maximum fibre strain on the test board is proportional to the square root of its density. An ideal PCB for minimum solder joint stresses is one that has low density, high flexural compliance, and in-plane compliances. In practice, it is near impossible to introduce a perfect half-sine excitation and this inconsistency is responsible for the poor reproducibility of the JESD22-B111 test method. The developed closed form solutions were used to investigate two forms of distortions to the half-sine excitation: general shape distortion and local spikes. The former has been shown to alter the response of the test board significantly and is responsible for the poor reproducibility of the JEDEC test.