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52 The PCB Design Magazine • August 2016 then bounces off the open circuit end-point and back to the trace for a total distance of a half wavelength. This half wavelength travel has the effect of shifting the phase of the signal by 180 degrees, creating resonance in the via stub. The phase-shifted, reflected signal has a maximum value at a time when the signal has a minimum value, and vice-versa. The Nyquist frequency of a discrete signal is defined as a half of the sampling rate of the signal and will have a strong frequency com- ponent at this frequency. In addition, the sig- nal can have strong power spectrum harmonic components at frequencies greater than the Nyquist frequency typically up to the 5 th har- monic. The resonant frequency of the via stub is inversely proportional to the dielectric con- stant of the material, surrounding the via, with a wavelength of four times the length of the unused portion of the via. This relationship is given by the following equations: Where is the time for the signal to propa- gate in a stub (~180ps/in for FR4), is the length of the via stub, Er is the dielectric constant, c is the speed-of-light and is the resonant frequen- cy of the via stub. When the resonant frequency is approxi- mately equal to the Nyquist frequency, one or more frequency components, of a signal trans- mitted through the via, can be strongly atten- uated which causes the impedance of the via drop. And although, it seems high enough to be outside consideration for most designs, the affects actually start to come into play above HOW TO HANDLE THE DREADED DANGLERS, PART 1 Figure 2: Differential 100Ω via with stub (red) vs. via with back-drilled stub (blue).

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