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August 2017 • The PCB Design Magazine 45 drops off with the inverse of frequency, since each harmonic is a higher frequency. Figure 3 shows the calculated harmonic amplitudes of an ideal 1GHz clock signal for the odd harmon- ics up to 100GHz. However, in practice, the signal rise time has an impact on the maximum signal band- width. Understanding the frequency band, that really matters, for digital design is very impor- tant. Traditionally, we used 0.35/Tr (where Tr is the rise time in ps) for the upper bandwidth. However, a more accurate approach is to use an upper knee frequency of 0.5/Tr, which forms a crude but useful translation between time and frequency domains. If, for instance, the rise time is 500ps, which is typical these days, then the upper bandwidth is actually 1GHz regard- less of the clock frequency. It is possible to have two different waveforms, with exactly the same clock frequency but different rise times and therefore different bandwidths. When selecting the most appropriate dielec- tric materials for a design, one should consid- er the bandwidth up to the 5 th harmonic. The bandwidth of an interconnect refers to the high- est sine wave frequency that can be transmitted by the interconnect with- out significant loss. For our 1GHz example, the maximum bandwidth to consider is the 5 th har- monic at 5GHz if the rise time is unknown. FR-4, the glass epoxy material commonly used for multilayer printed circuit fabrication, has negligible loss at frequen- cies below 1GHz. But since the dielectric loss is frequency-dependent, at higher frequencies, the dielectric loss of FR-4 increases. So, for high- frequency digital, RF and microwave designs, al- ternative materials that exhibit lower losses need to be considered. (To make this selection process easier, over 31,000 rigid and flexible materials, up to 100GHz, can be sourced from the iCD dielectric materials library.) Electromagnetic emissions arise from each frequency component of the signal. For the worse offender—the common-mode currents— the amount of radiated emissions will increase linearly with frequency. Although the amplitude of each harmonic drops off with the inverse of frequency, the ability to radiate increases linear- ly, so all harmonics contribute equally to EMI. To minimize EMI, the design goal is to use the absolute lowest bandwidth possible whilst still maintaining the specified data throughput. Any ringing in the circuit may increase the amplitude of higher-frequency components and thus increase the magnitude of radiated emissions. High-frequency harmonics can also beat with the resonant frequency of the plane pairs, as they approach half wave length, creat- ing a rough wave effect which, in extreme cases, can cause total system failure. This is the reason why solving signal integrity issues is always the best starting place to minimizing EMI. WHEN LEGACY PRODUCTS NO LONGER PERFORM Figure 3: Odd harmonics of a 1GHz fundament clock.