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74 DESIGN007 MAGAZINE I MAY 2020 the time and the frequency domains. The knee frequency is an estimate of the highest fre- quency content of the signal, which depends upon the rise time of the signal. For instance, if the rise time is 100 ps, then the upper band- width is actually 5 GHz regardless of the clock frequency. It is possible to have two different waveforms, with exactly the same clock fre- quency but different rise times and, therefore, different bandwidths. When selecting the most appropriate dielec- tric materials for a stackup design, one should consider the bandwidth up to the fifth har- monic. For the 1 GHz fundamental frequency in Figure 3, the maximum bandwidth to con- sider is the fifth harmonic at 5 GHz if the rise time is unknown. This assumes the worst case of a 100 ps rise time. For high-frequency sig- nals, it is more accurate to use the actual rise time to evaluate bandwidth, but unfortunate- ly, we do not always have the luxury of that information. It is important to note that the concept of bandwidth is inherently an approximation. It is roughly where the amplitude of the frequen- cy components in a waveform begins to drop off faster than an ideal square wave. One simple but often overlooked method of minimizing noise in a system is to limit the system bandwidth to only that required by the intended signal. The use of higher bandwidth than required allows additional noise into the system. The same principle also applies in the case of digital circuits. High-speed logic with a fast rise time is much more likely to gener- ate and be susceptible to high-frequency noise than its lower speed counterpart. Key Points • The shorter the rise time in the time domain, the higher the bandwidth in the frequency domain. • A signal must have a fast enough rise time to accommodate the data being processed. • A fast rise time may create ground bounce, reflections, crosstalk, and electro- magnetic radiation. • One should limit the bandwidth so that the system performs to expectations, but at the same time, avoid high-frequency effects, which cause electromagnetic compatibility issues. • Depending on the logic family, the fall time is usually slightly shorter than the rise time. • Signal-integrity problems are more likely to occur when switching from a high-to-low transition than from a low-to-high transition. • The rise time is typically measured from the 10% point to the 90% point on the rising edge of the signal. • The 3 dB point is where the signal is reduced down to 70% of the amplitude of the input signal. • As rise times become faster, a more accurate approach is to use an upper knee frequency. • The knee frequency is an estimate of the highest frequency content of the signal, which depends upon the rise time of the signal. • When selecting the most appropriate dielectric materials for a design, one should consider the bandwidth up to the fifth harmonic. DESIGN007 Further Reading • B. Olney, "Beyond Design: When Legacy Products No Longer Perform," The PCB Design Magazine, August 2017. • D. Brooks, "Rise Time vs. Frequency: What's the Rela- tionship?" I-Connect007, June 7, 2011. • E. Bogatin, Signal and Power Integrity: Simplified, Prentice Hall, 2008. • H. W. Johnson & M. Graham, High-Speed Digital De- sign: A Handbook of Black Magic, Prentice Hall, 1993. Barry Olney is managing director of In-Circuit Design Pty Ltd (iCD), Austra- lia, a PCB design service bureau that specializes in board-level simulation. The company developed the iCD De- sign Integrity software incorporating the iCD Stackup, PDN, and CPW Planner. The software can be downloaded at To read past columns or contact Olney, click here.

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