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62 DESIGN007 MAGAZINE I NOVEMBER 2019 the fastest rise time. When dealing with 1-ns rise times, the emissions can easily exceed the FCC/CISPR Class B limits for an unterminated transmission line. At high frequencies, traces on a PCB act as a monopole or loop antennas. Unfortunately, the high-frequency components of the fundamental radiate more readily because their shorter wave - lengths are comparable to trace lengths (particu- larly stubs), which act as antennas. Consequent- ly, although the amplitude of the harmonic fre- quency components decreases as the frequency increase, the radiated frequency varies depend- ing on the antennas/traces characteristics. Computer-based products tend to radiate on the odd harmonics. High emissions are gener- ally detected at the third, fifth, and sometimes seventh harmonic of the fundamental clock frequency. If this also occurs where the AC im- pedance of the PDN is high, then the radiation is projected even farther. Being able to view a problem in the frequen- cy domain is a powerful tool that provides an- other perspective that often reveals structure to a problem that isn't obvious in the time do- main alone. Key Points • The frequency domain can provide valuable insight to understand and master many SI effects • In the time domain, the system is evaluat- ed according to the progression of its state with time; however, in the frequency domain, the system is analyzed according to its response for different frequencies • The system is changed from time to frequency to make it easy to understand the response • The Fourier series expansion of a square wave is made up of a sum of harmonics • Impedance is defined in both the time and frequency domains; however, it is far easier to understand and apply the concepts of AC impedance in the frequency domain • If the square wave has an even mark-to- space ratio, then the even harmonics cancel • The high-frequency content of a square wave is significantly affected by the rise time of the waveform; a fast rise time results in higher-frequency components • One needs to consider the maximum bandwidth of a signal, including harmon- ics, rather than assume the perfect square wave fundament frequency model • Power consumption in FPGAs has become a primary factor for FPGA selection • To reduce power consumption, IC manu- facturers have moved to lower core voltages and higher operating frequencies, which of course mean faster edge rates • A faster edge rate creates ringing in the unterminated transmission line; this also has a direct impact on radiated emissions • The high-frequency components of the fundamental radiate more readily because their shorter wavelengths are comparable to trace lengths (particularly stubs), which act as antennas Further Reading • B. Olney, "Beyond Design: When Do Traces Become Transmission Lines," The PCB Design Magazine, October 2017. • B. Olney, "Beyond Design: Signal Integrity, Part 1," The PCB Design Magazine, October 2014. • E. Bogatin, Signal and Power Integrity: Simplified, Prentice Hall, 2008. DESIGN007 Editor's Note: Figures 1 and 3 drawn by Barry Olney. Barry Olney is managing director of In-Circuit Design Pty Ltd. (iCD), Australia, a PCB design service bureau that specializes in board- level simulation. The company developed the iCD Design Integ- rity software incorporating the iCD Stackup, PDN, and CPW Planner. The software can be downloaded www.icd.com.au. To read past columns or contact Olney, click here.