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20 The PCB Design Magazine • October 2017 At low frequencies, traces and components on a PCB behave simply as lossless lumped el- ements—as taught in Circuit Theory 101. But as the frequency increases, the copper trace and adjacent dielectric(s) become a transmission line, the skin effect forces current into the outer regions of the conductor and frequency depen- dant losses impact on the quality of the signal. The PCB trace now behaves as a distributed sys- tem with parasitic inductance and capacitance characterized by delay and scattered reflections. The behavior we are now concerned about oc- curs in the frequency domain rather than the familiar time domain. This is the real world of high-speed design. Ideally, square wave signals are just that— perfect square waves with an evenly, sloping rising and falling edge. However, in the real world, things are quite different. Figure 1, illus- trates the rising edge of a square wave, in the ideal case (low frequency), compared to the real world (high frequency). The transmission line effects create under and overshoot resulting in ringing in the signal. If this ringing crosses the voltage input high threshold (VIH), at the re- ceiver, then it may cause false triggering. The Fourier theorem states that every func- tion can be completely expressed as the sum of sines and cosines of various amplitudes and frequencies. The Fourier series expansion of a square wave is made up of a sum of odd har- monics. Figure 2 shows the conversion of a square wave from the time domain to the fre- quency domain and the resultant amplitudes of the frequency components. If the waveform has an even mark-to-space ratio, then the even har- by Barry Olney IN-CIRCUIT DESIGN PTY LTD / AUSTRALIA When Do Traces Become Transmission Lines? FEATURE COLUMN: BEYOND DESIGN Figure 2: Harmonics of a square wave converted from the time domain to the frequency domain. Figure 1: Ideal vs real-world rising edges.