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Digital Waveform Signals – Crossing the Digital-Analog Divide

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Digital signals are an idealization and as data rates climb above a few Gb/s, they betray their microwave analog reality.  

To understand how to cope with the physical nature of signals that we might prefer to think of as bits, nibbles and bytes, let’s start with an ideal digital waveform. To get nice square edges, the perfect waveform requires an infinite sum of harmonic frequencies at odd multiples of the data rate. It’s easiest to see in the Fourier series representation of a square wave where ƒd is the data rate in Gb/s. 

Square Wave(t) = Vpp Σ — sin(nπƒd t) 

To extend Eq. (1) from a simple square wave to a digital data signal requires subharmonics to accommodate all runs of consecutive identical bits. For example, a 0011 sequence requires frequency components at half the data rate, a run of three identical bits requires components at 1/3 the data rate, and so on.

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