Keyword: pcb change shape, pcb
When we think of digital signals, we naturally think of logic highs and lows, signals rooted in the Fourier components of a square wave PCB. Of course, we also know its not like that.
At gigabit per second rates, conducting traces on PCB act more like ugly waveguides than tidy paths from transmitter to signal. Rather than a current propagating along a conductor, these signals are electromagnetic waves that travel through the dielectric, barely clinging to the trace.
Picture yourself as a bit on a zip-line crossing a dense forest canyon, clinging to the cable for your very existence PCB.
But its worse than that. As you zip through PCB the forest, your body smears out and interferes with bits ahead and behind you. You absorb elements of bits from others, you and the other bits on this trace interfere with each other.
Digital waveforms are built from a combination of high frequency harmonics and lower frequency subharmonics. Alternating PCB 1s and 0s carry the high frequency content of square waves. Consecutive identical bits are made of lower frequencies. For example, at 10 Gb/s, 1010 is mostly 5 GHz sine waves, a sequence like 11001100 mostly 2.5 GHz, and so on. When you think about a real signal, say
1110 0101 1000 0110 . . . , its easy to get tired-head trying to picture all the different frequencies that Fourier is shoving in there.
But wait, the tired-head has only just begun!
Dispersion Nightmares
The speed of light is given by
where and are, respectively, PCB the electric permittivity and the magnetic permeability. We like to think of as a constant, but electric permittivity varies with frequency, that is:
which means that different frequencies travel at different speeds. That is, the cheap fiberglass we use to make PCB is a dispersive medium. The dispersion also varies with the direction of the signal, so we should really say
where u is a vector pointing in the direction of the signal. PCB Yeah, its a mess. Instead of those tidy waveguides with rectangular or cylindrical cross sections that made solving wave equations so satisfying on homework problems, we getthis.
Your two favorite Maxwell equations, Amperes law (electric currents cause magnetic fields) and Faradays law (induction = changing magnetic flux causes electric fields), conspire to create the skin effect.
The skin effect house of horror
Start with the electric field required to push your signal from Tx to Rx. Amperes law produces a magnetic field about the trace. PCB But your signal is composed of tons of different frequencies, so those magnetic fields are constantly changing. Faraday demands that those changing magnetic fields induce electric fields that oppose the changes. Ampere requires that those electric fields produce magnetic fields. Those magnetic fields induce electric fields that produce. . . .
You end up with a combination of horrors. The induced electric fields cancel the field that was supposed to get your signal from Tx to Rx. The electromotive force drops to zero on the inside of the conductor, but a hint of your intended signal remains at the outer skin. As the data rate increases, PCB the thinner that skin becomes. The thinner the skin, the higher the effective resistance. The higher the effective resistance, the less of your innocent signal survives.
Ultimately, your innocent looking PCB trace acts like a low pass filter designed by an angry two-year-old.
Put it all together and the conducting trace is just a cable to which you cling while flying through the dielectric jungle. Each of the frequency components that gave you such a nice digital appearance at the transmitter output travel at different speeds. Your high frequency components are pushed ever farther from the trace, left to perish on the metaphorical vine. PCB You lose your hat, your shoes, your shirt buttons tear off, your pants start to tear, your zipper.
Different components of you go at different speeds, you stretch out, PCB change shape, overlap with the bits ahead and behind you. Those overlaps superpose into a waveform critically infected with ISI (inter-symbol interference).
