# When will PAM4 take over from NRZ?

We don’t like to think of conducting traces on PCBs (printed circuit boards) as waveguides because it forces us to confront the ongoing lie we’ve been living in our cozy, digital domiciles in this harsh analog reality.

Think back to the college version of waveguides and the friendly geometry presented in homework problems. It’s a simple boundary value problem: What are the cutoff frequencies for TE (transverse electric) and TM (transverse magnetic) waves propagating along a uniform conducting cylinder?

By solving Maxwell’s equations subject to the conditions that the tangential component of the electric field and the normal component of the magnetic field are zero on the conducting surface, we get a set of TE waves that happily propagate along the cylinder. The boundary conditions limit the waves that the guide can transmit to those above a cutoff frequency. That cutoff is easy to remember because the boundary conditions are the same for an oscillating guitar string: the longest wavelength the guide can hope to transmit is twice the largest transverse dimension of the wave guide. For a cylinder, the wave has to have a wavelength smaller than twice its diameter.

Optic fibers as waveguides are similar, but the boundary conditions are messier. Light propagates down the fiber core and evanesces in the cladding. Evanescence means that tiny fractions of the wave’s energy propagate within the cladding. The diameter of the core of a single-mode fiber is small enough that only one mode can propagate within the wavelength range of the transmitting laser.

“Modal dispersion” occurs in multimode fibers when the core has a diameter larger than a full wavelength of light, allowing two or more distinct modes of oscillation. The signal disperses because each mode travels at a different velocity.

In electrical signaling on good old circuit boards, “multimoding” results from the same physical effect. The problem with traces on circuit boards is that, without the tidy geometry of fibers or homework problem waveguides, you can’t jot down the onset frequency from simple boundary conditions and obvious geometric arguments.

Since digital signals include a few high-frequency harmonics—the ones that give square-wave like edges to bit transitions—and a slew of low-frequency subharmonics, modal dispersion means that some of those high frequency terms can propagate at radically different speeds and destroy Fourier’s carefully manicured phase relationships and the shape of the signal. That is, multimoding creates ISI (inter-symbol interference) nightmares.

The multi-moding onset frequency depends on the trace width, thickness, corners, orientation, and so on, as well as the dielectric geometry and, in principle, everything on the board.

Dr. Steinberger provided a few rules of thumb that can either help you sleep at night or give you nightmares, depending on your design: “Microstrip will multimode when the substrate is more than about one seventh of a wavelength thick. Stripline will certainly multimode when the ground planes are separated by more than half a wavelength, with wider center conductor widths reducing that distance somewhat.”

As for future designs, Dr. Steinberger suggests, “Thinner dielectrics and the concomitant narrower traces will help somewhat, but the resulting increase in losses won't help a bit. Going to a lower dielectric constant material such as teflon or air could help immensely.”

**Figure 1: PAM4 packs two bits per symbol and NRZ just one. Both eye diagrams cover 6 bits, but PAM4 does it with almost half the signal frequency bandwidth.**Moving to PAM4 (4-level pulse amplitude modulation) can buy us time. The idea of PAM4 is easy: you encode two bits in every symbol so that, for a given data rate, the high frequency content of the signal is half the NRZ equivalent. Building PAM4 systems, on the other hand, isn’t so easy.

- Along with multimoding, what would make you switch to PAM4?
- What do you think the biggest drawbacks are to PAM4? Transmitter and receiver architecture or dealing with transmission line signal impairments—that is, closing an already complicated eye?
- Do you see a maximum data rate on the horizon for standard FR-4 PCB (flame-retardant type-4 printed circuit board)?

**Also See:**

Don’t confuse PAM4 SER and BER

PAM4: Symbol levels and voltage compression measurements

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The tradeoff between crosstalk and loss

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DesignCon2016: Prepare for the PAM4 phase shift

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