Notes on Impedance - Part 1

April 17, 2018

John Burkhert

There's scarcely a printed circuit board that doesn't have some form of impedance control. The trend is more and still more because the "Things" part of the Internet of Things all want to talk to each other, and without wires. It's probably a good time to be an expert on printed antennas. RF is the extreme version of Ohm management, so why not start there? Single-ended 50 Ohm transmission lines are the most common form; let's break that down.

Image Credit: ProSound

The Misleading Double Single

Single-ended has an element at both ends, something that transmits on one end and something else that receives the transmission at the other. Misleading! The waveform is most often analog; usually a sine wave. You establish the connection from one end to the other by transmitting a particular sine wave at a set frequency and amplitude.

The carrier wave sends a set amount of energy in a fixed number of pulses per second. The frequency is the width of the pulse, and the energy is the height of the wave you see on an oscilloscope. If these two values are held constant at the output, you receive a continuous tone at the input of the target.

Image credit: Embedded.com

That by itself isn't very useful, but you can change either of those values: bigger and smaller pulses of the same width (amplitude modulation), or faster and slower pulses of the same height (frequency modulation), or AM/FM, etc. It's those differences in the tone, the pitch, or the volume that can be used to convey information. That's what modulators do. These RF signals are way too high in frequency for us to hear, so we use antennas as ears then a demodulator to transform the signal back into something cool – whatever was modulated in the first place.

Image credit: SynaptiCAD showing an amplitude modulation scheme.

There's a problem though: the world is not a friendly place. The world around your transmission line wants to change the tone and loudness of your pure signal. As Homer Simpson would say, "Stupid physics!" The longer the path, the more it's exposed to the cruel world. Signal degradation is unwanted changes in the wave you're transmitting. Changes suck unless they're the ones you put into the transmitter. They happen both over the air and along the signal path of your board.

We have a bag of tricks to take care of that second problem. Impedance matching is the first step. I've asked why use 50 Ohms, is it Ohm's Law? Nope. Same reason we drive on the right or left side of the road: pick one. You don't want to reflect off of on-coming traffic, and electrons don't want to reflect off of impedance mismatches, so we have a standard. Avoid losses in either case.

An impedance mismatch can be any change in width or abrupt change in direction. That's why the short and straight path is the right path. A trained eye can immediately spot potential problems. In digital systems, we've used those 50 Ohm termination resistors to suck up the reflections at the end of the line if you're wondering.

Why 50 Ohm?

Back in the era when this was decided, 50 Ohms was pretty easy to achieve with the materials and technology on hand, both within the big chunky devices and on the stone-age boards. We'd calculate the line-width starting with the size of the device footprint and call out the appropriate dielectric constant/thickness for minimal mismatch.

These days, using 50 Ohm lines is a pain. Dielectrics are so thin to accommodate the aspect ratio of the micro-vias and/or reduce the Z-stack of the product that we're down to super thin (and lossy) line widths. The skinny lines then meet the big fat pad of the 0201 chip cap and POW, the impedance changes and the signal scatters. Fillets help but only a little. So we cut out layer 2 ground and reference layer 3, or deeper, to get a reasonable outcome out of the impedance calculator.

The above geometry where you route on outer layers where the parts have (unless embedded, but that's another story) a ground plane below is called microstrip. Internal routing between a ground sandwich is known as stripline, and those are the typical transmission lines. Another technique for routing on the outer layer is called co-planar waveguide (CPW), and as the name suggests, the entire thing takes place on one layer.

Stone-age boards used that technique just before transitioning to a via. The idea being that we would have the lower loss microstrip leading into the narrower CPW that didn't need a reference plane below. You see, the air-gap between the signal via and the ground plane was quite a bit wider then, so we didn't want ungrounded microstrip over that 20 mil air-gap.

For all of that, transmission lines are the given and power is where all of the drama lies in our current cruel world. We've mostly solved the analog noise problem by changing to the square waves of digital standards over the air and using differential pairs to cancel on-board noise. We'll discuss the thinner and edgier protocols next time around.

Dear EEs: I'm sure there are mistakes or omissions here. It's just an off-the-cuff explanation as I remember it being explained to me by magnanimous people such as yourself. Corrections appreciated.

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