w_daniel_hillis's picture
Physicist, Computer Scientist, Co-Founder, Applied Invention.; Author, The Pattern on the Stone
Impedance Matching

“Impedance” is a measure of how a system resists the inflow of energy. Often, a system can be changed to accept energy more efficiently, by adding an element called an “impedance matcher.” Most people have never heard of an impedance matcher, but once you know about them, you begin to see them everywhere: in the shape of a trumpet, the anti-reflective coating on a lens, and the foam spikes on the inside of a recording booth.

A familiar example of an impedance matcher is the transmission of an automobile, which couples the energy from the engine into the wheels by converting the relatively fast rotation of the engine into the slower, stronger rotation required to propel the car. The transformer on an electric pole solves an analogous problem, converting the high-voltage electricity on the transmission lines to the high-current electricity required to power your home. Lots of machines, from jet engines to radios, depend on impedance matchers to move energy from one part of the system to another.

Some of the most interesting impedance matching occurs when energy comes in the form of a wave. You have probably noticed in a swimming pool that waves from a splash reflect off the sides of the wall. Because there is an impedance mismatch between the water and the wall, the wave energy is unable to couple into the wall, and so it reflects back. If you watch a vertical seawall, you will notice that the reflected wave adds to the height of the original wave, creating a splash that is almost twice the height of the wave. This does not happen when a wave rolls up a gently sloped beach, because the slope acts as an impedance matcher, allowing the wave’s energy to flow into the sand. The foam spikes on the inside of an anechoic recording booth serve much the same function. The sound waves are much larger than the spikes, so they make the foam gradually denser as it gets closer to the wall. This couples the sound energy into the absorbing wall without reflection, so there is no echo.

The flare at the end of a trumpet works on the same principle, in reverse. Without the flare, most of the sound energy would just be reflected back into the trumpet instead of coupling to the outside air. A speaking cone, or megaphone, is another example. The cone acts as an impedance matcher, connecting the sound energy of the voice into the air. This kind of impedance matcher is so effective that it allows the tiny motion of an old Victrola record needle to fill a dance hall with music.

Impedance matching works with light waves as well as sound. The anti-reflective coating on a camera lens is very similar in function to the foam on the sound booth. A mirror, on the other hand, works like the seawall, creating a reflection with an impedance mismatch. By putting only a few molecules of aluminum on the glass we can tune the optical properties of the surface to create an impedance mismatch, a “half-silvered” mirror that reflects only a little bit of the light.

On a larger scale, we can think of atmospheric carbon dioxide as an undesired impedance matcher, coupling the infrared light waves of the sun into the planet. Someday, we may decide to cool our earth by adding tiny particles of dust to our stratosphere, tuning the optical surface to reflect away a tiny portion the infrared waves coming from the sun. The impedance mismatch between the atmosphere and sunlight would create a kind of half-silvered mirror to keep us cooler by reflecting away the unwanted energy flowing into our planet.