The Riddle of the Elusive Peanut Butter Property

With the gauntlet thrown down, a young engineer sets out to measure an electrical property of an important foodstuff

By Andrew Berding, Contributing Writer

Many years ago I had a boss by the name of Dan Murphy.  I often wondered if Murphy’s Law was named after him. (By the way, did you know that Murphy was an optimist?)

Whenever one of us employees would go in to him with a question (such as: “What happens if all logic outputs switch in the same direction at the same time?”), being a good manager he would habitually throw back the question to us with his own rhetorical question: “Well, what’s the dielectric constant of peanut-butter?”

This of course was frustrating. And annoying. And challenging. So I determined to find out!

As an experiment, I took a piece of copper-clad glass-epoxy board and made a transmission line by stretching a 12-inch piece of solid copper wire between a BNC connector and a ground post.

Using a high-speed Time Domain Reflectometer (TDR), I carefully measured the transmission line’s characteristic impedance Zo and its propagation delay Td.

For the second phase of the experiment I smeared the copper-clad glass-epoxy board, the BNC connector, the copper wire and the ground post with a whole jar of Skippy peanut butter (the smooth variety of course—not the chunky style)! Then using the TDR, I carefully re-measured the characteristic impedance and the propagation delay of the peanut-butter coated transmission line.

Since the only thing that had changed between the two measurements was the peanut-butter, I could now calculate the dielectric constant of the peanut-butter with a couple of simple computations. Knowing that Zo = sqrt(L/C) and that Td = sqrt(L*C), I then found that C = Td / Zo. Therefore, since capacitance is proportional to dielectric constant, the elusive dielectric constant of peanut-butter εpb = (Tdpb/Zopb) / (Tdair/Zoair).

Then I carefully wrote up the lab experiment in formal notation showing the various pieces of equipment used, their serial numbers, calibration dates, the “sell-by” date on the jar of Skippy peanut-butter, raw data, calculations, photos of waveforms, results, significance of results, recommendations for follow-on experiments, etc. I even added a section on error analysis of results. Since the inductance L = Zo * Td, capacitance cancels out of the equation and Lair should be exactly equal to Lpb. Any differences can be used to determine possible measurement errors.

Next time I went in to see my boss and he replied to my question with his typical rhetorical question: “Well, what’s the dielectric constant of peanut-butter?” I had an answer.

I said: “I’m glad you asked.” And I produced the experimental setup and the formal lab report. Needless to say, being a good guy he got a huge laugh out of it and complemented me on my “professionalism.”

The peanut-butter smeared experiment stayed on his desk for a couple of weeks then it migrated to the top of his book-case for a couple of months before it got really nasty and rancid and began to grow a half-inch of gray fuzz on it. One day it disappeared—for good reason.

He never asked that (or a similar) question again!
By the way, in case you ever really need to know (and your job depends on it), the dielectric constant of Skippy smooth peanut-butter is exactly 3.22!

Contributing Writer and BSEE Andrew Berding is an inventor with nine patents and serial entrepreneur, having founded six companies including Advanced Memory Systems (Intersil) and was a major participant in the founding of two others. He has been a consultant to the industry for 30 years and will soon be celebrating his 50th wedding anniversary. Though unfortunately no documentation exists from his most famous investigation, Andrew sends a sketch he drew of the ohm-meter used: