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A Plugged Nickel

What's with all these dB figures anyway? 

I got to thinking about the problem of detecting and quantifying distortion.  It's all because of the blessing and problem of preamp 'color'.   As near as I can tell, a preamp's color is a matter to the special blend of the relative amounts of transient 2nd, 3rd, and 4th harmonic distortions that will pop up as signals pass through the preamp. From what I have observed during my preamp measurements, the relative amounts of those distortions also differ in proportion depending on signal level, and the gain setting of the preamp.

The preamps in my Behringer X32 mixer/interface are described as transparent. That means that their 2nd, 3rd, 4th, and 5th harmonic distortion values are pretty low. The 6th, 7th, 8th and so on, are very small values relative to the 2 thru 5 group, and only the 7th seems in the technical literature to be particularly objectionable in small amounts.

 

As part of the research I did in buying the X32, I found an article produced by a German company that did a bunch of laboratory measurements on the preamps. Among the measurements was a distortion profile test at 0dB gain. The graph showed a peak of -85dB for the 3rd harmonic.  All other harmonics were -105dB and smaller. Since tape machines are famously strong in their 3rd harmonic profile (best case -45dB on mastering grade tape),  I chose to commit, and bought the X32.  All has been well since, but I've wanted to put that -85dB in a perspective that I could confidently reproduce in my head, and compare to other things.

It turns out that pocket change is a great reference.  It’s readily available, consistent, safe to handle, and gluten free.  So, I went to the US Mint website, and they had already dutifully documented the weight of all US coinage.  Here’s the list:

  • Cent 2.500 grams

  • Nickel 5.000 grams

  • Dime 2.268 grams

  • Quarter Dollar 5.670 grams

  • Half-Dollar 11.340 grams

  • Presidential Dollar 8.100 grams

  • Native American US coin 8.100 grams

 

While I have you trapped here, I might as well let you know the nickel was originally released as a 1-cent coin,  and then graduated to be a 3-cent coin before being standardized as a 5-cent coin.  Continuing our tour, the expression “ain't worth a plugged nickel” that we hear in the black-and-white gangster movies is related to the fact that a center disk of silver was pressed into the middle of the coin blank before being struck with the giant press that embosses the images on the coin. The silver increased the value of the hybrid coin up to face value.  A ‘plug nickel’ was one that was missing its center, thereby decreasing its value.  Just as today, people say “I could care less” when they really mean they “couldn’t care less”, the expression for the nickel should have been “not worth a plug nickel”, or most properly, “not worth an unplugged nickel”.  But we know how these things go in spoken language. My wife just went to the kitchen to “unthaw” some frozen vegetables. Do you see the inversion?

 

Conveniently, the lowly nickel coin (made of 25% nickel and 75% copper) weighs in with a round figure of five grams.  Even more conveniently,  that happens to be 85 dB less than my body weight!  Yeah, do the math; 200 pounds is 90718 grams, which works out to 18,143 nickels, or $907.15, because I knew you’d want to know.  As a matter of full disclosure, I’ve gained 2dB of body weight in the 44 years since high school graduation.  Getting back on track here,  two things in proportion of 18,143-to-1 are 85.17 dB apart. 

All of the dB calculations and proportions are done as voltage gains/losses because that’s the way amplifiers are designed. Their gain is measured in proportional dB volts.  Equally, test measurements are shown in the FFT (Fast Fourier Transform) screen shots as voltage proportions on a logarithmic (dB) scale. 

In the follow-on articles, we’ll be bandying about figures of  -96dB, -100dB, -108dB, -120dB, and even -143dB. It’s important to get these numbers into perspective because we audiophiles are too quick to imagine that we’ve got a handle on how loud or soft things are. 

 

  • 96dB is a proportion of 64,096-to-1: a nickel in the saddlebag of a 706-pound British Exmoor pony that's 12 hands high

  • 100dB is 100,000-to-1: a nickel in the mouth of a 1102-pound 12-foot 4-inch white sturgeon (Acipenser transmontanus)

  • 108dB is 251,189-to-1: a nickel on the dashboard of a 2768-pound 2012 Nissan Cube

  • 120dB is 1,000,000-to-1 : a nickel on the tow hitch of an 11,023-pound, class-3 GVWR truck (5.5-ton) Hummer H1

  • 143dB is 14,125,375-to-1: a nickel taped to the front shovel of a 155,705-pound Caterpillar D10T2 grading bulldozer (77 tons) used for reclaiming mined lands. 

 

The point of all this is ... calm down, and be skeptical. Stop worrying about the relative noise floors of microphones when the self-noise SPL is quieter than interstellar space. Stop being concerned about events that are -100dB down from the 0dBFS levels of your DAW. Be skeptical of people who want you to buy product 'X' because it promises to improve the noise floor of your already minus 100dB playback system.

 

Most of those claims ain’t worth a plugged nickel.

- Ted Gary of TedLand

June 7, 2016