When we talk about a “bell curve,” most technical people understand we mean a Gaussian or “normal” distribution. My introduction to the Gaussian distribution came in an analytical-chemistry course when our professor talked about how experimental results would fit a Gaussian curve. But he stressed we would need the results of many experiments to approximate the shape of an ideal curve, or peak.
Although we tend to take the Gaussian distribution for granted, some information fits other types of distributions. So, if you blindly try to force fit a Gaussian distribution to experimental data, you may lead yourself to an incorrect analysis of test results. The “shape” of many Gaussian-like peaks depends on three parameters; peak height (a0), peak position (a1) and half the peak width at half height (a2).
The equation below will produce data for a Gaussian peak as shown by the red line on the chart, below.
y = a0 * exp[-0.5((x-a1)/a2)2]for -x to +x
Note the blue line, which represents a Lorentzian peak, aka a Cauchy-Lorentz distribution:
y = a0 * (4 * ((x-a1)/a2)2 + 1)for -x to +x
Note the Lorentzian-peak data produces a sharper peak but a wider distribution. Although not found frequently in engineering work, engineers still might encounter this and many other types of distributions peaks such as Logistic peaks and Extreme-Value peaks. So, don't automatically assume every distribution falls on a Gaussian curve. The TableCurve 2-D software, for example, lists 37 nonlinear peak functions. This type of software can quickly find the best distribution curve that fits experimental data.
I scanned an old article from my paper archives about data peaks that provides more information and equations.
More on Surge Suppressors
In the April 4 Tips column, “Suppress Those Surges,” I discussed the need to suppress power surges on power lines that connect to instruments. Lou Garner responded with a thought about surge suppression and he supplied a circuit he built and continues to use to good effect.
Garner wrote: “The suppressor I built for my computer system uses three shunt MOVs, a series-connected inductor and three high-current Zener-diodes that serve as shunts. The let-thru voltage is less than 180V peak at 125V — the maximum line voltage — and during the five years I have used this circuit, the MOVs have not been degraded.”
The “secret” is the inductor, which does not change its performance with use and there are no voltage changes to worry about. As line surges occur, more instantaneous current will flow and the inductor will inherently resist it. You can find Lou's schematic diagram and component values above.
|Jon Titus, a former designer and chief editor of EDN and Test & Measurement World magazines, remembers when storage scopes used Polaroid instant film to capture transient signals.