[NLRS] piezoresistive transducers

[Dr. Gerald N. Johnson]

On 12/26/2012 9:33 AM, Douglas H Reed wrote:
>
>
> Based on Jerry's research, my guess would be that some Marketing type
> has confused "resolution" and "accuracy" when creating the advertising
> for the device. Resolution is easy to achieve but accuracy is
> something entirely different.

And some of that fine resolution will be used up in random noise, the 
user's task is to separate circuit noise from microclimate.
>
> We all do it. Haven't you ever used a cheap DVM to measure a voltage
> and written down a result with 4 digits? When the rated accuracy of
> the DVM was spec'ed at maybe 2% full scale?

Is the HF el cheapo that good. I have one somewhere, I figured it for no 
better than 10 to 20%, more of an indication of presence or absence than 
a reliable value.

> My first exposure to this
> was over 40 years ago when my Physics teacher told me that he didn't
> want to see results to 7 decimal places from my shiny new calculator,
> when the numbers involved only had 2 decimal places. Since then I've
> never forgotten that 1.5 volts is not the same as 1.500 volts because
> the implied accuracy of the reading is much different.

A lesson well learned that needs to be passed on daily, with computer 
programs giving many significant figures for data of ill repute taken by 
instruments or persons of questionable character. The point of W0PFP's 
oft repeated phrase, "Measured with micrometer, marked with chalk, cut 
with axe." Sometimes we need to add, "Micrometer made of jelly."

And its so often forgotten that taking extensive calculations of numbers 
with limited precision even to the 7 digits of double precision can give 
results of much poorer accuracy because each number has that limited 
precision in its approximation in floating point. One example I learned 
more than 50 years ago was iterating the solution to a polynomial. In 
single precision a good polynomial of 5th order would begin to oscillate 
at about 4 digits precision in the solution. Double precision could 
extend that to 7th order IF there were no repeated roots. x^n = 1 is a 
most obnoxious polynomial to interate to a solution. And those are using 
the most precise methods of polynomial evaluation. When looking for a 
solution you want to evaluate the polynomial to a value of zero which 
means you are taking very small differences of what can be large numbers 
if you plow in figuring ax^n + bx^(n-1)... What works better is (((ax + 
b)x + c)x + d... Its easy in the first case to have the least 
significant bit of the large number greater than the final result which 
means the final result has zero significant digits correct.

While the book I read on chaos didn't admit it, I believe that the 
looping of values they find is strictly due to round off error 
increasing until its as great as the magnitude of the computed result.

I used to read a 10" slide rule to 3 or 4 places and most were good 
digits, I'm sure some were noise. One time I eyeballed the 1KHz 
increment dial scale on my 75S-3B in an ARRL FMT on 7 MHz to 1ppm error 
in the reported results. I had improved the internal 100 kHz calibrator 
by encasing the crystal in a block of styrofoam with a layer of aluminum 
foil facing the adjacent tube to reflect radiated heat. And I set it 
with my in house double oven frequency standard with a few parts in 
10^-9 stability based on comparing it to WWVB or maybe WWBL in those 
days and I used harmonic birdies in the receiver to get more calibration 
marks than every 100kHz. I suspect that the receiver I bought as a 
Collins employee was selected to have better than average PTO linearity. 
It is possible to interpolate a scale accurately, and its equally 
possible to interpolate it inaccurately whether by eye or computer with 
excess resolution in the display.
>
> In practical terms, Jerry has shown that you can safely disregard what
> the article says about accuracy since you probably don't have enough
> money to ensure a level of calibration which would let the readings
> mean something in the outside world. But that level of resolution
> might be useful when making relative readings, assuming there is a
> useful amount of correlation between the original reference and the
> final target of the adjustment.

> OTOH, if you decide to make a voltage reference standard to calibrate
> your cheap DVM, there are a number of high-accuracy voltage reference
> chips available as free samples from Analog Devices and Maxim IC's.
> W1GHZ wrote an article about building one many years ago. And for
> sensors, a lot of new chips are just black boxes with a simple serial
> interface to a microprocessor and laser-trimmed factory calibration.
> The whole series of Maxim One-Wire devices come to mind......

There once was a series of digital voltmeters where the user dialed up 
individual decades to balance a meter to zero which used a precision 
divider set of decades and a wet standard voltage cell. Much like the 
technique used at NBS (in those days before the NIST name). The standard 
cell was fairly dependable though if moved it had to be moved carefully 
and not shaken or stirred. I have one of those meters, haven't applied 
power in decades but I kept it quiet, thinking I might want to calibrate 
some meter some time. While carrying it down the stairs to the basement 
in the new place, the leather handle broke (its that old) and it tumbled 
end over end down a dozen steps thoroughly stirring the standard cell. I 
figure its no longer trustworthy because the electrolyte in the standard 
cell is supposed to be stratified with different brews in the two sides 
of the H shapped cell. Probably didn't do the nulling meter any good 
either. Its a John Fluke model 803 differential voltmeter. 10" wide, 13" 
tall, about 20" deep. Weighs at least 30 pounds. Today we can probably 
find the same function with better accuracy in a chip this size of the 
dot at the end of this sentence. The beauty of a standard cell is that 
its not dependent on factory calibration, its dependent on standard 
metals in the electrodes and a standard electrolyte chemistry. Based on 
physical constants, not another voltmeter. Unfortunately laser 
calibration is based on another meter, not physical constants that can 
be measured independently and that standard reference used in the 
production setup can drift introducing more error as time passes.

73, Jerry, K0CQ
>
> 73, Doug Reed, N0NAS.
> ______________________________________________________________
>