Re: Electric pulse attenuation

On Dec 7, 10:50 am, "William R. Frensley" <frens...@xxxxxxxxxxxx>
wrote:
Rich L. wrote:
On Dec 6, 12:37 pm, Efthimios <eangelopou...@xxxxxxxxx> wrote:

(on the subject of the decibel)

Let me add one thing to Rich's excellent summary: While the formula
10\log_{10}(r) looks completely arbitrary, ratios of 1 dB \approx 1.26
turn up in a surprising number of places, always in some way associated
with human perception. The association of dB with audio technology is
well-known, and the quantization of modern digital volume controls is
almost certainly 1 dB steps.

A number of years ago, I needed to design an optical resolution test
pattern, consisting of different sets of lines with varying pitch.
After a bit of drawing I concluded that stepping the pitch such that
it doubled every three patterns was just right. In other words, the
ratio between two steps was cube root of 2, \aprox 1.26.

The most surprising occurrence of a dB scale was found when a
colleague and I attempted to estimate the salary scale at the company
for which we worked. The annual stockholder's meeting report gave us
enough information to estimate the salary of the Vice President at the
top of our reporting chain, and a simple calculation gave us a factor of
about 1.25 per level of management.

- Bill Frensley

I recall an article in Scientific American in the 70's or early 80's
making a similar observation about such random things as the first
digit of street addresses, the area of lakes (irrespective of the
units used), etc. It appears that any measurement that spans a
population of more than a few factors of 10 shows a similar
logarithmic frequency of the first digit. Not quite your observation,
but possibly related.

As for Efthimios' question: I was assuming that the "e" in that
expression was the voltage (sometimes represented by "e" or "E" for
electric field. If he is using the natural logarithim, it seems like
he is doing some conversion from a base 10 log to a base e log, but
that doesn't make sense for decibels. By definition dB is base 10
log.

One point that I didn't cover that might be key to understanding
this. What makes dB so handy in electronics is that amplifier gains
and attenuator losses are multiplicative properties. That is the gain
is 2x or the loss is 0.75x, and to get the output level you multiply
the input by the gain/attenuation. Since dB is a log of the signal
level, when working with dB signal levels you add/subtract the gain/
attenuation to get the output level in dB.

What you are describing does not make sense to me. If you would like
me to look at the paper I'd be happy to try to figure out what they
are doing. That is assuming it is in English, however. I'm an
American and thus monolingual...

Rich L.

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