#### Re: Risetime calculator (in tekwiki)

GerryR <totalautomation1@...>

Never mind, then-came-the-dawn; three different scales to get from 0 to 20 and I assume that proportionally you can try to put your values as close to center dial as possible for greater accuracy by using the different scales. I can be thick, sometimes!
GerryR
KK4GER

----- Original Message -----
From: "Chuck Harris" <cfharris@erols.com>
To: <TekScopes@groups.io>
Sent: Tuesday, January 21, 2020 10:26 AM
Subject: Re: [TekScopes] Risetime calculator (in tekwiki)

The dial scale values indicate numbers you want to
feed the equation SQRT(A^2 + B^2 + C^2) = f

In this case, if you set them to microseconds, f will
be in microseconds... nanoseconds, f will be in nanoseconds...

Obviously, you will have to interpolate your settings and
results, to gain more than integer accuracy... which you
should be able to do by eye to at least quarters.

-Chuck Harris

GerryR wrote:
Dennis,
What do the dial scales values indicate??
GerryR
KK4GER

----- Original Message ----- From: "Dennis Tillman W7PF" <dennis@ridesoft.com>
To: <TekScopes@groups.io>
Sent: Tuesday, January 21, 2020 12:09 AM
Subject: Re: [TekScopes] Risetime calculator (in tekwiki)

Hi Everyone,
Before getting caught up in the concept of an analog computer take a step back to
consider what an analog is. It is something that is similar to something else; the
two are said to be analogous.

THE RISETIME CALCULATOR IS AN ANALOG COMPUTER BASED ON LOGARITHMS
The risetime calculator is a simple, but clever, analog computer that relies on an
analogy between the angle of the dial on each pot and the resistance of the pot at
that angle. This in turn relies John Napier's discovery of logarithms, which he first
published in 1614. Logarithms are a method to multiply two numbers together by adding
their exponent. Anyone familiar with a slide rule knows the C and D scales on a slide
rule are logarithmic and not linear. The A and B scales increase twice as fast as C
and D because they represent a number times itself or the square of a number. If I
wanted to multiply 7 times 5 I simply had to add together the logarithm of 7 (in base
10) to the logarithm of 5 (in base 10). The log (short for logarithm in base 10) of 7
is 0.845. The log of 5 is 0.699. 7 x 5 = log 7 + log 5 = 0.845 + 0.699 = 1.544. If we
look up the number whose log is 1.544 it is our answer: 35. Commonly available 10"
slide rules are accurate to 2 or 3 decimal places. This is accurate enough for an
enormous variety and number of calculations so they were widely used until the
introduction of mechanical and then electronic calculators.

HOW IT WORKS
If the three pots on the left side of the risetime calculator have a logarithmic
taper and the current coming out of each was added together the sum would = A + B +
C. That's not what we want. We want A*A + B*B + C*C. To do that the taper has to
change logarithmically but twice as fast as an ordinary logarithmic taper. If the
first pot's taper increases twice as fast as an ordinary logarithmic taper the
current that comes out of it will be analogous to A*A. The same taper used for the
second pot will produce a current analogous to B*B, and the third pot will produce a
current analogous to C*C. Now if we sum together the currents coming from the three
pots we will get A*A + B*B + C*C. Our next step is to find the number, using the pot
on the right side, whose current equals the sum of the 3 pots on the left side. The
minimum current from a pot on the left side will be when it is counterclockwise
representing 1. 1*1 = 1, and the log of 1 is 0 so there would be 0 units of current
coming out of the pot. If the pot were set to 10, then 10*10 = 100 and the log of 100
is 2. So there would be 2 units of current coming from the pot. The currents are
summed from all three pots and the total can range from 0 to 6 units of current. With
the meter we have to balance (or null) the current on the left side with an equal
current from the right side knob. There is no need to take the square root of the
left side provided we square the right side instead. So on the right side we can use
one more pot as long as it has the same taper as the other three pots. We can even
use the same scale. One small drawback to doing this is there exists the possibility
that if all three risetimes happen to be greater than 5.773nSec you won't be able to
balance the bridge since the total risetime will be larger than 10nSec.

ANALOG VS DIGITAL OSCILLOSCOPES
High quality oscilloscopes strive to present an accurate analog of the voltages or
currents in a circuit being probed. Until recently all of the oscilloscopes in the
world were analog and there was no need to use the word analog to describe them. I am
absolutely certain no one gave that word a second thought until another way to make
an oscilloscope became possible in the 1970s. Suddenly it was important to
distinguish whether the oscilloscope made every attempt to present you with a wiggly
line on a CRT that was an analog of what was happening in the circuit you were
measuring or if what you saw looked like a connect the dots page from a coloring book.

How closely the analog displayed on the CRT compared to the actual potential in the
circuit being measured was an indication of the quality of the instrument. Enormous
amounts of money were spent over 100+ years to insure the trace on the CRT was an
accurate analogue of the voltage in the circuit. The result was something that could
be within +/-1%. Today there are two kinds of oscilloscopes. One important attribute
distinguishes analog oscilloscopes from digital oscilloscopes.

* The representation on the CRT of an analog oscilloscope is a CONTINUOUS analog of
the signal being measured (except for sampling plugins). One advantage of an analog
oscilloscope, as long as you use it within its specified limits, is the
representation on the CRT has a high likelihood of being a good analog of the signal
being measured.

* The representation on the display of a digital oscilloscope is a SERIES OF DISCRETE
DOT PAIRS that may (or may not) appear to form one or more patterns that humans will
assume, sometimes erroneously, are continuous and then they might conclude it is an
analog of the signal being measured. The interpretation of the pattern of dots on a
digital oscilloscope requires a detailed understanding of how the samples are taken,
how the samples are displayed, the type of sampling used, and the limitations of
sampling itself.

Analog oscilloscopes are desirable for new or unsophisticated users because the
results are less likely to be misunderstood. Digital oscilloscopes have many
limitations and pitfalls that analog oscilloscopes do not. They require that their
results be interpreted carefully. The digitized data from a signal can be further
processed mathematically to extract additional information from it or, for example,
to reduce the noise in the digitized data. There are many other things that can be
done to a digitally sampled signal after it has been captured to further process it.

Dennis Tillman W7PF

Join TekScopes@groups.io to automatically receive all group messages.