#### Re: 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

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Dennis Tillman W7PF
TekScopes Moderator

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