I’m a big fan of slide rules. I’m old enough to be a real user – my physics master and I were the last two people in the class using slide rules when the rest were using those new-fangled electronic calculators. We would race every time a calculation was required and the slide rules invariably won – to the three significant digits needed for scientific and engineering notation.
I have something of a collection of slide rules – including the Boots Ringplan 10 inch duplex I was using back then in the physics class ...
(which is actually a low-rent version of a Faber-Castell 52/82) and many others I’ve collected subsequently.
I like the way slide rules let you do math by touch. Not out of some romantic, touchy-feely notion. Rather out of the conviction that this is actually teaching something about how math works, through a different kind of interaction – a different kind of knowing.
Last weekend I got a great deal on a beautiful Pickett N-515-T on a familiar auction site...
It comes in a nice leather sheath, with a belt loop, so you can wear it like a sword by your side, ready for a quick-draw calculation. The original wearers would have had pocket protectors on their shirts to stop pens making marks when they were packed away after frenzied note-taking; the original nerds and geeks. Sorry – I shouldn’t laugh.
Whilst slide rules are a private passion, which ordinarily I wouldn't bore you with, the N-515-T is of interest on these pages, because it is built for use in electronics – specifically, it was produced for students at the Cleveland Institute of Electronics (formerly the Smith Practical Radio Institute).
Not only is some of the back of the rule stuffed with useful formulae...
but the whole rule is set up to do some useful calculations, which other ‘ordinary’ slide rules can’t do in the same direct way. Let me show you...
We’ll choose as an example a section of one of George’s bandpass filters, mentioned in the last post.
The G-QRP technical page describes the bandpass filter recipe as follows (in which I’ve pulled out the 40m version)...
If we look on the back of the N-515-T slide rule, there’s a little section on the left hand end which allows you to figure the resonant frequency of any LC filter, such as the combination of the 55uH and 100pF in each of the coupled 2nd order resonators in the bandpass design above.
You simply move the slide until 100pF (at ‘a’) and 5.5uH (at ‘b’) coincide...
and then read off the resonant frequency (in MHz) from below the arrow labelled ‘fMHz’ (at ‘c’)...
In this case, the result (which we know to be 7MHz - this was a 40m filter, remember) is seen to be somewhere between 6 and 10 MHz.
This is only supposed to return a rough answer – in fact, the section is only supposed to be a ‘Decimal Point Locator’ (as you see from the label on the slide rule at the top of the picture). That’s to say, this is an aid to get you the right ballpark, the right order of magnitude. But boy – is it quick!
If you’re not satisfied with the accuracy of that quick-and-dirty estimate, the slide rule offers another, more accurate way, just as fast...
The formula for the resonant frequency of an LC circuit is:
If you square both sides of equation 1:
and re-arrange, to solve for the LC product, you get:
The N-515-T has a special scale, called the H scale, which implements the function required in equation 3, allowing you to enter the resonant frequency on the D scale and read off the LC product on the H scale (or vice-versa).
The D scale of a slide rule usually carries the independent variable, named as ‘x’, so if we make the substitution f=x, then equation (3) becomes:
As you see from the photo segment of part of the slide rule next to equation 4, highlighted by my red line and dashed red box, the H scale directly implements equation (4).
So – for the 5.5uH and the 100pF components specified for the filter, we know that there is an LC product of 550 e-18 and we already have a rough idea (from the 'Decimal Point Locator') that the resonant frequency is between 6 and 10 MHz.
Putting the cursor's hairline over 5.5 on the H scale (the upper red dashed circle) and reading down to the D scale (the lower one) ...
returns a value of about 6.8 - i.e. 6.8 MHz.
(For those who understand slide rules, the value of the decimal point locator is in avoiding putting the cursor over the 55 on the H scale and returning a false reading – analogous to the problem of finding square roots on a slide rule).
The people in my physics class would still be boring each other rigid by reading out the ‘answer’...
6.786389575745699563327694285 and so on.
Actually, they wouldn't have had nearly that many (in-)significant figures to play with on their seventies calculators - that numerical shrapnel came from the 'calculator' bundled with Windoze 10 on the machine I'm typing on!
From the ridiculous noise of the calculator back to the sublime elegance of this N-515-T slide rule where, in pretty much a single step, you can calculate the resonant frequency of any LC combination. Of course, you can also directly calculate the frequency using equation 1 - as you can on any slide rule - but you can only do that in a single step on the N-515-T, with its special electronics scales.
If you thought that was neat, there’s a bunch of other stuff the N-515-T can do. You can download the instruction leaflet to explain all the other stuff (which, for this model isn’t an instruction leaflet at all, but an entire course on using the slide rule - and the N-515-T in particular - in electronics, produced by the Cleveland Institute for its students) from Kirt Blattenberger, kb3uon’s RF Cafe website.
I just happen to be going back to Ohio in a couple of months and Tom has kindly arranged a trip to Cleveland (to visit the Rock and Roll Hall of Fame). I wonder if we get to swing by Carl Smith's old Radio Institute?
...-.- de m0xpd