# Handy Gadgets and Resistor Divider Calculations

Handy gadgets make our engineering life easier—the little special purpose computer programs or spreadsheets that you might find or create yourself.

Back in the old days, engineers used nomographs. These are graphical aids that solve common multivariable problems of all sorts. Calculators and desktop computing caused their decline so you seldom see them today. I still use a variant of one—an old cardboard R-L-C reactance slide rule given to me in my first electric circuits class back in the ‘60s. It helps me find approximate values in the right impedance range when I’m positioning poles and zeros. I think better with it in my hands. I believe that the graphical nature of a nomograph can aid in visualization and optimization. Has something has been lost when we just plug numbers into a computer?

In previous blogs, I’ve provided gadgets for calculating op amp noise and 1/f noise. Here is another, an Excel sheet that calculates resistor values for a three-resistor divider with a voltage reference to offset the output voltage. For example, if you have a -10V to +10V input and you want attenuate and shift it to a 0 to 3V output, this gadget calculates the resistor values.

It’s a sub-circuit that is often needed in signal processing. The math is a bit messy, so if you solve it once you probably don’t want to do it again. It’s the type of task that is worth the time to create a gadget. The equations are in figure 2, if you don’t want to use the worksheet. I refined it a bit, adding some checking for out-of bound values and minimum required value for the reference voltage. Try it and see. With the annotations I think you’ll find it easy to use. Excel (or equivalent) is pretty handy for calculations like this but I find it awkward for some types of programs. I have some gadget programs that parse long files to manipulate data. I’ve used various forms of BASIC for this through the years but now I use Excel’s Visual Basic (macros), loading data into the associated worksheet to use its graphing capabilities. I wouldn’t publish these gadgets. Excel macros are so easily written or modified to create serious damage that they’re scary. I only give them to close associates and I’m not even sure they trust me. :-)

What handy gadget design aids have you made? What ones do you wish you had? Do you use any old-style nomographs or slide-rules like mine?

Bruce       email:  thesignal@list.ti.com (Email for direct communications. Comments for all, below.)

• When it comes to Excel, I'm working my way through creating a series of spreadsheets. I'm getting my head around I & Q demodulation, along with DSP.

I've started with a series of sinewaves, assorted magnitudes, rounded as 14-bit integers. 4096 samples along with a FFT (and windowed FFT!) makes a big spreadsheet.

My second sheet takes the samples from the 1st, splits into I & Q, and has a very basic FIR. FFT results too!

Third spreadheet [in progress]: Hilbert transform!

Final spreadsheet: Sum and difference of I & transformed Q: hopefully showing upper vs lower sidebands of original mix of sinewaves...

• Bravo, Alan. You're a serious gadget man!  --  Bruce

• 55 years ago, when a junior engineering student I was using my slide rule inherited from my grand-father (an artillery officer !) to

compute R/2R , R/10R, Pi/Ratio of Pi, etc...networks ...........Sorry, it took me 20 years to get a TI handheld calculator to execute the

same computations,! By the way, I was so good, that I executed  60% of the computations by head ( and still to day !!! )

• This is very simple:This is for a potential divider where only preferred values can be used. I did an Excel spreadsheet where cells in the first row were populated with preferred resistor values.  Cells in the first column were likewise populated.  The other cells had a formula in for calculating the division ratio from these resistors. It was then an easy matter to scan the table and find the combination that gave the best result required.  I did a similar one for series combinations and for parallel combinations.

• Sounds useful, Percy. Note that the Excel sheet provided above has cells that calculate the nearest 1% (R96) resistor value. For example, cell M8 calculates the nearest standard 1% resistor for the value of cell F7. The formula in M8 can be easily copied and used for the types of calculations you've done. -- Bruce