There are a couple of threads on making decade boxes and at least one asking about performance of an inexpensive decade box. The latter pushed me back into action on a project which had been set aside for a number of non-elx related activities. I have been fascinated with substitution boxes/decade boxes since first introduced in a high school electronics course. Going to university and learning how to calculate proper resistance values dropped the urgency, but the fascination remained. And a luck find at a surplus store turned up a box containing literally dozens of decade thumbwheel switches. I carefully salvaged them and had plans to build such a box, but then marriage, kids, career and other hobby interests took over and they sat in storage for decades. Somewhere along the line I acquired a GR five decade box and it satisfied my needs for quite a while. Then I saw the threads on fabrication of multidecade boxes and my interest went up. Comments in these threads pointed out the errors in such devices and I wondered just how good they can be.
The GR box I have is a wonder. It can be set to any value between 0.0 ohms and 9999.9 ohms and is accurate to within a few tenths of an ohm over the range. When opened up you can see what went into achieving this. Huge switches with contact area approximating a square centimeter and carefully hand wound and trimmed resistors, presumably made with a wire having as close to zero temperature coefficient as possible.
My approach was to be simpler and use those beautiful decade switches stored for so long.
The goals: Seven decades with lowest range being ohms and error less than an ohm.
Each resistance element in the box would be a small network of standard one percent resistors, selected to get the network as close as possible to the ideal value. I find it easier to work on computer and paper than with soldering iron and parts so the first step was some calculations. The attached spreadsheet includes the key calculations and results.
The first approach was a network with two resistors in series chosen to provide a value just above the desired value, and then a third resistor in parallel with that series combination to trim the resulting network down to the desired value. The tab named 3 Resistor Net 1 shows how that worked out. The results for low values are very promising, with predicted errors a tiny fraction of an ohm for resistances up to 100k ohms. But two problems crop up. First the error is larger than an ohm for the megohm series. And for the larger resistances the parallel resistor to trim down gets to large to be practical. While it is somewhat possible to obtain resistors with values in the hundreds or thousands of megohms, it is exceeding difficult to control leakage resistances and get an actual operating value near the desired value.
The second approach placed the paralleling trim resistor in parallel with the smaller of the other two resistors. This resulted in comparable errors and reduced the size of the largest trim resistor required to a couple of megohms, much more practical.
After briefly toying with more complex networks to trim the highest value resistors I took a moment to evaluate stability over temperature. Typical metal film resistors have a temperature coefficient of 250 ppm/Deg C. It is relatively easy to buy resistors with lower temperature coefficient, but the price rises rapidly. 5-10 ppm/Deg C is about the best you can buy at "reasonable" prices, which for me was under $10 per resistor. Your personal threshold may vary. Columns to the right in the spreadsheet show this evaluation. The results show that accuracy of one ohm or better is not practical at this price point. The highest range will change by roughly five ohms per degree and even the next higher range will vary by a few tenths of an ohm per degree. My lab varies by a couple of degrees over short intervals and by significantly larger amounts over the course of the year.
Even though the numbers showed that a seven decade box couldn't be achieved at this level of effort and expense, I decided to proceed. It will still be fine for use as a substitution box and can achieved very good results on a percentage basis. Two more theory points in this post. A later post will show design and construction and initial trimming, which is still a work in progress.
Self heating was mentioned in another thread as an error problem. The results from working out the math surprised me. First I had to measure the thermal resistance to ambient of the through hole metal film resistors I planned to use. I found that to be in the range of 30 to 100 depending on orientation, airflow and other factors. The math then showed that the change in resistance depends only on the thermal resistance, the applied voltage and the tempco. Not on the resistor value. The values are quite acceptable for lower tempco resistors, although a bit large for standard 250 ppm units. This calculation also shows what is a common fault mode in these boxes. If set to a low resistance value while connected to a significant source of power they can easily burn themselves up.
Next post should be along in a day or two.