In the last post we had a look at the short circuit performance of a decade. This time I want to address the question whether we can make the resistor decade more accurate, despite the fact that the design doesn’t feature any mechanism (e. g. potentiometer) to *adjust* resistance values. The short answer: Yes, partially. But first things first.

Let’s have a look at another example of a programmable resistor: The Fluke 5450A is a resistance calibrator from the 80’s (or so) that uses fancy precision resistors and relays to provide 17 different resistance values. It misses any adjustment options too – stability is most important for a calibrator. Instead, the calibrator displays a calibrated value of the currently selected resistance that can be programmed by a calibration lab. This is an idea I’d like to adopt. Given the required equipment, performing the calibration of 17 resistance values isn’t that big of a deal, doing it for each of the 1,000,000 resistance values of the programmable decade resistor, however, is a non-starter.

In contrast a reasonable approach would be to calibrate the decade individually and then calculate an estimate of the total resistance. This approach requires a closer look at the contact resistance of the relays and other “parasitic” resistances in the signal path.

### Calibration procedure

The basic idea of the calibration procedure is as follows:

- Estimate the average contact resistance
- Short all decades avoiding the bypass relays
- Measure the resistance at the input of the programmable resistor
- Calculate the average by dividing the measured value by the number of relays in the signal path.

- Determine the calibration values of all 9 resistance values \(\neq 0\Omega\) of each decade individually, while keeping the other decades shorted. The bypass relays can be used. For a total of 6 decades there will be 54 additional calibration values.
- Set up the resistance value
- Measure the resistance at the input of the programmable resistor
- Determine the number of relays in the signal path
- Subtract the sum of the contact resistances of those relays from the measured value

In step 1 we assume that the contact resistance is significantly larger than other “parasitic” resistances – like the PCB traces, the wires to the terminals, their contact resistance and so on. Having a large number of relays in the signal path during the measurement – by not using the bypass relays – makes sure that the assumption is valid, at least to some extent.

### Estimation of the total resistance

Now, when we want to estimate the resistance of any given combination of the decade, we do the following:

- Determine the theoretical resistance value by adding up the calibration values of all 6 decades according to the selected total resistance
- Determine the number of relays in the signal path
- Add the contact resistance according to the current switch state to the resistance value calculated in first step

For obvious reasons this approach won’t be perfect. In a future post in this series I hope to do a comparison between the estimated values and the measured values for a few exemplary resistance values.