# Programmable Decade Resistor: Switching (2)

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:

1. 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.
2. 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:

1. Determine the theoretical resistance value by adding up the calibration values of all 6 decades according to the selected total resistance
2. Determine the number of relays in the signal path
3. 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.

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