Resistor Divider Layout

A project log for Precision Voltage and Current Reference

A little something to check your digital multimeter accuracy occasionally.

Obtaining an exact 25:1 ratio is a difficult task. I wanted to keep the output resistance of the divider relatively low to help minimize any loading effects. A 20kΩ divider resistance with a 10MegΩ load from a volt meter will cause a 0.2% (200µV) error in the measurement. The 833Ω divider resistance yields a more reasonable 8µV error.

But the metal interconnect resistance between 24 parallel 20kΩ resistors causes significant errors. 1 oz. copper PCB traces have a sheet resistance of about 0.5 mΩ/square, with a tempco of 3900ppm/°C. The large tempco will destroy any accuracy the divider has if the trace resistances connecting the divider to the input source don't match correctly. This means that PCB trace resistances must be calculated as part of the divider ratio.

My first attempt to layout the resistors resulted in too much distance between the resistors -- I had to remove the reference designators from the top silk screen in order to pack the resistors more closely. My best effort to date yields about 7 squares of copper trace from the 2V5N kelvin connection at the GND pin of the REF5025 IC. That's only 3.5mΩ of resistance -- I was pretty proud of myself until I calculated the static error and temperature effect on the ratio and got 10µV of error with a 17°C change. Here's the top of the PCB layout:

It turns out that the ratio of the PCB trace resistances must match the resistor divider ratio in order to cancel out the errors of the traces. I needed to get 7x24 = 168 squares of trace resistance to the top of the divider. That's more difficult than it first appears. The trace width needs to be less than 10 mils to obtain 168 squares of metal from the top of the divider to the VOUT pin on the REF5025. The variation of a 10mil trace is not something I want to depend upon. The approach that I took was to use a serpentine route using a 20 mil wide trace. There should be much less width variation on a 20mil trace than a 10mil trace.

My rough calculations now show a +0.17µV error at room temperature, which expands to +3µV with a change of 17°C. If I choose to use 2 oz copper, then the error drops to +1.5µV over temp. Still paranoid that I missed something, I added pad openings along the trace so that I could measure the error and possibly short out some of the trace to correct some of the error. If the trace needs to be longer, then I can cut the shorted trace on the left and short between pads to get the desired result.

In addition, I added three pads for different pick off points along the length of the parallel resistors. If there is a measurable difference between the three points then just pick the best one to feed to the terminal.

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