Resistance ranges and maths

[eeka chu]

I was wondering if anyone could help with a resistance problem.

I wanted to sweep a range, say 10k and at 0.01k intervals, but using the fewest number of discrete step as possible.

So for instance, instead of sweeping the entire range at 0.01k steps I'd start by compressing one range into a single 5k step, then splitting the remaining 5k into 2.5k, then 1.25k and so on.

My problem is how do I find the most efficient way of doing this in the smallest number of steps whilst maintaining a 0.01k step between each?

At the moment I'm thinking about each step in my head but since this is obviously following a logical pattern I figured there must be a mathematical way of working out what value steps I should use and how many of each.

I know I could work out something that would work for this in my head but my concern is that it won't be with the fewest steps possible, which is quite important. Particularly once the decimals of the steps start going below the 0.01k intervals since then you're dealing with positive and negative percentages of the 0.01k steps.

Sorry if the answer is really obvious to some of you, maths isn't my best subject!

Any help with this would be great!

[Stocker]

Even in 1 ohm steps you don't need very many resistors. Think about a regular decade box... 10x 1R, 10x 10R, 10x 100R, 10x 1k etc.

For 10k in 100 ohm steps, you could have 10x 100 and 10x 1k and be done.

If you can't use two knobs however, the clockworks could get tricky.

[AndrewT]

Hi,
build a decade box with 0.1% resistors. Look at one in www.rs-components.com webpage for ideas
Or buy one second hand from Ebay or similar.
Or start with your smallest value (10R) and double up until you exceed half your desired maximum (only 10 steps needed). You need to be able to switch each value in or bypass using a 2 pole change over switch for each value.