There are circumstances where very accurate resistance are necessary as in the case of standard resistors and step up from 7V to 10V circuits.

The main resistor is often of fixed in value, adjustment would be impossible or degrade the performance significantly. Therefore, some peripherals will be added for the adjustment.

The adjustment may be performed with trimmers or without, let's look at them in turn.

**Part one, adjustment with trimmers.**Trimmer adjustment often used in places where re-adjustment or regular adjustments are required by the user. Trimmer range is the total relative change in the resistor when trimmer adjust from 0 to the max.. Trimmer range multiply the accuracy should be less than the uncertainty required. For instance, if the trimmer range is 100ppm, and your trimmer is 0.5%, the overall resistor will add 0.5ppm uncertainty because of the trimmer. Therefore, you need either to decrease the trimmer range or increase the trimmer accuracy to get a better result.

1. Series connection

This is the simplest way, but the performance is questionable, because the variation of contact resistance has direct impact on the final value.

Example, Fluke 887A differential voltmeter, trimmer range is 400ppm.

2. The common way

This is done by adding two fixed resistors from above circuit and is common used in metrology instruments.

The added resistor in series with the main resistor decreases the trimmer range considerably and range is easily changeable . Also, the added resistor in series with the trimmer will decrease the none-linearity of the adjustment.

Example one: esi RS925D, this is the precision 4-wire resistor box used in esi 242D bridge, the trimmer range is 100ppm.

Example two: Fluke 720A, 0.1ppm KVD, the trimmer range is 43ppm

Example three: IET SRX-10k standard resistor, the trimmer range is 66ppm

3. The parallel way.

Useful when the main resistor is small in value. The trimmer and R2 is parallel connected to the main resistor Rm, which should be made a bit larger than nominal value. The trimmer in this example has 48ppm trim range.

**Part two, Trimmerless Adjustment**This kind of adjustment was often performed in the factory when they made, thus not mean user adjustable.

When properly designed, this configuration provide the best, as if the adjustment add very little side effect.

1. Custom made small value WW

A simple, effective, widely used method.

The main resistor, when made, should be close to but less than the nominal value.

For instance, the main resistor made as 9999.78 Ohm, need a 0.22 Ohm in series to reach the perfect 10k

This 0.22 Ohm, only 22ppm of the total value, a normal WW will be sufficient.

The downside, of course, it has to be custom made.

Example, SR104, the best 10k ever produced.

2. Pairing

Parallel or series connection of two resistors of opposite deviation will cancel the resulting deviation.

For instance, a resistor of 4999.3 Ohm in series with 5000.7 Ohm makes 10000 Ohm exact.

A resistor of 19998 Ohm parallel with 20002 Ohm gives 9999.9999 Ohm, this in effect is 10k with only 0.01ppm difference.

Downside: need a large number of resistors to select from.

Example: Guildline 9250-1k Hamon transfer standard.

There are 10 arms and each arm consist of four 1k hermetic foils connected in mixed mode. They must be paired for tempco and also for tolerance.

3. Statistical

This means a lot resistors of the same value put together in series or in parallel or mixed.

The apparent benefit for doing so is to achieve large power/thermal mass, to achieve low value(when in parallel), and to achieve high value(when in series).

This also create a better opportunity for easy resistor adjustment.

Example one, Fluke 742A-1, twenty 20.01 Ohm in parallel to get 1.005 Ohm, and parallel another resistor of around 2000 to achieve the final 1 Ohm

Example two, Fluke 752A, nine 120k and one 119.8k in series, and series connect another small WW of about 200 Ohm to achieve the final 1200k resistor.

4. Binary

Binary number such as 0.110100110101..., although long, may represent any figure to any precision.

There is a series of resistors in binary value, pre-made, already soldered onto the PCB to be cut open, or soldered to as required.

Example one: Fluke 732A

Example two: Fluke 732B,

They use switches instead of cut/soldering, this is useful for re-adjust but prone for errors because of the contact resistance variations(although very small) and mechanical failure(although very little chance).

One thing worth noticing when design is that the errors of the binary resistors mus be considered. Otherwise there exist dead zone(some value cannot be achieved). In order to cover the entire adjustment area with margins, the resistor series should be designed not in the order of 2 for neighbor, but 1.9 instead. To be specific, the resistor series should not be like 10k, 20k, 40k, 80k, 160k, 320k. Rather, it should be 10k, 19k, 36k, 68k, 129k, 245k.

Similar way is adopted when they adjust foils resistors at the production line.

5. Grinding

This is the photo of one of the twelve resistors in an esi SR1010-1k Hamon transfer standard. I'm speechless.