Resistance source?

[NorthGuy]

That's one value, you need the whole 2ⁿ series and have to put up with roughly tolerancing to hit values like 4096 (nearest E96 402 or 412), 8192 (nearest E96 806 or 825) to some nominal accuracy,

So, you do it with 2 resistors when you can't do it with ones. Resistors are small and cheap compared to relays, not to mention driving circuits.

just as you've done with 523k for  524.288k. That's going to throw any idea of linearity out of the window.

Resistors are not exactly nominal values. They have tolerances. If you had 1% resistor with 524.288, the actual resistance could be way below 523 (or above 526 for that matter). The difference is 0.24%. Doesn't really matter if resistor tolerances are 1% as OP wants.

If you want better accuracy, you can always add compensating resistors (e.g. 523k + 1.29k)  to get closer to the value that you want. The compensating resistors don't even need to be precise. Even a dozen of extra resistors is still better than 4 extra relays.

Whereas if you stick with decades you don't have to do any fudging, you keep linearity and you get to choose a straightforward tolerance from the standard ranges available, 1% 0.1%, 0.05% and so on to as arbitrary a level of accuracy as your wallet will allow.

Accuracy-wise, it's exact the same properties as with binary. Linearity error depends on the tolerance of the resistors you use. 1% resistors will yield approximately 1% errors. 0.1% resistors will yield approximately 0.1% errors. I don't see any difference here.

[LazyJack]

How about this? Instead of having something that you set up with some values and hope it will be accurate, use a feedback loop. For example a motorized pot (maybe several one in ranges) and you set it up while measuring the value. Depending on accuracy requirement, you could use an Arduino or a bench meter via gpib. Once set, a relay disconnects the meaduring device and connects your test setup.
This takes some setup time, of course, but can be fully automated.

[Cerebus]

Accuracy-wise, it's exact the same properties as with binary. Linearity error depends on the tolerance of the resistors you use. 1% resistors will yield approximately 1% errors. 0.1% resistors will yield approximately 0.1% errors. I don't see any difference here.

No, it's not. A decade scheme doesn't need a 4096+/-1% resistor that gets implemented as a 4020+/-1% or 4120+/-1%, it needs a 4000 that gets implemented as a 4000+/-1%. The decade option has 1% error and at that point my error analysis is complete and I can go for a beer. The 'pick the nearest to 2ⁿ' scheme has, for 4096, -3% to +1.6% error for that single resistor, and you're stuck at your desk with another 19 resistors left to do the error analysis for, or work out a series/parallel combination that will keep the error to 1%, while I'm in the pub. You'll spend 1/2 a day working everything out (at whatever marginal cost your time has), I'll spend < £20 on four more relays and resistors.

[NorthGuy]

No, it's not. A decade scheme doesn't need a 4096+/-1% resistor that gets implemented as a 4020+/-1% or 4120+/-1%, it needs a 4000 that gets implemented as a 4000+/-1%. The decade option has 1% error and at that point my error analysis is complete and I can go for a beer. The 'pick the nearest to 2ⁿ' scheme has, for 4096, -3% to +1.6% error for that single resistor, and you're stuck at your desk with another 19 resistors left to do the error analysis for, or work out a series/parallel combination that will keep the error to 1%, while I'm in the pub. You'll spend 1/2 a day working everything out (at whatever marginal cost your time has), I'll spend < £20 on four more relays and resistors.

Of course, if it takes half a day to figure out that 4096 = 4020 + 76, it is better to use more relays.

[Cerebus]

No, it's not. A decade scheme doesn't need a 4096+/-1% resistor that gets implemented as a 4020+/-1% or 4120+/-1%, it needs a 4000 that gets implemented as a 4000+/-1%. The decade option has 1% error and at that point my error analysis is complete and I can go for a beer. The 'pick the nearest to 2ⁿ' scheme has, for 4096, -3% to +1.6% error for that single resistor, and you're stuck at your desk with another 19 resistors left to do the error analysis for, or work out a series/parallel combination that will keep the error to 1%, while I'm in the pub. You'll spend 1/2 a day working everything out (at whatever marginal cost your time has), I'll spend < £20 on four more relays and resistors.

Of course, if it takes half a day to figure out that 4096 = 4020 + 76, it is better to use more relays.

Given that 76 isn't a standard value, yes. Because if you're doing the job properly you have to look up and check standard values, then you have to check they're available in the tolerance, tempco, aging and power you require. All that time adds up. An actual complete, accurate, engineered solution always takes time. It's not as simple as reaching for a calculator and doing some subtraction.

We're back to my original argument. A decade solution makes the engineering trade off between using standard single, easily sourced, off the shelf resistors with 4 extra relays, drivers and resistors with little NRE cost against using a mixed selection of resistors with four fewer relays, drivers and resistors that will require extra time to calculate, source and confirm the solution against the error budget. If you're making a few dozen you can afford the NRE and your approach is probably overall cheaper, but we're talking about a one off and in that case I contend that my trade off with less NRE cost wins.

[john_c]

How about this? Instead of having something that you set up with some values and hope it will be accurate, use a feedback loop. For example a motorized pot (maybe several one in ranges) and you set it up while measuring the value. Depending on accuracy requirement, you could use an Arduino or a bench meter via gpib. Once set, a relay disconnects the meaduring device and connects your test setup.
This takes some setup time, of course, but can be fully automated.

Yeah, that's what I'm saying. All of this switching with huge (by modern standards) arrays of relays is a brute force approach.

[Fungus]

How about this? Instead of having something that you set up with some values and hope it will be accurate, use a feedback loop. For example a motorized pot (maybe several one in ranges) and you set it up while measuring the value. Depending on accuracy requirement, you could use an Arduino or a bench meter via gpib. Once set, a relay disconnects the meaduring device and connects your test setup.

How will you measure the value? Normally these resistors are inserted in a circuit.

[rs20]

How about this? Instead of having something that you set up with some values and hope it will be accurate, use a feedback loop. For example a motorized pot (maybe several one in ranges) and you set it up while measuring the value. Depending on accuracy requirement, you could use an Arduino or a bench meter via gpib. Once set, a relay disconnects the meaduring device and connects your test setup.

How will you measure the value? Normally these resistors are inserted in a circuit.

He said it's disconnected from circuit via relay.

[Fungus]

How about this? Instead of having something that you set up with some values and hope it will be accurate, use a feedback loop. For example a motorized pot (maybe several one in ranges) and you set it up while measuring the value. Depending on accuracy requirement, you could use an Arduino or a bench meter via gpib. Once set, a relay disconnects the meaduring device and connects your test setup.

How will you measure the value? Normally these resistors are inserted in a circuit.

He said it's disconnected from circuit via relay.

I guess you could disconnect it from the circuit every time you change the value, but:
a) That might harm other components in the circuit (depending on the circuit)
b) He said "I may end up with around 50V across the pot" so a simple pot won't do (it will burn if you set it 'wrong').

[LazyJack]

How about this? Instead of having something that you set up with some values and hope it will be accurate, use a feedback loop. For example a motorized pot (maybe several one in ranges) and you set it up while measuring the value. Depending on accuracy requirement, you could use an Arduino or a bench meter via gpib. Once set, a relay disconnects the meaduring device and connects your test setup.

How will you measure the value? Normally these resistors are inserted in a circuit.

He said it's disconnected from circuit via relay.

I guess you could disconnect it from the circuit every time you change the value, but:
a) That might harm other components in the circuit (depending on the circuit)
b) He said "I may end up with around 50V across the pot" so a simple pot won't do (it will burn if you set it 'wrong').

Yes, these are requirements, that we do not know about. Open circuit may be avoided by having a fixed resistor switched in, while taking measurement on the pot. If you want really complex setup, there may be two pots on the same shaft, one into the circuit, and one to take measurements. Obviously, with appropriate calibration tables (even those could be created automatically).
For high voltage, one would need to sense the voltage and disconnect if required. Just like some scopes do if you overload the 50ohms termination in the input.
So there are various ways to solve problems, but until the requirements are clear, it's just a brainstorming session.

[Fungus]

Maybe you could have a dual pot, or two pots attached to the same motor.

One channel is in-circuit, the other is used for the control feedback loop.

If it's all nicely calibrated then there's no reason it won't work well enough.

There's still the problem of whether a pot is a good solution though, given their power limitations, etc. It doesn't take much power to burn a permanent spot on the track.

[Fungus]

How about this? Instead of having something that you set up with some values and hope it will be accurate

What do you mean 'hope'?

Do we not own enough multimeters?

[john_c]

@Fungus, There are adjustable power resistors. I linked to one earlier in the thread.

[forrestc]

Very interesting. 1,2,4 and there you stopped. Lets proceed: how do you plan to buy 2^19? That is 524288R. I am afraid power-of-two decade box cannot be made with 20 x E24 resistors. BTW, anyone wishes to count how many 1% E24 resistors are needed to match 2^19=524288R to within 1%??

Since we are dealing with software here, and can calibrate, there is a very easy way to make a "almost power of two" decade box.

Start with a 1 ohm 1% resistor resistor.   This resistor is going to be at minimum 0.99 ohms. 
Double it.   1.98 ohms
Look at the E24 range, pick the largest value which will never be above that value.  in this case, we're talking a 1.8 ohm resistor, maximum value +1 % of 1.818 ohms.

Now repeat.   A 1.8 ohm resisistor has a minimum value of 1.782.  Double it you get 3.564. Look at the E24 resistors... you get 3.3 ohms (max value 3.333).
Repeat until you reach 10Mohm....

I'm going to roughly choose the following values, there may be one or two which is not accurately calculated based on above - i.e. I may need to reduce one and the successive value.

1, 1.8, 3.3, 6.2, 12, 22, 43, 82, 160, 300, 560, 1K1, 2K0, 3K9, 7K5, 13K, 24K, 47K, 91K, 180K, 330K, 620K,  1.2M, 2.2M, 4.3M, 8.2M.

Wire them up.  Measure each one individually in circuit.  You'll get the exact value, calibrated, of each.   Let's just assume they're all perfect for the next part.

Let's say you need a 132K245 ohm resistor, you enable the following resistors:

91K, 24K, 13K, 3K9,  300, 43, 1.8.  For a total of 132,244.8 Ohms.

So:  decade box to just under 16.4M with 26 resistors and relays.    Note that because of it being software driven, it doesn't matter the exact resistance values, as long as you have covered the entire range without any holes not able to be 'covered' by the lower value resistors.

I will need to do some math as to how tempco/drift does in relation to this.

[tszaboo]

Let's say you need a 132K245 ohm resistor, you enable the following resistors:

91K, 24K, 13K, 3K9,  300, 43, 1.8.  For a total of 132,244.8 Ohms..

The temperature changes 0.2 degrees, your 91K resistor drifts 20ppm so your 1.8 Ohm resistor is suddenly pointless. And don't get me started with things, like relay contact resistance and Thermal EMF because of relay self heating.

I would just design a relay card with turret standoffs for resistors, 4 relay per card, maybe a 5th one to bypass the entire card. 4 relays are switching 1R 2R 4R 3R in series, or bypassed SPDT. Each card is a decade. Place card in series. controlled by a I2C GPIO extender.
Probably it will be in the end slightly more expensive than buying the test gear.

[NorthGuy]

The temperature changes 0.2 degrees, your 91K resistor drifts 20ppm so your 1.8 Ohm resistor is suddenly pointless.

OP is interested in relative (%), not absolute (Ohm) errors. Therefore when you move to 100K range all the small resistors become pointless. This will happen no matter how you arrange your resistors.

If you want 1 Ohm accuracy across the range (so that the small resistors get pointless), then the biggest problem is that you would need 0.0005% 200K resistors.

In the realm of reasonable, IMHO the biggest problem is to figure out power ratings for the low end resistors, or possibly some sort of protective measures against applying too much voltage.

[rs20]

If you want 1 Ohm accuracy across the range (so that the small resistors get pointless), then the biggest problem is that you would need 0.0005% 200K resistors.

You need 0.0005% 200k resistors OR feedback OR a half-intelligent controller + one-off characterization.

[forrestc]

The temperature changes 0.2 degrees, your 91K resistor drifts 20ppm so your 1.8 Ohm resistor is suddenly pointless. And don't get me started with things, like relay contact resistance and Thermal EMF because of relay self heating.

I'm really only worried about 1% (or less) across the range.  Admittedly my example was piss-poor to illustrate this.   And I agree about the thermal issues.

So the bottom end (as you point out) really will be useless at the higher ranges.....  even with a decade scheme.   

One trick I have learned over the years though is that something like this can be calibrated on the fly  if you really really care about the exact value.   Use your relay matrix to connect it to your DMM, measure the value, and adjust to be exactly where you want it based on the DMM, then switch it into the test circuit.

[tszaboo]

The temperature changes 0.2 degrees, your 91K resistor drifts 20ppm so your 1.8 Ohm resistor is suddenly pointless. And don't get me started with things, like relay contact resistance and Thermal EMF because of relay self heating.

I'm really only worried about 1% (or less) across the range.  Admittedly my example was piss-poor to illustrate this.   And I agree about the thermal issues.

So the bottom end (as you point out) really will be useless at the higher ranges.....  even with a decade scheme.   

One trick I have learned over the years though is that something like this can be calibrated on the fly  if you really really care about the exact value.   Use your relay matrix to connect it to your DMM, measure the value, and adjust to be exactly where you want it based on the DMM, then switch it into the test circuit.

That will work with a current source, or a zero source resistance voltage source. With the resistor string, as soon as you connect a different voltage to it (different from DMM test current), the resistors will start to self heat, and you have a different resistance there.

[boggis the cat]

The way this is done in e.g. Transmille calibration instruments is to put resistors in a switchable array.  If you want high precision, then you'd want to select close values then trim with pots across each base resistor.  This approach looks simple on paper, but quickly turns problematic and expensive.

An alternative if you intend this for DC applications would be an electronic load.  If you characterise it then you should be able to dial in very accurate settings, and they are designed to sink power.

[Fungus]

What's really needed is feedback on voltage and current so it can continuously recalibrate itself as it drifts.

[NorthGuy]

If only 1% precision is needed then the temperature drift may not be a significant problem.

At the high end the heating will be minimal.

It may become a problem at the low end if voltages are relatively high, but it depends on what are voltage/current requirements for the low end.

[Fungus]

It may become a problem at the low end if voltages are relatively high, but it depends on what are voltage/current requirements for the low end.

Yep. It may not actually be a problem in real life.

Me? I'd put in a current sensor to light up a warning LED and disconnect the box if it detects dangerous levels of current.

(or at least put in a fuse)

[forrestc]

That will work with a current source, or a zero source resistance voltage source. With the resistor string, as soon as you connect a different voltage to it (different from DMM test current), the resistors will start to self heat, and you have a different resistance there.

Let me see if I can re-state my thinking here:

I need 1% accuracy. Ignore setting errors at the low end...  We're talking around 10K here...

If my box is make up of 50PPM/C resistors (widely available, not that expensive), once I 'calibrate it', even if I self-heat by 100*C (not even close to likely), I'm only at 5000PPM, which is still 0.5%.  Unless I don't understand the math here...

[tszaboo]

That will work with a current source, or a zero source resistance voltage source. With the resistor string, as soon as you connect a different voltage to it (different from DMM test current), the resistors will start to self heat, and you have a different resistance there.

Let me see if I can re-state my thinking here:

I need 1% accuracy. Ignore setting errors at the low end...  We're talking around 10K here...

If my box is make up of 50PPM/C resistors (widely available, not that expensive), once I 'calibrate it', even if I self-heat by 100*C (not even close to likely), I'm only at 5000PPM, which is still 0.5%.  Unless I don't understand the math here...

I was pointing out the errors in others calculations. They were making assumptions that you can easily create lots of digits accuracy by online calibrations and using lots of ranges.
You are absolutely right it is off topic for 1% accuracy.