Designing an OHM Meter

[HLA-27b]

Hello folks

I am stuck at the Ohms metering part of the OSHW multimeter that I am trying to figure out. Basically what I think I need is a precision current source that can supply a current to the Resistor under test so I can measure the voltage across the resistor and determine its value according to the Ohm's Law. There are two ways of implementing this and I don't know which one would be more suitable.

The first method is connecting a reference voltage source across a reference resistor and the resistor under test in series. Like this:



And measuring the voltage V across Rref.
The value of the R under test would be   Rut = ( Vref - V ) * Rref / V

The other method is having a precision current source connected across the R under test and measuring the voltage V directly across Rut like this:


The resistance of Rut is then V / Iref

I have no clue why to select one over the other. Your advice is needed.

[amspire]

I am going to suggest a third method.

If you look at your first suggestion, the accuracy will depend on the sum or the errors of 3 things:

Rref, VRef and the accuracy of the Voltmeter, then  I am assuming that the voltmeter input current is small enough to be negligible.

If you look at your second suggestion, the error is the sum of the errors in:

VRef and sense resistor in the current source, and the voltmeter. I am assuming here that again the voltmeter input current is negligible, and the output resistance of the current source is also high enough to be negligible.

So my 3rd option will just depend on the accuracy of one item. Rref only. Nothing else has to be particularly accurate.

Apply a voltage across Rref and Runder_test from a stable voltage - it doesn't need to be very accurate.

Set up the voltmeter so it can be switched across Rref and Runder_test. This switching can be done with switching ICs, discrete MOSFETS or relays, but the leakage current of the switches has to be negligible.  The switch resistance will be too low to effect the voltmeter reading. The voltmeter lead in the junction of the two resistors doesn't have to be switched - just the other voltmeter lead.  You also want it so the voltmeter lead can also be shorted to the other voltmeter lead so you can auto zero the voltmeter, so that offset voltages are not an issue. If the voltage source to the two resistors can be made floating, then the junction of the two resistors can be made measurement ground, and it all becomes much easier to implement.

Now all you need to do is to to accurately measure the ratios of the two voltages. Again the accuracy doesn't matter - ratios only depend on linearity and nothing else.

If the voltmeter is a dual slope converter, then you use Runder_test voltage  to charge for a fixed period, then use RRef voltage to discharge and measure the discharge time.

If Rref is 1K precision resistor , the charge time was 1 second, and the discharge time was 0.43678 seconds, then you have a 436.78 ohm resistor.

Hope that makes sense. If it is useful to you, I could do a sketch tomorrow.

Now if you want to stick to your two solutions, I would probably go with the first with a twist.  Arrange so the voltmeter can measure both the voltage across Rref and also VRef. Having an auto-calibrate stage where the voltmeter full scale is set to equal VRef exactly, it eliminates the errors caused by Vref and the voltmeter totally, and so like my suggestion, the accuracy depends only on Rref.

Once you add that step, you will realize that the only difference between the two methods is in my method, you are measuring the relative voltages across the two resistors, and in the modified method 1, you are measuring the relative voltages across Rref and Vref so it comes down to which ones works out easiest. If you know any two voltages, you know the third.

Richard

[HLA-27b]

Thank you Richard, this makes a lot of sense.

Am I getting this correctly?



If we call the current across both resistors Iref (because it will be the reference for the subsequent measurement) Then

Iref = 5V / Rref + Rut

Subsequently we can calculate Rut

Rut = V(rut) / I ref

which is the same thing as

Rut = V (rut) * Rref / 5V

It should work but I think I messed up the maths. 5V should not be necessary for finding the value of Rut

[ejeffrey]

If you look at the data sheet for the max 133/134 DMM on a chip, the technique they use is to connect Vref across a range setting resistor and the DUT.  Vref is the same voltage reference used by the ADC, so as amspire suggests, the result is a ratiometric output that doesn't depend on the value of the voltage reference.  This works for both dual/multi-slope integrators and sigma-delta converters.  This is a very common technique.  For instance, most high resolution ADCs designed for strain gauge or other resistance bridge applications will do the same: the bridge excitation voltage is connected to the ADC reference input in order to cancel Vref variation.

In the max133 design, the range setting resistor is the same one used by the attenuator in volts mode, which doesn't have any impact on performance but is an economical use of precision resistors.

[Zad]

It depends how much precision and resolution you want. The way my LCR meter design does it is to drive the device under test at a known voltage (DAC+buffer amp) and then measure the current with a transimpedance amplifier. Drive voltage is initially set at a minimum level, and then increased until it nears a predefined current limit. For higher impedances, the gain on the transimpedance amplifier is increased.

So long as you use reasonably low ppm components in the gain switching, the components don't have to be ultra high precision as they can be calibrated relative to external test components.

[HLA-27b]

In the light of all of the above, let's consider that we are using a resistive ladder as a reference resistor and range switch at the same time. The resistive ladder consists of 5 steps, 1k 10k 100k 1M 10M. ADC operates between 0V - 5V however it is a good idea to switch to the upper range when we measure 4 V across the Resistor under test. In this case we have:

Vref	Rref		Range
5 V	1k		4k
5 V	10k		40k
5 V	100k		400k
5 V	1M		4M
5 V	10M		40M

So far so good, but I'd like to have 400R and 40R ranges as well. Also what about 4 wire measurements and 4R and 0.4R ranges?

[Kiriakos-GR]

Also what about 4 wire measurements and 4R and 0.4R ranges?

What about them ?
When a Fluke 8012A haves 2R & 20R ranges and needs just two wires 
And about accuracy it managed to amaze me, this is why I do not care about the age of it.
Some models, are keepers but not all. 

[amspire]

HAL-42b, what accuracy are you after? If it is just 0.1% then Zad's suggestions are the way to go. No switching needed.

If you are after as much accuracy as you can achieve, my suggestion may be the way to go.

Now as far as the equations for my circuit, just assume the current trough the two resistors is I .

You are measuring:

  V_Rref = I * Rref
  V_Rut =  I * Rut

Now what you are measuring is the ratio

V_Rut/V_Rref  = I*Rut/(I*Rref) = Rut/Rref

So

Rut =  Rref  * V_Rut/V_Rref

Calibration inaccuracies in the voltage applied to the resistors and in the voltmeter don't affect the result at all.

In the light of all of the above, let's consider that we are using a resistive ladder as a reference resistor and range switch at the same time. The resistive ladder consists of 5 steps, 1k 10k 100k 1M 10M. ADC operates between 0V - 5V however it is a good idea to switch to the upper range when we measure 4 V across the Resistor under test. In this case we have:

Vref	Rref		Range
5 V	1k		4k
5 V	10k		40k
5 V	100k		400k
5 V	1M		4M
5 V	10M		40M

So far so good, but I'd like to have 400R and 40R ranges as well. Also what about 4 wire measurements and 4R and 0.4R ranges?

If you are going after accuracy, you may want to minimize the number of precision resistors - really stable resistors are very expensive, particularly if you are going to use Vishay foil resistors.

A trick HP has used is to add a switchable precision x1/x10 amplifier in front of the voltmeter. A single switch can turn the x10 on and off, and it is pretty easy to make a x10 divider that you can calibrate to at least 0.001% without special equipment and you can get up to 0.00001% if your divider resistors were stable  enough (I didn't miscount the zeros there - that is 1 part in 10-7).

This way, you get 3 ranges out of one precision resistor.

1K ohms can do the 100ohm, 1K and 10K ranges.
1M can do the 100K, 1M and 10M ranges

With these ranges, then if you did a 6 1/2 meter, you can read down to 0.0001 ohms.

For 4 wire ohms, you need to be able to switch the fixed voltmeter lead separately to each resistor.

Anyway, it all comes down to what you are after here.

Richard

[NiHaoMike]

If you're going to measure an impedance more complex than just a resistor (something that would be very important in a DMM), you'll be better off with a variable frequency (10Hz-100kHz or so, only going up to 1kHz or 10kHz would be easier) AC current source and synchronous sampling of the actual current and voltage. Then do some DSP work to determine the real and imaginary parts of the impedance.

As a bonus, that also gives you a very basic function generator and maybe even a curve tracer.

[ejeffrey]

So far so good, but I'd like to have 400R and 40R ranges as well. Also what about 4 wire measurements and 4R and 0.4R ranges?

Something I would prefer to see is an AC resistance measurement to cancel circuit voltages.  Basically you flip the polarity of the reference voltage at ~12 Hz or so.  Since this flips the reference to the DAC and the current through the DUT, it doesn't change the result, but DC offsets present are averaged out over alternating half-cycles.

Of course 4 wire measurements are nice too

[amspire]

Something I would prefer to see is an AC resistance measurement to cancel circuit voltages.  Basically you flip the polarity of the reference voltage at ~12 Hz or so.  Since this flips the reference to the DAC and the current through the DUT, it doesn't change the result, but DC offsets present are averaged out over alternating half-cycles.

This method cancels out offset voltage which eliminates the need for adding an auto-zero cycle and circuitry, but it cannot correct for test lead and connector  resistance. For sub-ohm resistance measurement, the only way to get very accurate measurements is 4 wire.

[HLA-27b]

Richard The short term reproducibility I am after is 6 digits +-1 count. Absolute accuracy +-10 counts / 1 year or better.

I'd like it to be able to source reference voltage and reference current so it will have voltage to current converter (transimpedance amplifier) on board, as well as voltage buffer for the reference voltage. In this case it may be better to use the current source for the lowest range measurements.

The reason for wanting to have sourcing is because I want to have two independent meters on the same PCB. This would take care of things like power metering and 4 wire measurements. The added benefit would be that the two meters will be able to check each other thus compensating for systematic errors.

Being able to reduce the number of the reference resistors by adding an amplifier is really good, but I suspect there is a tradeoff hidden in there, a thing to consider.

So the big picture for the moment is like this (times 2 on each PCB) I forgot to delete two of the range resistors btw.


Speaking of which, how about if we change the switch with a difference amplifier?


Or an analog divider?


Ideas?

[ejeffrey]

This method cancels out offset voltage which eliminates the need for adding an auto-zero cycle and circuitry, but it cannot correct for test lead and connector  resistance. For sub-ohm resistance measurement, the only way to get very accurate measurements is 4 wire.

True, I wasn't suggesting that one was a replacement for the other: I just put AC measurement higher on my priority list than 4-wire probing.

I don't like typical auto-zero approaches because they tend to use a short auto-zero measurement with low duty cycle, so they have very poor rejection against even slow drift.

[amspire]

Richard The short term reproducibility I am after is 6 digits +-1 count. Absolute accuracy +-10 counts / 1 year or better.

Very ambitious, but go for it. It definitely is possible.

I'd like it to be able to source reference voltage and reference current so it will have voltage to current converter (transimpedance amplifier) on board, as well as voltage buffer for the reference voltage. In this case it may be better to use the current source for the lowest range measurements.

You can but it doesn't solve the big problem - lead and wiring resistance. The ONLY solution for low resistances is 4 wire which means you have to switch the voltmeter ground to Rut and Rref separately. To test 1 ohm and below to a real 6 digit resolution, you actually need a lot of current - more then any standard lab DVM uses. This is why specialized milliohm meters exist. It is bad form in a general purpose DVM to output 1 to 20A into a resistor under test.

Remember this in all your figuring - if Vref is 1K, then to get 6 1/2 digit resolution, you have to have less then 1 milliohm circuit and switch resistance (probably impossible) unless you use 4 wire to eliminate these errors.

The reason for wanting to have sourcing is because I want to have two independent meters on the same PCB. This would take care of things like power metering and 4 wire measurements. The added benefit would be that the two meters will be able to check each other thus compensating for systematic errors.

Hmmm. It is hard enough to make one 6 1/2 digit meter. I can't quite see how two meters helps.

Being able to reduce the number of the reference resistors by adding an amplifier is really good, but I suspect there is a tradeoff hidden in there, a thing to consider.

It all comes down to noise. If the lowest voltage you can read reliably is, say 1 uV, then to get 6 1/2 digits resolution, you need 2 Volts or more across the Rut. If you use my x10 multiplier, then that might means putting 20V across Rref. Two problems - 20V may be enough to destroy components, and 20V on a 1K resistor is almost half a watt. That heat is a really big deal in a reference resistor. Not many resistors can hold a 6 digit stability while dissipating half a watt.

Noise is not just noise generated in the voltmeter. It is mains hum and any other electrical noise picked up by the wiring to the part being tested.  At very least, you need to measure the average voltage for a period of one mains cycle.  For a full 6 1/2 digit resolution, you probably need to measure the average voltage over 5 or 10 mains cycles.

Most hi end meters allow you to set the averaging period from sub millisecond for 4 digits of resolution to 20 to 100 mains cycle periods for 7 1/2 digits resolution.

Dual slope conversion is particularly good at averaging the voltage. A bit harder to do with ADC converters.

For 4 wire measurement you either need a fully differential input to the voltmeter, or a fully isolated voltage that is applied to the resistors.  It all comes down to which method has the least errors. The fully isolated supply bay be easier..

You are not going to get a 6 1/2 digit analog divider, but if you go back to the example in my first email, a dual slope converter measure a ratio - it is an analog divider and it has no accuracy problems.

Richard

[ejeffrey]

You are not going to get a 6 1/2 digit analog divider, but if you go back to the example in my first email, a dual slope converter measure a ratio - it is an analog divider and it has no accuracy problems.

A 6.5 digit dual slope(or multi-slope) converter is *slow*.  Delta-sigma has most of the advantages of a dual slope converter, and a 22 ENOB delta-sigma is easy and cheap.