How to squeeze a bit more precision from your multimeter

[Mr Happy]

One of the snags when measuring lithium ion voltages is that most inexpensive meters only read up to 1.999 or 3.999. If you want to read a voltage like 4.2 you have to switch to the next range up that gives you only 4.20 worth of digits rather than 4.200. The snag with this is that the last digit tends to be very unreliable. If the meter says 4.20 you can only really trust the 4.2 part of it.

Here's an example with one of the cheap meters that can be obtained from Harbor Freight for pocket change ($3.99 right now):

The meter on the left has a 2 V range and a 20 V range, so for this battery it has to be on the 20 V range. It says the voltage is 3.35 V, but unfortunately we cannot trust the "5".

Let's try the meter on the right:

It says 3.35 V as well. We can be fairly confident about the "3.3" part, but can we do better?

Well, perhaps we can. Let's put both meters on the 2 V range and connect them in series:

"What?" I hear you say. Can we do this? As it happens, we can. The two meters in series act like a potential divider, and the sum of the voltages across each meter is equal to the total voltage.

Let's try it: 1.665 V + 1.670 V = 3.335 V

As before, we can't really trust the last digit ("5" in this case), but we have more confidence about the second last digit. In all probability the voltage is 3.33 V to three significant figures.

We can do a comparison with another voltmeter to see if it agrees:

It says 3.326 V, which is closer to 3.33 than to 3.35.

This same technique will work with any two meters. They do not have to be identical as they are in this example.

Of course, we cannot improve on the basic accuracy of the meters being used in this way, but by switching to a scale with more digits we can access a bit more of whatever accuracy the meter has.

 

[TakeTheActive]

Nice *FREE* way to get MORE precision out of TWO (or MORE!) inexpensive DVMs. :thumbsup:

 

[Kestrel]

I like it.

 

[tolkaze]

Does the resistance of the connecting wire have any effect on the result?

 

[Lumencraft (Matt)]

I love your creativity, and determination to overcome cheap obstacles.

I enjoy your posts Mr Happy, Thanks.

Now if only Harbor freight would sell a clamp meter that would measure DC voltage for 3.99$

 

[HKJ]

Does the resistance of the connecting wire have any effect on the result?

Not really, the meters each has 10000000 ohms and the wires has maybe 0.1 ohm.

But I would prefer a meter with more digits, it is usual around 4.2 volt it is interesting to measure with best precision and this needs 3 meters in series of the 1999 types!

 

[Lion251]

Nice method! :thumbsup:

 

[march.brown]

Why not solder three high value resistors in series ... Say for example "ten megohm" resistors ... Clip these across the battery and then measure across each resistor , then add the three voltages ... You only need one meter that way ... The resistors don't have to be high-grade for this.

To check the calibration , you could use a "Precision Voltage Reference Source 5.000 Volt" which is what I bought for $14-55 on 3bay ... Mine is actually 5.0002 Volts so this could be put across the three resistors and will act as your reference to check the accuracy of the meter on the two volt range ... Once you know the difference at five volts , you can make the necessary allowance for the four volt reading of the battery.
.

 

[Mr Happy]

Why not solder three high value resistors in series ... Say for example "ten megohm" resistors ... Clip these across the battery and then measure across each resistor , then add the three voltages ... You only need one meter that way ... The resistors don't have to be high-grade for this.

That could work, but not with 10 megohm resistors. The resistors need to have a much lower resistance than the meter to prevent the meter disturbing the measurement. However, something like about 10 k would be reasonable.

 

[subwoofer]

I agree your results look good and using the lower part of a range is always less accurate (therefore using two of the lower range might be more accurate than one of the higher). However each of the multi-meters will have a certain accuracy, and with regard to trusting the last figure, if you put two multi-meters in series you also put their 'inaccuracy/uncertainty' in series so must add that together and apply it to the result.

A statistician may have more to add to this as there may be a way of analysing errors that results in some error cancelling, but on a basic level, with two multi-meters each with + or - 0.01V accuracy, two in series has an accuracy of + or - 0.02V, if you keep adding more multi-meters, especially from the same manufacturer who may have calibrated them against the same reference, you keep adding error to the result.

You may end up with more precision, but what is precision without accuracy?.... it is precisely inaccurate!

 

[Justin Case]

Sometimes the DMM has a bit more digits than advertised, and you can access it. This method mainly works when the voltage you want to measure is just slightly greater than the magnitude that would allow you to use a lower range on the DMM. In the case of a 3999 digit DMM, perhaps you want to measure something that could be at ~4.1V.

Measure something like the OCV of a 123A cell. Put the DMM in "relative" mode. Then measure the higher voltage item of true interest. If you are lucky, you will get a relative measurement with 3 decimal places, which you would then add to the OCV value of the 123A cell that you measured first. That gives you to absolute voltage magnitude of the higher voltage item to 3 decimal places, when normally you would only get 2 decimal places when using the higher range setting.

For example, with a cheap Chinese DMM, I measured 3.037V for a random Duracell 123A. I measured 4.15V for an IMR26650. But in relative mode, I measured 1.116V. Adding this to 3.037V gives 4.153V.

An AW18650 measured 4.18V. In relative mode, it measured 1.147V, giving 4.184V.

 

[Justin Case]

I agree your results look good and using the lower part of a range is always less accurate (therefore using two of the lower range might be more accurate than one of the higher). However each of the multi-meters will have a certain accuracy, and with regard to trusting the last figure, if you put two multi-meters in series you also put their 'inaccuracy/uncertainty' in series so must add that together and apply it to the result.

A statistician may have more to add to this as there may be a way of analysing errors that results in some error cancelling, but on a basic level, with two multi-meters each with + or - 0.01V accuracy, two in series has an accuracy of + or - 0.02V, if you keep adding more multi-meters, especially from the same manufacturer who may have calibrated them against the same reference, you keep adding error to the result.

You may end up with more precision, but what is precision without accuracy?.... it is precisely inaccurate!

The DMM accuracy is % of reading plus digits. So if the reading is halved, then % of reading is also halved. When you add the two together, you get the same error as with just one DMM. The difference is in the digits. At the more accurate voltage range, the digits affect the 3rd decimal place. At the less accurate voltage range, the digits affect the 2nd decimal place. Thus, shifting to a more accurate voltage range greatly reduces the impact of the digits that you add to the DMM reading by a factor of 5X (you get 10X improvement, but you add the digits twice so you lose 2X).

 

[march.brown]

That could work, but not with 10 megohm resistors. The resistors need to have a much lower resistance than the meter to prevent the meter disturbing the measurement. However, something like about 10 k would be reasonable.

Yes , you are right , as long as the three resistors are high enough in value to draw minimal current from the battery ... We are trying to measure the open circuit voltage ... I suppose ideally the meter impedance should be at least 100 times the resistor value for the shunting effect to be minimal.
.

 

[xoomercom]

That actually made me laugh. :twothumbs

I give you A for being original. Not only did you move the decimal point, you've actually doubled the capacity. If the probes allow 2 of 200V meters can now measure up to 400V.

 

[Mr Happy]

Here's another trick along the same lines. I have a 3999 count meter, and when I measure something over 4 V I necessarily end up on the 40 V range. For instance a certain cell I have here reads between 4.09 - 4.10 V (the reading actually flickers between the two measurements).

To get the voltage into the 4 V range I can take an NiMH cell and place it reversed in series with the original cell, thus subtracting the NiMH cell voltage from the measurement. If I do this the meter reads 2.724 V. The NiMH cell alone reads 1.370 V. Therefore, the original voltage can be recovered by adding these two together:

2.724 + 1.370 = 4.094 V

In this case it looks like the reading on the 40 V range was consistent with the more precise measurement.