Experimenting with AC Current Sensing

After watching James Lewis' Work Bench Wednesday presentation a couple weeks ago on Clamp Meters and sensing current

Workbench Wednesday 24: No-Contact Current Measurements

and reading some of the comments I decided that it would be fun to run some experiments to verify as true of false some of my own conceptions about the physics involved. Some of the questions that I want to explore are:

Can I simply (without a complicated circuit) read the presence of AC currents of less than an Amp in a wire?

Will the AC voltage applied to the load have any affect on the output if the current is held constant?

Will the output reading I get be linear with respect to the current in the wire?

Will the position or orientation of the wire in the sensing coil have any effect on the Output reading?

After giving it a lot of thought and doing a few small empirical experiments with coils and different cores I settled on using a large toroidal transformer with a 5 cm internal hole as my sensing coil.

The black wire coming through the toroid will be considered the Primary winding for our experiment and the toroid's original 115 Volt winding will be considered the secondary. The original secondary of the toroid (Red Wires) will be ignored. In addition to the Toroid transformer I will be using an AC power Supply that I built a while back.

and some 115 Volt light bulbs which will serve as loads for the AC power supply. If you happen to try to read the Ammeter on the power supply in any of the following pictures please be aware that it is set to display Deci-Amps. This is a bit strange but it was dictated by Ammeter that I used when I built the power supply. The meter will also display in Amps but the Deci-Amp setting gives me one more digit of precision. In addition to the meters on the power supply I will have a Radio Shack digital multimeter in line to give a more accurate reading of the primary current and a Fluke multimeter to read the millivolt output from the secondary winding of the Toroid transformer. None of my meters or test equipment can be considered of very high quality or precision but they will suffice for this simple general exploration. The AC power supply has a small variac for the output and this makes it difficult to get any precision as the slider on the variac takes steps of a volt or two from one winding to the next.

Here is a picture of the test setup:

In the picture you can see that the Radio Shack meter is reading 0.35 Amps and the power supply is reading 3.4 deci-Amps.

With a load of a 72 Watt incandescent bulb I began at a 50 mA current and took 50 mA steps up until I reached a 600 mA current level. Each step of the way I noted the output voltage on the secondary of the toroidal transformer. This voltage varied from 125 mV at 50 mA on the primary to 5812 mV when the primary was at 600 mA AC. Once I had accumulated the data I began to experiment with it.

One of my original questions was whether the output in mV would be linear with the primary current. One method to prove this is to assume that it is true and then do an experiment to verify it. My first experiment was to divide the mid-range of the output 2171 mV  by the mid-range of the primary current 300 mA. This gave me a result of approximately 7.24 mV per mA. If the relationship between input and output was indeed linear we should be able to predict an output from an input and all of our data points should match up. I tried a couple experiments using my new linear factor. While the factor gave me a ballpark result it was obviously not linear. The closer my test point was to the mid-range the more accurate it was. For example if we apply the factor to out first 50 mA input we should get an output of 362 mV not the 125 mV actual reading and this factor applied to the 600 mA input gives us 4344 mV not the actual 5812 mV that we recorded.

I used Xcel to chart and plot the data which gave a more accurate picture:

Not bad but definitely not linear. My speculation for this effect is that the lower primary currents are inefficient at coupling with the core of the transformer. While it is well beyond my ability to test we would probably continue to see a slight increase in the slope of the curve up until the core's magnetic saturation point. This effect must also be present for the manufacturers of clamp meters and they must have to use software or other techniques to compensate for the non-linearity.

My next experiment was to see if the voltage would make any difference in the output if the current were to remain constant. Everything I have been taught and the mathematics say that voltage should not affect it but why not have a little seeing is believing. To do this experiment I used a different light bulb (25 Watt) to raise the load resistance. Now I had 55 Volts applied to the circuit in order to have a current of 200 mA. The output from this experiment was 1235 mV which is well within the error of my instruments compared to the 200 mA at 15 Volts from the original data collection where the output was 1254 mV. As expected voltage does not make a difference. The output is tied to the current in the wire and not the voltage producing that current.

My next question was whether the position of the wire in the hole of the toroid would make any difference in the output. The physics and mathematics say that it should not but the vendors of Clamp Meters usually advocate the placement of the wire in the center of the jaws so we will see. Here is a video of this experiment.

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The movement of the wire had no more affect on the output than the background fluctuations produced by my equipment so the answer is that position and orientation do not matter. Perhaps the inability of the clampmeter manufacturers to produce a clamp with a symmetrical and closed core makes it necessary for the wire to be in a sweet spot but with a symmetrical closed core it doesn't matter.

Even with simple experiments like these I always learn something and I always have a lot of fun in the process.

Thanks for looking over my shoulder.

John