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Why is the gradient of the voltage potential field not equal to the electric field?

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Hi,

I have been working on a 3D model of a resistive current sensor, and I am trying to verify the high frequency (50-500Mhz) response. Essentially, i want to make sure that at a fixed current excitation of 1A, I measure as close as possible to 0.1V, corresponding to a resistance of 0.1Ohm. The challenge is to avoid coupling the measurement loop to the rapidly changing magnetic flux.

I initially used boundary probes to measure the average voltage potentials at the two boundaries corresponding to the sensor output, but this gave erroneous result. I then tried to do a line integral of the electric field between the two sensor outputs, and I was surprised to find the expected voltage of 0.1V. After further investigation, I have discovered that the electric field in general corresponds well with my expectations, in that the electric field is strong across the resistive elements, and weak at the copper. The voltage potential field does not make much sense in this regard - the total voltage between the terminal and ground is close to the expected 0.1V, but by plotting the 3D voltage potential field over the model, it seems that the entire voltage drop appears in an area very near the terminal, with apparently nearly zero voltage drop over the resistive elements.

I have attached screenshots of d(V,y), and Y component of E field, respectively, plotted in the same plane. From my understanding, these should be equal, which is clearly not the case in my simulation.

Is the V field somehow calculated based on the bulk impedance seen at the terminals, ignoring the geometry? This is the only explanation I can come up with...

I would be grateful if you would help me solving this discrepancy. I have attached the model file with all cleared as the uncleared file is too big, but I would not expect anyone to run the simulation themselves as it took about an hour to run for me with a modern workstation. Let me know if you want me to upload a screenshot of a plot of anything.

Best regards,
Kristian

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