EMC Question of the Week: January 3, 2022

oscilloscope displaying a sine wave

At 1 MHz, which electrical quantity is difficult to measure because it's not well-defined?   

  1. voltage between two points on a copper plane
  2. current density on the surface of a copper plane
  3. signal voltage on a transmission line
  4. electric field at a point in space


The best answer is “a.” The voltage between any two points is defined as the voltage between points a and b is the integral from a to b of E dot dl.

Voltage is a function of the electric field strength and the chosen path of integration. At 0 Hz, the same voltage is obtained regardless of the integration path. However, at high frequencies, the path of integration is critical.

Anyone attempting to measure the voltage between two points on a copper plane at 1 MHz will generally observe that the measured voltage is a function of the position of the probe leads. Current on the planes creates a magnetic field that is captured by the loop area of the probe producing the majority of the measured voltage. In most cases, neither minimizing nor maximizing this loop area produces the desired result. If the purpose of the measurement is to determine the voltage that will couple to a signal path or the voltage that will drive an antenna, then the measurement must emulate the coupling. Usually, it is easier to measure the result of the coupling rather than try to define and measure the voltage directly.

Unlike a voltage between two points on a plane, voltages on a transmission line are generally well-defined. For TEM propagation, the electric field between two conductors in the same plane is conservative. In other words, the voltage obtained is independent of the path of integration.

Current densities and electric fields are both well-defined vector quantities. Anyone measuring them correctly should get the same value independent of the measurement technique.

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