These notes are applicable to the MC Series of sensors (or "probes"): www.magneticsciences.com/magnetic-field-sensors/ which are calibrated multi-turn solenoids for 5Hz to 1 MHz, which provide a strong voltage output.
These notes are also generally applicable to single loop sensors (or “probes”), used for RF and microwave frequencies up to 6 GHz, these have better spatial resolution but weaker output: www.magneticsciences.com/EMI-probes/
These sensors measure magnetic fields over a range of frequencies as shown on those web pages. These do not measure static (DC) magnetic fields. You will connect the sensor to your own display instrument to view the AC or RF output from the sensor.
The sensor only measures magnetic fields parallel to the sensor axis. Therefore, rotate the sensor to all pointing directions (while keeping the sensor at the location you want to measure). When you see the maximum output, then the sensor is parallel to the maximum magnetic field polarization. Then use the curves or calibration data to determine the maximum field at that location.
The entire length of the MC sensor is used to make the measurement. Therefore, if the field is not uniform (not the same) over the length of the MC sensor, then the output will show you the approximate average field over the length of the sensor. So it is suggested that you center the MC sensor at the location you want to measure. The closer you measure to the source, the more non-uniform the field will generally be. The farther away, the more uniform the field will be.
A possible cause of measurement error is if connecting cables or other test equipment is radiating or picking up electromagnetic fields. This may be noticed if moving the cables or equipment (while keeping the MC sensor unmoved) is seen to cause a change of the measured result. This is not desired, since the test equipment and cables should not be radiating any fields, only your selected source of fields (DUT) should be radiating, and only the sensor receiving.
Reflections from the room and equipment, table, shelves, chairs, etc near the test area are also possible.
If you are driving a DUT it often requires coaxial input from a generator or oscillator. Or if your DUT needs a 'balanced' input it may require a balun or two-wire input. If using two-wires then a twisted pair would eliminate most radiation from those wires.
If using a series resistor to measure current into your DUT: some resistor types are only accurate at lower frequencies. The resistor should be a type that does not have a large error in resistance at the frequencies being tested. And the voltage displayed for the traces on scope (from resistor and from MC sensor) should be both RMS or both Peak voltage: set to the same, not one to RMS and the other to Peak, for input to your measurement calculations.
In elliptically polarized fields the maximum reading of the sensor will be in the polarization direction of the major axis of the polarization ellipse. Therefore these single-axis sensors avoid a large error seen with most triple-axis meters when measuring elliptically or circularly polarized fields (or near 3-phase power lines), due to the sequential (not simultaneous) sampling of X,Y,Z field polarizations done by most triple-axis meters.
B-dot Sensors: These solenoid and loop sensors are "B-dot" sensors since the voltage output is the time-derivative of the magnetic field. This is based on Faraday's Law which says the electromotive force around a closed loop is equal to the negative of the time rate of change of the magnetic flux enclosed by the loop: e = -dF/dt. So, on an oscilloscope if the magnetic field is CW (sinusoidal) then the voltage output from the sensor will show a -cosine trace on the scope. For other waveforms the output voltage is likewise the first derivative (B-dot) of the magnetic field.
If 180 degree phase reversal is seen on the scope trace it may be the negative sign of the cosine (since its B-dot of sine). It can also result from 'inverse’ button in scope channel, or the polarity of the internal coil wire connection inside the MC sensor, or flipping the sensor around so its oriented the opposite direction, or due to trigger setting for the trace on the scope.
Magnetic field flux density B emitted by a small loop:
Below is shown the equations for the magnetic field flux density B radiated by a small loop or multiturn loop with current Io (in spherical coordinate system). This field is also very similar to the field radiated by many types of small magnetic field sources which resemble loop currents. In the diagram the loop lies in the XY plane with axis along the Z axis. The range to observation point is r.
Br is the radially polarized field, with maximum on axis of loop (at q= 0°), minimum in plane of loop (at q = 90°)
Bq is theta q polarized field (along theta vector), maximum is in plane of loop (at q = 90°), and minimum on axis of loop (q = 0°).
(The phi f polarized field component is not radiated by a small loop).
m = IoNA is “Magnetic moment”, where N is number of turns of the loop, with current Io.
For Br equation: bringing the 1/r inside parenthesis: if r is very small 1/b2r 3 is the largest term, so fields diminish as 1/r3 in near field.
As r is increased, the largest term is 1/br2 so there the field is inversely proportional to r2 , this is the main term in Br
For example, the voltage output Vo was measured using an MC sensor placed along Z axis to measure Br the radially polarized field, at two distances from a small loop: ra=80 cm and rb=100cm. So the ratio of range squared = 1002/802 = 1.56
Measured at ra the sensor output voltage Vo = 5.9V, and measured at rb output Vo = 3.8V. So ratio of voltages = 5.9/3.8 = 1.55 which is almost exactly proportional to inverse range squared which is the correct theoretical result.
Very close to the source it can decline faster vs r due to Br proportional to 1/r3 term.
Bq has a different equation as is shown above, so it may decline more slowly vs distance: proportional to 1/r.