How Fluxmeters, sense coils and voltage integrators work
Fluxmeters: more than a century of applications
Moving a coil in a magnetic field induces a voltage proportional to the change in flux seen by the coil. Similarly, a varying field induces a voltage on a stationary coil. These principles have been understood and exploited since the 19th century to precisely measure, for example, the earth’s magnetic field. Fluxmeters also continue to play an important role in the measurement of the hysteresis of magnetic materials and in magnet design, for example to determine the losses in a magnetic circuit.
A coil: the most flexible of all magnetic probes
The use of coils is limited only by the imagination. How do you measure the flux density inside a solid piece of iron? Certainly not with a Hall sensor – try a search coil tightly wrapped around the block. How about the field induced by an MRI gradient coil, with frequencies in the MHz range? Again, you’ll have better luck with a single turn of wire than with the most elaborate Hall instrument.
Since the voltage induced on the coil is proportional to the flux change, we need to integrate the voltage to obtain the change in flux:
There are two commonly used approaches to building an integrator; each has its limitations:
- A standard analogue integrator circuit, using a high-gain amplifier with a capacitive feedback. The low-end bandwidth is limited by the size of the capacitor, and there are numerous analogue noise sources, such as leakage currents and temperature dependence. In addition, we usually want a digital result, so we have to digitize the output anyway.
- Digitize the voltage at periodic intervals and perform a numerical integration. This method has to limit the high-end bandwidth to satisfy the Nyquist criterion, it depends critically upon the linearity of the ADC, and can suffer from quantification noise.
The magnetic flux is defined as the integral of the field strength B over the area of the coil A:
If the field strength is constant over the area of the coil, the integrated voltage gives the change in field strength B:
where A is the effective area of the coil and theta is the angle between the coil’s axis and the field. To precisely measure magnetic field strengths with a fluxmeter, it is therefore essential to know the effective area of the coil with a great deal of precision. This is usually achieved by calibrating the coil in a known magnetic field. For measurements with 100 ppm or better precision, this requires an NMR-controlled or -stabilized reference magnet.
FDI2056 Fast Digital Integrator
The first off-the shelf instrument to quantify magnetic field transients
Mapping accelerator magnets
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