Mirnov calibration Helmholtz coil

Fig. 1: Mirnov calibration Helmholtz coil

A Helmholtz coil used for the calibration of Mirnov coils, which produce a voltage in response to a changing magnetic field.

Parameters

• Wire gauge: 14 AWG
• Number of turns (N): 12
• Helmholtz radius (r): 3.5" (8.89cm)
• Resistance (R): 53.4mΩ
• Inductance (L): 161μH
• Access:
  • Coil-Coil Height: ~2.75" (6.99cm)
  • Bore Diameter: ~6.25" (15.88cm)
• Calibration:
  • Induction: 115±3 µT/A (tested at 10.2 A)

Design

Mirnovs are calibrated on a 3.5" Helmholtz coil. The Helmholtz frame is constructed in G10 with nylon screws and bolts. Using the ideal Helmholtz expression, with N the number of turns per coil, I the current per winding, and R the Helmholtz radius, and the ideal wire gauge and associated amplifier output parameters can be estimated. The limitations of available power supplies strongly influenced the optimal choice of wire gauge: smaller gauge wire provides more windings per coil, resulting in higher field per ampere but also increasing inductance and therefore required supply voltage per ampere. This essentially means that smaller gauge (i.e. heavier wire) allows higher field at low frequency, but constrains maximum field at high frequency. Schematics for the Helmholtz form can be found here.

A BOP100-4M power supply is available from the calibration lab as an amplifier; alternatively, a Crown-style Techron7560 audio power amplifier may be borrowed from the electrical engineering department. The BOP is a 400W supply with a 100Vx4A swing; the Techron is rated for 1350W at 4Ω, although its V-I graph suggests the limit of its operational range is roughly 110Vx15A with a mainly inductive load.

Given these power supply specifications, the following magnetic fields and frequencies are accessible, either current limited (C) or voltage limited (V):

		BOP100-4M			Techron 7560			Crown XLS 2502
Gauge (AWG)		1kHz (G)	10kHz (G)		1kHz (G)	10kHz (G)		1kHz (G)	10kHz (G)
20		21 (C+V)	2 (V)		26 (C+V)	2.4 (V)
18		14 (C)	3.5 (V)		42 (C)	4.5 (V)
16		9 (C)	6 (V)		32 (C)	7 (V)
14		5.5 (C)	5.5 (C)		20 (C)	12.5 (V)		21 (V)	11.5 (V)
12		3.5 (C)	3.5 (C)		12.5 (C)	12.5 (C)
10		2 (C)	2 (C)		7.5 (C)	7.5 (C)

Operation

As of Feb. 2020, the Helmholtz is driven primarily by a Crown XLS 2502 audio amplifier purchased for this purpose. The Crown amp has been used to drive the Helmholtz at more than 18A (~21G) at low frequencies (~1kHz and lower), and up to ~10A at 10kHz. Rather than reaching a hard current limit in this application, the Crown amp either begins to distort, or reaches a thermal limit and throttles itself down.

The Crown amp is operated by providing input from a signal generator through a BNC-to-phono adapter. The amp output knob should always be turned down completely when not in use, and whenever making any large change to the input signal voltage. The signal generator should not be set higher than ~4V, to avoid damaging the Crown amp input. If the Crown thermal limits during use, the output knobs should be turned down to zero with the power on to keep the fans running, and the amp allowed to cool. Thermal stress on the amp is audible as the fans work harder and visible as a thermal warning indicator lights.