Air-gapped Ferrite Toroid Data

For an upcoming Circuit Cellar column on Hall effect current sensing, I slit another pair of toroids:

Slitting FT37 ferrite toroid
Slitting FT37 ferrite toroid

Then wound them with grossly excessive amounts of wire (the up-armored core on the right appeared earlier):

Slit Ferrite Toroid current sensors
Slit Ferrite Toroid current sensors

The smaller toroid is an FT37-43 that barely covers the active area of an SS49-style Hall effect sensor, but experience with the FT50 toroid suggests that’ll be entirely enough:

slit FT37 toroid trial fit to SS48-style Hall effect sensor
slit FT37 toroid trial fit to SS48-style Hall effect sensor

Data on the uncut toroids:

Property FT50-61 FT37-43
Outer diameter (OD) – inch 0.50 0.375
Inner diameter (ID) – inch 0.281 0.187
Length – inch 0.188 0.125
Cross section area – cm2 0.133 0.133
Mean path length (MPL) – cm 3.02 2.15
Volume – cm3 0.401 0.163
Relative Permeability (μr ) 125 850
Saturation flux G @ 10 Oe 2350 2750
Inductance factor (AL) – nH/turn2 68.0 420

Those overstuffed windings improved the sensitivity, but increased the winding resistance far beyond what’s reasonable.

Data on the slit toroids:

Toroid ID FT50-61 FT37-43 FT50-61
Measured air gap – cm 0.15 0.15 0.17
Winding data
Turns 120 80 25
Wire gauge – AWG 28 32 26
Winding resistance – mΩ 530 920 100
Predicted B field – G/A 872 660 163
Hall effect sensor @ 1.9 mV/G
Predicted output – mV/mA 1.7 1.3 0.31
Actual output – mV/mA 1.9 1.9 0.37
Actual/predicted ratio – % +12 +46 +19

The last few lines in that table show the transimpedance (transresistance, really, but …) based on the winding current to Hall sensor output voltage ratio (in either mV/mA or V/A, both dimensionally equivalent to ohms), which is why the toroid’s internal magnetic flux doesn’t matter as long as it’s well below saturation.

Gnawing the 80 turn winding off the FT37-43 toroid and rewinding it with 15 turns of 24 AWG wire dropped the winding resistance to 23 mΩ and the transimpedance to 0.36 mV/mA:

FT37-43 with 15 turns 24 AWG - Hall sensor
FT37-43 with 15 turns 24 AWG – Hall sensor

However, applying a voltage gain of about 28 (after removing the sensor’s VCC/2 bias) will produce a 0-to-5 V output from 500 mA input, which seems reasonable.