It works best with ring cores (toroids) but should be usable with other shapes having a closed magnetic path. The circuit, as shown, will plot the hysteresis loop for a half-inch diameter, high permeability ferrite ring; adaptations for other components are also given.

- The circuit diagram.
- Winding the core.
- The equipment
- Adjusting the circuit.
- Interpreting the curves.
- Finding the hysteresis losses.
- Troubleshooting.

See also ...

[
Producing wound components]
[A guide to the terminology used in the science of magnetism]
[ Power loss in wound components]
[ Faraday's law]

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Tolerances are only significant on R2, R6 and C1 (which is polyester or polycarbonate). C2 and C3 are ceramic.

The secondary can be made from wire that is as thin as you like, while the primary need only be sufficiently thick not to get hot enough to heat the core much (the saturation level falls fairly rapidly with temperature). I used 0.2mm and 0.5mm respectively.

Note: if you wish to measure very small rings with low permeability (such as those used in radio receivers) then you may need a source running at a few kilohertz in order to get sufficient secondary voltage. If you do this then you should also decrease C1.

The oscilloscope must be a dual channel model able to operate in an 'X-Y mode' (with the horizontal deflection controlled by a signal input rather than the timebase). I used an HP 54600 digital storage 'scope. A DSO is handy if you wish to plot initial magnetization curves.

Component tolerances for R_{2}, R_{6} and C_{1}
will affect the accuracy of your results.

X-axis = voltage on R2. Y-axis = V_{o} (voltage on U1 pin 1)

This shows the characteristic hysteresis
effect. Looking at the horizontal axis you see that the limits of the
curve span a change in voltage of 146mV. Because R2 is 1 ohm you know that
the primary current, I_{p}, changes by 146mA. From this you can
find the change in field strength as:

H = N_{p}×I_{p}/ l_{e}Am^{-1}

Where N_{p} is the number of turns on the primary. For the core
I used this gives H = 22×0.146/0.0276=116Am^{-1}.

OK, that's the field strength found. flux density is a bit trickier. Faraday's Law tells us:

V_{s}= N_{s}×d /dt volts

Where V_{s} is the voltage on the secondary winding and
N_{s} is the number of turns on the secondary and is the the magnetic flux in the core. Now, all text books on
op-amps give the result:

dV_{o}/dt = -V_{s}/(C_{1}R_{6}) volts

Where V_{o} is the voltage on pin 3. Substituting the previous
result for V_{s} we get:

dV_{o}/dt = -N_{s}(d/dt)/(C_{1}R_{6})

We have time rates of change on both sides of this equation so we can integrate wrt time and get:

V_{o}= -N_{s}/(C_{1}R_{6}) volts

This is a good result because it establishes that the op-amp voltage is proportional to the core flux.

= -V_{o}(C_{1}R_{6})/N_{s}webers

Putting in the known values:

= 0.239(1e^{-6}×1e^{3})/25 = 9.56e^{-6}webers

We now get the flux density from:

B = /AThe core has a roughly rectangular cross section of 6.3 × 3.2 = 20.2 mm_{e}tesla

B = 9.56eNow we can work out the permeabilty (at this level of field strength) from:^{-6}/20.2e^{-6}= 0.473 tesla

µ = µ_{0}µ_{r}= B/H H m^{-1}

4 e^{-7}µ_{r}= 0.473/116 H m^{-1}

Giving µ_{r} = 3240.

W_{R}= H × B = 116 × 0.473 = 54.9 J m^{-3}

However, the actual area of our loop is smaller by the fraction 4605/45122 giving an actual energy value of

W_{A}= 54.9 × 4605/45122 = 5.60 J m^{-3}

If we ran the core at 25 kHz this would mean a hysteresis loss rate of

P = 5.60 × 25e^{3}= 140 kW m^{-3}

The mean core diameter is 9.5 mm so the volume is

V_{T}= 20.2e^{-6}× 9.5e^{-3}= 6.03e^{-7}m^{3}

So the total core hysteresis loss is

P = 140e^{3}× 6.03e^{-7}= 84.4 mW

Now, the above calculation isn't to be taken too seriously - there are several shaky assumptions, but as an indication then it should be worthwhile.

When the primary current is increased you will see a curve something like this:

X-axis = voltage on R2. Y-axis = voltage on U1 pin 1

Note the change of scale on the X-axis. The difference in shape is due to the onset of saturation.

If you repeat this measurement at different values of primary current then you can get a curve like this:

X-axis = Field strength (Am^{-1}).
Y-axis = relative permeability

Incidentally, as you raise the primary current the tip of the hysteresis
loop traces out a *normal magnetization curve*. It is similar in
shape to the initial magnetization curve,
and is a useful way of describing the material behavior.

E-mail: R.Clarke@surrey.ac.uk

Last revised: 2001 April 16th.