Experiment C2. Magnetic Properties of a Ferrite Pot-core Inductor

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```					M AGNETIC P ROPERTIES OF A F ERRITE P OT- CORE I NDUCTOR                                C2–1

Experiment C2. Magnetic Properties of a
Ferrite Pot-core Inductor

Objectives

In this experiment you will investigate the properties of an inductor and transformer en-
closed in a ferrite pot-core. In addition to being strongly ferromagnetic, ferrite is a good
electrical insulator. This makes it useful for constructing inductors and transformers for use
at high frequencies, since it helps to avoid problems with eddy currents. You will:

• measure the inductance L, resistance RL and quality factor Q of two inductor coils
with an air core

• repeat these measurements with one coil short-circuited to determine the leakage in-
ductance

• repeat the previous measurements with a ferrite core and obtain a value for the relative
permeability µr for ferrite

• examine the behaviour of the coils as a transformer.

If you have not done experiment A5, you should ﬁrst read the short Background section of
that experiment. Also, if you are unfamiliar with AC circuits you should read Appendix C
in the pink section at the end of these notes.

Prework Questions.

1. Consider an LCR circuit, where the inductor has an air-core.

(a) How do the inductance of the inductor, and the resonant frequency of the circuit,
change if the number of turns of wire in the coil is doubled?
(b) How do they change if the core is replaced with ferrite?

2. Sketch a diagram for a concentric air-core transformer in operation, with the outer
coil as the primary. Assume that the secondary coil is not connected, and that the
current in the primary coil is increasing and near maximum. Include the ﬁeld lines
in your sketch. (Don’t worry about the gap in between the primary and secondary
coils.)

3. Sketch a similar diagram, assuming the secondary coil is short circuited. Also include
current for the inner coil, if any. Explain any differences between this sketch and your
previous one.
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Background

For a long air-cored inductor with N turns, length              , radius a and cross-sectional area
A = πa2 , the inductance is given by:
L = µ0 N 2 A/ .                                        (1)
By ‘long,’ we mean that       a. If the inductor is not long relative to its other dimensions,
the inductance is more accurately represented by (see Figure C2-1 ):
µ0 N 2 A
L=               .                                      (2)
+ 0.90a

Fig. C2-1 Parameters of a short air-cored inductor

The inductance is increased substantially if a ferromagnetic material is placed inside or
around the coil. If the magnetic ﬂux is conﬁned entirely within the magnetic material (e.g.,
as in the toroidal geometry of Figure C2-2(a)), then the inductance is given by (see Figure
C2-2)
L = µr µ0 N 2 A/ ,                                   (3)
where µr is the relative permeability of the core and is now the length of the magnetic
circuit (dotted line in Figure C2-2(a)), not the length of the winding.

magnetic circuit
N           S

A = effective cross-
Hg
sectional area
Hc

(a)                                                 (b)

Fig. C2-2 Examples of (a) a closed magnetic circuit, and (b) a magnetic circuit with an air gap

If a small gap is introduced into the magnetic circuit, as in Figure C2-2(b), we need to apply
the boundary conditions for B and H to determine L. If Bc , Hc refer to the core and Bg , Hg
to the gap, we have
Bc = B g       since           B · dS = 0.

Since B = µr µ0 H,
µr µ0 H c = µ 0 H g .
M AGNETIC P ROPERTIES OF A F ERRITE P OT- CORE I NDUCTOR                                  C2–3

Since    H · dl = N i, we have
N i = Hg g + Hc ,

where g is the gap width and is the path length in the magnetic material.

Using the deﬁnition for inductance, L = N φ/i, where φ is the magnetic ﬂux, we ﬁnd that

µr µ0 N 2 A
L=                                                   (4)
+ µr g

If i changes with time, the voltage across L is given by

di    dφ
v=L       =N
dt    dt

Procedure

1. A ferrite core kit may be obtained from the service counter. It contains two halves of
a ferrite pot core which can be assembled around two coils wound on a plastic former;
the arrangement is shown in Figure C2-3. Please handle these carefully since ferrite
is a ceramic which chips easily.

Fig. C2-3 Ferrite pot core components

Measure L, Q and RL for air-cored coils

Select one of the two coils wound on the plastic former. Measure the inductance
L of this ﬁrst coil (without the ferrite core), by using the circuit in Figure C2-4 to
determine the resonance frequency

1
f0 =     √   .
2π LC

The non-ideal nature of the inductor may be represented with either a series or parallel
resistor. Obviously, for an ideal inductor the series RL would be zero, whereas the
parallel RL would be inﬁnite. In Figure C2-4, RL represents the equivalent parallel
loss resistance of the inductor.
The circuit should be constructed using the trainer board provided. The unused coil
must be left open circuit. An accurate value for C and R1 may be obtained using the
DigiBridge impedance bridge available in the laboratory - it is more convenient to
measure these before wiring the circuit.
Resonance should be determined by looking for zero phase shift between v in and
vout .
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R1 = 100kΩ
v in                                                                              vout
(to Oscilloscope)                                                                    (to Oscilloscope)

C
~                                              L            RL
0.01µF

Fig. C2-4 Parallel resonant circuit used to determine L and RL

The sharpness of the resonance is expressed in terms of Q, the quality factor. By
comparing vin and vout at resonance, you can calculate RL and hence the Q of the
inductor, using
RL                      vout     RL
Q=                and              =         .
ω0 L                    vin    R1 + RL
When measuring vin and vout it is best to use one oscilloscope probe to avoid cali-
bration differences between two probes. If you want to use two probes, their voltage
response to a common source must ﬁrst be compared over the relevant frequency
range.

2. Repeat the measurements described above to determine L, Q and R L for the second
coil.

3. Compare your values of L with the predictions of eqns. (1) and (2) and comment.
C1

Flux linking and leakage for air-cored coils

4. With an air core, the magnetic ﬂux produced by one coil will not be strongly linked
to the other coil. The proportion of magnetic ﬂux which is not linked between the
coils is called the leakage ﬂux. A direct method of measuring the leakage ﬂux is to
measure the inductance of one coil when the second coil is short-circuited. If the coils
formed an ideal transformer the inductance would be zero. This is because the current
in the secondary coil would produce a ﬂux which completely cancels the ﬂux due to
the current in the primary coil (why?). Any inductance measured in the primary coil
when the secondary is shorted is known as leakage inductance.
Measure the inductance of the smaller (fewer turns) coil again, but now with the
second coil short-circuited. Comparing this result with your earlier measurements of
L (with the secondary open circuit) you should be able to estimate the fraction of the
ﬂux of the primary coil which is linked by the secondary coil.

5. Make a sketch of the magnetic ﬁeld around the two coils when the secondary is open
circuit.
C2
M AGNETIC P ROPERTIES OF A F ERRITE P OT- CORE I NDUCTOR                                 C2–5

Measure L, Q and RL for ferrite-cored coils

6. Insert the coils in the ferrite core. You will again use the circuit in Figure C2-4. Since
Q, RL and L depend strongly on vin , you should record the input level used. Use
a value of 2V p-p (peak to peak) for vin . Repeat the measurements described to in
steps 1 and 2 to ﬁnd L, Q and RL for each coil. Check that L ∝ N 2 by comparing
the inductance of the two coils.

Determine µr for ferrite

7. Calculate the value of µr from eqn. (3) assuming that the effective area A = 198 mm 2
and the effective magnetic path length = 70.0 mm.
The problem with this calculation is that the values of A and are difﬁcult to estimate
and A varies in different places within the ferrite. As a result, the magnetic ﬂux varies
dramatically within the ferrite. The values you have used are effective values supplied
by the ferrite manufacturer.

Flux linking and leakage for ferrite-cored coils

8. Repeat part 4, with the coils now inserted into the ferrite core, to determine the leak-
age ﬂux with the ferrite present. Comment on the difference between the results with
and without the ferrite.

9. Make a sketch of the magnetic ﬁeld around the coils when they are in the ferrite, with
the secondary open circuit.
C3

Importance of air gaps

10. Insert small pieces of plastic (0.10 mm thickness) on opposite sides of the ferrite cores
so the two halves are separated by a gap of one thickness of plastic. Measure the new
resonance frequency of the smaller turn coil and compare the measured inductance
with the value calculated using eqn. (4) above. Hint: Is there one gap or two?
The two halves of the core are well polished to ensure close contact in normal use.
Give an explanation, in your log book, of why even a small gap makes a big difference
to L.

11. Determine the leakage ﬂux with the gap between the halves of the ferrite core present
by repeating the procedure used in item 4. Comment on the difference between this
case and the case with no gap.

Transformer

12. Set up a transformer by connecting the sinewave generator to the coil with 240 turns
and measure the voltage across this coil and the voltage induced in the other coil.
These measurements should be made at a frequency chosen to lie somewhere in the
range 10 − 20 kHz and with an input signal ∼ 10 V p-p. Check the validity of the
relation v2 /v1 = N2 /N1 for the two cases :
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(a) a ferrite core with no air gap, and (b) no ferrite core.

How do these results relate to your previous measurements of leakage inductance for
these two cases?

Conclusion

Collect the results of this experiment together into a table and compare the different cases
you have examined. What conclusions can you draw - especially regarding the importance
of the core to the performance of the coils as a transformer?

C4

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Description: Experiment C2. Magnetic Properties of a Ferrite Pot-core Inductor