October 1932 RadioCraft
[Table
of Contents]
Wax nostalgic about and learn from the history of early electronics.
See articles from RadioCraft,
published 1929  1953. All copyrights are hereby acknowledged.

One very satisfying aspect of 'rolling your own' audio frequency
coils (aka chokes, aka inductors),
is how well the simple inductance equations match measured end results.
Unless you really manage to mangle the job, if you use the right
equation and are reasonably careful to observe wire size, spacing
(including insulation), and core diameter,
you will be amazed at how close practice matches theory. Although
strictly speaking audio frequencies run from a few Hertz up to maybe
15 kHz for people with really good hearing. My experience
is that similar success can be had even into the low MHz realm with
just a little tuning required. It's not until you get into the realm
of selfresonance that everything starts falling apart with basic
equations.
Building Your Own A.F. Choke Coils
By C. H. W. Nason
Fig. 1  Magnetization flux and hysteresis curves.
Fig. 2  Inductor core lamination.
Fig. 3  Coil turns vs. air gap inductance chart.

For a given inductance and D.C. through the core, the number
and size wire may easily be determined by means of the chart above.
For an inductance of 20 henries, with 120 ma. through the core,
6,700 turns of No. 35 wire should be used on the core indicated
in Fig. 2.
Filter chokes designed for a given inductance require calculations
far outside the abilities of the average amateur. Before discussing
actual simplified design methods it might be well, however, to discuss
briefly the factors involved. Certain relations are involved in
the design of the magnetic circuit which are briefly as follows:
Factor
Equation Unit of Expression
H (the magnetic force 4 pi N I
Gilberts per Cm.
Φ (the flux)
u H A
Maxwells
B (the flux density) Φ/A
Gausses
u (the permeability)
B/H
Numeric value.
In these equations:
1 = the magnetic path in cms.
A = the cross section of the core in sq. cms.
N =the number of turns.
I = the current in amperes.
pi = 3.1416
If we pass a gradually increasing current through the winding
surrounding a magnetic material the relation of B to H is as shown
in Fig. 1A. If the current through the winding is now decreased
it will not follow the original path of the curve but will take
another course as shown in Fig. 1B. Thus for a given value of H
a twofold value of B corresponding to Q and to R in Fig. 1B are
found. (This is due to the residual magnetism in the core and the
condition is known as "hysteresis." Naturally, the smaller this
loop the better is the core material for magnetic purposes.)
If with a fixed D.C. magnetizing force a small A.C. voltage is
superimposed, a minor hysteresis loop appears as is indicated in
Fig. 1C. It is from the minor loop that we determine the permeability
of the core material to alternating currents, and it is u_{a.c.}
that we employ in calculating the inductance of a transformer or
choke. The factor u_{a.c.} is defined as being equal to ΔB ΔH
or the increment in B divided by the corresponding increment in
H for a given A.C. flux. It may be readily seen that the value for
u_{a.c.} is something quite different from the arithmetical
value for u obtained from the original B/H curve. This value is
not really a constant as it varies over a range of A.C. flux densities.
The relation of u_{a.c.} to the A.C. flux is shown in Fig.
1D for two values of D.C. magnetizing force. These values are for
a particular core material and are consequently not for design purposes.
With u_{a.c.} determined for a given D.C. flux density
the inductance of the winding may he calculated from the equation.
It will be noted in Fig. 1D that the value u_{a.c.} increases
slightly for the higher values of A.C. flux density but the increase
has the effect of slightly adding to the inductance of the winding
and is therefore beneficial in its effect except where sharply tuned
circuits are involved.
It an airgap be provided in a magnetic core the D.C. flux density
will fall off but an increase in the A.C. permeability will obtain.
There is an optimum value for this relation which depends upon the
characteristics of the particular iron chosen for the core material.
That is to say: for some length of airgap  for some substitution
of a material having unit permeability for a portion of the magnetic
path  the A.C. permeability will be at a maximum. Not only this,
but the D.C. flux density may be varied over a wide range with but
slight effect upon the inductance of the winding.
In most A.F. transformers a certain percentage of airgap is
necessary (although it is provided in the case of the highest quality
transformers only). The airgap may be dispensed with only when
the D.C. flux density is at zero through the use of parallel feed
systems. In pushpull transformers the D.C. components are assumed
to cancel but there are high values of A.C. in the core and a certain
amount of D.C. is always present due to tube irregularities so that
an airgap is still essential to an economical design.
In order to offer a series of chokes for the average experimenter
to construct with a full knowledge of the characteristics that will
obtain it is first necessary that a particular lamination be chosen
which will be available to him. A core form which will offer a range
in the neighborhood of 30 henries for all normal values of D.C.
flux and which will at the same time lend itself to an economical
design in so far as D.C. resistance is concerned may be achieved
around the EI11 lamination of the Lamination Stamping Company (located
at Brackenridge, Pa.)
Fig. 4  Coil turns vs. wire resistance inductance graph.

The dimensions of this core are as shown in Fig. 2. The characteristics
of a core having a square crosssection are as follows:
Window area, 0.575sq.in.;
Volume, 4.03 cu. in.;
Core weight, 1.13 lbs.;
Area, 4.94 sq. cm. or .766sq. in.;
Length of path, 15.61 cm. or 6.13 in.
Winding data from the charts is based on the use of enamel wire
of the size indicated and with glassine paper between layers. The
ends of windings should be straightened with pieces of fiber and
the core itself should be protected with several layers of brown
paper.
In forming the windings a piece of wood should be cut to slightly
less than the core dimensions and wrapped with one layer of string.
After winding. this string may be pulled out and the coil removed
from the wood form. The values for the airgap given in the chart
refer to the total gap and in the case of EI laminations the gap
at the center and in each leg should be just half the value read
from the chart. Any machinist will lend you a micrometer to assist
in building up wafers of paper or of fiber to insert in the legs.
The holes provided in the core offer ready means for mounting and
for clamping in position by means of iron or brass straps in methods
which will readily suggest themselves to the experimenter.
Variations from the data in the charts may be achieved by varying
the "stack" of the laminations. For double the stack (2 x 0.875in.)
the inductance will be doubled for a given current density and number
of turns; while the resistance of the windings will be increased
by but onethird. For onehalf the stack specified, the inductance
will be halved; and the resistance will be reduced by about 16 percent.
We may thus achieve with this single type of lamination any value
of inductance up to 60 henries with D.C.; or up to over 200 henries
where no D.C. is employed. The core material employed in calculating
the charts was Allegheny Super Dynamo Grade Steel Sheets and the
calculations are based on the assumption that 1 volt of A.C. is
superimposed on the D.C.; for high A.C. flux densities a slightly
higher inductance will prevail.
As an example, let us suppose that we desire a choke having an inductance
of 20 henries at a current of 120 ma. on the core specified . Tracing
through from the 20 henry line at the left edge of the curve we
find that this cuts the 120 ma. line at 6,700 turns. We find from
the wire sizeresistance curve, that the wire size for this number
of turns is No. 35 enamel; and that the resistance of the choke
will be 1,100 ohms. Under these conditions the second chart shows
that the airgap is about 0.045in. This means that 0.0225in. of
insulating material will be required in each leg of the choke core.
Now, an efficient choke should not have a resistance so high
as this unless designed for a specific purpose  for instance, let
us suppose that a receiver employing a 2,500ohm dynamic field in
its filter system must be used with an external speaker and we desire
to replace the original speaker field with a choke. In this case
we would work backwards from the specifications that our choke must
have a 2,500ohm resistance. On the basis of economy, let us see
what we can do with our choke design in order to reduce the resistance.
As we noted before. increasing the height of the core stack by
100% increases the inductance of any form of winding by a like degree.
On the basis of a square stack we start with an inductance of 10
henries at 120 ma. This calls for 5,000 turns of No. 33 wire, a
total resistance of 450 ohms. Increasing the stack by 100% likewise
increased the resistance by onethird. Our total resistance is therefore
600 ohms. Reference to the second chart indicates a total airgap
of 0.035 in. or .0175in. in each leg.
Posted December 26, 2014
