Ease of C.W. Transformer Design

Ease of C. W. Transformer Design
Radio for February, 1922
By A.H. Babcock

A year or so ago, one of my sons came to me with a transformer core he had traded-in, and asked, "How can I tell how many turns to wind on this for a 110 volt circuit ?" Here was a practical question that demanded an answer in terms a school-boy could understand and apply to every-day use. The answer was found in such simple form that he wound that core, tried it in service, and then went around the neighborhood hunting up transformers to design-for an adequate fee - which his father did not share; another example of the manner in which a business man commercializes the technical knowledge of an engineer.

But here is where the engineer gets back at him, by publishing the information, so that any radio, or about-to-be radio, experimenter can do it himself. Usually the problem presents itself in one of two forms:

(1) I have a transformer core; how many turns and of what size shall I wind on it;

(2) How much iron must I pile up, and how many turns must I put on it ?

He who looks in books for the equations used in transformer design, finds this one:


from which he shies, as a rule, because it looks formidable. In fact, it is simple.

E = the volts of the circuit,

N =the cycles of the circuit,

A = the number of square inches of the magnetic circuit,

B = the number of magnetic lines per square inch of the magnetic circuit,

T = the number of turns.

The proper value for B usually is the sticking point, but it has been found by long experience that for small transformers, and for ordinary grades of sheet iron, such as are now being considered, we may safely use, B= 75,000 for 25 cycle transformers, and 50,000 for 50 or 60 cycle transformers. First we rewrite our equation in this form:

and since we know N and B, we may write:

from which:

That is, for a transformer to be used on a 60 cycle circuit, we can get the proper number of turns for the primary coil by multiplying the house-circuit volts by 7.5 and dividing this product by the number of square inches cross-section of the magnetic circuit. "EASY!"

On a 25 cycle circuit, the 7.5 becomes 12, and on a 50 cycle circuit it becomes 9; which makes that simple expression good for any power circuit likely to be used.

One example will illustrate:

Let us assume we have a core that we wish to use on a 115 volt, 60 cycle circuit for two tubes, each of which takes 1000 volts on the plate and 15 volts on the filament, to be used in a self-rectifying circuit on both half waves. The core measures 2.25x4.5 inches; hence:

(to the nearest 2.25 x 4.5 - turn), and the volts per turn:

which is the same for all coils.

Now the secondary coil must have two windings in series, each to give 1000 volts, and with a middle tap. Then the secondary turns will be:

with a tap taken out at the 739th turn.

The filament coil must have two similar windings, each to give 15 volts and with a middle tap. Its turns then will be:

with a tap taken out at the 11th turn.

For two 50 watt tubes, such as are assumed for this example, the primary current will be about 6 amperes. Allowing 1500 c.m. per ampere, the primary wire should be No. 10; and the filament winding may be the same size for a 6 ampere filament current when the filaments are in series. If they are connected in parallel, the wire should be No. 8 and the number of turns should be 11, with the middle tap at 5.5 turn (for ground
connection). The size of wire on the plate coils may be No. 20 or No. 22. One word of caution: Frequently in "Answers to Questions," transformer
cores as small as 1x1 or even 1.5x2 inches are recommended. How thoughtless! Remember that the turns increase in the same ratio that the core area decreases; and that iron is cheaper than copper wire. Even more important is the labor of winding. For example, suppose the core of the transformer taken for the illustration above had been half as large; then the primary turns would have to be 170, and the secondary 2956.
Think of the labor to put all those turns on, and possibly to take off in case of a burn -out ; and then to put back again. 

So, if you want to determine how much iron to pile up for a core, remember that about 1 to 1.5 volts per turn is a conservative range. For trial assume 1.25 volts per turn. Then by transforming our first equation we have:

or, the area required is 7.5 times the volts per turn ; in this case 7.5x1.25=9.38 sq. in.

Method of Measuring Magnetic Cross Section.

The magnetic cross section must be measured at right angles to the laminations that are enclosed by the coil ; the center leg when the core is built up around the coil; and either leg where the core is built up inside the coil, i. e., between the arrows in the sketches.