These days it is probably rare that a person would find the need to construct a custom transformer for a power supply since just about anything you need can be found on websites like eBay and Amazon. However, there are still many homebrew types out there who enjoy the challenge (and maybe nostalgia) of creating a transformer for a special need. For those folks, this article from a 1952 issue of Radio−Electronics magazine will be a welcome bit of information. Author T.W. Dresser presents the fundamental equations and design methodology needed for winding a transformer on a laminated steel core frame. There are plenty of abandoned transformers which can be stripped down and rebuilt as required. Even the newest electronic devices - radios, TVs, Blu−ray players, kitchen appliances, etc. - have a transformer of some sort.

Transformers

By T. W. Dresser*

Knowing the principles of transformer design, the technician can often modify an existing transformer, or construct his own to meet special voltage or space requirements.

This article will discuss power transformer design, show the methods by which the design data is arrived at, and illustrate these methods by working out the details of a typical radio power transformer.

Power transformers, generally speaking, are fairly easy to design; essentially they are based upon the fundamental theory of induction which states that the E.M.F. induced in a coil inserted in a changing magnetic field is directly proportional to:

The number of turns in the coil.

The rate of change of flux (frequency).

The maximum number of flux lines. A numerical constant (to make the figures read in inches, centimeters, or whatever units may be used).

Expressed as a formula, the relation-ship becomes:

E = (4.44 x T x F x B x A)/108

where E = the voltage across the coil

T = the number of turns in the coil

F = the rate of change of flux

B = the maximum number of flux lines per square inch of core area

A = the cross-sectional area of the core in square inches

4.44/108 = a numerical constant

It will be apparent from the requirements listed that the greater the number of turns on the coil or the faster the flux changes the greater will be the voltage across the coil. Equally, the greater the flux density or lines of force linked by the coil the greater will be the induced voltage.

For our purpose it is more convenient to use the formula in its transposed form:

T = (E x 108)/(4.44 x F x B x A)

in which T is the number of turns required for the transformer primary; E is the line voltage, the factor F is the line frequency in c.p.s.; and the value of B can be taken as 60,000 for standard silicon steel core material. For standard 117-volt, 60-cycle-line operation the formula becomes:

T = (117 x 108)/(4.44 x 60 x 60,000 x A) = 732/A

Fig. 1 - Basic dimensions of the laminated transformer core.

The value of A depends on the power the transformer must handle, so the next step is to establish the transformer requirements. A typical radio power transformer would have the following characteristics:

Primary: 117 volts 60 cycles.

Secondary No.1: 700 volts at 0.05 amp center-tapped. (Note: For full-wave rectification this would represent a d.c. output of 0.1 amp at approximately 350 volts.)

Secondary No.2: 5.0 volts at 2 amp.

Secondary No.3: 6.3 volts at 3 amp. The total power required by the secondary windings is found by adding their volt/ampere products:

No. 1 - 700 v x 0.05 amp                  35.0 v/amp

No. 2 - 5.0 v x 2 amp                       10.0 v/amp

No. 3 - 6.3 v x 3 amp                       18.9 v/amp

Total secondary power                   53.9 v/amp

Due to copper and iron losses small transformers of this type require about 10% more input to the primary than is taken from the secondary, so that in this case the primary power would be: 1.1 x 53.9 = 59.3 v/amp.

For conservative design, A should be at least 0.04 square inches per volt/ampere. The cross-sectional area of the core is found to be

0.04 x 59.3 = 2.5 square inches approx. (Note: Britain is said to be a conservative country, and her transformer engineers are held to be conservative by most Britons. This will explain why the core areas given here are much larger than any the average American technician is likely to find on the transformers he tears down as a means of studying transformer design. For practical work, these figures can be cut almost in half, especially for transformers of 100 watts or over. -Editor)

It is unlikely the technician will have access to any variety of laminations. It is much more likely he will have to make his windings suit a core he already possesses, and he may not know what wattage the core is capable of carrying. The following formula will give him this information.

Watts = (Weight x Frequency)/2.5

where weight is in pounds

frequency is supply frequency

2.5 is a constant.

If a core of adequate weight is available, its effective core area can be found by multiplying the width of the center leg by the thickness of the lamination stack. (See Fig. 1).

The number of primary turns is found by substituting the core area in the formula T = 732/A

T = 732/2.5 = 293 turns

The turns-per-volt ratio is then 283/117= 2.5 turns per volt

The number of turns for each secondary winding is found by multiplying the required secondary voltage by the turns-per-volt ratio. In practice, about 5% is added to each secondary winding to compensate for voltage drop in the resistance of the wire. Time and computation may be saved by adding 5% to the turns-per-volt ratio:

1.05 x 2.5 = 2.63

Sec. 1: 700 x 2.63 = 1841 turns (This should be wound in two equal sections of 920.5 turns each.)

Sec. 2: 5.0 x 2.63 = 13.2 turns

Sec. 3: 6.3 x 2.63 = 16.6 turns

The next step is to select - with the aid of a wire table - the proper size wire for each winding. Wire tables are obtainable from wire manufacturers and appear in many manuals. For average intermittent operation, wire with a cross-sectional area of 1,000 circular mils per ampere is permissible. For continuous operation, at least 1,500 circular mils per ampere is required to prevent overheating.

The primary current is Ip = Wp/Ep = 59.3/117 = 0.5 amp.

From the wire table No. 23 is seen to be suitable for the primary. No. 33 can be used for secondary No. 1; No. 17 for secondary No. 2; and No. 15 for secondary No. 3. If the specified wire sizes are not readily obtainable, the next larger size should be used.

Filling the "window" and thereby insuring a well balanced transformer is not difficult. The majority of wire tables give the number of turns per square inch for each wire size. Calculate the window area in square inches, ascertain the number of turns per square inch for primary and secondaries and add about 50% for interleaving paper and board to insure that they fit in. If the windings will not fit, it is permissible to reduce the size of wire one or two gauges and thereby gain sufficient space to accommodate them.

The points to remember are:

The core wattage is determinable by weight and supply frequency.

Use a gauge of wire which will carry the current adequately.

Interleave each layer of primary and secondaries with insulating paper. Secondaries are insulated with thin "glassine," primaries and filament windings with electrical insulating paper of varying thickness, depending both on wire size and voltage. Check an old transformer for types of paper required, and your local armature winder for a source of supply.

If a transformer with a core of adequate size and weight is being rewound for different secondary voltages, it may be possible to utilize the original primary winding. In most radio transformers, the primary is wound next to the core, with the high-voltage secondary over it. The filament windings are generally on the outside.

Proper methods of insulating and anchoring the windings and making connections can best be learned by dismantling any good commercial transformer.

* Chief Designer, R.T.S. Transformer Co.; Bradford, England

Posted May 13, 2022