April 1952 RadioElectronics
[Table of Contents]
Wax nostalgic about and learn from the history of early electronics.
See articles from RadioElectronics,
published 19301988. All copyrights hereby acknowledged.

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
RadioElectronics 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, Bluray 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 relationship becomes:
E = (4.44 x T x F x B x A)/10^{8}
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 crosssectional area of the core in square inches
4.44/10^{8} = 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 10^{8})/(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
117volt, 60cycleline operation the formula becomes:
T = (117 x 10^{8})/(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 centertapped. (Note: For fullwave 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 crosssectional 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 turnspervolt 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 turnspervolt 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 turnspervolt 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 crosssectional
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 I_{p} = W_{p}/E_{p} = 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 highvoltage 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
