The single phase transformers used in power supplies of various instruments are small transformers which required to deliver few amperes at small voltages having VA ratings from 10 VA to 1000 VA. Such transformers are mainly used to drive the rectifier circuit of the power supply.

The design of such transformers divided as,

1. Core design

2. Winding design

3. Stamping design

**1. Core design** The first step in designing such small transformers is to select turns per volt value depending upon VA rating of the transformer. The table 1 gives the values of turns per volt (T

_{e}) for various VA ratings.Table 1 |

From the e.m.f. equation,

E = 4.44 Φ

_{m }f T**.**T/E = 1/(4.44 Φ

^{.}._{m }f) = T

_{e}..........(1)

Knowing the frequency of operation which is generally 50 Hz, the value of Φ

_{m }can be decided using equation (1).**Key Point**: Assume maximum value of the flux density in the core B

_{m }as 1 Wb/mm

^{2}which is enough for small transformers.

A

_{c }= Net core area = Φ_{m}/B_{m }..........(2) Assuming stacking factor as 0.9,

A

_{gc }= Gross area of core = /0.9 .............(3)**Key Point**: The shell type construction is generally used for small transformers. The core is made up of stampings as the construction of core is laminated. The stampings can be a) E and I, b) T and U or c) E type as shown in the Fig. 1.

Fig. 1 Types of stampings |

The companies manufacturing the stampings provide the information of the values of A, B, C, D and E for various standard available stampings.

**Key**

**Point**: For central limb, square section is generally preferred.

Thus for the central limb, the depth and width is made equal.

W

_{c }= Width of central limb = √A_{gc }............(4) Referring to stampings tables provided by the manufacturers, a standard stamping with W

_{c }nearly equal to the value A is selected.

**2. Winding design** The VA ampere rating of such transformers is known. Assume efficiency to be between 80 to 95% the primary current can be obtained as,

I_{p }= (VA/η V

_{p }) A .............(5)

where V

_{p }= Primary voltage

Assume current density in the primary winding conductors to be 2.5A/mm

^{2}which is sufficient for small transformers.**.**δ

^{.}._{p }= Current density in primary conductors = 2.5A/mm ........(6)

But δ

_{p }= I

_{p }/a

_{p }where a

_{p }= Area of primary winding conductors

**.**a

^{.}._{p }= I

_{p}/2.5 mm

^{2}...........(7)

For small transformers enamelled around conductors are used. The standard tables for the sizes of enamelled round conductors are provided by the manufacturers. Referring the tables, properly sized conductors can be selected.

As turns per volt T_{e }and primary voltage V

_{p }is known, the number of turns can be obtained on primary side as,

T

_{1 }= V

_{p }T

_{e }

_{ }.....(8)

The current in the secondary winding is,

I

_{s }= V

_{A }/V

_{s }............(9)

where V

_{s }= Secondary voltage

**.**a

^{.}._{s }= I

_{s }/δ

_{s }mm

^{2}..........(10)

where δ

_{s }= Current density in secondary conductors in A/mm

^{2}

Referring standard table, proper conductors can be selected.

While calculating secondary number of turns, allowance of 5% is selected so as to compensate for the voltage drop in the windings.

T_{2 }= 1.05 V

_{s }T

_{e }

_{ }............(11)

**3. Stamping Design**1. Primary winding

2. Secondary winding

3. Insulation and former used to support the windings.

The steps to design the stampings are,

Space factor S = 0.8 (d

_{ }

_{ }/d

_{1})

^{3}............(12)

where d = diameter of bar conductor

d

_{1 }= diameter of insulated conductor

The values of d

_{1}and can be obtained from the standard tables provided for conductor sizes.

**.**Space required for primary winding = T

^{.}._{1 }a

_{p }/S ............(13)

and space required for secondary winding = T

_{2 }a

_{s }/S ..........(14)

While the space for insulation and former is assumed to 20 to 25% of the space required for both the windings.

A_{w }= Total window area

= 1.2 (Window area required for both windings) .........(15)

**Key Point**: Standard table can be referred to select the proper stampings which gives window area slightly greater than the value calculated above.

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