Designing Your Own TransformerDesigning a transformer is not easy simply because the criteria involved with these devices are critical and elaborate. However some meticulously arranged data regarding the various calculations can make the procedure easier. Learn how to make a transformer through using simple formulas.

Introduction

We have already studied a lot about transformers in Bright Hub and we know that it’s simply a device used for either stepping-up or stepping down an applied input AC through magnetic induction in-between its two windings.

Basically a transformer will have the following main components:

Iron core stampings (configured either as U/T or E/I, generally the later is used more extensively)

Central plastic or ceramic bobbin surrounded by the above iron core stampings Two windings (electrically isolated and magnetically coupled) using super

enameled copper wire made over the bobbin Normally the winding which is designated to receive the input supply is termed as

the “Primary” and the winding which in response to this input produces the required induced voltage as the output is termed as the “secondary” winding.

Designing your own transformer as per a specific application can be interesting, but not feasible without calculating the various parameters typically involved with them. The following discussion will take you through a few important steps and formulas and explain how to make a transformer.

Calculating the Core Area (CA) of the Transformer

The Core Area is calculated through the formula given below:

CA = 1.152 ×√ (Output Voltage × Output Current)

Calculating Turns per Volt (TPV)

It is done with the following formula:

TPV = 1 / (4.44 × 10-4 × CA × Flux Density × AC frequency)

where the frequency will depend on the particular country’s specifications (either 60 or 50 Hz), the standard value for the flux density of normal steel stampings may be taken as 1 Weber/sq.m, for ordinary steel material the value is 1.3 Weber/sq.m

Primary Winding Calculations

Basically three important parameters needs to be figured out while calculating the primary winding of a transformer, they are as follows:

Current through the primary winding Number of turns of the primary winding Area of the primary winding

Let’s trace out each of the above expressions:

Primary Winding Current = (Secondary Volts × Secondary Current) ÷ (Primary Volts × Efficiency), the average value for the efficiency of any transformer nay be presumed to be 0.9 as a standard figure.

Number of Turns = TPV × Primary Volts

Primary Winding Area = Number of Turns / Turns per Sq. cm (from the table A)

Reading Table A is easy – just find out the relevant figures (wire SWG and Turns per sq.cm.) by tallying them with the closest matching value of your selected primary current.

Secondary Winding Calculations

As explained above, with the help of Table A you should be able to find the SWG of the wire to be used for the secondary winding and the TPV simply by matching them with the selected secondary current.

The Number of turns for the secondary winding is also calculated as explained for the primary winding, however considering high loading conditions of this winding, 4 % extra turns is preferably added to the over all number of turns. Therefore the formula becomes:

Secondary Number of Turns = 1.04 × (TPV × secondary voltage),

Also secondary winding area = Secondary Turns / Turns per sq. cm. (from table A).

Calculating the Core Size of the Steel Laminations or the Stampings

The core size of the steel stampings to be used may be easily found from Table B by suitably matching the relevant information with Total Winding Area of the transformer. The Total Winding Area thus needs to be calculated first, it’s as follows:

Total Winding Area = (Primary Winding Area + Total Secondary Winding Area) × Space for External Insulations.

The third parameter i.e. the space for the insulations/former etc. may be taken approximately 25 to 35 % of the sum of the first two parameters.

Therefore, the above formula becomes:

Total Winding Area = (Primary Winding Area + Total Secondary Winding Area) × 1.3

Normally, a core having a square central pillar is preferred and used - other factors involved are also appropriately illustrated in the adjoining figure and calculated as follows:

Gross Core Area = Core Area from Table B / 0.9 (sq.cm.)

Tongue Width = √Gross Core Area (cm)

After calculating the Tongue Width, it may be used as a reference value and matched appropriately in Table B to acquire the actual CORE TYPE.

Your quest regarding how to make a transformer gets over when you finally finish calculating the stack height, using the formula:

Stack Height = Gross Core Area / Tongue Width.

The present article explains through a practical example the process of applying the various formulas for making an inverter transformer. The various formulas required for designing a transformer has been already discussed in one my previous articles.

Designing a Transformer with the Help of a Practical Example

An inverter is your personal power house, able to transform any high current DC source into readily usable AC power, quite similar to the power received from your house outlets. Although inverters are extensively available in the market today, but designing your own customized inverter unit cab make you overwhelmingly satisfied and moreover it's great fun.

At Bright Hub I have already published of inverter circuits, ranging from simple to sophisticated sine wave and modified sine wave designs. However folks keep on asking me regarding formulas that can be easily used for designing a inverter transformer. The popular demand inspired me to publish one such article dealing comprehensively with transformer design calculations.

Although the explanation and the content was up to the mark, quite disappointingly many of you just failed to grasp the procedure. This prompted me to write this article which includes one example thoroughly illustrating how to use and apply the various steps and formulas while designing your own transformer. Let’s quickly study the following attached example:

Suppose you want to design a transformer for a 120 VA inverter using a 12 Volt automobile battery as the input and need 230 Volts as the output. Now, simply dividing 120 by 12 gives 10 Amps, this becomes the required secondary current.

Referring the article, let’s try and design the above transformer through the following steps:

The data in hand are:

Primary Voltage = 230 Volts,

Secondary Current (Output Current) = 10 Amps.

Secondary Voltage (Output Voltage) = 12-0-12 volts, that is equal to 24 volts.

Output Frequency = 50 Hz

First we need to find the core area CA = 1.152 × √ 24 × 10 = 18 sq.cm

We select CRGO as the core material.

Calculating Turns per Volt TPV = 1 / (4.44 × 10-4 × 18 × 1.3 × 50) = 1.96

Calculating Primary Current = (24 × 10) / (230 × 0.9) = 1.15 Amps,

By matching the above current in Table A we get the approximate Primary copper wire thickness = 21 SWG.

Therefore the Number of Turns for the primary winding is calculated as = 1.96 × 230 = 450

Next, Primary Winding Area becomes = 450 / 137 (from Table A) = 3.27 sq.cm.

Now, the required secondary current is 10 Amps, therefore from Table A we match an equivalent thickness of copper wire = 12 SWG.

Calculating Secondary Number of Turns = 1.04 (1.96 × 24) = 49.

Calculating Secondary Winding Area = 49 / 12.8 (From Table A) = 3.8 Sq.cm.

Therefore, the Total Winding Area Comes to = (3.27 + 3.8) × 1.3 (insulation area added 30%) = 9 sq.cm.

Calculating Gross Area we get = 18 / 0.9 = 20 sq.cm.

Next, the Tongue Width becomes = √20 = 4.47 cm.

Consulting Table B yet again through the above value we finalize the core type to be 6 (E/I) approximately.

Finally the Stack is calculated as = 20 / 4.47 = 4.47 cm

Transformer Design Calculations - Table ATransformer Design Calculations - Table A

The table below helps you to select the gauge and turns per sq. cm of copper wire by matching them with the selected current rating of the winding appropriately.

SWG------- (AMP)------- Turns per Sq.cm.

10----------- 16.6---------- 8.7

11----------- 13.638------- 10.4

12----------- 10.961------- 12.8

13----------- 8.579--------- 16.1

14----------- 6.487--------- 21.5

15----------- 5.254--------- 26.8

16----------- 4.151--------- 35.2

17----------- 3.178--------- 45.4

18----------- 2.335--------- 60.8

19----------- 1.622--------- 87.4

20----------- 1.313--------- 106

21----------- 1.0377-------- 137

22----------- 0.7945-------- 176

23----------- 0.5838--------- 42

24----------- 0.4906--------- 286

25----------- 0.4054--------- 341

26----------- 0.3284--------- 415

27----------- 0.2726--------- 504

28----------- 0.2219--------- 609

29----------- 0.1874--------- 711

30----------- 0.1558--------- 881

31----------- 0.1364--------- 997

32----------- 0.1182--------- 1137

33----------- 0.1013--------- 1308

34----------- 0.0858--------- 1608

35----------- 0.0715--------- 1902

36----------- 0.0586---------- 2286

37----------- 0.0469---------- 2800

38----------- 0.0365---------- 3507

39----------- 0.0274---------- 4838

40----------- 0.0233---------- 5595

41----------- 0.0197---------- 6543

42----------- 0.0162---------- 7755

43----------- 0.0131---------- 9337

44----------- 0.0104--------- 11457

45----------- 0.0079--------- 14392

46----------- 0.0059--------- 20223

47----------- 0.0041--------- 27546

48----------- 0.0026--------- 39706

49----------- 0.0015--------- 62134

50----------- 0.0010--------- 81242

Make Your Own Transformer Design - Table BThis Table B enables you to make your own transformer design by comparing the calculated Winding Area with the relevant required Tongue Width and Lamination Type number.

Type-------------------Tongue----------Winding

No.---------------------Width-------------Area

17(E/I)--------------------1.270------------1.213

12A(E/12I)---------------1.588-----------1.897

74(E/I)--------------------1.748-----------2.284

23(E/I)--------------------1.905-----------2.723

30(E/I)--------------------2.000-----------3.000

21(E/I)--------------------1.588-----------3.329

31(E/I)--------------------2.223-----------3.703

10(E/I)--------------------1.588-----------4.439

15(E/I)-------------------2.540-----------4.839

33(E/I)--------------------2.800----------5.880

1(E/I)----------------------2.461----------6.555

14(E/I)--------------------2.540----------6.555

11(E/I)---------------------1.905---------7.259

34(U/T)--------------------1/588---------7.259

3(E/I)-----------------------3.175---------7.562

9(U/T)----------------------2.223----------7.865

9A(U/T)----------------------2.223----------7.865

11A(E/I)-----------------------1.905-----------9.072

4A(E/I)-----------------------3.335-----------10.284

2(E/I)-----------------------1.905-----------10.891

16(E/I)---------------------3.810-----------10.891

5(E/I)----------------------3.810-----------12.704

4AX(U/T) ----------------2.383-----------13.039

13(E/I)--------------------3.175-----------14.117

75(U/T)-------------------2.540-----------15.324

4(E/I)----------------------2.540----------15.865

7(E/I)----------------------5.080-----------18.969

6(E/I)----------------------3.810----------19.356

35A(U/T)-----------------3.810----------39.316

8(E/I)---------------------5.080----------49.803