Designing Your Own Transformer

written by: Swagatam • edited by: Lamar Stonecypher • updated: 11/1/2011

Designing 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.

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• 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 Insulation.

    The third parameter i.e. the space for the insulation/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.

  • 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

  • Table B

    This 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