Design Center
SIMPLIFIED DESIGN OF
POWER SUPPLY TRANSFORMERS
POWER SUPPLY TRANSFORMERS
Almost every electronic circuit needs a separate power supply, which may be a battery or a rectified power supply. Here we will deal with the design of small transformers that are normally used in conjunction with mains-operated power supplies. This will help electronic hobbyists to design and construct their own transformers according to their needs. In the following pages, a simplified design procedure is given so as to obtain satisfactorily designed transformers. However, the design procedure is often a matter of trial and error.
The tables provided here cut calculations short and help the designer to choose the proper size of wire or core lamination. Only relevant data and calculations are provided so that the designer is not confused by unnecessary details.
The tables provided here cut calculations short and help the designer to choose the proper size of wire or core lamination. Only relevant data and calculations are provided so that the designer is not confused by unnecessary details.
The transformer
A transformer has two or more windings of insulated copper wire over an iron core. They are, one primary winding and one or more secondary windings. Each winding is electrically isolated from the other, but they are magnetically coupled with the help of a laminated iron core. Small transformers have a shell type construction, i.e. the windings are surrounded by the core as shown in Fig. 1. The power delivered by the secondary is actually transferred from the primary, but at a voltage level determined by the turns ratio of the two windings.
Preliminary design
As the first step to the design of a transformer, the primary and secondary voltage ratings and the secondary current rating must be clearly stated. Then decide on the core material to be used: ordinary steel stampings or cold rolled grain oriented (CRGO) stampings. CRGO has a higher allowable flux density and lower losses.
The optimum cross-sectional area of the core is approximately given by:
A transformer has two or more windings of insulated copper wire over an iron core. They are, one primary winding and one or more secondary windings. Each winding is electrically isolated from the other, but they are magnetically coupled with the help of a laminated iron core. Small transformers have a shell type construction, i.e. the windings are surrounded by the core as shown in Fig. 1. The power delivered by the secondary is actually transferred from the primary, but at a voltage level determined by the turns ratio of the two windings.
Preliminary design
As the first step to the design of a transformer, the primary and secondary voltage ratings and the secondary current rating must be clearly stated. Then decide on the core material to be used: ordinary steel stampings or cold rolled grain oriented (CRGO) stampings. CRGO has a higher allowable flux density and lower losses.
The optimum cross-sectional area of the core is approximately given by:
For transformers with multiple secondaries, the sum of the output volt-amp, product of each winding is to be used.
The number of turns on the primary and secondary windings is decided by the turns per volt ratio as :
Turns per volt = 1\(4.44 X 10- 4 frequency X core area X flux density)
Here, the frequency is 50Hz for Indian domestic mains supply. The flux density can be taken as about 1.0 Weber/sq, m. for ordinary steel stampings and about 1.3 Weber/sq, m. for CRGO stampings.
Primary winding design
The current in the primary winding is given by:
Sum of (output volts X output amps)
Primary current = -----------------------------------------
Primary volts X efficiency
The efficiency of small transformers varies from 0.8 to 0.96. A value of 0.87 can be used for ordinary transformers.
The proper wire size has to be selected for the winding. The wire diameter depends on the current to be supplied by the winding and the allowable current density of the wire. The current density may be as high as 233-amps/sq. cm. in small transformers and as low as 155-amps/sq. cm. in large ones. Usually, a value of 200-amps/sq. cm. can be taken, on whose basis Table I is given. The number of turns in the primary winding is given by:
Primary turns = Turns per volt X primary volts.
The number of turns on the primary and secondary windings is decided by the turns per volt ratio as :
Turns per volt = 1\(4.44 X 10- 4 frequency X core area X flux density)
Here, the frequency is 50Hz for Indian domestic mains supply. The flux density can be taken as about 1.0 Weber/sq, m. for ordinary steel stampings and about 1.3 Weber/sq, m. for CRGO stampings.
Primary winding design
The current in the primary winding is given by:
Sum of (output volts X output amps)
Primary current = -----------------------------------------
Primary volts X efficiency
The efficiency of small transformers varies from 0.8 to 0.96. A value of 0.87 can be used for ordinary transformers.
The proper wire size has to be selected for the winding. The wire diameter depends on the current to be supplied by the winding and the allowable current density of the wire. The current density may be as high as 233-amps/sq. cm. in small transformers and as low as 155-amps/sq. cm. in large ones. Usually, a value of 200-amps/sq. cm. can be taken, on whose basis Table I is given. The number of turns in the primary winding is given by:
Primary turns = Turns per volt X primary volts.
The space taken up by the winding will depend on the insulation thickness, method of winding and the wire diameter. Table I gives the approximate values of the turns per square cm. from which we can estimate the window area occupied by the primary winding.
Primary turns
Primary winding area = ------------------------------------
Turns per sq cm. from Table I
Secondary winding design
Since we have assumed that we know the secondary current rating, we can find out the wire size for the secondary winding by referring to Table I directly.
The number of turns on the secondary is calculated in the same way as for the primary, but about 3% extra turns are to be added to compensate for the internal drop of secondary voltage of the transformer, upon loading.
Primary turns
Primary winding area = ------------------------------------
Turns per sq cm. from Table I
Secondary winding design
Since we have assumed that we know the secondary current rating, we can find out the wire size for the secondary winding by referring to Table I directly.
The number of turns on the secondary is calculated in the same way as for the primary, but about 3% extra turns are to be added to compensate for the internal drop of secondary voltage of the transformer, upon loading.
Thus, Secondary turns = 1.03 (turns per volt X secondary volts)
The window area required for secondary winding is found from Table I as
Secondary turns
Secondary window area = -----------------------------
Turns per sq. cm. from Table I
Core size
The main criterion in selecting the core is the total window area of winding space available.
Total window area = Primary window area + sum of secondary window areas + space for former & insulation.
Some extra area is required to accommodate the former and insulation between windings. The actual amount of extra area varies, although 30% may be taken to start with but may have to be modified later. The suitable core sizes having a larger window area are selected from Table II. Taking into account the gap between laminations while stacking them (the core stacking factor taken as 0.9), we have
Core area
Gross core area = ----------- sq. cm.
0.9
In general, a square central limb is preferred. For this, the width of the tongue of lamination is
The window area required for secondary winding is found from Table I as
Secondary turns
Secondary window area = -----------------------------
Turns per sq. cm. from Table I
Core size
The main criterion in selecting the core is the total window area of winding space available.
Total window area = Primary window area + sum of secondary window areas + space for former & insulation.
Some extra area is required to accommodate the former and insulation between windings. The actual amount of extra area varies, although 30% may be taken to start with but may have to be modified later. The suitable core sizes having a larger window area are selected from Table II. Taking into account the gap between laminations while stacking them (the core stacking factor taken as 0.9), we have
Core area
Gross core area = ----------- sq. cm.
0.9
In general, a square central limb is preferred. For this, the width of the tongue of lamination is
Now refer to Table II again and finally select the proper core size, with sufficient window area and a close value of the tongue width as calculated. Adjust the stack height as required to obtain the required core section.
The stack should not be much less than the tongue width but may be more. However, it should not be more than 1 half times the tongue width.
Assembly
The windings are wound on an insulating former, which fits over the center limb of the core. The primary is usually wound first, then the secondary, with insulation between windings. A final insulating layer is provided over the windings to protect them from mechanical damage.
When thin wires are used, their ends must be soldered to thicker wires for bringing the terminals outside the former. The laminations are assembled over the former with alternate laminations reversed in assembly. The laminations must be held together tightly by a suitable clamping frame or by screws (if holes are provided in the laminations).
Shield
It is a good practice to use an electrostatic shield between the primary and secondary windings to prevent disturbances from passing through to the secondary from the primary. The shield is made out of a copper foil, which is wound between the two windings for slightly over a turn. Insulation must be provided along the length of the foil and care taken so that the two ends of the foil do not touch each other. A wire soldered to the foil is brought out and connected to the ground.
Assembly
The windings are wound on an insulating former, which fits over the center limb of the core. The primary is usually wound first, then the secondary, with insulation between windings. A final insulating layer is provided over the windings to protect them from mechanical damage.
When thin wires are used, their ends must be soldered to thicker wires for bringing the terminals outside the former. The laminations are assembled over the former with alternate laminations reversed in assembly. The laminations must be held together tightly by a suitable clamping frame or by screws (if holes are provided in the laminations).
Shield
It is a good practice to use an electrostatic shield between the primary and secondary windings to prevent disturbances from passing through to the secondary from the primary. The shield is made out of a copper foil, which is wound between the two windings for slightly over a turn. Insulation must be provided along the length of the foil and care taken so that the two ends of the foil do not touch each other. A wire soldered to the foil is brought out and connected to the ground.
Design example
Primary voltage : 230 V
Secondary voltage : 7.5 V
Secondary current : 500 mA
Primary voltage : 230 V
Secondary voltage : 7.5 V
Secondary current : 500 mA
Selecting CRGO as the core material,
Turnspervolt= l/(4.44 X 10-4 X 50 X 2.231 X1.3)= 15.5
Primary current =(7.5 X 0.5)/(230 X 0.87)= 18.7 mA
From Table I, the wire selected is 41 SWG Thus primary turns = 15.5 X 230 = 3565
Primary window area = 3565/6543 =0.5448 sq. cm
Secondary current = 500 mA
From Table I the wire selected is 24 SWG Secondary turns = 1.03 (7.5 X 15.5) = 120 Secondary window area = 120/286 = 0.4196 sq. cm.
Total window area = 1.3 (0.5448 + 0.4196)= 1.2537 sq. cm.
From Table II, note that core No. 12A & 74 are suitable. Gross core area = 2.231/0.9 = 21479 sq. cm.
Turnspervolt= l/(4.44 X 10-4 X 50 X 2.231 X1.3)= 15.5
Primary current =(7.5 X 0.5)/(230 X 0.87)= 18.7 mA
From Table I, the wire selected is 41 SWG Thus primary turns = 15.5 X 230 = 3565
Primary window area = 3565/6543 =0.5448 sq. cm
Secondary current = 500 mA
From Table I the wire selected is 24 SWG Secondary turns = 1.03 (7.5 X 15.5) = 120 Secondary window area = 120/286 = 0.4196 sq. cm.
Total window area = 1.3 (0.5448 + 0.4196)= 1.2537 sq. cm.
From Table II, note that core No. 12A & 74 are suitable. Gross core area = 2.231/0.9 = 21479 sq. cm.
Referring back to Table II, out of the previous selections we finally choose Core No. 12A. Therefore,
2 479
Stack height =--------- =1.56 cm
1.588
Thus, the resultant data are: Primary winding: 3565 turns of 41 SWG wire
Secondary winding: 120 turns of 24 SWG wire Core: Size 12A, Stack height 1.56 cm.
2 479
Stack height =--------- =1.56 cm
1.588
Thus, the resultant data are: Primary winding: 3565 turns of 41 SWG wire
Secondary winding: 120 turns of 24 SWG wire Core: Size 12A, Stack height 1.56 cm.
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