Transformer Design
A transformer transfers electric power from one circuit to another circuit without a change in frequency. It contains primary and secondary winding. The primary winding is connected to the main supply and secondary to the required circuit. In our project circuit, we have taken the design of low power (10 KVA) single phase 50 hertz power transformer as per our requirement in the project.
The transformer is basically of three types:
 Core Type
 Shell Type
 Toroidal
In core, type windings surround a part of the core whereas in shell type core surrounds windings. In the Core type, there are two main types namely EI type and UT type. In this transformer design, we used EI core type. We chose EI core as the winding is much easier when compared to toroidal, but efficiency is very high (95%96%). It is so because flux loss is very less in toroidal cores comparatively.
The transformers employed in the project are
 Series transformer: To provide the required boost or buck voltage and
 Control transformer: For sensing the output voltage and for power supply.
Design Formulas:
Here we take the reference of winding data on enameled copper wire table and dimensions of transformer stampings table to select input and output windings SWG and core of the transformer for given specifications.
The design procedure is followed assuming that the following specification of a transformer are given:
 Secondary voltage (Vs)
 Secondary current (Is)
 Turns ratio (n2/n1)
From these given details we calculate Tongue width, stack height, core type, window area as follows:
 Secondary VoltAmps (SVA) = secondary voltage (Vs) * secondary current(Is)
 Primary VoltAmps (PVA) = Secondary VoltAmps (SVA) / 0.9 (assuming efficiency of the transformer as 90%)
 Primary voltage (Vp)= Secondary voltage(Vs)/ turns ratio(n2/n1)
 Primary current (Ip) = Primary VoltAmps(PVA)/ Primary voltage(Vp)
 The require crosssectional area of the core is given by: Core area (CA) = 1.15 * sqrt (Primary Voltamps(PVA))
 Gross core area (GCA) = Core area(CA) * 1.1
 The number of turns on the winding is decided by the ratio given as: Turns per volt (Tpv) = 1/(4.44 * 104 * core area* frequency * flux density)
Winding data on Enameled copper wire
(@ 200A/cm²)
Max. Current Capacity (Amp.) 
Turns/Sq. cm 
SWG 
Max. Current Capacity (Amp.) 
Turns/Sq. cm 
SWG 

0.001 
81248 
50 
0.1874 
711 
29 

0.0015 
62134 
49 
0.2219 
609 
28 

0.0026 
39706 
48 
0.2726 
504 
27 

0.0041 
27546 
47 
0.3284 
415 
26 

0.0059 
20223 
46 
0.4054 
341 
25 

0.0079 
14392 
45 
0.4906 
286 
24 

0.0104 
11457 
44 
0.5838 
242 
23 

0.0131 
9337 
43 
0.7945 
176 
22 

0.0162 
7755 
42 
1.0377 
137 
21 

0.0197 
6543 
41 
1.313 
106 
20 

0.0233 
5595 
40 
1.622 
87.4 
19 

0.0274 
4838 
39 
2.335 
60.8 
18 

0.0365 
3507 
38 
3.178 
45.4 
17 

0.0469 
2800 
37 
4.151 
35.2 
16 

0.0586 
2286 
36 
5.254 
26.8 
15 

0.0715 
1902 
35 
6.487 
21.5 
14 

0.0858 
1608 
34 
8.579 
16.1 
13 

0.1013 
1308 
33 
10.961 
12.8 
12 

0.1182 
1137 
32 
13.638 
10.4 
11 

0.1364 
997 
31 
16.6 
8.7 
10 

0.1588 
881 
30 
Dimension of Transformer stampings (Core table):
Type Number 
Tongue Width (cm) 
Window Area (Sq. cm) 
Type Number 
Tongue Width (cm) 
Window Area (Sq. cm) 

17 
1.27 
1.213 
9 
2.223 
7.865 

12A 
1.588 
1.897 
9A 
2.223 
7.865 

74 
1.748 
2.284 
11A 
1.905 
9.072 

23 
1.905 
2.723 
4A 
3.335 
10.284 

30 
2 
3 
2 
1.905 
10.891 


1.588 
3.329 
16 
3.81 
10.891 

31 
2.223 
3.703 
3 
3.81 
12.704 

10 
1.588 
4.439 
4AX 
2.383 
13.039 

15 
2.54 
4.839 
13 
3.175 
14.117 

33 
2.8 
5.88 
75 
2.54 
15.324 

1 
1.667 
6.555 
4 
2.54 
15.865 

14 
2.54 
6.555 
7 
5.08 
18.969 

11 
1.905 
7.259 
6 
3.81 
19.356 

34 
1.588 
7.529 
35A 
3.81 
39.316 

3 
3.175 
7.562 
8 
5.08 
49.803 
For operation on mains supply, the frequency is 50HZ, while the flux density can be taken as 1Wb/sq cm. for ordinary Steel stampings and 1.3Wb/sq cm for CRGO stampings, depending on the type to be used.
Hence
 Primary turns (n1) = Turns per volt(Tpv) * Primary voltage(V1)
 Secondary turns (n2) = Turns per volt(Tpv) * secondary voltage(V2) * 1.03 (Assume that there is 3% drop in transformer windings)
 The width of the tongue of laminations is approximately given by:
Tongue width (Tw) = Sqrt * (GCA)
Current density
It is the current carrying capacity of a wire per unit cross sectional area. It is expressed in units of Amp/ cm². The above mentioned wire table is for a continuous rating at current density of 200A/cm². For noncontinuous or intermittent mode of operation of transformer one can choose a higher density up to 400A/cm² i.e., twice the normal density to economize the unit cost. It is opted as, the temperature rise for the intermittent operational cases are less for the continuous operational cases.
So depending on the current densities choosen we now calculate the values of primary and secondary currents that are to searched in wire table for selecting SWG:
n1a = Primary current (Ip) calculated / (current density/200)
n2a = Secondary current (Is) calculated / (current density/200)
For these values of primary and secondary currents we choose the corresponding SWG and Turns per sqcm from the wire table. Then we proceed to calculate as follows:
 Primary area(pa)= Primary turns(n1) / (Primary turns per sqcm)
 Secondary area(sa)= Secondary turns(n2) / (Secondary turns per sqcm)
 The total window area required for the core is given by:
Total area (TA) = Primary area (pa) + Secondary area (sa)
 Extra space required for the former and insulation may be taken as 30% extra space of what is required by the actual winding area. This value is approximate and may have to be modified, depending on the actual winding method.
Window area (Wacal) = Total area (TA) * 1.3
For the above calculated value of tongue width, we choose core number and window area from the core table ensuring that the window area chosen is greater than or equal to the Gross core area. If this condition is not satisfied we go for a higher tongue width ensuring the same condition with a corresponding decrease in the stack height so as to maintain approximately constant gross core area.
Thus we get available tongue width (Twavail) and window area ((avail)(aWa)) from the core table
 Stack Height = Gross core area / Tongue width ((available) (atw)).
For commercially available former size purposes, we approximate stack height to tongue width ratio to the nearest following figures of 1.25, 1.5, 1.75. At the worst case we take the ratio equal to 2. However any ratio till 2 can be taken which would call for making ones own former.
If the ratio is greater than 2 we select a higher tongue width (aTw) ensuring all the conditions as above.
 Stack height(ht) / tongue width(aTw) = (some ratio)
 Modified stack height = Tongue width(aTw) * Nearest value of standard ratio
 Modified Gross core area = Tongue width (aTw) * Modified stack height.
Same design procedure applies for control transformer, where in we need to ensure that stack height equals Tongue width.
Thus we find core number and stack height for the given specifications.
Designing a transformer using an example:
 The given details are as follows:
 Sec. voltage(Vs) = 60V
Sec current(Is) = 4.44A
 Turns per ratio (n2/n1) = 0.5
Now we have to calculations as follows:
 Sec.VoltAmps(SVA) = Vs * Is = 60 * 4.44 =266.4VA
 Prim.VoltAmps(PVA) = SVA / 0.9 = 296.00VA
 Prim.Voltage (Vp) = V2 / (n2/n1) = 60/0.5= 120V
 Prim.current (Ip) = PVA/Vp = 296.0/ 120 = 2.467A
 Core Area(CA) = 1.15 * sqrt(PVA) = 1.15 * sqrt(296) = 19.785 cm²
 Gross core area(GCA) = CA * 1.1 = 19.785 * 1.1 = 21.76 cm²
 Turns per volt(Tpv) = 1 / (4.44 * 104 * CA *frequency * Flux density) = 1 / (4.44 * 104 * 19.785 * 50 *1) = 2.272 turns per volt
 Prim.Turns(N1) = Tpv * Vp = 2.276 * 120 = 272.73 turns
 Sec.Turns(N2) = Tpv * Vs * 1.03 = 2.276 * 60 * 1.03 = 140.46 turns
 Tongue width(TW) = Sqrt*(GCA) = 4.690 cm
 We are choosing the current density as 300A/cm², but the current density in the wire table is given for 200A/cm², then
 Primary current search value = Ip / (current density/200) = 2.467 / (300/200) = 1.644A
 Secondary current search value = Is / (current density/200) = 4.44 / (300/200) = 2.96A
For these values of primary and secondary currents we choose the corresponding SWG and Turns per sqcm from the wire table.
SWG1=19 SWG2=18
Turn per sqcm of primary = 87.4 cm² turns per sqcm of secondary =60.8 cm²
 Primary area(pa) = n1 / turns per sqcm(primary) = 272.73 / 87.4 = 3.120 cm²
 Secondary area(sa) = n2 / turns per sqcm(secondary) = 140.46 / 60.8 = 2.310 cm²
 Total area(at) = pa + sa = 3.120 + 2.310 = 5.430 cm²
 Window area (Wa) = total area * 1.3 = 5.430 * 1.3 = 7.059 cm²
For the above calculated value of tongue width, we choose core number and window area from the core table ensuring that the window area chosen is greater than or equal to the Gross core area. If this condition is not satisfied we go for a higher tongue width ensuring the same condition with a corresponding decrease in the stack height so as to maintain approximately constant gross core area.
Thus we get available tongue width (Twavail) and window area ((avail)(aWa)) from the core table:
 So tongue width available (atw) = 3.81cm
 Window area available (awa) = 10.891 cm²
 Core number = 16
 Stack Height = gca / atw = 21.99 / 3.810 = 5.774cm
For performance reasons, we approximate stack height to tongue width (aTw) ratio to the nearest following figures of 1.25, 1.5, and 1.75. At the worst case we take the ratio equal to 2.
If the ratio is greater than 2 we select a higher tongue width ensuring all the conditions as above.
 Stack height(ht) / tongue width(aTw) = 5.774 / 3.81 = 1.516
 Modified stack height = Tongue width(aTw) * Nearest value of standard ratio = 3.810 * 1.516 = 5.715cm
 Modified Gross core area = Tongue width (aTw) * Modified stack height = 3.810 * 5.715 = 21.774 cm²
Thus we find core number and stack height for the given specifications.
Design of a small control transformer with example:
The given details are as follows:
 Sec. voltage(Vs) = 18V
 Sec current(Is) = 0.3A
 Turns per ratio (n2/n1) = 1
Now we have to calculations as follows:
 Sec.VoltAmps(SVA) = Vs * Is = 18 * 0.3 = 5.4VA
 Prim.VoltAmps(PVA) = SVA / 0.9 = 5.4 / 0.9 = 6VA
 Prim. Voltage (Vp) = V2 / (n2/n1) = 18/1 = 18V
 Prim. current (Ip) = PVA/Vp = 6 / 18 = 0.333A
 Core Area(CA) = 1.15 * sqrt(PVA) = 1.15 * sqrt(6) = 2.822 cm²
 Cross core area(GCA) = CA * 1.1 = 2.822 * 1.1 = 3.132 cm²
 Turns per volt(Tpv) = 1 / (4.44 * 104 * CA *frequency * Flux density) = 1 / (4.44 * 104 * 2.822 * 50 *1) = 15.963 turns per volt
 Prim. Turns(N1) = Tpv * Vp = 15.963 * 18 = 287.337 turns
 Sec.Turns(N2) = Tpv * Vs * 1.03 = 15.963 * 60 * 1.03 = 295.957 turns
 Tongue width(TW) = Sqrt*(GCA) = sqrt * (3.132) = 1.770 cm
We are choosing the current density as 200A/cm², but the current density in the wire table is given for 200A/cm², then
 Primary current search value = Ip / (current density/200) = 0.333 / (200/200) = 0.333A
 Secondary current search value = Is / (current density/200) = 0.3 / (200/200) = 0.3A
For these values of primary and secondary currents we choose the corresponding SWG and Turns per Sq. cm from the wire table.
SWG1=26 SWG2=27
Turn per Sq. cm of primary = 415 turns Turns per Sq. cm of secondary = 504 turns
 Primary area(pa) = n1 / turns per sqcm(primary) = 287.337 / 415 = 0.692 cm²
 Secondary area(sa) = n2 / turns per sqcm(secondary) = 295.957 / 504 = 0.587 cm²
 Total area(at) = pa + sa = 0.692 + 0.587 = 1.280 cm²
 Window area (Wa) = total area * 1.3 = 1.280 * 1.3 = 1.663 cm²
For the above calculated value of tongue width, we choose core number and window area from the core table ensuring that the window area chosen is greater than or equal to the Gross core area. If this condition is not satisfied we go for a higher tongue width ensuring the same condition with a corresponding decrease in the stack height so as to maintain approximately constant gross core area.
Thus we get available tongue width (Twavail) and window area ((avail)(aWa)) from the core table
 So tongue width available (atw) = 1.905cm
 Window area available (awa) = 18.969 cm²
 Core number = 23
 Stack Height = gca / atw = 3.132 / 1.905 = 1.905cm
Hence the control transformer is designed.
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