Transformer Designing | The Definitive Guide

Q: How do you design a transformer?

The details shown are as follows: Sec. voltage (Vs) = 60V Sec current (Is) = 4.44A Turn per ratio (n2 / n1) = 0.5 Now we have to calculate as follows: Sec.Volt-Amps (SVA) = Vs * Is = 60 * 4.44 = 266.4VA Prim.Volt-Amps (PVA) = SVA/0.9 = 296.00VA Primary 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 * 10-4 * CA * frequency * Flux density) = 1/(4.44 * 10-4 * 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 in the table of wires the current density is given for 200A/cm², then Primary current detection value = Ip/(current density/200) = 2.467/(300/200) = 1.644A Secondary current detection value = is/(current density/200) = 4.44/(300/200) = 2.96A

Q: What is the transformer formula?

Vp = −NpΔΦΔt V p = - N p Δ Φ Δ t. This equation is known as the transformer equation, and it simply states that the ratio of the secondary and primary voltages in the transformer is equal to the ratio of the number of loops in their coils.

A transformer transfers power from one circuit to another without any change in frequency. There are two types of windings in a transformer, one is primary winding and the other is secondary winding. This involves connecting the primary winding to the main supply while the secondary winding is connected to the required circuit.

In our project circuit, we have taken the design of low power (10 KVA) single-phase 50 Hz power transformer as per our project requirement.

There are basically three types of transformers in the market which are as follows:

Core Type.
Shell Type.
Toroidal.

The type winding in the core encloses a part of the core while the shell type encircles the core winding. There are two main types of core such as E-I type and U-T type. In such a transformer we have used the E-I core type. We have chosen the E-I core as the winding is very easy compared to the toroidal, but the efficiency is very high approximately 95 to 96%. This is because the flux loss in the toroidal core is relatively low.

The transformers used in the project are as follows:

Series Transformer: Used to give the required boost or buck.

Control Transformer: This is used to sense the output voltage and for the power supply.

Suggested Read: What is a Single Phase Transformer

In This Post

Transformer Designing Formula:

We refer to the winding data on the parameters of the enameled copper wire table and the transformer stamping table to select the input and output winding SWG and transformer core for the specification shown here.

The design process is followed by assuming that the following specifications of a transformer are given:

Secondary voltage (Vs).
Secondary current (Is).
Turns ratio (n2 / n1).

From the details given here, we calculate the width of the tongue, the height of the stack, the core type, and the window area as follows:

Secondary Volt-Amps (SVA) = Secondary Voltage (Vs) * Secondary Current (Is)
Primary volt-amps (PVA) = secondary volt-amps (SVA)/0.9
(Assuming 90% efficiency of the transformer)
Primary voltage (Vp) = secondary voltage (Vs)/turn ratio (n2/n1)
Primary current (Ip) = primary volt-amps (PVA)/primary voltage (Vp)
The required cross-sectional area of the core is given by: – Core area (CA) = 1.15 * square (Primary Volt-AMPS (PVA))
Gross Core Area (GCA) = Core Area (CA) * 1.1
The number of turns on the winding can be determined by a given ratio
Turn per Volt (TPV) = 1/4.44 * 10-4 * Core Area * Frequency * Flux Density)

Data of winding on the enameled copper wire:

Max. Current Capacity (Amp.)	Turns/Sq. cm	SWG
0.001	81248	50
0.0015	62134	49
0.0026	39706	48
0.0041	27546	47
0.0059	20223	46
0.0079	14392	45
0.0104	11457	44
0.0131	9337	43
0.0162	7755	42
0.0197	6543	41
0.0233	5595	40
0.0274	4838	39
0.0365	3507	38
0.0469	2800	37
0.0586	2286	36
0.0715	1902	35
0.0858	1608	34
0.1013	1308	33
0.1182	1137	32
0.1364	997	31
0.1588	881	30
0.1874	711	29
0.2219	609	28
0.2726	504	27
0.3284	415	26
0.4054	341	25
0.4906	286	24
0.5838	242	23
0.7945	176	22
1.0377	137	21
1.313	106	20
1.622	87.4	19
2.335	60.8	18
3.178	45.4	17
4.151	35.2	16
5.254	26.8	15
6.487	21.5	14
8.579	16.1	13
10.961	12.8	12
13.638	10.4	11
16.6	8.7	10

Dimension of transformer stamping (Core table):

Type Number	Tongue Width (cm)	Window Area (sq. cm)
17	1.27	1.213
12A	1.588	1.897
74	1.748	2.284
23	1.905	2.723
30	2	3
–	1.588	3.329
31	2.223	3.703
10	1.588	4.439
15	2.54	4.839
33	2.8	5.88
1	1.667	6.555
14	2.54	6.555
11	1.905	7.259
34	1.588	7.529
3	3.175	7.562
9	2.223	7.865
9A	2.223	7.865
11A	1.905	9.072
4A	3.335	10.284
2	1.905	10.891
16	3.81	10.891
3	3.81	12.704
4AX	2.383	13.039
13	3.175	14.117
75	2.54	15.324
4	2.54	15.865
7	5.08	18.969
6	3.81	19.356
35A	3.81	39.316
8	5.08	49.803

The frequency to work on the main supply is 50Hz, while the density of the current can be taken as 1Wb/square cm. 1.3Wb/sq. Cm for the general type of steel stamping and for CRGO stamping, depending on the type used.

Hence

Primary turn (n1) = Turns per volt (TPV) * Primary voltage (V1)
Secondary winding (n2) = Turns per volt (TPV) * Secondary voltage (V2) * 1.03 (Suppose the transformer windings have a 3% reduction)
The width of the lamination tongue is given by approx.
Tongue width (Tw) = Sqrt * (GCA)

Current Density:

Here the unit is the current carrying capacity of the wire per cross-sectional area. It is expressed in units of Amp/cm². The wire table shown above is for continuous rating at a current density of 200A/cm². One can choose a high density up to 400A/cm² for an uninterrupted or intermittent mode of transformer operation.

That is double the normal density to make the unit cost economical. For continuous operational cases, it is preferred for intermittent operational cases as the temperature rise is low.

So based on the selected current density we now calculate the value of primary and secondary current which is to be found in the wire table for selecting SWG:

n1a = Primary current (Ip) calculated/(current density/200)
n2a = Secondary current (Is) calculated/(current density/200)

For the value of primary and secondary current, we select the corresponding SWG and turn per square from the wire table shown above. We then proceed to the following calculation.

Primary area (pa) = Primary turns (n1)/(Primary turns per sq cm)
Secondary area (sa) = Secondary turns (n2)/(Secondary turns per sq cm)
The total window area required for the core is given by: –
Total area (TA) = Primary area (pa) + Secondary area (sa)

The former requires additional space and the insulation can be taken as 30% of the additional space required by the actual winding area. This value is approximate and may need to be modified depending on the actual winding method.

Window area (Wacal) = Total area (TA) * 1.3

For the calculated value above the width of the tongue, we select the core number and window area from the core table to make sure that the window area is greater than or equal to the gross core area.

If not satisfied with this position we go for higher tongue width. This ensures a uniform position with a corresponding reduction in stack height so that an approximately stable total main area is maintained.

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 pre-shaped purposes we estimate the ratio of the height of the stack to the width of the tongue for the following figures close to 1.25, 1.5, 1.75. In the worst case, we take the ratio equal to 2. However, any ratio up to 2 can be taken which would call for making one’s own former.

If the ratio is greater than 2, we choose a higher tongue width (aTw) by ensuring all the conditions outlined above.

Stack height(ht)/tongue width(aTw) = (some ratio)
Modified stack height = Tongue width(aTw) * Nearest value of the standard ratio
Modified Gross core area = Tongue width (aTw) * Modified stack height.

A similar design procedure applies to the control transformer, where we need to make sure that the height of the stack is equal to the width of the tongue.

Suggested Read: Difference Between Step-up And Step-Down Transformer

Transformer Design Calculation:

The details shown are as follows:

Sec. voltage (Vs) = 60V
Sec current (Is) = 4.44A
Turn per ratio (n2 / n1) = 0.5

Now we have to calculate as follows:

Sec.Volt-Amps (SVA) = Vs * Is = 60 * 4.44 = 266.4VA
Prim.Volt-Amps (PVA) = SVA/0.9 = 296.00VA
Primary 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 * 10-4 * CA * frequency * Flux density) = 1/(4.44 * 10-4 * 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 in the table of wires the current density is given for 200A/cm², then
Primary current detection value = Ip/(current density/200) = 2.467/(300/200) = 1.644A
Secondary current detection value = is/(current density/200) = 4.44/(300/200) = 2.96A

For the values of primary and secondary currents, we select the corresponding SWG and turn per square from the wire table.

SWG1 = 19 SWG2 = 18

Turn per sq cm of primary = 87.4 cm²

Turns per sq cm of secondary = 60.8 cm²

Primary area (pa) = n1/turns per sq cm (primary) = 272.73/87.4 = 3.120 cm²
Secondary area (sa) = n2 / turns per sq cm (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 the width of the tongue, we select the core number and window area from the core table to ensure that the window area is greater than or equal to the gross core area. If this position is not satisfied we go for the width of the tongue which ensures a uniform position with a corresponding reduction in the height of the stack so that an approximately stable total main area is maintained.

Thus the width of the tongue and the window area are obtained from the main 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 estimate the height of the stack with the following tongue width ratio close to 1.25, 1.5, and 1.75. In the worst case, we take the ratio 2 exactly.

If the ratio is greater than 2 we choose the width of the upper tongue to ensure all the conditions outlined 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 the core number and stack height for the given specifications.

Custom Transformer Design:

Custom-made transformers are uniquely designed for related parameters, physical constraints, and termination. So they offer more effective solutions than standard transformers that may not fit properly. Equipped with various advanced custom transformer winding equipment enables the quality and fast change time provided by us in the vast industry.

Suggested Read: What is Armature Winding | Types of Armature Winding

Custom Wound Transformers:

Custom Wound Transformers are used to step up, step down and isolate the voltage. Isolation can be used to help provide secondary-side immunity from primary-side spot voltage spikes and noise.

Isolation allows separate ground on both the input and output sides of the transformer. Osborne designs with a range of electrostatic shielding to provide many levels of sound immunity.

Flyback Transformer Calculation:

The flyback voltage VOR is equal to VO (the secondary Vout plus the VF for the secondary diode D6) multiplied by the transformer winding ratio Np: Ns. Setting the flyback voltage VOR determines the winding ratio Np: Ns and the Duty ratio.

Core	Size
Lp	Inductance
Np	Number of turns
Ns	Number of turns
Nd	Number of turns

Most Commonly Asked Questions:

Most Commonly Asked Questions

What are the design parameters of the transformer?

The calculated design parameters include the required core cross-section primary turn/current and secondary turn/current. During the design process of a transformer, the design engineers need to quickly verify that their design meets the various interrelated transformer design requirements.

What Is the Basic Design of a Transformer?

The two most common and basic designs of transformer construction are closed-core transformers and shell-core transformers. In a “closed-core” type (core form) transformer, the primary and secondary windings are wound outside and around the core ring.

How do you design a transformer?