**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

**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****:**

**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?**

**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

**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.

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Many thanks for posting this informative paper -much appreciated

This explanation is awesome thank you ❤