# Design of High Frequency Pulse Transformer

We were commonly aware of 50 Hz fundamental frequency in Distribution and Power Transformers which are commonly used in the chain of Power Generation, Transmission and Distribution network. The main purpose of transformer is to either step up or step down the voltage level of power at various point of network for efficient power transmission and distribution.The power at generating stations is generated at low voltage and high current so as to minimize the ohmic loss in the lines and to transfer the power to the load centers with less power loss efficiently this low voltage level of power is to be stepped up to reduce line current hence to reduce ohmic loses and to get better voltage regulation. Since in this journey of power from generating stations to the load centers, due to line resistance there will be ohmic loss and due to the line impedance there will be voltage fall or poor voltage regulation. For efficient distribution and supply this high voltage power is again stepped down at desired distribution and supply voltage level. All the way the frequency of the transformer and power remain constant.

## What is High frequency Transformers or Pulse Transformer

As the name prefaces the operating frequency of these transformers would be typically around few hundred kilo hertz. The main significance of these transformers is in “Switched Mode Power Supplies”. The main conceptual idea of Switched Mode Power Supply is that it is using energy efficient devices to transfer/convert the Power (A.C./D.C) from the source to the sink/load. One such energy efficient device is High Frequency Pulse Transformer. The switching frequency of these SMPSs (Switched Mode Power Supply) system will be very high as a concern it reduces the size of magnetics (like transformer and inductor) and and it reduces the ripple and so on. In later sessions we will be discussing about complete design of High frequency transformer from fundamentals for a DC-DC converter as an application.## High Frequency Transformer Designing

There are two main core requirements of High Frequency Transformer in the SMPS system.- To match the voltage levels of Source and the Load
- To provide electrical isolation between the power circuits.

The schematic diagram of the Transformer is as shown below, We can basically categorize the transformer circuitry as “Electrical Circuit” and “Magnetic Circuit”. The electrical equivalent circuit of a transformer is shown below, Where primary electric circuit is represented with a current source representing the relation and secondary electrical circuit is represented with a voltage source representing the relation

The magnetic equivalent circuit is shown taking a Toroid Core as magnetic medium for common flux,
Where μ= permeability of the magnetic medium
V_{1} = primary voltage
V_{2}= Secondary voltage
N_{1}= Primary turns
N_{2}= Secondary turns
A_{c}= Effective Core Area.
I_{1} = Primary Current
I_{2} = Secondary Current
The normal frequency (50HZ) transformer is classified depending on the Core used as

- Core type transformer
- Shell type transformer

Generally Shell type core is preferred for High frequency transformer. The prime reason for selecting shell type topology of core for high frequency application is the 3^{rd} harmonic components will circulate with in primary without entering in to the secondary power circuit which is similar to “delta connection”. Also as the flux divides in the outer limbs it offers less core losses. The commonly used shell core is EE - Core. In general CRGO (Cold Rolled Grain Oriented) Silicon Steel Ferromagnetic material is used as magnetic core for Power transformers and Distribution transformers. How so ever in some of the distribution transformers “Amorphous Core” is used. But in High frequency transformers generally “Ferrite Cores” are used. Commonly for frequencies less than 5 MHz manganese-zinc ferrites are used above which nickel-zinc ferrites are of common choice. These ferrites offers very low coercivity, that means the material's magnetization can easily in reverse direction without dissipating much energy (hysteresis losses), Even they do not need core lamination to reduce “Eddy Current” losses as the Powder core itself offers High resistance. Only concern with ferrites is its operating maximum flux density is limited to maximum of 0.5 T while it is a maximum of 2.2 T for ferromagnetic cores and 1.8 T for amorphous cores.

Popularly EE Cores is used to form the Shell type High frequency transformer. Its geometric version is as shown below,
Where A_{c} = Effective Core Area of the transformer where the actual magnetic flux passes. A_{w} = Window Area, which provides the accommodation to primary winding, secondary winding and a portion of it to the insulation. Deducing a relation for A_{c} (Core Area) and A_{w} (Window Area) :
The high frequency transformers are also called Pulse transformer as the input voltage wave form commonly applied to it is a pulse train as depicted in the figure below. The flux waveform is also shown in it which is integral of voltage waveform from the relation
Faradays law of electromagnetic induction.
Where T_{s} = total switching time period
**A) From the above waveform we shall now derive a relationship for Aw (Core Area) :**
**B) Secondly we shall derive an equation for Aw (Window Area) :**
Let, a_{1} = area of primary winding
a_{2} = area of secondary winding
J = Current density of copper
K_{w} = window space factor.
N_{1}, N_{2}, I_{1}, I_{2} = No. of turns and current corresponding to primary and secondary respectively.
As discussed earlier Window area of a transformer provides accommodation for primary and secondary winding. But entire window area is not used for the winding a portion of it is used for insulation therefore a factor K_{w} is introduced which is called window space factor or window utilization factor.
From equation 1 and equation 2,

##### Now consider an example of DC-DC converter

V_{1}= 48 V, V

_{2}= 400 V and I

_{2}= 3 A. High Frequency (50 kHz) Application. Now we need to design transformer for above application, Assumptions: Let the B

_{m}= 0.2 T, J = 3 A/mm2, K

_{w}= 0.35. Step 1: Selection of Core. From the equation (3) that we have derived, there substituting all the values and finding the value of window and core area. After we derive this value, from the data sheets of the Core we need to select the appropriate core. A typical data for ETD Cores is given below,

#### ETD Core Series Data

Type Number | A_{c} (mm^{2}) | A_{w} (mm^{2}) | A_{c}A_{w} (mm^{4}) |

ETD 29/16/10 | 76 | 128 | 9728 |

ETD 34/17/11 | 97 | 171 | 16587 |

ETD 39/20/13 | 125 | 234 | 29250 |

ETD 44/22/15 | 173 | 279 | 48267 |

ETD 49/25/16 | 211 | 343 | 72373 |

ETD 54/28/19 | 280 | 412 | 115360 |

ETD 59/31/22 | 368 | 473 | 174064 |

_{1}and N

_{2})

`NOTE: The Core Area (Ac) Value is taken from the ETD/49/25/16 Core `

Step 3: Deriving primary and secondary conductor size/gauge(a_{1}and a

_{2}) Generally for copper conductor the current density ‘J’ is taken as 3A / mm

^{2}. Step 4: Deriving primary resistances and secondary resistances. Once on calculating the mean length of the turn from the geometry of ETD/49/25/16 core the resistance is derived from formula, For ETD 49/25/16 core mean length of a turn = 83 mm Primary Resistance = 10 μΩ, Secondary resistance = 629 μΩ Step 5: Deriving primary inductance and secondary inductance. Note: The value of ‘l

_{e}’ and ‘A

_{c}’ is taken from the core magnetic characteristics as shown in the below for ETD 49/25/16 Core. The value of ‘μ

_{r}/ μ

_{e}’ is taken from core material characteristics. For instance let the core material is “ungapped N27 material”. The data for ETD 49/25/16 Core is shown below. This completes the

**design of High frequency Pulse Transformer**.