Transformer Construction & EMF Equation

• Construction

• Working Principle

• EMF Equation

• Transformation Ratio (K)

• Rating of a Transformer

• Losses in a Transformer

• Ideal and Practical Transformers

• Phasor Diagram of a Transformer on No Load

• Phasor Diagram of a Transformer on Load

• Equivalent Circuit

• Voltage Regulation

• Efficiency

• Open Circuit (OC) Test and Short-Circuit (SC) Test

• Static device which can transfer electrical energy from one circuit to another circuit without change of frequency .

• \(V~\uparrow~\Rightarrow~I~\downarrow\) and vice versa

• Works on the principle of mutual induction .

• Works with ac voltage i.e. time varying.

• A major application is to increase voltage before transmitting electrical energy over long distances through wires and to reduce voltage at places where it is to be used.

• Used in electronic circuits to step down the supply voltage to a level suitable for the low-voltage circuits they contain.

• Signal and audio transformers are used to couple stages of amplifiers and to match devices such as microphones to the input of amplifiers.

• Mainly consists of two coils or windings placed on a common core.

• With the increase in size (capacity) and operating voltage, it also needs other parts such as a suitable tank, bushing, conservator, breather, etc.

• Two basic parts— core and windings will be discussed.

Transformer Core:

• composition depends on voltage, current and frequency

• core materials are soft iron and steel

• Air-core transformers are used when the voltage source has a high frequency (above 20 kHz) and Iron-core when frequency is low (below 20 kHz).

• constructed of laminated steel to provide a continuous magnetic path

• high-grade silicon steel is used where hysteresis loss is very low

• alternating flux induced eddy currents in the core.

• cause eddy current loss in the core

• Silicon content in the steel increases its resistivity to eddy-current loss, thereby reducing eddy-current losses.

• To reduce eddy-current losses further, the core is laminated by a light coat of varnish or by an oxide layer on the surface

• two main shapes of cores used in laminated steel-core transformers
  

  

Transformer Windings:

• Two coils, called windings, are wrapped around a core

• primary winding in which electrical energy is fed

• secondary winding which is connected to the load

• Windings made up of an insulated copper conductor in the form of a round wire or strip

• The windings are insulated from each other and the core, using cylinders of insulating material such as a press board or Bakelite

• For simplicity, the primary and secondary windings are shown on separate limbs of the core.

• If such an arrangement is used in actual practice, all the flux produced in the primary winding will not link with the secondary winding.

• Some of the flux will leak out through the air known as leakage flux

• leakage flux cause poor performance of the transformer.

• Hence, to reduce leakage flux, the windings are placed together on the same limb in actual transformers

• When an alternating voltage \(V_1\) is applied to a primary winding, an alternating current \(I_1\) flows in it producing an alternating flux in the core.

• \[e_{1}=-N_{1}{\frac{d\phi}{d t}}\]
  is induced in the primary winding. As per Faraday’s laws of electromagnetic induction, an emf

• Assuming leakage flux to be negligible, almost the whole flux produced in the primary winding links with the secondary winding.

• \[e_{2}=-N_{2}{\frac{d\phi}{d t}}\]
  is induced in the secondary winding. Hence, an emf

• Thus, energy transfer from primary to secondary winding

• If \(N_2>N_1~\Rightarrow\) step-up transformer

• If \(N_2<N_1~\Rightarrow\) called a step-down transformer

• step-up transformer increase the voltage at the output, whereas a step-down transformer is used to decrease the voltage at the output.

• \[\phi = \phi_m\sin\omega t\]
  sinusoidally varying flux in the core alternating current flows in the winding sinusoidal alternating voltage Primary winding
• \[\begin{aligned} e_1& =-N_{1}\frac{d\phi}{d t} \\ &=-N_1\frac{d}{dt}(\phi_m\sin\omega t) \\ &=-N_1\phi_m\omega\cos\omega t \\ &=N_1\phi_m\omega\sin{(\omega t-90^{\circ})} \\ &=2\pi f\phi_m N_1\sin{(\omega t-90^{\circ})} \end{aligned}\]
  is induced in the primary winding. As per Faraday’s laws of electromagnetic induction, an emf

• Maximum value of induced emf \(=2\pi f\phi_m N_1\)

• \[E_1=\frac{E_{\max}}{\sqrt{2}}=\boxed{\frac{2\pi f\phi_mN_1}{\sqrt{2}}=4.44f\phi_m N_1}\]
  RMS value of induced emf in primary winding
• \[\begin{aligned} &\boxed{E_2 =4.44f\phi_m N_2 } \\ \text{Note:}~ \Rightarrow~&\boxed{\frac{E_{1}}{N_{1}} =\frac{E_2}{N_2}=4.44f\phi_m } \end{aligned}\]
  RMS value of induced emf in the secondary winding

• Thus, emf per turn is same in primary and secondary windings

• Also equal emf is induced in each turn of the primary and secondary windings.

• The rating of a transformer indicates the output power from it.

• Load is not fixed and power factor continuously changes.

• Rating is not expressed in terms of power but in terms of the product of voltage and current, known as the VA rating.

• \[\text{kVA rating of a transformer} = \frac{V_{1}I_{1}}{1000}=\frac{V_{2}I_{2}}{1000}\]
  Rating is generally expressed in kilovolt-ampere (kVA).

• We can calculate full-load currents of primary and secondary windings from kVA rating of a transformer.

• \[\begin{aligned} \text{Full-load primary current}~ I_1 & =\frac{\mathrm{kVA rating}\times1000}{V_1}\\ \text{Full-load secondary current}~ I_2 & =\frac{\mathrm{kVA~rating}\times1000}{V_2} \end{aligned}\]
  Full-load current is the maximum current which can flow through the winding without damaging it.