Chapter 1. Theory and Principles

Chapter 1. Theory and Principles - 1 Theory and Principles...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon
1 Theory and Principles Denni s J. Al lan Merlin Design Harold Mo ore H. Moore and Assoc iates 1.1 Air Core Transformer. ......................................................... 1 -1 1.2 Iron or Steel Core Transformer . ......................................... 1 -2 1.3 Equivalent Circuit of an Iron-Core Transformer . ............ 1 -4 1.4 The Practical Transformer . ................................................. 1 -8 Magnetic Circuit . Leakage Reactance . Load Losses . Short-Circuit Forces . Thermal Considerations . Voltage Considerations Transformers are dev ices that transfer energ y from one circuit to another by means of a common magnetic field. In all cases except autotransformers, there is no direct electrical connection from one circuit to the other. When an alternating current flows in a conductor, a magnetic field exists around the conductor, as illustrated in Figure 1.1 . If another conductor is placed in the field created by the first conductor such that the flux lines link the second conductor, as shown in Figure 1.2 , then a voltage is induced into the second conductor. The use of a magnetic field from one coil to induce a voltage into a second coil is the principle on which transformer theory and application is based. 1.1 Air Core Transformer Some small transformers for low-power applications are constructed with air between the two coils. Such transformers are inefficient because the percentage of the flux from the first coil that links the second coil is small. The voltage induced in the second coil is determined as follows. E ¼ Nd f = dt 10 8 (1 : 1) where N is the number of turns in the coil d f = dt is the time rate of change of flux linking the coil f is the flux in lines At a time when the applied voltage to the coil is E and the flux linking the coils is f lines, the instantaneous voltage of the supply is: e ¼ p 2 E cos v t ¼ f = dt 10 8 (1 : 2) d f = dt ¼ ( p 2 cos v t10 8 ) = N( 1 : 3) The maximum value of f is given by: f ¼ ( p 2E10 8 ) = (2 p fN ) (1 : 4) ß 2006 by Taylor & Francis Group, LLC.
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Using the MKS (metric) system, where f is the flux in webers, E ¼ N d f = dt (1 : 5) and f ¼ ( p 2E) = (2 p f N ) (1 : 6) Since the amount of flux f linking the second coil is a small percentage of the flux from the first coil, the voltage induced into the second coil is small. The number of turns can be increased to increase the voltage output, but this wi ll increase costs. The need then is to increase the amount of flux from the first coil that links the second coil. 1.2 Iron or Steel Core Transformer The abilit y of iron or steel to carr y magnetic flux is much greater than air. This abilit y to carr y flux is called permeabilit y. Modern electrical steels have permeabilities in the order of 1500 compared w ith 1.0 for air. This means that the abilit y of a steel core to carr y magnetic flux is 1500 times that of air. Steel cores were used in power transformers when alternating current circuits for distribution of electrical energ y were first introduced. When two coils are applied on a steel core, as illustrated in Figure 1.3 , almost 100% of the flux from coil 1 circulates in the iron core so that the voltage induced into coil 2 is equal to the coil 1 voltage if the number of turns in the two coils are equal.
Background image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 12

Chapter 1. Theory and Principles - 1 Theory and Principles...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online