AUTO TRANSFORMERS

AUTO TRANSFORMERS

By Engr. Aneel Kumar   February 19, 2016   No comments:

An autotransformer is a transformer which has part of its winding common to the primary and secondary circuits. Fig. 1(a) shows the circuit for a double-wound transformer and Fig. 1(b) that for an auto transformer. The latter shows that the secondary is actually part of the primary, the current in the secondary being (I₂-I₁). Since the current is less in this section, the cross-sectional area of the winding can be reduced, which reduces the amount of material necessary.

Figure 1: (a) double-wound transformer (b) auto transformer

ADVANTAGES OF AUTO TRANSFORMERS

The advantages of autotransformers over double wound transformers include:

1) a saving in cost since less copper is needed

2) less volume, hence less weight

3) a higher efficiency, resulting from lower I²R losses

4) a continuously variable output voltage is achievable if a sliding contact is used

5) a smaller percentage voltage regulation.

DISADVANTAGES OF AUTO TRANSFORMERS

The primary and secondary windings are not electrically separate, hence if an open-circuit occurs in the secondary winding the full primary voltage appears across the secondary.

USES OF AUTO TRANSFORMERS

Auto transformers are used for reducing the voltage when starting induction motors and for interconnecting systems that are operating at approximately the same voltage.

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EMF EQUATION OF A TRANSFORMER

EMF EQUATION OF A TRANSFORMER

By Engr. Aneel Kumar   February 19, 2016   No comments:

The magnetic flux ϕ set up in the core of a transformer when an alternating voltage is applied to its primary winding is also alternating and is sinusoidal.

Let ϕm be the maximum value of the flux and f be the frequency of the supply. The time for 1 cycle of the alternating flux is the periodic time T, where T = (1/f) seconds

The flux rises sinusoidally from zero to its maximum value in (1/4) cycle, and the time for (1/4) cycle is (1/4f) seconds. Hence the average rate of change of flux = (ϕm/ (1/4f)) = 4f ϕm Wb/s, and since 1Wb/s D 1 volt, the average emf induced in each turn = 4f ϕm volts. As the flux ϕ varies sinusoidally, then a sinusoidal emf will be induced in each turn of both primary and secondary windings.

For a sine wave,

Form Factor = r.m.s Value / Average Value

= 1.11

Hence r.m.s. value = form factor*average value = 1.11 * average value Thus r.m.s. e.m.f. induced in

each turn

=1.11 * 4fϕm volts

=4.44fϕm volts

Therefore, r.m.s. value of e.m.f. induced in primary,

E1 = 4.44 f ϕmN1 volts

and r.m.s. value of e.m.f. induced in secondary,

E2 = 4.44 f 8ϕN2 volts

Dividing E1 by E2

E1E2=N1N2

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AIR CORE TRANSFORMER

AIR CORE TRANSFORMER

By Engr. Aneel Kumar   February 12, 2016   No comments:

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=NdΦ/dt108

where N is the number of turns in the coil, dϕ/dt is the time rate of change of flux linking the coil, and ϕ is the flux in lines.

At a time when the applied voltage to the coil is E and the flux linking the coils is ϕ lines, the

instantaneous voltage of the supply is:

Since the amount of flux ϕ 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 will increase costs. The need then is to increase the amount of flux from the first coil that links the second coil.

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