Unformatted text preview: Summary: Irrespective of several practical eﬀects, transformers are simplest devices. A
tranformer simply consists of several coils coupled by a magnetic path. Electrically all
coils are physically uncoupled. Many transformers have eﬃciency exceeding 98%. Some
transformers even have eﬃciency in the order of 99.9%. Two basic principles guide the
behavior of an ideal transformer:
• Voltage induced per turn is the same in any coil.
• The mmf of primary coil has to balance the mmfs of all other coils.
In the case of two coils denoted by p (primary) and s (secondary) with turns Np and Ns , we
have
Vp
Np
=
and Ip Np = Is Ns .
Vs
Ns
In the case of three coils denoted by p (primary), s (secondary), and t (tertiary) with turns
Np , Ns , and Nt , we have
Vp
Np
Vp
Np
=
,
=
, and Ip Np = Is Ns + It Nt .
Vs
Ns
Vt
Nt
The above guiding principles lead to impedance transformation. That is, a coil feeding an
impedance can equivalently be thought of as primary coil feeding another impedance called
reﬂected impedance. In the case of two coils denoted by p and s, the secondary impedance
Zs is reﬂected as primary impedance Zp ,
Np 2
Zs .
Ns
If the primary coil is supplying more than one coil, each such coil reﬂects an impedance into
the primary. All such reﬂected impedances are in parallel.
Zp = Practical Eﬀects:
• A current called excitation current is necessary to magnetize the medium. The excitation current is often not sinusoidal, it contains several harmonic frequencies. There
are two kinds of excitation losses, hysteresis loss and eddy current loss. These losses
together are known as core losses or iron losses.
• Not all the ﬂux generated by one winding links the other windings. This leads to
leakage reactances.
• Every coil has a resistance, and it leads to what are known as copper losses. ...
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This note was uploaded on 10/23/2011 for the course ECON 103 taught by Professor Ruhe during the Spring '11 term at Baptist Bible PA.
 Spring '11
 Ruhe

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