TABLE OF CONTENTS An ideal transformer is one in which the coefficient of coupling is almost unity, and both the primary and secondary inductive reactances are very large in comparison with the load impedances. The primary and secondary coils have many turns wound around a laminated iron-core and are arranged so that the entire flux links all the turns of both coils.
An important parameter of an ideal transformer is the turns ratio a which is defined as the ratio of the number of turns on the secondary, N 2, to the number of turns of the primary N 1, that is,
The flux produced in a winding of a transformer due to a current in that winding is proportional to the product of the current and the number of turns on the winding. Therefore, letting ? be a constant of proportionality which depends on the physical properties of the transformer, for the primary and secondary windings we have:
The constant ? is the same for the primary and secondary windings because we have assumed that the same flux links both coils and thus both flux paths are identical. We recall from (9.8) and (9.14) that
Then, from (9.78) and (9.79) we obtain:
or
Therefore,
From (9.69),
or
and since j ?L 2 Z LD, (9.84) reduces to
For the case of unity coupling,
or
and by substitution of (9.87) into (9.85) we obtain:
From (9.82) and (9.88), we obtain the...
