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# Closely Coupled Circuits

When the primary and secondary of an inductively coupled circuit are on a closed ferromagnetic core a closely coupled transformer, or transformer, exists. In communication, transformers are often regarded as impedance changers, a viewpoint that will now be discussed.

Assume that a transformer, or repeating coil, as it is often called in telephony, has a closed core of Permalloy and that all the magnetic flux φ produced by the primary winding Np links with the secondary turns Ns; also, assume that the losses in the transformer are negligible. The magnitude of the back voltage induced in the primary is given by the fundamental expression ep = Npdφ/(108 dt), and this will approximately equal the impressed voltage. The magnitude of the voltage induced in the secondary will be es = Nsdφ/(108 dt). Dividing the second equation by the first, and in terms of effective instead of instantaneous values, gives

To determine the approximate impedance transforming equations, suppose that the transformer secondary is delivering power to a load. The magnitude of the load impedance will be ZL = Es/Is and the impedance measured across the primary terminals will be Zp = Ep/Ip. From equation 20, Ep = EsNp/Ns, and Ip = IsNs/Np, and, when these are substituted in the equation for the primary impedance,

This equation shows that the transformer acts like an impedance changer because the impedance Zp measured at the primary will be (Np/Ns)2 times the impedance connected as a load to the secondary.

Last Update: 2011-05-30