Reflected Impedance

Author: J.B. Hoag

Fig. 5 D. A simple transformer circuit

Consider the case of a transformer with a simple resistance load as in Fig. 5 D. Here R₁ is the total primary resistance including that of coil L₁ and R₂ is the total secondary resistance, not only of the load but also of coil L₂. As the alternating current generator sends current back and forth through coil L₁, its magnetic field rises and falls, cutting coil L₂, generating an alternating e.m.f. between its terminals, and driving an alternating current through the secondary circuit L₂R₂. But this current, in turn, produces a magnetic field around the coil L₂ which, in cutting coil L₁ generates a voltage between the primary terminals and causes a current to flow in the primary circuit. This "reflected" current then reacts upon the secondary and the process continues back and forth, with ever-diminishing intensity. The final result is that the current flowing in the primary is altered in such a manner as though the primary resistance had been increased and its inductance decreased, i.e., the total primary circuit's reactance, or, in general, its "impedance" is altered. The amount of the reflected resistance or inductance is greater when the primary and secondary coils are closer together and when they are so oriented with respect to each other that more of the lines of force from one of them can cut the other. The increase of resistance and the decrease of inductance is greater at higher frequencies of the alternating current. It is also affected by the resistance and inductance of the secondary circuit.