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primary would have to supply a different loss power. Must be equal to . does in fact reduce to .Similarly the stored magnetic energy in the leakage field which is proportional to will be found to check as . The referred secondary .The argument is sound, though at first it may have seemed suspect. In fact, if the actual secondary winding was removed physically from the core and replaced by the equivalent winding and load circuit designed to give the parameters ,and , measurements from the primary terminals would be unable to detect any difference in secondary ampereturns, demand or copper loss, under normal power frequency operation.There is no point in choosing any basis other than equal turns on primary and referred secondary, but it is sometimes convenient to refer the primary to the secondary winding. In this case, if all the subscript 1’s are interchanged for the subscript 2’s, the necessary referring constants are easily found。 . ,。 similarly and .The equivalent circuit for the general case where except that has been added to allow for iron loss and an ideal lossless transformation has been included before the secondary terminals to return to .All calculations of internal voltage and power losses are made before this ideal transformation is applied. The behavior of a transformer as detected at both sets of terminals is the same as the behavior detected at the corresponding terminals of this circuit when the appropriate parameters are inserted. The slightly different representation showing the coils and side by side with a core in between is only used for convenience. On the transformer itself, the coils are, of course, wound round the same core.Very little error is introduced if the magnetizing branch is transferred to the primary terminals, but a few anomalies will arise. For example, the current shown flowing through the primary impedance is no longer the whole of the primary current. The error is quite small since is usually such a small fraction of. Slightly different answers may be obtained to a particular problem depending on whether or not allowance is made for this error. With this simplified circuit, the primary and referred secondary impedances can be added to give: And It should be pointed out that the equivalent circuit as derived here is only valid for normal operation at power frequencies。 capacitance effects must be taken into account whenever the rate of change of voltage would give rise to appreciable capacitance currents,. They are important at high voltages and at frequencies much beyond 100 cycles/sec. A further point is not the only possible equivalent circuit even for power frequencies .An alternative , treating the transformer as a threeor fourterminal network, gives rise to a representation which is just as accurate and has some advantages for the circuit engineer who treats all devices as circuit elements with certain transfer properties. The circuit on this basis would have a turns ratio having a phase shift as well as a magnitude change, and the impedances would not be the same as those of the windings. The circuit would not explain the phenomena within the device like the effects of saturation, so for an understanding of internal behavior.There are two ways of looking at the equivalent circuit:(a) viewed from the primary as a sink but the referred load impedance connected across ,or(b) Viewed from the secondary as a source of constant voltage with internal drops due to and. The magnetizing branch is sometimes omitted in this representation and so the circuit reduces to a generator producing a constant voltage (actually equal to ) and having an internal impedance (actually equal to ).In either case, the parameters could be referred to the secondary winding and this may save calculation time.The resistances and reactances can be obtained from two simple light load tests.Introduction to DC MachinesDC machines are characterized by their versatility. By means of various bination of shunt, series, and separately excited field windings they can be designed to display a wide variety of voltampere or speedtorque characteristics for both dynamic and steady state operation. Because of the ease with which they can be controlled, systems of DC machines are often used in applications requiring a wide range of motor speeds or precise control of motor output.The essential features of a DC machine are shown schematically. The stator has salient poles and is excited by one or more field coils. The airgap flux distribution created by the field winding is symmetrical about the centerline of the field poles. This axis is called the field axis or direct axis.As we know, the AC voltage generated in each rotating armature coil is converted to DC in the external armature terminals by means of a rotating mutator and stationary brushes to which the armature leads are connected. The mutatorbrush bination forms a mechanical rectifier, resulting in a DC armature voltage as well as an armature . wave which is fixed in space. The brushes are located so that mutation occurs when the coil sides are in the neutral zone, midway between the field poles. The axis of the armature . wave then in 90 electrical degrees from the axis of the field poles, ., in the quadrature axis. In the schematic representation the brushes are shown in quadrature axis because this is the position of the coils to which they are connected. The a