【正文】 ondary winding or simply secondary. The flux is changing。 therefore, it induces a voltage in the secondary by electromagnetic induction in accordance with Lenz’s law. Thus the primary receives its power from the source while the secondary supplies this power to the load. This action is known as transformer action.3. TRANSFORMER PRINCIPLESWhen a sinusoidal voltage Vp is applied to the primary with the secondary opencircuited, there will be no energy transfer. The impressed voltage causes a small current Iθ to flow in the primary winding. This noload current has two functions: (1) it produces the magnetic flux in the core, which varies sinusoidally between zero and φm, where φm is the maximum value of the core flux。 and (2) it provides a ponent to account for the hysteresis and eddy current losses in the core. There bined losses are normally referred to as the core losses.The noload current Iθ is usually few percent of the rated fullload current of the transformer (about 2 to 5%). Since at noload the primary winding acts as a large reactance due to the iron core, the noload current will lag the primary voltage by nearly 90186。. It is readily seen that the current ponent Im= I0sinθ0, called the magnetizing current, is 90186。 in phase behind the primary voltage VP. It is this ponent that sets up the flux in the core。 φ is therefore in phase with Im.The second ponent, Ie=I0sinθ0, is in phase with the primary voltage. It is the current ponent that supplies the core losses. The phasor sum of these two ponents represents the noload current, orI0 = Im+ IeIt should be noted that the noload current is distortes and nonsinusoidal. This is the result of the nonlinear behavior of the core material.If it is assumed that there are no other losses in the transformer, the induced voltage In the primary, Ep and that in the secondary, Es can be shown. Since the magnetic flux set up by the primary winding，there will be an induced EMF E in the secondary winding in accordance with Faraday’s law, namely, E=NΔφ/Δt. This same flux also links the primary itself, inducing in it an EMF, Ep. As discussed earlier, the induced voltage must lag the flux by 90186。, therefore, they are 180186。 out of phase with the applied voltage. Since no current flows in the secondary winding, Es=Vs. The noload primary current I0 is small, a few percent of fullload current. Thus the voltage in the primary is small and Vp is nearly equal to Ep. The primary voltage and the resulting flux are sinusoidal。 thus the induced quantities Ep and Es vary as a sine function. The average value of the induced voltage given byEavg = turnswhich is Faraday’s law applied to a finite time interval. It follows thatEavg = N = 4fNφmwhich N is the number of turns on the winding. Form ac circuit theory, the effective or rootmeansquare (rms) voltage for a sine wave is times the average voltage。 thusE = Since the same flux links with the primary and secondary windings, the voltage per turn in each winding is the same. HenceEp = andEs = where Ep and Es are the number of turn on the primary and secondary windings, respectively. The ratio of primary to secondary induced voltage is called the transformation ratio. Denoting this ratio by a, it is seen thata = = Assume that the output power of a transformer equals its input power, not a bad sumption in practice considering the high efficiencies. What we really are saying is that we are dealing with an ideal transformer。 that is, it has no losses. ThusPm = PoutorVpIp primary PF = VsIs secondary PFwhere PF is the power factor. For the abovestated assumption it means that the power factor on primary and secondary sides are equal。 thereforeVpIp = VsIsfrom which is obtained = ≌ ≌ aIt shows that as an approximation the terminal voltage ratio equals the turns ratio. The primary and secondary current, on the other hand, are inversely related to the turns ratio. The turns ratio gives a measure of how much the secondary voltage is raised or lowered in relation to the primary voltage. To calculate the voltage regulation, we need more information.The ratio of the terminal voltage varies somewhat depending on the load and its power factor. In practice, the transformation ratio is obtained from the nameplate data, which list the primary and secondary voltage under fullload condition.When the secondary voltage Vs is reduced pared to the primary voltage, the transformation is said to be a stepdown transformer: conversely, if this voltage is raised, it is called a stepup transformer. In a stepdown transformer the transformation ratio a is greater than unity (a), while for a stepup transformer it is smaller than unity (a). In the event that a=1, the transformer secondary voltage equals the primary voltage. This is a special type of transformer used in instances where electrical isolation is required between the primary and secondary circuit while maintaining the same voltage level. Therefore, this transformer is generally knows as an isolation transformer.As is apparent, it is the magnetic flux in the core that forms the connecting link between primary and secondary circuit. In section 4 it is shown how the primary winding current adjusts itself to the secondary load current when the transformer supplies a load.Looking into the transformer terminals from the source, an impedance is seen which by definition equals Vp / Ip. From = ≌ ≌ a , we have Vp = aVs and Ip = Is/ terms of Vs and Is the ratio of Vp to Ip is = = But Vs / Is is the load impedance ZL thus we can say thatZm (primary) = a2ZLThis equation tells us that when an impedance is connected to the secondary side, it appears from the source as an impedance having a magnitude that is a2 times its actual value. We say that the load impedance is reflected or referred to the primary. It is this property of transformers that is used in impedancematching applications.4. TRANSFORMERS U