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Finite Load Resistance
The real power output of the ac source with zero output impedance, when the resistance of the gate windings and the core losses are neglected, as under the assumed ideal conditions, must be zero. This is also evident from the current and voltage waves shown in Fig. 713(a), from which it is apparent that the average of the instantaneous power taken over a complete cycle is zero. When a noninductive load R_{L} is connected in series with the gate windings, the real power output of the source must equal (k_{f}I_{L})^{2}(R_{L} + 2R_{G}), where R_{G} is the resistance of each gate winding. The current wave is then advanced in phase from the wave shown in Fig. 713(a). If the value of R_{L} + 2R_{G} is in the range for linear operation, i.e., low enough so that the law of equal ampere turns is practically satisfied, the current wave form will again be rectangular and of an amplitude determined by Eq. 737. The wave forms of applied voltage and output current including the fundamental component of output current for a noninductive load are shown in Fig. 714. Since sinusoidal voltage is assumed, the real power output of the ac source is
where I_{L1} is the rms value of the fundamental component in the gate current. It was shown in Section 54 that only the harmonics that are present in both the voltage and the current waves contribute to the real power. The applied voltage has no higher harmonics, and for that reason, only the fundamental in the current need be considered for the real power. The values of V and I_{L1} in Eq. 740 are rms. The fundamental component of a periodic rectangular wave has an amplitude that is 4/π times that of the rectangular wave. Therefore
and
The angle α, found by substituting Eq. 741 in Eq. 740, is
where R_{G} is the resistance of each gate winding.
For a given value of ac supply voltage and premagnetizing current, if the load resistance is increased beyond a certain value, the gate current is no longer entirely a function of the control current, but of the load resistance as well. This can be seen from the extreme case in which the load resistance R_{L} approaches infinity, causing the gate current to approach zero, regardless of the value of premagnetizing current i_{c}. With a given load resistance R_{L}, increasing the premagnetization causes the angle α to decrease and to shift the current wave to the left, which follows from Eq. 740. However, when the resistance reaches a value such that (2V/R_{L} + 2R_{G}) sin α is less than N_{C}i_{c}/NG, the wave form of the current is no longer rectangular, and the critical value of a is determined as follows
from Eq. 749
Hence, from Eqs. 743 and 744, we get
and
Therefore, the range of load resistance over which the wave form of the output is rectangular is
where V is the rms value of the ac supply voltage. When the average value V_{av} instead of the rms value V of the sinusoidal supply voltage is used, Eq. 746 becomes
since V = 1.11 V_{av}.


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