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Home Saturable Reactors Applied Voltage and Conduction Angle  
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Relationship Between Applied Voltage and Conduction Angle for Noninductive Load
The differential equation describing the operation of the basic circuit in Fig. 72 in the unsaturated or presaturated region is, on the basis of negligible winding resistance and the idealized magnetization curve
If A_{c} is the effective core area, B_{c} the critical flux density, and N the number of turns in the winding, then, when these quantities are substituted in Eq. 74, the result is
Integrating
in which K_{i} is the initial flux density, i.e., at t = t_{i}. Wave forms of flux density, voltage, and current for resistance loading are shown in Fig. 73(a). At ωt = π the load current goes through zero and the voltage changes sign, which means that dB/dt must become negative also, and the reactor becomes unsaturated. The current, therefore, is extinguished at ωt = π. The flux density starts to build up from a value of B_{c} at ωt = 0, and t_{i} is the value of t at ωt = 0, so that Eq. 75 can be put into the more definite form
Firing occurs when B reaches the saturated value +B_{C}, which occurs at ωt = α_{f} in Fig. 73(a). When these quantities are substituted in Eq. 76, there results
which yields


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