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The load current through the 74- resistor is: 2 200 sin (2 250t) 75 iL (t) = 0 and the triggering voltage is: vt (t) = Vt sin [(2 250t) ]
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The triggering voltage will go positive at the desired ring angle, , thus injecting a current into the gate of the thyristor, turning it on Thus, the requirement that the average load current be equal to 1 A is equivalent to requiring that 1 2 200 iL (t) = sin 2 t d t = 1 A 1 75 Performing the integration, we determine that the requirement is 2 200 (1 + cos( )) = 1 2 75 Solving for , we nd = 4823 Now, to determine the value of R, we observe that the AC source voltage appears across the RC circuit; thus, vt can be computed from an impedance voltage divider by
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using phasor methods: 1 VS j C VS (j ) = arctan ( RC) Vt (j ) = 1 1 + 2 R 2 C 2 R+ j C We then observe that the phase of Vt (j ) is the ring angle , and we can therefore determine by setting arctan( RC) = = 4823 R= tan( ) tan(4823) = 713 = C 2 250 10 6
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circuit analyzed in this example is supplied in the accompanying CD-ROM You may wish to experiment with changing the value of R to see its effect on the average load current
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