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Homework Statement
I am having quite a bit of difficulty with the problem I have attached. We need to determine the period of operation and the critical inductance. Solving for the period is not as difficult. However, determining [itex]τ[/itex] has proven to be rather tedious. Any help is appreciated.
The output voltage can be expressed as [itex]V_o = \frac{t_{on}V}{T} + \frac{V_C(Tt_x)}{T}[/itex] where [itex]t_x[/itex] represents the point that the load current falls to zero. In this instance, this value falls to zero at the boundary where the current is just discontinuos ([itex]t_x=T[/itex]). Therefore, [itex]T=\frac{t_{on}V}{V_c}[/itex].
I then can do a bunch of manipulations to the current equations to come up with [itex]t_x = τln[1+3(e^{t_{on}/τ}  1)][/itex]
At this point, I cannot seem to solve this equation by hand or with my TI89. Any ideas?
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