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I was wondering how one would go about the derivation for the output to input voltage ratio for a DC-DC Buck converter given the critical max current that is found to be $$ I_{crit} = \frac{V_{in}T}{8L} $$ The final result of the output to input voltage ratio is $$ \frac{V_{out}}{V_{in}} = \frac{D^{2}}{D^2 + \frac{I_{load}}{4I_{crit}}}$$

Edit: For clarification: T is the period and L is the inductance and D is the duty cycle and we assume the system to be in discontinuous current mode

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  • \$\begingroup\$ DCM or CCM? What is T and what is L and why is there a critical value of output current. Many things you should explain. \$\endgroup\$ – Andy aka May 7 '18 at 12:38
  • \$\begingroup\$ T is the period and L is the inductance and D is the duty cycle and we assume the system to be in discountinous current mode. \$\endgroup\$ – Sam May 7 '18 at 13:23
  • \$\begingroup\$ And \$I_{crit}\$? Is it at the boundary condition? \$\endgroup\$ – Andy aka May 7 '18 at 13:55
  • \$\begingroup\$ @Andyaka $$I_{crit} $$ is at the boundary condition \$\endgroup\$ – Sam May 7 '18 at 14:51

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