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Boost converters boost the input voltage higher

Analysis Edit

$V_dDT_s = V_0T_S(1-D)$ $\frac{V_o}{V_D} = \frac{D}{1-D}$

Boundary between dis and cts ConductionEdit

Discontinuous conduction mode is the preferred method of operation for a buck-boost converter. $I_{LB} = \frac{V_dT_sD}{2L}$

note $V_d = \frac{V_o(1-D)}{D}$ & $I_o = I_L - I_d$ average current through inductor equates to the current through the inductor minus that which flows back to the source. The capacitor has zero average current.

$\therefore I{oB} = \frac{V_o(1-D)^2T_s}{2LD}$

Output Voltage Ripple Edit

The diode current $i_D$ carries both the ripple current from capacitor and the average current through the load. Hence $\Delta V_o = \frac{\Delta Q}{C} = \frac{I_o D T_s}{C} = \frac{V_oDT_S}{RC}$