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Boost converters boost the input voltage higher

Circuit Diagram Edit

Picture 18

Analysis Edit

Picture 19

Voltage Relationship Edit

$ V_dT_sD = (V_o-V_d)T_s(1-D) $ $ \therefore \frac{V_o}{V_d} = \frac{1}{1-D} $

Boundary between dis and cts ConductionEdit

$ i_{min} = I_L - \frac{\Delta i}{2} $ $ \therefore I_{Lb} = \frac{V_dT_sD}{2L} $ & $ Insert formula here $





Output Voltage Ripple Edit

Picture 14

If our output voltage is constant the output capacitors average current is zero.

Hence $ I_L = I_o $ and $ i_{ripple} = i_c $ So capacitor essentially smooths the output current wave form, filling in the supply gaps when the inductor is out of energy.

Ok so we know


$ C = \frac{dq}{dv} $ so

$ \Delta V_o = \frac{\Delta Q}{C} $

We then have $ \Delta V_o = \frac{1}{C} \frac{1}{2} \frac{\Delta I_L}{2} \frac{T_s}{2} = \frac{\Delta I_L T_s}{8C} $ essentially the area under capacitor current shown in figure above(triangle).


$ \Delta I_L = \frac{V_o}{L}(1-D)T_s $ during Toff the voltage across the inductor is Vo.

$ \therefore \frac{\Delta V_o}{V_o}\frac{T_s V_o}{8CL} (1-D)T_s $


Note:

$ f_c = \frac{1}{2\pi\sqrt{LC}} $ is the cut off frequency of the LC filter, hence it is very desirable for $ f_s>>f_c $

Practical Considerations and Ratings Edit

Transformer Considerations Edit

Switch Ratings Edit

Two Switch Flyback Converter Edit