## FANDOM

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Boost converters boost the input voltage higher

## Analysis Edit

### 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

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 $f_s>>f_c$