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A buck converter delivers a lower DC voltage than the supplied voltage.


Circuit Diagram[]

Picture 15

Analysis[]

Picture 16


Input output voltage relationship[]

For continous conduction mode. Remember energy is conserved! Energy coming into inductor leaves the inductor each cycle.

This is best expressed in using

and conservation of energy




Boundary between dis and cts Conduction[]

Discontinuous conduction is more likely the lower the duty cycle, as the inductor has less time to store energy and more time dispensing it.

find when the minimum current is zero.




from the inductor equations



the load current for which we will enter into discontinuous mode.


Note: maximum current supplied when D=0.5, so the maximum boundary current is when D=0.5


It is useful to find the minimum conditions for the inductor and frequency to avoid discts conduction mode



For CTS


DCM[]

Picture 17


Start anaylsis similar method as to ccm.


But now we need to find an expression for





Output Voltage Ripple[]

Picture 14

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

Hence and 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


so

We then have essentially the area under capacitor current shown in figure above(triangle).


during Toff the voltage across the inductor is Vo.


Note:

is the cut off frequency of the LC filter, hence it is very desirable for


In practice, the voltage drop across the equivalent series resistance (ESR) of the capacitor may contribute significantly to the output voltage ripple. This drop has been neglected.

Practical Considerations and Ratings[]

Transformer Considerations[]

Switch Ratings[]

Two Switch Flyback Converter[]

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