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

## Circuit Diagram Edit

## Analysis Edit

### Input output voltage relationship Edit

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 Edit

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 Edit

Start anaylsis similar method as to ccm.

But now we need to find an expression for

### Output Voltage Ripple Edit

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 Edit

### Transformer Considerations Edit

### Switch Ratings Edit

### Two Switch Flyback Converter Edit