or Step Down

http://schmidt-walter.fbe.fh-darmstadt.de/snt/snt_eng/snte_pdf.html

http://alpha400.ee.unsw.edu.au/elec4240/Lecture_12.pdf

The output voltage is determined by the switch duty cycle:

Initial State (simplified circuit)

The output voltage is controlled by the switch ON time. The circuit operation can be observed by turning the switch ON and OFF.

Step 1 – Close the switch.

When the switch closes:

The inductor starts to store energy.

Current starts to flow in the capacitor and load.

The diode does not conduct.

The voltage drop across the switch is quite low and is equal to the saturation voltage of the particular transistor used.

The current during the ON period is:

and reaches a maximum of:

Step 2 – Open the switch.

When the switch opens:

The voltage across the inductor reverses polarity.

The inductor releases its stored energy to the capacitor and load.

The diode starts to conduct.

The current during the OFF period is:

The slope of the falling inductor current is:

Step 3 – Close the switch.

When the switch closes:

The voltage across the inductor reverses polarity.

The process repeats.

Current Waveforms

The direct currents in the inductor, diode, and load resistance are quite easy to approximate. The capacitor current however is more complex since it is AC.

The capacitor will alternately accept current from the inductor, thus storing charge when the switch is ON, and discharge through the load when the switch is OFF. The capacitor current can be approximated by using Kirchoff’s current law: the sum of all currents in a node is zero.

Positive values in the above diagram represent currents entering the node and negative values represent currents leaving the node.

From this we observe that the inductor and load currents are DC, however the capacitor current is AC. The positive capacitor currents represent it discharging current to the load and the negative values represent it being recharged by the inductor.

The principle losses will be the voltage drop across the switch (a transistor) and the resistive loss across the inductor (generally very small).

Deriving the Minimum Inductor Value

From the falling inductor current waveform, (assuming continuous operation) we can deduce:

Rearranging we obtain the minimum inductor value: