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# DC-DC Buck converter

This example shows a DC-DC Buck converter with:

• an input voltage of 50 V,
• an output voltage of 25 V for duty cycle D=0.5,
• a power of 125 W transferred ( $$P_{output}=P_{input}$$ ).

A Buck converter is a class of switch mode power supply (SMPS) which is a DC-DC Step-Down converter that steps down voltage from its supply to load while stepping up the current depending upon the duty ratio.

## Model

In this model, all components are ideal. When the switch is ON (closed), the diode in the circuit is in reverse biased condition and the energy is transferred from the input supply to the inductor. Hence, the inductor stores the energy during the switch ON period.

However, when the switch is OFF (open), the diode in the circuit is in forward biased condition and the polarity of the inductor reverses so that the energy transfer takes place from the inductor to the load. In conclusion, the energy is transferred from inductor to the load when the switch is off.

## Switch control

The switch model can be directly connected with a control signal. For this control, we use a PWM block with an amplitude of 1, a duty cycle of 0.5 and 0.25 respectively, and a frequency of 5KHz.

Here are the values of the other components :

• Inductor L1 : 1 mH
• Capacitor C2 : 100 µF
• Load R1 : 5 $$\Omega$$

## Simulation

The results below show the output voltage across R1 with a duty cycle= 0.5. A zoom shows a measure of the average value of this voltage : 25 V. The results below show the output voltage across R1 with a duty cycle= 0.25. A zoom shows a measure of the average value of this voltage : 12.5 V. The results follow the equation: $$V_{out} = V_{in}*{D}$$

With:

• D: duty cycle
• $$V_{in}$$: Input voltage
• $$V_{out}$$: Output voltage