Avatar

Buck Converter with Arduino

Dec 20th, 2020 | by: ELECTRONOOBS
Views 1165
A buck converter (step-down converter) is a DC-to-DC power converter which steps down voltage (while stepping up current) from its input (supply) to its output (load). It is a class of switched-mode power supply (SMPS) typically containing at least two semiconductors (a diode and a transistor, although modern buck converters frequently replace the diode with a second transistor used for synchronous rectification) and at least one energy storage element, a capacitor, inductor, or the two in combination. To reduce voltage ripple, filters made of capacitors (sometimes in combination with inductors) are normally added to such a converter's output (load-side filter) and input (supply-side filter).

1.0 DC to DC buck converter


A buck converter (step-down converter) is a DC-to-DC power converter which steps down voltage (while stepping up current) from its input (supply) to its output (load). It is a class of switched-mode power supply (SMPS) typically containing at least two semiconductors (a diode and a transistor, although modern buck converters frequently replace the diode with a second transistor used for synchronous rectification) and at least one energy storage element, a capacitor, inductor, or the two in combination. To reduce voltage ripple, filters made of capacitors (sometimes in combination with inductors) are normally added to such a converter's output (load-side filter) and input (supply-side filter).

In this tutorial we will learn how to build and how a DC to DC buck converter works. The circuit is very basic using just one diode, an inductor and a capacitor. The switch will be a MOSFET transistor and to create the PWM signal we will use a 555 timer in the PWM configuration, boost adjustable controller or one Arduino NANO. But first let's study a little bit of theory. We have the Buck converter circuit in the next figure where we can see the switch, inductor and capacitor and of course we add a load to the output.

2.0 Buck converter theory


Ok, so we have the next circuit. In order to study how it works, we will divide it in two stages. The ON and OFF stages. In the ON part, the switch is closed as we can see in the next figure where the diode is open becasue the cathode voltage is higher than the anode. When the switch is first closed (on-state), the current will begin to increase, and the inductor will produce an opposing voltage across its terminals in response to the changing current. This voltage drop counteracts the voltage of the source and therefore reduces the net voltage across the load. Over time, the rate of change of current decreases, and the voltage across the inductor also then decreases, increasing the voltage at the load. During this time, the inductor stores energy in the form of a magnetic field. If the switch is opened while the current is still changing, then there will always be a voltage drop across the inductor, so the net voltage at the load will always be less than the input voltage source. When the switch is ON the inductor will charge up and the voltage on the inductor will be the difference between the output and the input. But we also know that the inductor voltage is the inductance L multiplied by the inductor current derivate. As we can see in the next figure we obtain the ON current through the inductor.

When the switch is opened again (off-state), the voltage source will be removed from the circuit, and the current will decrease. The decreasing current will produce a voltage drop across the inductor (opposite to the drop at on-state), and now the inductor becomes a Current Source. The stored energy in the inductor's magnetic field supports the current flow through the load. This current, flowing while the input voltage source is disconnected, when concatenated with the current flowing during on-state, totals to current greater than the average input current (being zero during off-state). The "increase" in average current makes up for the reduction in voltage, and ideally preserves the power provided to the load. During the off-state, the inductor is discharging its stored energy into the rest of the circuit. If the switch is closed again before the inductor fully discharges (on-state), the voltage at the load will always be greater than zero.

In this case the voltage across the inductor is the output voltage. So once again using the next figure formulas we obtain the current of the OFF part.

Ok, now if we want to obtain the output depending on the input and the duty cycle of the PWM all we have to do is to make the sum of the On and Off current equal to 0. That means that the On current is equal to the Off current. So the will give us:

So we've obtain that the output is the input multiplied by the duty cycle. The duty cycle of the PWM can have values between 0 and 1. So te only posible output will be equal or lower than the input. That's why this configuration is called step down converter.


3.0 Buck converter Arduino NANO No Feedback


Sincerely, this circuit has no other sense but to learn. The Arduino NANO already has a 5V linear voltage regulator that will lower the efficiency of the circuit. So the main goal is to learn how the circuit, the feedback and the PWM signal work in order to achive the desired output. As you can see in the schematic above we have a potentiometer connected to the analog input A0. With this potentiometer we will choose the output value between 1 and 12 volts since the maximum input voltage in this case is 12V. With the Arduino's ADC we will read a value between 0 and 1024, next, in the code we map that value from 1 to 244 which are the values used with the analogWrite function of the arduino. With this we will apply a PWM signal on pin D3 where 1 is the lowest duty cycle and 244 the maximum. Since the arduino digital value is 5V we add a small BJT driver using one S8050 NPN and two resitors of 10k and 1k. The output of this driver is connected to the gate of the IRF4905 P-MOSFET.

Connect everything as in the schematic above and upload the next code to your Arduino and start moving the potentiometer. Observe the otput on the oscilloscope.
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

3.1 Buck converter Arduino NANO Feedback


Let's add the feedback to our circuit. As you can see in the schematic below we have a potentiometer connected to the analog input A0 as before. With this potentiometer we will choose the desired output value between 1 and 12 volts since the maximum input voltage in this case is 12V. At the output of the circuit we have nowa voltage divider that will lower the voltage from 12V to under 5 volts because that's the maximum input voltage of the Arduino ADCs. Check the formula below to understand how the voltage divider works. If you apply a higher voltage to the input than 12V you should change the values of R1 and R2 in order to always have a voltage below 5V for the ADC.


In the code we compare this two voltages and increase or decrease the PWM width in order to keep the output constant. Just copy and upload the next code to the Arduino for this example.
Connect everything as in the schematic above and upload the next code to your Arduino and start moving the potentiometer. Observe the otput on the oscilloscope.

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

0 Comments

Login or Sign Up to post comments on this tutorial.