Buck Converter

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- The values of all input fields can be changed.
- If an input field is left empty, a default value is chosen. This value is displayed after leaving the input field in question.
- The switch mode power supply operates within a certain input range i.e. between
*V*_{in_min}and*V*_{in_max}. - The program needs the output values
*V*_{out}and*I*_{out}. - The switching frequency
*f*is the operating frequency of the transistor. - If the field "proposal" is activated, the proposed choking coil
*L*and the current ripple Δ*I*_{L}are chosen such that Δ*I*_{L}= 0.4*I*_{out}, for*V*_{in_max}as the input voltage. - If you should not be content with the proposed values, you can change
*L*or Δ*I*_{L}. If this is the case, the field "proposal" is deactivated automatically. - The value
*V*_{in}is the value for the calculation of the current and voltage diagrams on the right side of the display.*V*_{in}must lie between*V*_{in_min}and*V*_{in_max}.

Illustration 1: Buck Converter |

For the following analysis it will be assumed that the transistor is simplified as an ideal switch and the diode has no forward voltage drop. In the program itself, the diode will take into account a forward voltage drop *V*_{F} = 0.7V.

During the on-time of the transistor, the voltage *V*_{1} is equal to *V*_{in}. Since *V*_{in} is higher than *V*_{out} the current through the diode increases linearly in correspondence to Faraday's Law.

When the transistor is turned off (blocking phase) the diode takes the inductor current. At this time the voltage across the inductor inverts. The voltage *V*_{1} becomes zero *(exact: -0.7V)* and the voltage across the inductor is now -*V*_{out}. The inductor current *I*_{L}
decreases linearly. If the current *I*_{L} does not decrease to zero during the blocking phase, this is called **continuous mode** (see illustration 2).

In this mode *V*_{1} is a voltage which changes between *V*_{in} and zero, corresponding to the duty cycle *t*_{1}/T. The Low Pass Filter, formed by *L* and *C*_{out}, produces an output voltage equivalent to the average value of *V*_{1}, i.e. *V*_{out} = *V*_{1}.

- For the continuous mode the output voltage is a function of the duty cycle and input voltage, it is independent of the load.

The inductor current *I*_{L} has a triangular shape, its average value is determined by the load. The peak to peak current ripple Δ*I*_{L} is dependent on *L* and can be calculated with the help of Faraday's Law. For *V*_{out} = (*t*_{1}/T) · *V*_{in} and a switching frequency *f* it follows that for continuous mode:

- The current ripple Δ
*I*_{L}is independent of the load. The output current*I*_{out}is equal to the average value of the inductor current*I*_{L}.

At low load current, namely if *I*_{out} < Δ*I*_{L}/2, the inductor current *I*_{L} falls to zero during every switching cycle. This mode is called **discontinuous mode** (see illustration 2). For this mode the calculations above are **not** valid.

At the moment when the inductor current becomes zero, i.e. *t*_{2}, the voltage *V*_{1} jumps to the value of *V*_{out} because in this case *V*_{L} = 0. The drain-source capacitance in parallel with the diode-junction capacitance forms a resonant circuit with the inductance *L*. This is stimulated by the voltage jump across the diode. The voltage *V*_{1} then oscillates and fades away.

Continuous Mode | Discontinuous Mode |

Illustration 2: Operating modes of the Buck Converter

- The larger the chosen value of the inductor
*L*, the smaller the current ripple Δ*I*_{L}. However this results in a physically larger and heavier inductor. - Choose Δ
*I*_{L}so that it is not too big. The suggestions proposed by us have adequately small current ripple along with physically small inductor size. With a larger current ripple, the voltage ripple of the output voltage*V*_{out}becomes clearly bigger while the physical size of the inductor decreases marginally. - The higher the chosen value of the switching frequency
*f*, the smaller the size of the inductor. However the switching losses of the transistor also become larger as*f*increases. - The smallest possible physical size for the inductor is achieved when Δ
*I*_{L}= 2*I*_{out}at*V*_{in_max}. However, the switching losses at the transistors are at their highest in this state.

** V_{in_min}**,

Using these parameters, the program produces a **proposal for L**:

with

From this it follows that:

- For
**Δ**the converter is in continuous mode and it follows that:*I*_{L}< 2*I*_{out}

- For
**Δ**the converter is in discontinuous mode and it follows that:*I*_{L}> 2*I*_{out}

,

Main page | | How to use the program | | Function principals | | Mathematics used in the program | | |

Top of page | | Application | | Tips | | Literature Notes | | Help for choking coils |