# Buck Converter

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## How to use the program

Reference: The shapes of current and voltage curves are calculated using Faraday's Law. They do not represent an incremental simulation like it is done normally by programs like P-Spice. In the calculations the forward voltages of the diodes are considered with VF = 0.7V, and the transistors are interpreted as ideal switches.
• 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 Vin_min and Vin_max.
• The program needs the output values Vout and Iout.
• 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 ΔIL are chosen such that ΔIL = 0.4Iout, for Vin_max as the input voltage.
• If you should not be content with the proposed values, you can change L or ΔIL. If this is the case, the field "proposal" is deactivated automatically.
• The value Vin is the value for the calculation of the current and voltage diagrams on the right side of the display. Vin must lie between Vin_min and Vin_max.

## Application:

The Buck Converter converts an input voltage to a lower output voltage. The buck converter often replaces the traditional analogue voltage regulator.

## Function principals

 Illustration 1: Buck Converter

The transistor works as a switch which is driven by a high frequency pulse-width-modulated control voltage. The switch is turned on and off by the pulse-width-modulated control voltage. The ratio between on-time and the period t1/T is called the Duty Cycle.

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 VF = 0.7V.

During the on-time of the transistor, the voltage V1 is equal to Vin. Since Vin is higher than Vout 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 V1 becomes zero (exact: -0.7V) and the voltage across the inductor is now -Vout. The inductor current IL decreases linearly. If the current IL does not decrease to zero during the blocking phase, this is called continuous mode (see illustration 2).

In this mode V1 is a voltage which changes between Vin and zero, corresponding to the duty cycle t1/T. The Low Pass Filter, formed by L and Cout, produces an output voltage equivalent to the average value of V1, i.e. Vout = V1.

• 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 IL has a triangular shape, its average value is determined by the load. The peak to peak current ripple ΔIL is dependent on L and can be calculated with the help of Faraday's Law. For Vout = (t1/T) · Vin and a switching frequency  f  it follows that for continuous mode:

• The current ripple ΔIL is independent of the load. The output current Iout is equal to the average value of the inductor current IL.

At low load current, namely if Iout < ΔIL/2, the inductor current IL 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. t2, the voltage V1 jumps to the value of Vout because in this case VL = 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 V1 then oscillates and fades away.

 Continuous Mode Discontinuous Mode

Illustration 2: Operating modes of the Buck Converter

## Tips

• The larger the chosen value of the inductor L, the smaller the current ripple ΔIL. However this results in a physically larger and heavier inductor.
• Choose ΔIL 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 Vout 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 ΔIL = 2Iout at Vin_max. However, the switching losses at the transistors are at their highest in this state.

## Mathematics used in the program

The following parameters must be entered into the input fields:

Vin_min, Vin_max, Vout, Iout and  f

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

with VF = 0.7V (Diode Forward-voltage) and ΔIL = 0.4Iout
For the calculation of the curve-shapes, and also for the calculation of "ΔIL for Vin_max", two cases have to be distinguished, i.e. continuous mode and discontinuous mode:

From this it follows that:

1. For ΔIL< 2Iout the converter is in continuous mode and it follows that:

2. For ΔIL> 2Iout the converter is in discontinuous mode and it follows that:

,

 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