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# LAB3 - Applications and Operating Principle

# Page Content

# Applications

Buck-boost converters are typically used when an input voltage source varies and may be either above or below the required output voltage at different times.

# Operating principle

The principle of the buck–boost converter is as follows:

- While in the On state, the input voltage source is directly connected to the inductor (L).

This results in accumulating energy in L.

In this stage, the capacitor supplies energy to the output load. - While in the Off state, the inductor is connected to the output load and capacitor, so energy is transferred from L to C and R.

Compared to the **buck** and **boost** converters, the characteristics of the buck–boost converter are mainly:

- The polarity of the output voltage is opposite to that of the input.
- The output voltage can vary continuously from 0 to -∞ (for an ideal converter).

The output voltage ranges for a buck and a boost converter are respectively 0 to and to -∞.

**Figure 16**: Buck-Boost Converter

With:

- : Input voltage
- : Input current
- : Output voltage
- : Output current
- : Inductor current
- : Inductor voltage

## Continuous Conduction Mode

In continuous conduction mode, the buck-boost converter assumes two states per switching cycle.

### State 1

The On state is when switch S is closed.

**Figure 17**: State 1 of a Buck-Boost Converter

** For the subinterval 1**:

When the switch pictured above is closed, the voltage across the inductor is:

From figure 17 above :

### State 2

The Off state is when the switch S is opened.

**Figure 18**: State 2 of a Buck-Boost Converter

Therefore, the energy stored in L increases during On-state and then decreases during the Off-state.

L is used to transfer energy from the input to the output of the converter.

** **** For the subinterval 2**:

When the switch is opened, the diode is forward biased.

Current flows through the diode and the voltage across the inductor is:

From figure 18 above:

The energy is stored in the inductor when the switch is closed and transferred to the load when switch is opened.

As the energy in an inductor is given by:

It’s obvious that the value of at the end of the OFF state must be the same with the value of at the beginning of the ON state; it means that the sum of the variations of during the ON and the OFF states must be zero.

So, we can write based on the above equations:

Substituting and by their expressions, we obtain:

Note

The output of a buck-boost converter is either higher or lower than the source voltage.

- If D>0.5: the output is higher (a boost converter)
- If D<0.5: the output is lower (a buck converter)

The output voltage is always negative. It’s never directly connected to the load.

We assume that there is no power loss in the converter, so the power absorbed by the load must equal the power supplied by the source, so we can write:

Unlike the buck power stage, the average of the inductor current is not equal to the output current.

To relate the inductor current to the output current, referring to figure 18 above, note that the inductor delivers current to the output only during the off state of the power stage.

This current averaged over a complete switching cycle is equal to the output current because the average current in the output capacitor must be equal to zero.

The relationship between the average inductor current and the output current for the continuous mode buck-boost power stage is given by:

By using equation (37):

The maximum value of inductor current is:

The minimum value of inductor current is:

The average inductor current is proportional to the output current, and since the inductor ripple current, , is independent of output load current, the minimum and the maximum values of the inductor current track the average inductor current exactly.

We assure continuous conduction mode when

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