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# LAB 2 - Applications and Operating Principle

# Page Content

# Applications

A buck converter can be remarkably efficient (up to 95 % for integrated circuits) and self-regulating.

This makes it useful for tasks such as converting a 12 V to 24 V typical battery in a laptop, down to the few volts needed by the processor.

This topology can be used not only to convert voltage but is also suitable to act as a current source, depending on the control method.

# Operating principle

When the switch is first closed, 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 is storing 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 opened again, the voltage source will be removed from the circuit, and the current will decrease.

The changing current will produce a change in voltage across the inductor, now aiding the source voltage.

The energy stored in the inductor’s magnetic field supports current flow through the load.

During this time, the inductor is discharging its stored energy into the rest of the circuit.

If the switch is closed again before the inductor fully discharges, the voltage at the load will always be greater than zero.

* Figure 10: Buck Converter*

## Continuous Conduction Mode

A buck converter operates in continuous mode if the current through the inductor never falls to zero during the commutation cycle.

In this mode, the operating principle is described by the plots in figure 11 and figure 12 below.

The principle of a buck converter consists of **two distinct states**.

### State 1

When switch S is closed, the current through the inductor rises linearly.

As the diode is reverse biased by the voltage source , no current flows through it.

**Figure 11**: State 1 of a Buck Converter

D is the duty cycle. It represents the fraction of the commutation period T during which the switch S is closed.

D is between 0 (S is never ON) and 1 (S is always ON).

With:

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

** For the subinterval 1**:

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

From figure 11:

### State 2

When the switch S is opened, the diode is forward biased. The current decreases.

The energy stored in inductor L is:

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.

**Figure 12**: State 2 of a Buck 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 12:

If we assume that the converter operates in steady state, the energy stored in each component at the end of a commutation cycle is equal to that at the beginning of the cycle.

That means that the current is the same at t =0 and at t = .

So, using the equations above, we can write:

Substituting and by their expressions, we obtain:

The voltage conversion ratio depends on D but is independent of the output load.

From this equation, the output voltage of the converter varies linearly with the duty cycle for a given input voltage.

As the duty cycle D cannot be more than 1, therefore this converter is referred to as step-down converter.

We assume that all components are perfect; the theoretical efficiency of this converter is equal to 1, so we can write that:

By using equation 23, we obtain:

When the load is resistive, the expression of the load current is:

The average capacitor current is zero in DC steady state, the average inductor current equals the output current by Kirchhoff’s current law applied at the output node.

The inductor current equals the output current so:

The maximum value of inductor current is:

The minimum value of inductor current is:

Continuous conduction mode is ensured when

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