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# LAB 1 - Applications and Operating Principle

# Page Content

# Applications

Battery powered systems often stack cells in series to achieve higher voltage values.

However, sufficient stacking of cells is not possible in many high voltage applications due to lack of space and the cost of implementation.

Boost converters can be used to increase the voltage and reduce the number of cells.

Two battery-powered applications that use boost converters are hybrid electric vehicles (HEV) and lighting systems.

# Operating principle

The DC/DC boost converters generally operate by applying a DC voltage across an inductor or transformer over a period of time which causes current to flow through it and store energy magnetically, the load is being isolated from the input voltage during that time, then connecting the load and causing the stored energy to be transferred to the voltage output in a controlled manner.

The output voltage is regulated by adjusting the ratio of on/off time. This is achieved using switched-mode, or chopper, circuits whose elements dissipate negligible power.

The main components of a boost converter are an inductor, a diode, and a high frequency switch.

These supply power to the load in a coordinated manner at a voltage greater than the input voltage magnitude.

The control strategy lies in the manipulation of the switch’s duty cycle, which causes the changes of voltage.

The switch is typically a MOSFET, IGBT, or BJT.

* Figure 2: Boost Converter*

## Continuous Conduction Mode

The principle of a boost converter consists of two distinct states, based on the closing and opening of the switch.

- The first state is when the switch is closed; this is known as the charging mode of operation.
- The second state is when the switch is open; this is known as the discharging mode of operation.

When a boost converter operates in continuous mode, the current through the inductor () never falls to zero.

### State 1

When the switch S is in ON state (closed), the whole circuit will be divided into two loops: one at the output side and another at the input side.

The closed loop at input consisting of an inductor gets charged by the current flowing through the loop during this period.

This current will increase linearly until the switch is in closed condition.

In the same time interval, inductor voltage is also high, as it is not delivered to any load but to itself. Diode is OFF during this mode.

The equivalent circuit representation of state 1 is shown in figure 3 below.

**Figure 3**: State 1 of a Boost Converter

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

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

With:

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

** For the subinterval 1**:

According to figure 3 above:

Using the two previous equations is:

### State 2

When switch S is in OFF state (Open), there will be a closed loop consisting of a power source, inductor, and RC load.

The energy stored in the inductor during ON state is discharged to the RC load circuit through the diode.

Thus, inductor current is reducing linearly, charging the capacitor at the load side.

The equivalent circuit for state 2 is shown in 0.

Therefore, for closed switch time the inductor gets charged, the capacitor is delivering the required power to the load, and for the opened switch time the inductor will discharge supplying the full power to the load and charging the capacitor simultaneously.

**Figure 4**: State 2 of a Boost Converter

** **

** For the subinterval 2**: D

**∙**T < t < T

When switch S is in the OFF state, the inductor current flows through the load.

If we consider zero voltage drop in the diode, and a capacitor large enough for its voltage to remain constant, the evolution of is:

According to figure 4 above:

As we consider that the converter operates in steady-state conditions, the amount of energy stored in each of its components must be the same at the beginning and at the end of a commutation cycle.

In particular, the energy stored in the inductor is given by:

The inductor current must be the same at the start and end of the commutation cycle.

This means the overall change in the current (the sum of the changes) is zero:

Substituting and by their expressions, we obtain:e

The above expression shows that the output voltage is greater or equal to the input voltage as the duty cycle goes from 0 to 1, and that it increases with D, theoretically to infinity as D approaches 1.

In a Boost converter, the inductor current equals the input current, whose average can be calculated from the output load current by equating the input and the output powers:

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

The inductor current equals the input current, so:

Using equation (11), the expression of average inductor current becomes:

The maximum value of inductor current is:

The minimum value of inductor current is:

Continuous conduction mode is ensured when

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