Northern Illinois University
Virtual Renewable Energy Laboratory
College of Engineering and Engineering Technology

A boost converter’s output voltage is always higher than the input voltage. Figure 1 shows the schematics of a boost converter. It has a dc input voltage, a transistor working as a switch, an inductor and a capacitor forming a low pass filter to smooth out the output voltage, and a load resistor. The diode provides a path for the inductor current when the switch is opened and is reverse biased when the switch is closed.

Figure 1. Schematics of a boost converter

When the switch is closed, the diode is reverse biased. The equivalent circuit is shown in Figure 2.

Figure 2. Equivalent circuit when the switch is closed

When the switch is open, the diode is forward biased. The equivalent circuit is shown in Figure 3.

Figure 3. Equivalent circuit when the switch is open

Output voltage of a boost converter is controlled by a pulse width modulated (PWM) signal shown in figure 4. The duty cycle is the ratio between the on time and the switching period shown in (1). By adjusting the duty cycle, we can obtain desired output voltage, which is shown in (2). When D increases, the output voltage increases. When D decreases, the output voltage decreases.

Figure 4. Pulse width modulated (PWM) Signal

If the inductor current is continuous, the boost converter is operating in continuous conduction mode. If the inductor current is reduced to zero, the boost converter is operating in discontinuous mode. We would like to keep the boost converter operating in continuous conduction mode. The minimum inductance to keep the boost converter in continuous conduction mode is the critical inductance. Value of the critical inductance is shown in (3).

Average inductor current is the same as the average load current in the load resistor. Value of the average inductor current is shown in (4).

The peak-to-peak inductor current is often a design criterion in the design of a boost converter. It is also called the current ripple. Equation (5) shows the value of the current ripple. The current ripple is inversely proportional to the inductance and the switching frequency. To reduce the current ripple, we can increase the inductance or the switching frequency.

The maximum inductor current is the average inductor current plus half of the current ripple, shown in (6). The minimum inductor current is the average inductor current minus half of the current ripple, shown in (7).

Another basic dc-dc converter is buck-boost converter shown in Figure 5. The output voltage of a buck-boost converter can be either higher or lower than the input voltage. Ratio of the output voltage over the input voltage is shown in (4). If D>0.5, the output voltage is greater than the input voltage. if D < 0.5, the output voltage is less than the input voltage.

Figure 5. Buck-boost converter