Discontinuous Operation

When the load resistor becomes high, the buck converter circuit operates in the discontinuous mode. The inductor current falls to zero when the switch is open and remains at zero till the switch becomes ON in the next cycle. Such a mode is the desirable mode of operation when variable frequency of operation is employed for voltage control. Additionally, discontinuous operation puts less stress on the diode and the circuit operates well. This aspect will be explained later.

The effect of load resistance on the inductor current is shown in Fig. 17. Given that the conduction is continuous, the average load current is V_o,avg/R. As the load resistance increases, the average load current decreases, but on the other hand, the change in inductor current as defined by equation (12) remains constant. As indicated by equation (13), the inductor current remains within the range specified below.

Fig. 16: Effect of Step Load Change: Reduction in Load

When the inductor current is continuous, the value of V_o,avg is as defined by equation (10) and it is not so if the conduction is discontinuous. After substituting for DI from equation (12), we get that

Hence a critical resistance, say R_C can be defined that makes the circuit operate at boundary of continuous conduction, a situation illustrated in Fig. 17. When the load resistance is higher than the conduction in inductor is discontinuous and it is continuous if the load resistance is less than R_C .

It can be seen from equation that at the boundary of continuous and discontinuous conduction,

Discontinuous operation is illustrated in Fig. 18. In Fig. 18, the duty cycle for the switch is defined to D₁, and the duty cycle for the diode is defined to D₂. It means that in each cycle, the switch conducts for a time interval equal to D₁T and the diode conducts for a time interval equal to D₂T, where T is the cycle period. It can be seen that for discontinuous conduction

At the boundary of continuous and discontinuous conduction, (D₁ + D₂) = 1. Given that the discontinuous, there is no current in the inductor for a time interval equal to (1 - D₁ -D₂)T.

The average load current is the average of the inductor current in Fig. 18. From Fig. 18,

Substituting for DI from equation (24), we get that

Solving for D₂,

When R > R_C, D₂ can be obtained from equation (27), assuming that D₁, f and L are known. Since the average of the inductor voltage over a cycle is zero, we obtain from Fig. 18 that,

Then

Substituting for D₂ from equation (27),

The second applet shows how D₂ and V_o,avg vary when R > R_C.

The first applet is shown below. It has a pull-down list of items, of which the only first item is displayed. On clicking on the downward arrow, the list is displayed. If any item of the list is high-lighted, its default value is displayed in the window adjacent to the label with the caption Set Value.. If one scrolls down or up the list, the default value of the item high-lighted is displayed in the window adjacent to the label with the caption Set Value. To change the default value of an item, highlight it first and then click inside the text-field window adjacent to the label with the caption Set Value. A line cursor would appear and the value can be changed. After changing the value, click on the Set Value label and then the program recognizes the change. It can be verified that the program has made the change out by inspecting the pull-down list again.

The default values of items in pull-down list are:

    Input Voltage,dc avg = 100
    Input Ripple Volt., pk-pk = 0
    Input Ripple Frequency = 100
    Switching Frequency,kHz = 20
    Inductance, microHenry = 500
    Capacitor, microFarad = 500
    Load Resistance, Ohms = 10
    Duty Cycle= 0.5
    Slow Response,0-200 = 0.

It is possible to see one of the four responses:

    Periodic response over one output cycle,
    Transient response over one output cycle,
    Periodic response over one input cycle, and
    Transient response over one input cycle.

Initially, the program sets '1' on the voltage axis of the plots equal to 100 V and sets '1' on the current axis to 10 A. If periodic response over one output cycle is chosen, the program assumes that the peak-to-peak ripple in input voltage is zero. The response can be slowed by varying the parameter called Slow Response. This parameter is effective only for periodic or transient response over one output cycle.

If the load resistance is changed from 10 W to 5 W, still '1' on the current axis would correspond to 10 A. If the Reset button is clicked, the program would make changes so that '1' on the voltage axis of the plots equal to input voltage and sets '1' on the current axis to (input voltage/load resistance).

When Start/Continue button is clicked, the program responds to the visible response type and starts with the values of inductor current and the capacitor voltage it had from the previous calculation. Initially they are set to zero values. If the Reset button is clicked, the program would make them zero again.

FIRST APPLET

The second applet takes in three parameters, namely the switching frequency, the inductor value and the duty cycle and plots the duty cycle of the diode and the output voltage as a function of the load resistance varying from R_C to (11 ´ R_C).

SECOND APPLET

 
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