The Buck Converter with R Load and Filter

The output voltage and current of the converter contain harmonics due to the switching action. In order to remove the harmonics LC filters are used. The circuit diagram of the buck converter with LC filter is shown in Figure 6 . There are two modes of operation as explained in the previous section.

The voltage drop across the inductor in mode 1 is

and                                                                         (25)

where i_L is the current through the inductor L_f

            i_sw is the current through the switch

The switching frequency of the converter is very high and hence, i_L changes linearly. Thus, equation 25 can be written as

                                                                                        (26)

where T_on is the duration for which the switch S remains on

            T is the switching time period

Figure 6: Buck converter with resistive load and filter	Figure 7: Voltage and current waveform

Hence, the current ripple is given by

                                                                                    (27)

When the switch S is turned off, the current through the filter inductor decreases and the current through the switch S is zero. The voltage equation is

                                                                                  (28)

where i_D is the current through the diode D

Due to high switching frequency, the equation 28 can be written as

                                                                             (29)

where T_off is the duration in which switch S remains off the diode D conducts

Neglecting the very small current in the capacitor C_f , it can be seen that

for time duration in which switch S conducts

and

for the time duration in which the diode D conducts

The current ripple obtained from equation 29 is

                                                                                          (30)

The voltage and current waveforms are shown in Figure 7 .