The Buck Converter With RLE Load

The buck converter is a voltage step down and current step up converter. The two modes in steady state operations are:

Mode 1 Operation

In this mode the switch S₁ is turned on and the diode D₁ is reversed biased, the current flows through the load. The time domain circuit is shown in Figure. The load current, in S domain, for mode 1 can be found from

                                                                     (6)

Where

I₀₁ is the initial value of the current and I₀₁ = I₁.

 

Figure 4: Time domain circuit of buck converter in mode 1	Figure 5: Time domain circuit of buck converter in mode 2

From equation 6 , the current i₁(s) is given by

                                                                              (7)

In time domain the solution of equation 7 is given by

                                                              (8)

The mode1 is valid for the time duration . At the end of this mode, the load current becomes

                                                                                            (9)

Mode 2 Operation

In this mode the switch S₁ is turned off and the diode D₁ is forward biased. The time domain circuit are shown in Figure 5 . The load current, in S domain, can be found from

                                                                                (10)

Where

I₀₂ is the initial value of load current.

The current at the end of mode1 is equal to the current at the beginning of mode 2 . Hence, from equation 9 I₀₂ is obtained as

I₀₂ = I₂                                                                                                             (11)

Hence, the load current is time domain is obtained from equation 10 as

                                                                        (12)