Mode2 : This mode is valid for the time duration

                                                                                        (8)

In this mode the switch S₁ is open and the inductor current flows through the RL load and the equivalent circuit is shown in Figure 6. The voltage equation in this mode is given by

                                                                            (9)

For an initial current of I₂, the solution of Equation 9 is given by

                                           (10)

The current at the end of mode 2 is equal to I₁:

   (11)

were Z = TR/L

 

Solving Equation 7 and Equation 11 gives the values of I₁ and I₂ as

                                               (12)

 

                                               (13)

The ripple current is given by

                                                                  (14)

The above equations are valid if . In case , the converter works in discontinuous mode.

 

Boost Converter with Filter and Resistive Load

A circuit diagram of a Buck with filter is shown in Figure 7. Assuming that the inductor current rises linearly from I₁ to I₂ in time t₁

                                                     (15)

Figure 7: Configuration of a Buck Boost Converter