The r.m.s value of output voltage v_o is given by

                                                                              (3)

The instantaneous output voltage (v_o) is rectangular in shape ( Figure 3 ). The instantaneous value of v_o can be expressed in Fourier series as:

                                                          (4)

Due to the quarter wave symmetry along the time axis ( Figure 3 ), the values of a_o and a_n are zero. The value of b_n is given by

                                          (5)

Substituting the value of b_n from equation 5 into equation 4 gives

                                                                                 (6)

The current through the resistor ( i_L) is given by

                                                                            (7)

For n = 1 , equation 6 gives the r.m.s value of the fundamental component as

                                                                                               (8)

Half Bridge DC-AC Inverter with L Load and R-L Load

The DC-AC converter with inductive load is shown in Figure 4 . For an inductive load, the load current cannot change immediately with the output voltage. The working of the Dc-AC inverter with inductive load is as follow is:

Case 1: In the time interval the swith S₁ is on and the current flows through the inductor from points a to b . When the switch S₁ is turned off (case 1) at t = T₁, the load current would continue to flow through the capacitor C₂ and didode D₂ until the current falls to zero , as shown in Figure 5 . Case 2: Similarly, when S₂ is turned off at t = T₂, the load current flows through the diode D₁ and the capacitor C₁ until the current falls to zero , as shown in Figure 6 .