The states of the K_j and K¢_j switches must be complementary. In order to allow the flow of the i_j current, without connecting in short-circuit the source U, we must have

• even K_j ON and K¢_j OFF
• even K_j OFF and K¢_j ON.

For passing from (K_j ON and K¢_j OFF) to (K_j OFF and K¢_j ON), two cases must be considered

• even the current i_j is positive
• even the current i_j is negative

Passing from (K_j ON, K¢_j OFF) to (K_j OFF, K¢_j ON) for i_j > 0.

If i_j is positive,

• when K_j is ON, the transistor T_j is conducting (figure 6).

  

  Figure 6

• when K¢_j is ON, the diode D¢_j is conducting (figure 7).

  

  Figure 7

The commutation from K_j ON (T_J conducting) to K¢_j ON (D¢_j conducting) is performed by commanding the turning off of the T_j (figure 8).

Figure 8

When T_j is OFF, we can command the ON state of T¢_j to ensure that K¢_j rests closed even the current i_j stops being positive and becomes negative

Passing from (K_j ON, K¢_j OFF) to (K_j OFF, K¢_j ON) for i_j < 0.

If i_j is negative,

• when K_j is ON, the diode D_j is conducting (figure 9)

  

  Figure 9

• when K¢_j is ON, the transistor T¢_j is conducting (figure 10).

  

  Figure 10

The commutation from K_j ON (D_J conducting) to K¢_j ON (T¢_j conducting) is performed by commanding the turning on of the T¢_j after previously turning off of the T_j, in order to avoid the simultaneous conduction of T_j and T¢_j and the short-circuit of the source U (figure 11).

Figure 11

Conclusion

For passing from K_j ON, K¢_j OFF to K_j OFF, K¢_j ON, we command the turning off of the T_j, then, after a delay t_d the turning on of the T¢_j:

• if i_j > 0, the turning off command of T_j determines the commutation

• if i_j < 0, the turning on command of T¢_j determines the commutation.

The delay t_d

• must be large enough to allow T_j to turn off if it was conducting
• no be too large because it fixes the distance that could exist (if i_j < 0) between the moment when the commutation is started, by the turning off command of T_j and the moment when the commutation really starts.