Two quadrant chopper:
There are two semiconductor controllable switches in the two-quadrant chopper.
Two quadrant type A chopper:
The figure shows the type A chopper. Both the switch never turn on at the same time because this will cause a short circuit. At the output, there is a freewheeling diode so the voltage is always positive. When the chopper 2 (or switch 2) is turned on then the voltage is zero and when chopper 1 is turn on then the output voltage Vo=Vs.
Two quadrant type B chopper:
The figure shows the two quadrant type B chopper. In this type of chopper, current is always positive. When both chopper 1 and chopper 2 are turned on then Vo=Vs. When chopper 1 and chopper 2 are off then Vo=-Vs.