Hi, thank you all for your replies but I still do not know how to fix this circuit. Please if someone knows a better (and simpler) H-bridge than this one would you posting it, please ? Or at least tell me exactly how to fix this one ? I am still learning how to design circuits and I can't use an IC H-bridge. Please any help would very much appreciated.
You could use the logic from a DFF (CD4013) and 4 NOR (CD4001) gates with a PWM input signal. The PWM input signal would be 2x as fast as the actual frequency of the H bridge, and if you want to use it up to 20V the PWM input would probably need to be stepped up to the logic voltage as function gnerators only usually go up to a 10Vp. The NOR gate outputs can directly gate the H-bridge at any duty cycle your PWM input is at, so if you use 1% duty cycle pulse, there would be a 0.5% duty cycle time between the ON times of the N and P channel mosfets.
The clock of the DFF is tied to the PWM, and 2 NOR gate legs. The DFF has Q not tied to the D input and 1 of the NOR gates that are tied with the PWM on it's other input. The other NOR gate that has the PWM on one of it's inputs, has Q tied to it's other input. The outputs of these NOR gates have their signals inverted by the last two NOR gates. The outputs of all four NOR gates can be used directly to their coresponding mosfet of the H bridge. You should be able to see for yourself how this 2 chip 20V circuit works without resistors, optocouplers, boot straps, or caps.
It's a simplistic circuit, it's my own creation. It's sort of cheating telling you about it, as it took me alot of thought into making it. You can use any mosfets with it depending on how good you want them to be, because you can decide how much shoot through, if any, you want there to be by manually changing the frequency and duty cycle of the PWM input signal. Old CMOS logic is good up to about 10Mhz
Hope that helps..