analogspiceman
Junior Member
Offline
Posts: 23
|
If the inductor is small enough so that its current never goes continuous, even at the heaviest load, then the RHP zero simply disappears. This is because then any change in inductor current called for can be achieved in one cycle.
When the inductor is relatively large so that its current is heavily continuous, then the RHP zero arises because in order to increase the output, duty cycle must be increased to build up inductor current, but this also immediately results in a smaller portion of the slowly building inductor current being directed to the output (so output current falls at first) with the increasing portion being dumped to ground in order to apply positive net voltage across the inductor.
A system with one or more RHP zeros is known as a non-minimum phase system (anything with pure delay falls into this category) and cannot be compensated via global feedback for loop gain bandwidth much past the frequency of the lowest RHP zero.
The article you linked includes a derivation of the expression for the frequency of the RHP zero: fz = Ro/Lb*(1-D)^2. This only holds if the inductor current is continuous where simple duty cycle averaged voltages drive its current. If the inductor current goes discontinuous, then a third system state is introduced, which alters the system's two-state dynamics, completely eliminating the RHP zero.
If a RHP zero exists under certain line/load conditions, this may not be a limit to system dynamics. It is only necessary that the RHP zero not be allowed to fall low below somewhere slightly above the switching frequency so that its phase effects don't come into play before the normal PWM limits to loop gain bandwidth.
Rather than work with equations, you can use the simulator to see how the RHP zero moves and various system parameters are stepped (e.g. inductor value, input voltage, output load, etc.). This zero is easy to see by plotting the ratio of current out of the boost diode divided by current through the boost inductor.
|