Answer :
Final answer:
Buck and boost converters in discontinuous-current mode present intervals where the inductor current falls to zero. For a buck-boost converter in this mode, the output voltage can be calculated using the formula Vout = (D / (1 - D)) * Vin, where D is the duty cycle.
Explanation:
The question involves describing the operation of buck and boost converters in the discontinuous-current mode and deriving an expression for the output voltage. In the discontinuous-current mode, the inductor current in these converters falls to zero during a portion of the switching cycle before the next cycle starts.
Buck Converters in Discontinuous Mode
A buck converter steps down the input voltage. In discontinuous mode, the current through the inductor drops to zero before the next switching cycle begins, resulting in a different behavior compared to continuous mode, where current always flows through the inductor.
Boost Converters in Discontinuous Mode
A boost converter, on the other hand, steps up the input voltage. The boost converter also operates differently in discontinuous mode, with intervals where no current flows through the inductor, affecting the output voltage.
In the case of a buck-boost converter operating in discontinuous mode, the output voltage is given by the formula:
Vout = (D / (1 - D)) imes Vin
Where D is the duty cycle of the switch (on time divided by the total period) and Vin is the input voltage. The derivation of this formula stems from analyzing the energy stored and released by the inductor over a complete cycle when the current is not continuous.
