ECEN 5817 Resonant and Soft-Switching Techniques in Power Electronics 1 Lecture 26 Discontinuous conduction mode (DCVM) Occurs at heavy load and low output voltage During the “discontinuous” interval, all four output diodes are forward-biased The capacitor voltage waveform exhibits an additional subinterval with v c = 0

ECEN 5817 Resonant and Soft-Switching Techniques in Power Electronics 2 Lecture 26 State plane trajectory: DCVM As predicted by CCM analysis DCVM trajectory DCVM occurs when

ECEN 5817 Resonant and Soft-Switching Techniques in Power Electronics 3 Lecture 26 DCVM solution Mode boundary Steady-state solution Output characteristics Solid lines: CCM Dashed lines: DCVM

ECEN 5817 Resonant and Soft-Switching Techniques in Power Electronics 4 Lecture 26 Design considerations Let’s now consider how to design a resonant converter in a dc-dc converter application in which the output voltage V is to be regulated over a range of operating points. Typical specifications are of the form P max ≤ P ≤ P min V gmax ≤ V g ≤ V gmin V is regulated How specifications map into the converter output plane M = V / nV g J = nR 0 I / V g The turns ratio n can be chosen to map the range of voltage operating points to any valid range of M: Current and power are related to J: Hence

ECEN 5817 Resonant and Soft-Switching Techniques in Power Electronics 5 Lecture 26 Mapping the specifications into the output plane

ECEN 5817 Resonant and Soft-Switching Techniques in Power Electronics 6 Lecture 26 PRC output plane

ECEN 5817 Resonant and Soft-Switching Techniques in Power Electronics 7 Lecture 26 Peak tank capacitor voltage stresses Proportional to output voltage in CCM Peak capacitor voltage, CCM: DCVM: (above equations are derived from the state plane trajectory) (the course notes include Fig. 5.26(b) that shows peak voltage stresses below the peak frequency in the double frequency region)

ECEN 5817 Resonant and Soft-Switching Techniques in Power Electronics 8 Lecture 26 Peak current stresses Proportional to output voltage in CCM Peak transistor current, CCM: DCVM: (above equations are derived from the state plane trajectory) (the course notes include Fig. 5.25(b) that shows peak current stresses below the peak frequency in the double frequency region)

ECEN 5817 Resonant and Soft-Switching Techniques in Power Electronics 9 Lecture 26 Design example Off-line dc-dc converter Design a dc-dc converter using a parallel resonant converter, to meet the following specifications: It is desired to operate MOSFET devices with zero- voltage switching

ECEN 5817 Resonant and Soft-Switching Techniques in Power Electronics 10 Lecture 26 Choice of range of operating points Here, “converter design” involves selection of a valid range of M and J, that is mapped into the range of converter specifications through selection of the turns ratio and characteristic impedance according to The values of L and C are then chosen as follows:

ECEN 5817 Resonant and Soft-Switching Techniques in Power Electronics 11 Lecture 26 One possible design A B C D Corners of the operating region for the design M max = 1.2, J max = 0.9 Operating region overlayed on the converter output characteristics

ECEN 5817 Resonant and Soft-Switching Techniques in Power Electronics 12 Lecture 26 Comparison of some other choices Choose M max, J max close to the boundary of allowed operation to minimize peak current stress Increasing M max leads to operation closer to resonance, with reduced range of switching frequencies