where Eo and Ei are the output and input voltages of the converter, a is the turns-ratio of output transformer and J is the pulse width angle. Equation (4.1) shows that the output voltage of the series-resonant converter is independent of output load and it can be controlled by varying the pulse width angle against any variation of input voltage. The output voltage level can be matched, as desired, by choosing a proper value of transformer turns-ratio (a) for a given application. The typical performance curves of the series converter for varying load conditions are shown in Fig. 19. The following points are observed from this figure: (1) The output current (Zs) of the converter decreases with a decreasing output load. This allows the converter to maintain an excellent efficiency from fullload to reduced-load. (2) The control circuit of the converter is easier to design as pulse width angle (<5) is relatively constant from full-load to no-load. 4.3.2 Parallel-resonant Converter Topology. The circuit diagram of a parallel-resonant DC/DC converter is shown in Fig. 20. This circuit is the same as shown in Fig. 5 except that a rectification and filtering stage has been added across the parallel resonant capacitor Cp. As discussed in Section 3.3.1, a large value of capacitor Cp is required to obtain a relatively constant output voltage for full-load to no-load operation. This results in excessive heating of the converter circuit and requires a higher volt-ampere rating of the inverter switches. One difference between the parallel-resonant DC/AC inverter and DC/DC converter circuits is that the latter circuit is not required to provide a high quality voltage source across capacity Cp as this voltage is rectified and filtered to obtain DC output voltage. Therefore, the emphasis is to optimize the components' rating in designing the DC/DC converter. The output voltage of the converter with this consideration is given by:
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