networks; in the typ ical dc–dc converter application, the input voltage sourceis effectively trans-formed into its dual, a n output current source o f value Series resonant converters have been pur-posely designed to operate in thek =2DCM, at power levels of several tens of kW.The complete control plane character istics c an now be plotted using Eqs . (19 .77) t o ( 19.89).

19.5Exact Characteristics of the Series and Parallel Resonant Converters745The result is shown in Fig. 19 .45, and the mode boundaries are explicitly diagrammed in Fig. 19 .46. Itcan be seen that, for operation above resonance, the only possible operating mode is thek =0 CCM, andthat the output voltage decreases monotonically with increasing switching frequency. Reduction in loadcurrent (or increase in load resistance, which decreasesQ) causes the output voltage to increase. A num-ber of successful designs that operate above resonance and utilize zero-voltage switching have been doc-umented in the literature [7,21].Operation below resonance is compl icated by the presence of subharmonic and discontinuousconduction modes. Thek =1 CCM andk =2 DCM are well behaved, in that the output voltage increasesmonotonically with increasing switching frequency. Increase of the load current again causes t he outputvoltage t o decrease. Successful designs that operate in these modes a nd employ zero-current switchingare numerous. However, operation in the h igher-order modes(k =2 CCM,k= 4 DCM, etc.) is normallyavoided.GivenFandQ,the operating mode can be evaluated directly, us ing the following algor ithm.First, the continuous conduction mode k corresponding to operation at frequencyFwith heavy loading isfound:where INT(x) denotes the integer part ofx. Next, the quantityis determ ined:

746Resonant Conversion

19.5Exact Characteristics of the Series and Parallel Resonant Converters747The converter operates in typekCCM provided that :Otherwise, t he converter operates in typeDCM. A simple algorithm can therefore be defined, in whichthe convers ion rat ioMis computed f or a givenFandQ.First, Eqs . (19 .90) t o (19.92) are evaluated, t odetermine the operating mode. Then, the appropriate equation (19.83), (19.85), or (19.88) is evaluated tofindM.OutputI–Vplane characteristics for thek =0 CCM, plotted using Eq. (19 .79), are shown in Fig.19.47. The constant-frequency curves are elliptical, and all pass through the pointM =1,J= 0. For agiven switching frequency, the operating point is given by the intersection of the elliptical converter out-put characteristic w ith t he loadI–Vcharacteristic.Output plane characteristics that combine thek =1 CCM,k =1 DCM, andk =2DCM areshown in F ig. 19.48. Thesewere plotted u sing Eqs . (19 .79), ( 19.85), a nd (19.88). Thesecurves wereplotted with the assumption that the transistors are allowed to conduct no longer than one tank half-cycleduring each switching half-per iod; th is e liminates subharmon ic modes and causes t he converter to oper-ate ink =2 ork =1 DCM wheneverIt can be seen that the constant-frequency curves are ellip-

Upload your study docs or become a

Course Hero member to access this document

Upload your study docs or become a

Course Hero member to access this document

End of preview. Want to read all 881 pages?

Upload your study docs or become a

Course Hero member to access this document