6.4 Coin-ener Evaiuanon and Вемцп

Tal>t 6.2 Spreadsheet design exainpie

The worst-case maximum ripple occurs in CCM at minimum duty cycle. Solution for L yields

DVT,

2Д,-

(6.62)

This equation is used to .select! such that the worst-case ripple is equal to the specified value of Al. The required value of L is listed in Table 6.2. The required value of С that leads to the specified voltage ripple Av is also comptited, using Eq. (2.60). Since Eq, (2,60) neglects capacitor esr, a larger valtie of Ctnay be required in practice.

If the converter operates in the discontinuous conduction mode at light load, then the controller must reduce the duty cycle D to maintain the required output voltage V. The conversion ratio MiD, K) of the DCM forward converter can be fotmd analytically, using the method developed in the previous chapter. Alternatively, the nonisolated buck converter solution, Eq. (5.29), can be applied directly if all element values are referred to the trajisformer secondary side. Hence, tlie output voltage in EtCM is given by

2v:k

(6,64)

The actual duty cycle i.s the smaller of Eqs. (6.60) and (6.64). The minimum duty cycle occurs at minimum load power and maximum V , and is given in Table 6.2.

Worst-case component .stresses can now be evaluated, The peak transistor voltage is given by Eq. (6.37). The rms transistor current is calculated with the help of .Appendix 1. With the assumption that the transformer magnetizing current can be neglected, the transistor cuirent is equal to the reflected inductor ctirrent iXOn/fi] during subinterval i, and is equal to zero during subintervals 2 and 3. The rnis transistor current is therefore

where /- Pi,JV. The worst-case value of /ц,. ,,occurs at maximum load power and at maximum duty cycle. Expressions for the worst-case stresses in the diodes and output capaciUir, as well as for the flyback converter, are found in a similar manner. Their derivation is left as an exercise for the student.

The designs of Table 6.2 are good ones which illustrate the tradeoffs inherent in .selection of an i.4olated converter topology, although some additional design optimization is possible and is left as a homework problem. Both designs utilize a turns ratio of 8:1. The rms transistor current is 22% higher in tlte flyback converter. This current could be reduced, at the expense of increased transistor voltage. The flyback converter imposes only 510 V on the transistor. A transistor rated at Ш) V or КХЮ V could be used, with an adequate voltage derating factor and some margin for voltage ringing due to transformer leakage inductance. The 780 V imposed on the transistor of the forward conveiter is 53% higher than in the flyback converter. Power MOSFETs with voltage ratings greater than l(XX) V are not available in 1ВД7; hence, when voltage ringing due to transformer leakage inductance is accounted for, this design will have an inadequate voltage design margin. This problem could be overcome by changing the reset winding turns ratio 2 t y using a two-transistor forward converter. It can be concluded that the transforiner reset mechanism of the flyback converter is better than that of the conventional forward converter.

Because of the pulsating nature of the secondary-side currents in the flyback converter, the rms and peak secondary currents are significantly higher than in the forward converter. The flyback convetter diode must conduct an rms current that is 47% greater than that of forward converter diode fJj, and 80% greater than the current in forward converter diode Dj.The secondary winding of the flyback transformer must also conduct this current. Furthermore, the output capacitor of the flyback converter must be rated to conduct an rms current of 9.1 A. This capacitor will be much more expensive than its counterpart in the forward converter. It can be concluded that the nonpulsating output current property of the forward converter is superior to the pulsating output current of the flyback. For these reasons, Ilyback converters and other converters having pulsating output currents are usually avoided when the application calls for a high-current output.

with АГ= and R = Solution lor the duty cycle D yields

6.5 Suujfijary of Key Points 177

6.5 SUMMARY OF KEY POINTS

1. The btJDSL ctmverler can be viewed an inverse butlt converter. whiJe the buclt-boost and Cuk converters arise from cascade connections of buck and boost conveners. The properties of these converters are consistent with their origins. Ac outputs can be obtained by differentia! connection of the load. An infinite number of converters are possible, and several are listed in this chapter.

2. For understanding the operadon of most converters containing transformers, the transformer can be modeled as a magnelijEing inductance in parallel with an ideal transformer. The magnetizing indnciance must obey all of the usual rules for indtictors, inckiJing the principle of volt-second balance.

3. The steady-stale behavior of transformer-isolated converters may be understood by first replacing the transformer v/iih the magnelizing-induciance-pks-ideal-transformer equivalent circuit. The techniques developed in the previous chapters can Ihen be applied, inclnding use of inductor volt-second balance and capacitor charge balance to find dc currents and voltages, use of equivalent circuits lo ratKiel ksses and efficiency, and analysis of the discontinuous conduction mode.

4. In the full-briJge, half-bridge, and push-pull isolated versions of the buck and/or boost converters, the transformer frequency is twice the output ripple frequency. The transformer is reset while it transfers energy: the applied voltage polarity alternates on successive switching periods.

5. In Ihe cimvenlional forward Converter, the transformer is reset while the transistor is off The transformer magnetizing inductance operates in the discontinuous conduction mode, and the maximum duty cycle Is limited.

6. The flyback converter is based tm the buck-boosl converter, The flyback transformer is actually a two-winding inductor, which stores and transfers energy.

7. The transformer turns ratio is an extra degree-of-freedom which Ihe designer can choose to optimize the converter design. Use of a computer spreadsheet is an effective way to delermine how the choice of turns ratio affects Ihe component voltage and current stresses.

8. Total active switch stress, and active switch udlization, are Iwo simplified figiires-tif-merit which can be used to corapaie the various convertercircuits.

References

[1] S. Cuk, Modeling. Analysis, and Design of,Switching Converters, Ph.D. thesis, California Institute of Technt>logy, November 1976.

[2] S. Cuk and R. D. MiDDLEBROOK, A New Optimum Toptilogy Switching Dc-to-Dc Converter, IEEE Fawer Electronics Specialisrs Conference, 1977 Record, pp. 160-179, June 1977.

[3] E. Landsman, A Unifying Eterivaliim of Switching Dc-Dc Converter Topologies, IEEE Power Electron-

ics Specialists Conference, 1979 Record, pp. 239-243, June 1У79.

[4] R. Tymerski and V. Vorperian, Generation, Classification, and Analysis of Switched-Mode Dc-to-Dc Converters by the Use of Converter Cells, Proceedings International Telecommunications E>ier}>\ Conference, pp. 1Й1-195, October 1986.

[5] S. twK and R. Erickson, A Conceptually New High-Frequency Switched-Mode Amplifier Technique Eliminates Current Ripple, Proceedings Fifth National Solid-State Power Conversion Conference (Pow-ercon 5). pp. G3.1-G3.22, May 1978.