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Problems

19.1 Analysis of a half-bridge dc-dc parallel resonani converter, operated above resonance. In Fig, 19,53,

the elements C , L , and C,. are large in value, and have negligible switching ripple. You may assume that all elements are ideal. You may use the sinusoidal approximatron as appropriate.

0 o.sr, T, t

Fig, 19.53 Half-bridge parallel resonant cunverter of Problem 19,1; (a) schematic, (b) switch voltage waveform.

Sketch the waveform of the current;(().

Construe tan equivalent circuit for this converter, similar to Fig. 19.22, which models the fundamental components of the tank waveforms and the dc components ofthe converter input current and oulpul voltage. Clearly label the values and/or give expressions for all elements in your model, as appropriate.

(c) Solve your model to derive an expression for the conversion ratio VIV - MiF, Q, n). At rated (maximum) load, this converter produces /= 20 A at V= 3.3 V.

(d) What is the converter switching frequency /, at rated load?

(e) What is the magnittide ofthe peak transistor current at rated load? At imnimum load, the converter produces /= 2 A at V= 3.3 V.

(f) What is tlie converter switching frequency f at luiiiimum load?

(k) What is the magnitade of the peak transistor current at minimuin load? Compare with your answer from part (e)-what happens to the conductioii loss and efficiency at minimum load?

19.2 A dc-dc resonant converter contains an LCC tank network Hig. I9.1(d)k with an OLitpLit filter contain-

ing a filter inductor as in the parallel resonant dc-dc converter.

(a) Sketch an equivalent circuit model for Ihis converler, based on the approximate sinusoidal analysis method of Section 19.1, Give expressions for all elements in your model.

(b) Solve your mode], to derive an expression for the conversion ratio Л/= V/V. Kxpress Л/ as a function of F-f!f , 2, = RJRa, and n = CJC, where/ is defined as in Eq. (I9.5D) and is

LC,C,

(t) floe .Vf vs. F, for = I and Q, = I , 2, and 5. (d) Plot M vs. F, for л = t).25 and = 1, 2, and 5.

19.3 Dual nf the series resonant convener In the converter illustrated in Fig. 19.54, tf-p ip2, and are large

filter elements, whose switching ripples are small. L and С are tank elements, whose waveforms iil) and Vflt) are nearly sinusoidal.

Fig, 19.54 Dual of the series resonant converter, Problein ]y.,l.

(a) Using the sinusnidal approximatioii inethod, develop equivalent circuit models for the switch network, tank network, and rectifier network.

fb) Sketch a Bode diagram of the parallel LC parallel tank impedance.

(c) Solve your model. Find an analytical solution for the converter voltage conversion ratio M= WVj, as a function of the effective and the normalized switching frequency F = JJff,-Sketch M vs. F.

(d) What can you say about the validity of lhe sinusoidal approximation for this converter*. iVhich