(a) Determine the eonvetter switching frequency, in Hz.

(b) Determine Lhe gain d{t)lv.(t] for (his circLiil.

(C) Over what range of v. is yoLir answer to (b) valid?

7.1i Use the averaged switch modeiing technique lo derive an iic equivalenL ciicuit model for the buck-boost

converter of Fig. 7.31:

(a) Replace the switches in Fig. 7.31 with the averaged switch model given in Fig. 7.50(c).

(b) Compare your result iviih the model given Ili Fig. 7. lu(b). Show thai lhe two models predict lire same small-signal linc-to-outpui transfer function c;,,{.v) = v/v.

7M Modify the CCM dc and smjll-signal ac averaged swiich models of Fig. 7.50, lo accotint for MOSFET

on-resislance R and diode forward voltage drop Vj.

717 Use the averaged swiich modeling lechniqiie [o derive a dc and ac equivaleni circuit model for the fly-

back converter of Fig. 7.18. You can neglect all losses and [he transformer leakage inductances.

(a) Define a swiich network containing the transistor Q] and the diode Dj as in Fig. 7.39(a). Derive я large-signal averaged switch model of the swiich network. The model should account for the iran.sformer turns ratio (i.

(b) Peilurb and linearize the model you derived in pari (a) to obtain lhe dc and ac small-signal averaged swiich model. Verify lhat for л = 1 your model reduces to the model shown in Fig. 7.39(d).

(c) Using lhe averaged swiich model you derived in part (b), sketch a complete dc and small-signal ac mode] of the flyback converter. Solve the model for the steady-.state conversion ratio m{d) =

(A) The averaged switch models you derived in parts (a) and (b) could be used in other converters having an isolation iiansfurmer. Which ones?

7,18 In the flyback converter of Fig. 7.18, the transistor on-resislance is .R , and the diode lorvvard voltage

drop is Vp,- Other losses and the transformer leakage inductances can be neglecied. Derive a dc and small-signal ac averaged switch model for the switch network containing the Iransistor Й] and the diode /Jj, The model shoidd account for the on-resislance R, lhe diode forward vultage drop V, and the ttansformer turns lalio n.

7J5 In the boost converter of Fig. 772(a), the v{t) and yO waveforms of Fig. 772(b) are observed. During

the transistor luin-on transition, a reverse current flows through lhe diode which removes lhe diode stored charge. As illusUated in Fig. 7.72(b), the reverse current spike has area - Q. and duration The inductor winding has resistance You may neglect all losses other than the switching loss due lo the diode stored charge and the conduction loss due to the inductor winding resistance.

(a) Derive an averaged switch model for the boost swiich network in Fig. 7.72(a).

(b) Use yoLir resLiIl of part (a) lo sketch a dc equivalent circuit model for the boost converter.

(c) The diode stored charge can be expressed as a function of the CLiirent J, as:

while the reverse recovery time t, is approximately constant. Given = 100 V, Л = 05,/, = 100 kHz,

= 100 пС/А , f,= 100 ns, fff = 0.1 Q., use a dc sweep simulation to plot lhe converlerefficiency as a function of the load current /др in the range:

p. пЛПп-p-

1(0 Q

Area -e.

Fig. 7.72 Boost cunvarter and waveforms illustrating reverse recovery of the diode. Averaged switth modeling in this converter is addressed in loblcm 7,19.

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