JS.13

iai4

be neglected. The lurns ratio of the flybtitk transformer is 1:1. The coutrolier varies the duty cycle such lhat {(0),; is equal to v{t}/R,v;btre R is the emulated resistance. The input voltage is vjl) = tjsiii (cur). The input Alter removes tlie switching hatmouics frotn the input current (j(0.but has itegligible effect on the low-frequency components of the converter waveforms,

(a) Derive an expression forthe rectifierefftctency, in terms of (\f, К D-Rmi and R

(b) Given the following values, find the value of MOSFET on-resistance which leads to an efficiency of 96%.

rms input voltage 120 V

DCoutput voltage 120V

Diode Dl forward voltage drop 1.5V Load power 2(Ю W

Derive an expression for the emulated resistance /f,(Vj R, (г , v., ) of the average-current-controlled boost rectifier with ac line voltage feedforward. Fig. 1S.14.

Derive the CPM boost rectifier static input characteristics, Eq. (18,57).

The boost rectifier system of Fig. 1S.47 employs average current control with ac line voltage feedforward.

The ac line frequency is 50 Hz, The rectifier drives a constant-power load of 5(Ю W, The pulse-width modulator contains a ramp having a peak-to-peak amplitude ail V. There is no compensator in the inner wide-bandwidth average current control feedback loop. The average current sensing circuit has gain

1 -f-

Peat, detector

Muttipiier

-1-1-<innp

v,(s)

Gate driver

Pulse wdlh modulator

Compensator

500W

Fig, 18,47 Average current controlled boost rectifier witli inpul vollage feedforward, Problem 18.14.

Other eonverter parameter values are

/,= l(X}kHz L = 2.5mH

/o = = iukHz й, = иг

v = 385V l, = 230V

(a) Construct the inagnitude and phase Btxle diagrams of the loop gainTj) of the average-current-

toncrol loop. Label impoitant features, (h) Determine iiumerieal values of the crossover frequency and phase margin of 7{j},

The outer iow-bandwidth feedback loop has loop gain TJ.s), The compensator of this loop has constant gain G,j) = 330.Themultipliergainis = 2.The capacitor value is C = 680RThe reference voltage is 3.85 V.

(t) Determine the peak inagnitude of the output 100 Hz voltage ripple.

(d) Determine the quiescent control vohage V ,

(e) Construct the magnitude and phase Bode diagrams of the loop gain T\,Cs) of the outer feedbaclt loop. Label important features.

(f) Determine numerical values of the crossover frequency and phase margin of TJ,s).

18.1S A critical conduction mode controller causes a boosi rectifier to exhibit an ac input cunent waveform simihu to Fig. lS.19(b). The ac input voliage is 120 Vrms at 60 IIz. The rectifier .supplies 225 Vdc to a 120 W load. The boost converter inductance i.s L =600 fill.

(a) Determine the emitlaced resi.stance K

(b) Write the numerical expression for the converter switching frequencyas a function of and the applied tenninal voltages. Slcetch/jVS. time.

(c) What i.s the maxiiiiuin switching frequency.What is the minimum switching frequency?

(d) Derive an analytical expression for the rms transistor current for this control method, as a function ofthe inagnitude of the sinusoidal line current. Compare the rms transistor current of this approach with a CCM boost rectifier having negligible current switching ripple.

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