hw4soln - So lather/x Homework Assignment 4 Resonant and...

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Unformatted text preview: So lather/x Homework Assignment 4 Resonant and Soft Switching Techniques in Power Electronics ECEN 5817 Spring 2006 Dynamic Analysis of a Parallel Resonant Inverter A certain parallel resonant inverter circuit includes a full bridge switch network as illustrated in Fig. 19.1 of the text, with the parallel tank network of Fig. 19.1(c). The element values are: L = 627 yI-l, C = 7.9 nF, R = 400 Q, and VE = 150 V. The controller includes a frequency modulator circuit whose control input is voltage vin(t). This frequency modulator generates the gate drive signals for the switch network; its switching frequency fs depends on vino) according to the formula f: = Km vi", with Km = 50 kHz per volt. Variations in vin(t) therefore cause the switching frequency to vary proportionally, leading to variations in the amplitude (envelope) of the ac output voltage v(t). The objective of this assignment is to work out analytical expressions for the control-to—output small-signal transfer function Gem,(s), i.e., the transfer function from perturbations in the control voltage vin(t) to variations in the envelope of the ac output voltage waveform v(t). You should accomplish this by application of the methods developed in lectures 12 to 14. 1 Quiescent operating point analysis. At what switching frequency does the converter operate with an out— put power of 50 W? For this quiescent switching frequency, determine the quiescent value of the peak ac output voltage. Sketch the elliptical output characteristic and label the values of the open-circuit voltage, short-circuit current, and tank output impedance. 2 Tank transfer function. Determine the numerical values (real and imaginary parts) of the poles and any zeroes of the tank transfer function H003). Sketch the pole locations in the complex s—plane. 3 Control-to-output transfer function. Apply the analysis derived in class to ﬁnd an analytical expression for the control-to—output transfer function Gem/(s). Hint: it is possible to derive relatively simple expres— sions for the zeroes and dc gain in this example. The result contains a dc gain, one zero, and four poles. 4 Root locus. Determine the numerical values of the poles and zero of Gm(s). Sketch the pole and zero locations in the complex s—plane. Which comer frequencies are lower than half of the switching fre- quency? 5 Frequency response. Construct a Bode diagram of the magnitude and phase of G m0). Label salient fea- tures. L~ TLQ Phe jt‘V'CS Viv» 30/‘d1‘ém above rﬂ\$8n®v~ce F: l. 201 W)“ ﬁrm 1 (“53%, 4W5 M9 “VD £5: '3 I u R \ @ 71m, OFQAA~Q‘(FCLL{+ od‘fuxv} “01% L5 5%)“ Um: : 1%“3‘ “RN 1 \$3! V m (was @5912 = ‘ 2%le m amt/mags} MN MM g 35% 4:3 Isa: La : OSGA U 290 C3“)ng 1. Tom», Mk {MKQM ‘ ( W9 :— Sk _ \+ h a A M ONLH'V 052;: 7—5—5 Q ,5 R [9‘00 600) ~ a Ea > J? m M9 r9063 05* Wgnd‘wgo)l>§ﬂwso> : M 917K093) (3%) “WW “55* P499 W Loco?\7:sw\ av? {>495 0‘0 @“(331 jws) @ F‘AMU ) co to ~ 1 2 ram2 33:..— Geml(g> Z Q kKM W s (H— w‘fng"wr ‘(Y 3 “’2? w? “A ‘ ’1 W 2 / f 1+ "’ ‘02 wk (H‘ QPW *(ma>)( Qﬁmﬂx (ado) L <_; WI” mam as w: (w:+w;o w); ) vr wFrwg—w‘c .— __ "/— W Sr “ML (j\;)04\ VQIMS“ So»\\‘e.2f w—g’eof‘mv-eg are ﬁkﬂaﬂ OV\ Mycf Pa? . a {OWQNW PaIeS ot’r BISMe) on‘es Z “byw‘fwg #53 0?} (gskHa)€Q= 34 6%;va above \ \$91M} ) I C W of“ H0 EH2 [LWJavae sﬁﬂgg AC 554% oxc ‘255 => WM AB By) For maﬁ— LOCVK} ACOSW) \$52K 19% 7 New HW#4 ECEN 5817 S 2006 Dynamic analysis of the parallel resonant converter 1.333333333 150 200 0.000627506 7.91186E-09 400 75000 50000 1.05 1.752266974 71428.57143 50 493.4802201 281 .6238777 Problem solutions 627.5056511 pH Hz/V stated element values and part 1 calcs .11 og<zévnwr 3‘3 || 200 | | Voc Isc wO wr wi 6.27E-04 400 7.90E-09 50 1.50E+02 1.33E+00 200 281.7216509 1.419841175 1.20E+00 7.15E+04 8.59E+04 7.64E+02 4.31E+02 5.64E-01 4.49E+05 1.58E+05 4.21E+05 69.38099844 5.40E+05 = 0990 2.52E+04 6.69E+04 @ Genv salient features wL 198094.5235 31527.72261=€[_ QL 6.26E-01 wH 973204.8861 154890.3683 =€H QH 3.08E+00 zero freq 8.82E+05r[9 1.40E+05 He dc gain -2.55E+02 :1) 4.81E+011,\£, WES Suﬁc'léwﬂj‘ [(235 W“: t I ‘Hmwx MUG 0'? +5.2 §W\+¢\Mv\\j mom \ _27bo> ...
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hw4soln - So lather/x Homework Assignment 4 Resonant and...

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