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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 yIl, 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 controlto—output
smallsignal 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 opencircuit voltage,
shortcircuit 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 Controltooutput transfer function. Apply the analysis derived in class to ﬁnd an analytical expression
for the controlto—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
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S 2006 Dynamic analysis of the parallel resonant converter 1.333333333
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 Spring '10
 Maksimovic
 parallel resonant inverter

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