parts of your M vs. F plot of part (c) are valid and accurate?

194 The converter of Problem 19.3 Operate. below resonance.

(a) Sketch the wuveform vf), Foreiich subintervul, lubel: ii) which ofthe diodes D, to and transistors Q to conduct current, and (i7) which devices block voltage.

(b) Does the reverse recover pnieess of diodes D[ to lead to switching loss? Do the output capacitance.* of transistors Q, to Й lead to switching loss?

(*) Repeat parts (a) and (b) for operatiun above re.*onance.

19.5 .\ parallel resonant converter operates with a dc input voltage of = 270 V. The converter supplies 5 V lo a dc load. The dc load power varies over the range 20 W to 200 W. It is desired to operate the power transistors with zero voltage switching. The lank element values are L = 57 IxH, = 0,9 nF, referred to the transformer primary. The parallel resonant tank network contains an isolation iranslormer having a turns ratio of 52:1.

(a) Define Fas in е4. (19.19). Derive an expression for F, as a function ofMand 0,.

(b) Determine the switching frequency, peak transistor current, and peak tank capacitor vuitage at the maximum loud power operating point.

(t) Determine the switching frequency, peak transistor current, and peak tank capacitor vuitage at the minimum load power operating point.

19.6 In a certain resonant inverter application, the dc input voltage is = 320 V. The inverter must produce an approximately sinusoidal output voltage having a frequency of 200 kHz. Under no load (output open-circuit) conditions, the inverter shuuld produce a peak-to-peak output voltage of 1500 V. The nominal resistive operating point is 200 Vrms applied to 100 Q. A nonisolated LCC inverter is employed, h is desired that the inverter operate with zero-vohage switching, at least lor load resistances less than 200 il

(й> Derive expressions for the output open-circuit voltage V iind short-circuil current /j. uf the LCC inverter. E.\prEss your results а.ч functions oi F = f/j, V, = L/C,\[Cp and n = CJC. The open-circuit resonant frequency/ is defined in Eq. (19.50).

(b) To meet the given specifications, how should the short-circuit current l be chosen?

(t) Specify tank element values that meet the specifications.

(d) Under what conditions does your design operate with zero-voltage switching?

( ) Cumpute the peak transistor current under nu-load and short-circuit conditions.

19.7 A series resonant dc-dc converter operates with adc input vuitage of = 550 V. The converter supplies 30 kV to a load. The dc load power varies over the range 5 kW to 25 kW. It is desired to operate the puwer transistors with zero-voltage switching. The ma.\imum feasible switching frequency is 50 kHz. An isolatitm transformer having a 1:л turns ratio is connected in series with the lank network. The peak lank capacitor voltage should be no greater than 2000 V, referred 10 the primary.

(a) Derive expressions fur the peak tank capacitor voltage and peak lank induclor current.

(b) Select values for the lank inductance, lank capacitance, and turns ralio, such thai the given specifications are met. Allempt to minimize the peak lank inductor current, while maximizing the worst-case minimum switching frequency.

19Л Figure 19.55 illustrates a full-bridge resonant inverter containing an LLC tank network.

(a) Sketch the Bode diagrams of the input impedance under short-circuit and open-circuit conditions: II Lfia) II and Zijto) . Give analytical expressions for the resununl frequencies and asymptotes.

(b) Describe the conJilions on switching frequency and load resistance that lead to zerij-voltage switching.

(C) Derive an expression Ior Ihe lrequency. . where II II = II Z- II.

с L,

-олпг

R < V

Fig. 19.S5 LLCinvorterof Pmblem 19.x,

(d) Sketch [he Bode plo[ ol II HJJiil) . Label (he lesOnanl fretjuency, anJ give analytical expressions for lhe asympiotes.

You are given the LLC inverter circLiit of Fig. 19.56. UnJer nominal conditions, this converter operates at switching frequency/, = 100 к H/.. All elements are ideal.

19.10

12V V

0.4 ЦР 2.5 цН

е. I

1 :n

15 цН

R f V

п = 7.5

19.S6 Iraiisformer-isolated LLC inverter, Pivbkm 19,9,

(a} Determine the numerical values of the open-circuit peak OUIpul voltage 1, anJ the shurt-circuit peak output current

(b) Sketch the elliptical output characteristic. Over what pordon of this ellipse Joes the converter operate with zero-voltage switching ? Does it operate with zero-voltage switching at matched luad?

(t) Sketch the Bode pints of Z.jj and [ Z , and label the numerical values iiffyf.f ,. and/,.

(d) What is the numerical value of the peak transistor current when R = 0? When R ?

(e) The inverter operates with load re.sistances that can vary between 500 ii und an open circuit. What is the resnlting range of output voltage? Does the inverter always operate with zero-voltage switching?

It is desired to obtain a cunverter with carrent soLirce characteristics. Hence, a series resonant converter is designed furoperatiun in the I: = 2 disconlinuoLis conduction mode. The switching frequency is chosen to be/, = 0.225/j, where/(, is the tank resonant frequency {consider only open-loop operation). The load К is a linear resistance which can assume any positive value: 0 < R <

(a) Plot the output characteristics (M vs. J), for all values of Д in the range 0 < Д < i=. Label mode boundaries, evaluate the short-circuit current, and give analytical expressions for the output characteristics.

(Ь) Over whii[ lange of R (referred lo ihe lank eharaelerislie impedance Лд) does ihe converler operate as intended, in die i = ! discontinuous conduction mode ?

19.11 The purullel resonant converter us j single-phuse high-quulily rectifier, il is desired to uliliie a trans-foriTier-isolaled parullei resonani dc-dc converter in j singie-phase low-haririonic reclifier system. By properly varying the converler switching frequency, a near-ideal reclifier System lhat can be niiideled as in Fig. 1S.I2 is obtained. You may utilize the results of Section 19.5.2 lo answer this problem. The parallel resonant tanli network contains an isoladon transformer having a 1: n turns ratio. You may use either appruximate graphical analysis or computer iteration lo answer parts (b) and (c).

(a) Plot the normalized input characierisdcs (normalized inpul voltage = fVglv vs. normalized input current - i lSo/v)of the parallel resonant converler, operated in the continuous conduction mode above resonance. Plot curves foг=Л/o= 1.0, 1.1, 1-2, 1.3, 1.5, and 2.0. Compare these characteristics wilh the desired linear resistive input characteristic vH = Л [;.

(b) The converler is operated open-loop, wilh F= I.I. The applied normalized input voltage is a rectified sinusoid olunilvmagnilude: mj,l\ = sin ((Uf) j. Sketch the resulting normalized input current waveform ;((). Approsimalely how large is the peak current? The crossover dead time?

(c) A feedback loop is now added, which regulates the inpul current to follow the inpul voltage such that ij,(/)= *j(/Vj, uj( nj.Yt>u may a.s.sume that the feedback Imip operates perfectly. Forthe ca.se р:ли1111Ы~ with the same applied w(r) waveform as in part (b), sketch the switching frequency waveform for one ac line period [i.e.. show how the conlroller musi vary F lo regulate Jj,(f)l. What is [he maximum value of f? Note: In practice, the converter would be designed U> operate with a smaller peak value of , so thai the switching frequency varialions would be belter behaved.

(d) Choo.se element values (lank inductance, tank Capacitance, and transformer turns rado) such that [he converter ofpart (c) meets the following specifications;

Ac inpul voltage 120 Vrms, 60 Hz

DC ouiput voltage 42 V

Average power SOO W

Maximum switching frequency 200 kHz

Refer the element values to the primary side oflhe transforraer.