Generalized Analysis for ZCS

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1 Generalized Analysis for ZCS The QRC cells (ZCS and ZS) analysis, including the switching waveforms, can be generalized, and then applies to each converter. nstead of analyzing each QRC cell (L-type ZCS, L-Type ZS, M-type ZS ) for each converter (buck, boost ) By using generalized parameters, it is possible to generate a single transformation table from which the voltage converter ratios and other important design parameters for each converter can be obtained directly. 1

2 The Generalized Switching-Cell Generalized switching-cell of the quasi-resonant ZCS L-type cell 2

3 The Generalized Transformation Table Each QRC cell can be analyzed separately, and then the transformation table is used to obtain the design parameters for a specific converter using the analyzed QRC cell 3

4 The following parameters, will be used Generalized Analysis Parameters The normalized cell input voltage : ng = g in ng where is the switching-cell average input voltage as shown in Figure 6.37 g The normalized cell output current nf : = nf F o where F is the switching-cell average output current. The normalized filter capacitor voltage nf : F nf = F in where is the filter capacitor average voltage. The normalized filter inductor current nt : T nt = T o where is the filter inductor average current (in the ZCS-QSW CC family). 4

5 EEL6246 Power Electronics Chapter 6 Lecture 7 Dr. Sam Abdel-Rahman The normalized cell output average voltage nbc : nbc = bc in Generalized Analysis Parameters where bc is the switching-cell average output voltage. The normalized current entering node b in the switching cell nb = b b o where is the average current entering node b. nb 5

6 Basic ZS QRC Topologies (a) (b) (c) Fig 6.38 The dc-dc ZCS QRC family. (a) Buck. (b) Boost. (c) Buck-boost. 6

7 Basic Operation of the ZCS-QRC Cell There are four modes of operation and their analysis is summarized as follows: Mode 1 ( t ) t o t 1 t is assumed that before t =, S was OFF and D was ON to carry F. t 0 Mode 1 starts when S is turned ON while D is ON, which causes L to charge up linearly until the current through it becomes equal to at t = t causing D to turn OFF. F 1 7

8 Mode 2 ( t1 t t 2 ) starts when D turns OFF while S is ON, causing a resonant stage between C and L to start until the current through L drops to zero at t = t2 causing S to turn OFF at zero current (soft-switching). Mode 3 ( t2 t t 3 ) starts when S turns OFF at zero current. The resonant capacitor starts discharging linearly causing the voltage across it to drop to zero again, causing D to turn ON at zero voltage at. t = t 3 Mode 4 ( t 3 t t o + T s ) is a steady-state mode and nothing happens in it until S is turned ON again to start the next switching cycle. 8

9 Typical ZCS QRC Waveform Fig 6.39 Main ZCS QRC switching-cell waveforms. 9

10 ZCS QRC Generalized Steady State Analysis Mode 1( t ) v c t o ( t) = 0 g t) = ( t t L ( t 1 ) = 0 l ( 0 i v C i ( t 1 ) = l F ) t 1 Mode 2 ( t t ) v c 1 t 2 [ 1 cos ( t t )] ( t ) = g ω o 1 g i ( ) sin ( t t l t = F + ω o 1) Z o ( t 2 ) = 0 i L Mode 3 ( t t ) 2 t 3 F vc ( t) = ( t t2 ) + g C i l v c ( t) = 0 ( t 3 ) = 0 [ 1 cos β ] Mode 4 ( t 3 t t o + T s ) v c ( t) = 0 ( t) = 0 i L (6.89) (6.90) (6.91) (6.92) (6.93) (6.94) (6.95) 10

11 Generalized ntervals Equations To simplify the analysis, the following time intervals are defined: α = ω o ( t 1 t0 ) β = ω o ( t 2 t1) γ = ω o ( t 3 t2 ) δ = ω o (( t0 + Ts ) t3) Fig 6.40 Equivalent circuits for (a) mode, (b) mode 2, (c) mode 3, and (d) mode 4. 11

12 These intervals can be derived as follows: From Eqs. (6.89) and (6.90), α is given by, α = ω t ) = o ( 1 t0 Z o g F Generalized ntervals Equations (cont d) By using the normalized parameters, we have α = ω t ) = o ( 1 t0 M Q nf ng From Eqs. (6.92) and (6.93); β is given by, 1 M nf β = ω o ( t2 t1) = sin ( ) Qng From Eqs. (6.94) and (6.95), γ is given by, Qng γ = ω o ( t3 t2 ) = (1 cos β ) M nf From Fig and the intervals α, β and γ, we have δ given by, δ = ω o (( t0 + Ts ) t3 ) = 2π α β γ f ns (6.96) (6.97) (6.98) 12

13 Generalized Gain Equation The cell output to input generalized gain can be found using the average output diode D voltage as follows: D ave = C ave 1 = T s t 0 + t 0 T s v C ( t) dt 1 sin β F 2 = g (( t2 t1) ) ( t3 t2 ) + g (1 cos β )( t3 t2 ) Ts ωo 2C By using the normalized parameters defined previously, we have: nd f ns M nf 2 = γ ng ( β + γ sin β γ cos β ) 2π 2Q (6.99) By substituting for the generalized parameters ( nd, ng, and nf ) from Table 6.1 in Eq. (6.99), we will have the gain equation for each converter in the family. 13

14 Generalized Peak Resonant nductor Current (Peak Switch Current) The peak resonant inductor current or peak switch current occurs at. ω ( t t1) = π 2 o L p n, L p = nf + Q M ng t = (6.101) t L p when The peak resonant capacitor voltage or peak diode voltage occurs at. : ω t t = π o ( C p 1) t = t C p when 2 n, C p = ng 14

15 Design Control Curves Fig shows the control characteristic curves of M vs. f ns for the ZCS-QRC family as an example, Fig shows the average and the rms switch currents as a function of the voltage gain. (a) (b) (c) Fig 6.41 Control characteristic curves of M vs. ƒ ns for (a) ZCS QRC buck, (b) ZCS QRC boost, (c) ZCS QRC buck-boost, Cuk, Zeta, and SEPC. 15

16 ZCS QRC Boost Switch/Peak alues (a) (b) Fig 6.42 Some of the ZCS QRC boost main switch (S) normalized stress. (a) Normalized average current, (b) Normalized rms current. 16

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