DC-DC Flyback Converters in the Critical Conduction Mode ...

1 DC-DC Flyback Converters in the Critical Conduction Mode: a Re-examination G. Spiazzi* D. Tagliavia** S. Spampinato**. *. Department of Electronics and Informatics University of Padova via Gradenigo 6/a - 35131 Padova - Italy Phone: + Fax: + e-mail: **. ST Microelectronics Via Stradale Primosole 50, 95121 Catania - ITALY. Phone: +39-095-740-1111 - Fax: +39-095-740-6006. e-mail: e-mail: Abstract - The Critical Conduction mode for DC-DC Flyback the beginning and at the end of each switching interval. This SMPS, in which the converter is forced to operate at the simplification leads to substantial errors in the prediction of boundary between continuous and discontinuous Conduction the switching frequency variation and of the component modes, represents an interesting alternative to the classical stresses in Converters designed with a low resonance constant-frequency PWM technique.

2 In fact, such operating mode allows for a soft turn off of the freewheeling diode, Zero frequency (for example in order to keep the switch dv/dt at Voltage commutations of the switch and reduction of the turn off below a specified limit). generated EMI. In this paper, a detailed analysis is reported which allows In this paper, this operating mode is re-examined with the aim for an accurate prediction of the converter behavior in all of accurately predict switching frequency variation and operating conditions. Moreover, a small signal model is component stresses in those applications in which the delay inserted between the turn off of the freewheeling diode and the N1:N2 D. turn on of the switch, used to achieve zero voltage commutations, cannot be neglected. The analysis presented allows for a correct iL +.

3 Prediction of the converter behavior in all operating conditions RL. as well as for a proper design of the feedback loop through a + L CL Uo suitable small-signal characterization. Ug The theoretical forecasts are verified by means of a Flyback prototype built using a new smartpower IC developed by ST Cr +. Microelectronics in VIPower M3 technology. uCr S. I. INTRODUCTION. a). Standard DC-DC Converters (buck, boost or buck-boost) in the Critical Conduction mode, at the boundary between continuous and discontinuous Conduction modes (CCM- i i . DCM), have the following advantages as compared to normal constant-frequency PWM operation: soft turn-off of the + L + L . freewheeling diode (like constant-frequency DCM operation Ug Ug but at a reduced current stress), self-protection capability Cr against short circuit conditions at the output, and reduced turn +.

4 On and turn off losses by exploiting the resonance between the uCr S S. inductance and the switch output capacitance. This feature is b) c). particularly appealing for off-line Flyback power supplies in i . which the high switch voltage stress increases both switching Uop losses and EMI. L +. Analysis of Flyback Converters in the Critical Conduction d). mode has already been reported in literature [1], but it is Fig. 1 a) Basic scheme of a Flyback converter in the Critical usually done neglecting the resonant intervals that occur at Conduction mode; b) equivalent circuit during subintervals Td and Trise;. c) equivalent circuit during Ton; d) equivalent circuit during Toff 0-7803-6404-X/00/$ (C) 2000. developed in order to design properly the feedback loop. Ug+Uop A multioutput Flyback prototype employing a new uCr smartpower IC developed by ST Microelectronics in I pk VIPower M3 technology was built and tested in order to verify the theoretical expectations [2].

5 I . II. REVIEW OF THE converter OPERATION. The basic scheme of the Flyback converter in the Critical Conduction mode is shown in Fig. 1a in which the resonant Trise t capacitor Cr accounts for any parasitic capacitance (of the Td Ton Toff switch, of the freewheeling diode and of the transformer windings) as well as added ones. The circuit operation is very t0 t1 t2 t3 t4. similar to a standard Flyback except for the resonant intervals a). at the beginning and at the end of each switching period. Two different situations can occur depending on the value of the Ug+Uop uCr U op voltage conversion ratio M = , where Uop is the output Ug voltage reported to the primary side: when M > 1 zero voltage I pk turn on of the switch is achieved as can be seen from the i . converter main waveforms shown in Fig. 2a, while if M < 1.

6 The situation becomes as depicted in Fig. 2b. In both cases the switching period TS = t4-t0 can be divided in four subintervals Trise t which are analyzed in the following, assuming a new time origin at the beginning of each subinterval. Td Ton Toff A. Interval Td = t1-t0. t0 t1 t2 t3 t4. b). At instant t0 the magnetizing current zeroes causing the Fig. 2 Magnetizing current i and resonant capacitor voltage uCr turn-off of the freewheeling diode D. The equivalent circuit waveforms in a switching period. a) case M > 1; b) case M < 1. during this subinterval is shown in Fig. 1b: the magnetizing inductance L resonates with capacitor Cr bringing its voltage 0 if M >1. toward zero. The magnetizing current and the capacitor u Cr (Td ) = ( ). voltage are given by the following equations U g U op if M <1. (uCr(0) = Ug+Uop, i (0) = 0): B.

7 Interval Ton = t2-t1. u Cr (t ) = U g + U op cos ( R t ) The second interval (Ton = t2-t1) corresponds to the normal U op (1) charging phase (see Fig. 1c) in which the magnetizing current i (t ) = sin ( R t ) i increases linearly starting from an initial value which is ZR. zero only in the case M < 1 and if the switch is turned on at 1 L the valley point of voltage uCr (this is the case of Fig. 2b). In where R = and Z R = are the angular L C r Cr the general case we can write: Ug frequency and the characteristic impedance of the resonant i (t ) = I 0 + t (4). L . circuit respectively. If M > 1 this interval ends when voltage uCr reaches zero, At the end of the switch on-time, the magnetizing current while if M < 1 Td is chosen to be one half of the resonant reaches its maximum value (indeed, its maximum occurs period so as to turn the switch on always at the minimum during the next resonant period but it differs only slightly value of the voltage across it, as shown in Fig.)

8 2b: from this value): ( ). 1 Ug L . 1 1 i (Ton ) = I pk = I 0 + Ton Ton = I I 0 (5). cos M if M > 1 L U g pk Td = R (2). if M < 1 C. Interval Trise = t3-t2. R. i (Td ) = I 0 = The third interval (Trise = t3-t2) is the time between the switch turn off instant and the turn on of the freewheeling U op 2 diode at the secondary side which occurs when uCr becomes 1 1 if M >1. ( ). greater than Ug+Uop. The equivalent circuit during this stage = Z M . R is, again, that shown in Fig. 1b. Due to the high value of the 0 M <1. if energy stored in the magnetizing inductance, it seems 0-7803-6404-X/00/$ (C) 2000. reasonable to consider a linear increase of the resonant are not negligible, substantial errors are introduced in the capacitor voltage at a constant charging current, : prediction of the switching frequency variation as well as of I pk (.

9 C r U g + U op ) the component stresses. In the following section, a rigorous u Cr (t ) = t Trise = ( ) analysis is performed with the aim of precisely forecast the Cr I pk converter behavior at different output power and voltage i (t ) = I pk ( ) conversion ratios. However, this approximation can lead to a substantial error III. DC ANALYSIS. in Converters designed with a low resonant frequency (for example in order to keep the dv/dt across the switch at turn In order to derive the relation between the voltage off below a specified limit), expecially when M becomes conversion ratio and the switching frequency for a given set lower than one. In these cases an exact analysis must be of the converter parameters, let's start with the determination performed, with the following result: of the average (in a switching period) current delivered to the u Cr (t ) = U g + Z R I sin ( R t + ) load.

10 From Fig. 2 we can write: (7) T. i (t ) = I cos ( R t + ) I Dp = I off off (14). 2TS. where where IDp is the secondary diode current reported to the 2 primary side. This current equals the average load current, I = I 2 + g . U. Lpk Z ( ) : R U op I Dp = (15). Ug R L. = tg 1 . ( ). Z R I pk where a non unity converter efficiency was assumed. Using The interval duration is given by: (12) and (15) into (14) we obtain: L 2 U 2op 1 1 U op . I off = (16). Trise = sin (9) R L. R . 2 TS. ZR I . Now, substituting (2), (5), (9) and (12) into (13) the and the value of the magnetizing current at the end of this switching period results: interval results: 2. U op 1. ( ). TS = I pk I 0. L . M+. U op I off = i (Trise ) = + . I 2pk . M 2 1 (10) (17). Z. R 1 1 U op L . + sin + I off + Td Note that, this current is lower than I pk for M > 1 meaning R Z I U op a reduction of the energy transfered to the output.