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					                             Small-Signal Characterization of the
                        Forward-Flyback Converters with Active Clamp

                      Ionel Dan Jitaru                                    Serban Birc5-G515teanu,Senior Member, IEEE
Rompower Inc., Phone (520) 326-8401, Fax. (520) 326-8366                LR 2EP - GE 44, IRESTE, Fax. +33 240 68 30 66
 4400E Broadway, Suite 414, Tucson, AZ 85711, U.S.A.                 La Chantrerie, BP 60601,44306Nantes cedex 3, FRANCE


   Abstract     - Linear equivalent models of the                       The for-fly with hybridge rectifier has a single transformer
forward-flyback converters with active clamp are                     secondary which always conducts half of the output current.
deduced, using the Vorpbrian model of the PWM                        Transformerratio is then the same for the forward and for the
switch.    Control-to-output transfer functions are                  boost-buck sections.
plotted against frequency, for a 36-72 V    to    -
                                                5 V     -               The for-fly with tapped secondary has separate windings for
converter, for different load resistances, thus
allowing the design of the error amplifier as to                     the two sections, thus allowing for different transformer
ensure circuit stability.       Experimental results                 ratios, but the two sections are connected towards the output
confirm models validity.                                             at the same filter inductance. This leads to dynamic behavior
                                                                     different from the preceding topology when the converter is
                       I. INTRODUCTION                               controlled by a feedback loop.

   The trend towards higher power density and higher                                  II THE LINEARIZED MODEL
                                                                                       I.
efficiency imposed converter topologies which can use the
entire range of quasi-linearity of the transformer core: push-          To deduce the small-signalbehavior of the converters, the
pull, bridge, half-bridge and active-clamp forward. In these         method of the PWM model [31] will be used, rather than the
converters, in steady state, the transformer magnetizing             state-space average method [30]. The PWM model is
current has the average value zero for any value of the load         versatile and may be applied to the complex, non-standard
current. In the active-clamp flyback and forward-flyback             topologies, as the converters with active clamp are.
converters, the average value of the magnetizing current is             The for-fly converter with hybridge rectifier (Fig. 1.a) may
proportional to the load current. The magnetizing current            be considered as being the association of two dc-dc converters
may even not change the polarity - at medium and heavy               connected at the same output (Fig. 1.c) :
loads. Transformer core is used less well than in push-pull or          - a forward converter with the duty factor D , and
active-clamp forward converters, but these topologies still.            - a boost converter with the duty factor D ,the transformer
have high efficiency and other advantages. The forward-              and a buck converter with the duty factor (1 - D ) . Indeed, the
flyback converter (hereafter called "for-fly") has lower losses      operation of the circuit L2-D2-D1 is that of a buck converter
in the secondary than the push-pull converter.                       where D2 is the freewheeling diode and D , is the control-
   This paper aims to deduce small-signal equivalent circuits        led switch (called the "active" switch in [31]), because it
for the for-fly converters, in order to make it possible to          conducts when energy is stored in inductance L2 . The input
calculate the error amplifier phase correction as to ensure          voltage for this one is ideally E D / (n (1 - D)) .
circuit stability when controlled by a feedback loop. The               If the clamping circuit is connected across the transformer
circuits were deduced using the versatile model of the PWM           primary, as in [33] and others, than the clamping circuit is a
switch [3 11. Experimental verification demonstrated the             flyback [27]. For this reason we maintained in this paper the
validity of the models.                                              same name offorward-flybackconverter, though the operation
                                                                     is slightly different.
                     I
                    I. CIRCUITS OPERATION                               Consequently, the linear equivalent circuit for duty cycle
                                                                     variations only is that of Fig.2, with the parameters' values:
   Two active-clamp converters are studied: the for-fly with
hybridge (current-doubler)rectifier (Fig.1) and the for-fly with                                              I
tapped transformer secondary (Fig.5). In both converters,                                                Ic1= -
when the main switch Q conducts, energy is transferred from                                                     2
the dc source E to the filter inductor (L1 or L ) . At the same                                        E
                                                                         VDI= Vapl - ICI rEl (1 - D) = - - I,, rEl (1 - D)
time the magnetizing current increases, hence energy is stored                                         n
in the transformer magnetic field. When Q switches off,                                    +
                                                                         RI = D (1 - D)rE1 r,,
energy stored in the transformer is eliminated: partly through           The transformer ratio n = np / ns .
QA in C A ,partly towards the output as in a boost or flyback
                                                                         rE = 'CA R A =rcA                     1  v
converter. Circuit operation is mixed: forward and boost-buck                                            IC= --- - 0
[I1 - WI.                                                                     rCA   RA                       1-D RA


0-7803-4340-9/98/$10.000 1998 IEEE.                                626
rt 5     ’
              ------l




                   At   w   ’

tf           ‘ f

     U                          *



                                    A




              w
                                                               ~




                                1                         E          parameters: E = 36 -72 V , U = 5 V , R L = 0.25 - 1 Q , L , =
                                                                     4 pH , L 1 = L z = 2 pH , L p = 64 pH , n = 4 , rL1= rL2 = 3
                                                                     m a , r , = 3 mQ ,rp = 50 m a , Rg = 0.15 a , C = 390 pF ,
                                                                     rc = 60 m a ,CA= 10 nF and 47 nF ,r,-A = 10 mQ .
                                                                         The calculated and measured gain and phase curves are close
                                                                     to each other for different E and load values, at frequencies
   V is the voltage across capacitor CA . R A is the load            lower than half the switching frequency. The load resistance
resistance of the boost section, that is the resistor connected      values seems not to have a dramatic impact on these
in parallel with CA. In the for-fly converters R A is infinite,      functions. As it was always noticed, the gain and the phase
hence relationships for R E , I c and V are simpler. rL1             shift are larger for higher values of the load resistance. On
and rLz are the series resistances of inductors L1 and Lz ,          the contrary, variations of the duty factor lead to significant
respectively.                                                        variations of the curves (Figs.3 and 4). The curves are
                                                                     relatively smooth, because of the very low value of the ratio
                                               I                     L1IC , which leads to a very low value of the critical series
                                            la=-                     damping resistance (= 0.14 a).This is an advantage of the
                                               2
                                                                     switching power supplies with very low output voltage.
                            E    D
  VD2= Vap2- IC, rm D =    - -- IC2 m         D                      Phase lead at high frequencies is due to the transfer function
                           n 1-D                                     zero produced by the equivalent series resistance rc of the
                                                                     output capacitor C  .
                                                                         Capacitor CA value is a key parameter, because the reso-
   A transformer must be inserted before, between or after the       nance of C A and transformer primary inductance creates a
equivalent circuits of the boost and the buck converters (even       right-half-plane zero with a strong impact on the gain and
with unity tums ratio), in order to avoid a short-circuit due to     phase curves. The position of this zero strongly depends on
the crossed-connection of the ground nodes of the two                the input voltage and its damping - on the load. CA value is
converters. First, the transformer was inserted in front of the      to be chosen low, in order this zero to have a frequency as
equivalent circuit of the forward converter and between the          high as possible. Also an RD C D damping circuit may be
boost and the buck converters as to be equally taken into            added in parallel with CA to reduce phase shift. We used C    ,
account. Inserting the transformer limits the domain of              = (8 - 10) CA and RD =180 .
model validity towards low frequencies, because in the real               The same method was used to deduce the model of the for-
circuit the duty-factor variations are transmitted by PWM and        fly converter (Fig.5) with transformer tap (previously deduced
rectification, not directly as slow signals through the              by the averaging method [331). The small-signal equivalent
transformer. This leads to completely false results at               circuit (Fig.6) is very similar to the previous one, with two
relatively low frequencies. Consequently, the isolation task         remarks. First, the transformer ratio in the forward section
was left to the ideal transformer from the equivalent circuit of     ( 1 ) may be different from the ratio for the boost-buck section
the buck converter. The real transformer was moved in front          (2); thus the weights of the two sections may be different.
of the boost converter and the other component values of the         Second, the circuit contains a single output inductor L and
boost equivalent circuit converted according to the turns ratio      the two sections are connected together in front of this
(voltages divided by n ,currents multiplied by n and impe-           inductor.
dances divided by n2 ). Now, the two transformer icons may               For this topology, the curves are very sensitive to the
be put together in a single one, with the converters connected       transformerratios. The higher the contribution of the forward
at the secondary. The real transformer initially appears in the      section, the higher the high-frequency phase shift. The phase
boost equivalent circuit with opposite primary/secondary             shift is larger than for the for-fly converter with current-
polarities. In order to make it possible to unify the two icons      doubler rectifier, hence the dynamic stability is more difficult
of the real transformer, it must appear with the same winding        to obtain.
polarities. Therefore, the relative windings' polarity of the
ideal transformer from the buck converter equivalent circuit                                 CONCLUSION
was inverted and that of the current and voltage generators of
the equivalent circuit, too. Finally, the real transformer could
even be eliminated from the equivalent circuit and only the             Small-signal equivalent circuits of the forward-flyback
generator and winding resistances be taken into account.             converters were deduced, in order to make it possible to
                                                                     calculate the error amplifier phase correction as to ensure
   The model is deduced for all inductances operating in
continuous mode (with never-zero current), for two reasons.          circuit stability when controlled by a feedback loop. The
First, it was noticed that the stability conditions are more         circuits were deduced using the model of the PWM switch.
easily satisfied in the discontinuous than in the continuous         Experimental verification demonstrated models' validity. The
mode [32]. Second, the model is simpler for the continuous           curves are relatively smooth, because of the very low value of
mode. Anyway, the boost section always operates in the               the ratio L I / C (which leads to a very low value of the
continuous mode, because the auxiliary switch QA conducts            critical series damping resistance). The phase shift is larger
in both directions, therefore the current in the transformer         for the converter with tapped secondary than for the converter
                                                                     with current-doubler rectifier, hence the current-doubler
primary never remains zero for an interval during each cycle.
   We have consbvcted for-fly converters with the following          rectifier is to be preferred.



                                                                   628
                                                  lk                            10k

                                                                    frequency      (HZ)


Fig.3. Calculated and measured gain and phase curves of the for-fly converter with hybridge rectifier delivering 15 A and 5 A           ,




         ?/d-7 2v




                                                   lk                           10k                               lOOk       ’
                                                                                                                             iI
                                                                    frequency      (Hz)

 Fig.4. Gain and phase curves of the for-fly converter with hybridge rectifier delivering   l!j   A , at 3 different supply voltages.


                                                              629
      Fig.5. Forward-flyback converter with secondary tap.


                           n




I-------------i--c--i----c--l
                             a




                             b

Fig.6.Linear equivalent circuit of the converter with secondary tap



                                 630
           __
                                          1   measured                                                                      1

                         1I               I                                                                       E=4av     I




               //(j-bA




           I


           I                  a

           j                          0 -.

           I"/d-lSA


           ~                        -10-1


           1
           I
           I
           I
               v/d_5A                                                          calculated




                                                                measured
                              2
               v/d_lSA




                                                  lk                        1Gr

               -                                                        frequency ( H z )


                    Fig.7. Gain and phase curves of the for-fly converter with tapped secondary delivering 15 A and 5 A.


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