A push-pull transformer of a push-pull current-fed DC-DC converter is arranged so that the inductance of the primary side of the transformer diminishes equivalently, thereby reducing a conversion loss attributable to a distributed capacitance of the transformer. To equivalently reduce the inductance of the primary side, for instance, a gap is formed in the core of the transformer and/or an inductor is connected in parallel to any one of the windings of the transformer.

BACKGROUND OF THE INVENTION 
The present invention relates to a low-loss, push-pull current-fed DC-DC 
converter for yielding DC voltage. 
FIG. 1 is a circuit diagram of a conventional push-pull current-fed DC-DC 
converter. An input capacitor 6 is connected across an input DC power 
supply 5. One end of DC power supply 5 is connected to respective first 
ends of a diode 7 and the primary winding a choke coil 8. The other end of 
the diode 7 is connected via a secondary winding, or feedback winding, of 
the choke coil 8 to the other end of the DC power supply 5. The primary 
winding of the choke coil 8 is connected at the other end thereof to the 
junction of primary windings 2 and 3 of a push-pull transformer 110, and 
the other ends of the primary windings 2 and 3 are, in turn, connected to 
the other end of the DC power supply 5 via MOSFETs 9 and 10 serving as 
main switching elements The MOSFETs 9 and 10 include parasitic diodes 11 
and 12, respectively. Across a secondary winding 4 of the transformer 110 
there is assumed a capacitor 13 which represents a distributed capacitance 
of the secondary winding 4. The output of the secondary winding 4 is 
connected to the input side of a bridge circuit composed of rectifying 
diodes 14 to 17. Connected to the output side of the bridge circuit are a 
smoothing capacitor 18 and a load resistor 19. 
FIG. 2 shows waveforms occurring at respective parts of the converter 
depicted in FIG. 1. The switching elements 9 and 10 are supplied at their 
gates with gate signals V.sub.G1 and V.sub.G2 of the same frequency f and 
the same ON-OFF ratio but displaced 180 degrees apart in phase. When the 
switching element 9 conducts and current I.sub.D1 flows therethrough at 
time t.sub.0, current I.sub.L flows from the choke coil 8 into the primary 
side of the transformer 110 at the same time. As a result, a voltage 
-V.sub.T is created in each of the primary windings 2 and 3 of the 
transformer 110, and current flows in the secondary winding 4, charging 
the distributed capacitance 13. When the voltage across the capacitance 13 
(corresponding to voltage V.sub.T on the primary side) exceeds the voltage 
V.sub.out of the output capacitor 18, the rectifying diodes 14 and 17 are 
turned ON, charging the output capacitor 18 by current I.sub.Dr. The 
current I.sub.Dr shown in FIG. 2 represents a rectified current which 
flows through either of the pair of diodes 15 and 16 or the pair of diodes 
14 and 17 in FIG. 1, although the current flow is indicated by arrows in 
FIG. 1 beside only the pair of diodes 14 and 17. 
When the switching element 9 is turned OFF at time t.sub.3, the diode 7 is 
immediately turned ON and conducts for a period (t.sub.3 -t.sub.4) during 
which the switching elements 9 and 10 are both OFF, by virtue of the 
continuity of the current flowing through the choke coil 8 for the period 
(t.sub.0 -t.sub.3) during which only the switching element 9 was ON; so 
that current flows via a route [feedback winding of the choke coil 8 
.fwdarw.diode 7 .fwdarw.input power supply 5], thus feeding back the 
excitation energy of the choke coil 8 to the input power supply 5. 
Similarly, since the exciting current for the transformer 110 cannot flow 
to the primary side thereof during this period (t.sub.3 -t.sub.4), a 
voltage is generated in the transformer winding when the exciting current 
flows to the secondary side. The exciting current of the transformer 110 
acts as a discharging current of the distributed capacitance 13. As a 
result of this, voltage V.sub.T of the transformer 110 gradually 
approaches zero. Next, when the switching element 10 is turned ON at time 
t.sub.4, current I.sub.D2 flows therethrough owing to voltage V.sub.DS2 
applied across the switching element 10 immediately prior to its 
conduction, and at the same time current I.sub.L flows into the primary 
side of the transformer 110 from the choke coil 8. In consequence, current 
flows across the secondary winding 4 as is the case with the above, 
charging the distributed capacitance 13 in a reverse direction. When the 
voltage across the capacitance 13 exceeds the output voltage V.sub.out 
across the capacitance 18 at time t.sub.6, the rectifying diodes 15 and 16 
are turned ON to cause a current I.sub.Dr therethrough, by which the 
output capacitor 18 is charged. 
In this way, a voltage which is a multiple of the turns ratio of the 
transformer 110 is obtained, in the same form as the waveform V.sub.T 
shown in FIG. 2, on the secondary side of the transformer 110, and this 
voltage is rectified and output from the DC-DC converter as the output 
voltage V.sub.out. 
Such a conventional push-pull current-fed DC-DC converter as shown in FIG. 
1 employs, in the transformer 110, a no-gap core 100 as depicted FIG. 3, 
and its excitation inductance is so large that the rate of exciting 
current contained in the current flowing in the primary winding (2 or 3) 
of the transformer is very low. The value of this exciting current 
represents the value of energy stored in the excitation inductance of the 
transformer. In the case of the transformer of the prior art converter, 
the energy stored in the excitation inductance is discharged to the 
secondary side in the first half of the ON period of the main switching 
element and is stored in the latter half of the ON period. Even if the 
exciting current is large, its energy will not be entirely lost, but since 
it is partly consumed as an increase in the copper loss in the transformer 
windings, it is usually considered preferable that the value of the 
exciting current be small. However, the present inventors' analyses have 
revealed that where a transformer of a high turns ratio is employed in the 
conventional converter for the purpose of generating a particularly high 
voltage, an increased distributed capacitance of the transformer would 
cause an increase of the conversion loss because of the small exciting 
current. Next, a description will be given, with reference to FIGS. 1 and 
2, of the mechanism of the increase in the loss. 
In the period during which the main switching element 9 is ON (t.sub.0 
-t.sub.3 in FIG. 2), the distributed capacitance 13 on the secondary side 
of the transformer 110 is charged by a voltage which is negative at the 
side of the transformer winding marked with the black dot, relative to the 
other side thereof. When the main switching element 9 is turned OFF at 
t.sub.3, the exciting current of the transformer 110 reduces the charges 
stored in the distributed capacitance 13 and hence decreases its voltage, 
because the exciting current flows from the secondary winding 4 at the 
side indicated by the black dot. The variation in the voltage across the 
distributed capacitance 13 is similar to the variation in the primary 
winding voltage V.sub.T. Where the charges stored in the distributed 
capacitance 13 are not reduced to zero until time t.sub.4, the turning ON 
of the main switching element 10 causes the charges in the distributed 
capacitance 13 to constitute a short-circuit current I.sub.S which is 
discharged via a route [primary winding 3 of the transformer 110 
.fwdarw.main switching element 10 .fwdarw.parasitic .fwdarw.diode 11 of 
the main switching element 9 .fwdarw.winding 2], resulting in the loss of 
the energy stored in the distributed capacitance 13 until just before time 
t.sub.4. After the short-circuit current period (t.sub.4 -t.sub.5) the 
distributed capacitance 13 is charged by current I.sub.L of the boosting 
choke coil 8 and becomes positive at the black-dot side of the transformer 
winding. As will be seen from the above, the less the exciting current is, 
the more the voltage of the distributed capacitance 13 remains 
undissipated just before time t.sub.4 (see waveform V.sub.T in FIG. 2), 
causing an increase in the loss. Incidentally, in a converter for creating 
high voltage through use of a transformer having a higher turns ratio, 
n.sub.T (=N.sub.T2 /N.sub.T1), of the number of turns N.sub.T2 of the 
secondary winding 4 to the number of turns N.sub.T1 of the primary winding 
2 (or 3), since the value of the distributed capacitance as viewed from 
the primary side increases correspondingly, the loss by the distributed 
capacitance will increase; further, the loss increases as the switching 
frequency, i.e. the conversion frequency f rises. 
The above phenomenon will occur also in the case of employing EI or EE 
cores in the transformer of the push-pull current-fed DC-DC converter, 
because the cores are joined together with no gap therebetween, providing 
a large transformer inductance. 
In addition to the loss by such a short-circuit current, the prior art has 
presented a problem that an increase in the conversion frequency f causes 
an abrupt increase in the loss, since the excitation inductance of the 
choke coil 8 has heretofore been determined taking only input current 
ripples into account. 
SUMMARY OF THE INVENTION 
It is therefore an object of the present invention to reduce the loss 
attributable to the distributed capacitance of the transformer of the 
push-pull current-fed DC-DC converter. 
It is another object of the present invention to suppress an increase in 
the loss accompanying an increase in the exciting current of the push-pull 
transformer and an increase in output ripples, by specifying the ranges in 
which to select the excitation inductances of the push-pull transformer 
and the choke coil. 
The present invention has a primary feature of setting the excitation 
inductance of the push-pull current-fed DC-DC converter so that the 
voltage of the distributed capacitance of a main transformer can be 
inverted during the period in which both switching elements are in the OFF 
state. 
Moreover, the present invention has another primary feature of defining 
either one or both of the ranges in which to select the excitation 
inductances of the push-pull transformer and the choke coil, thereby 
implementing a high-efficiency, low-ripple and high-frequency push-pull 
current-fed DC-DC converter.

DESCRIPTION OF THE PREFERRED EMBODIMENTS 
[Principle of the Invention] 
To hold down an increase in the loss by the distributed capacitance of the 
transformer, the polarity of its voltage is inverted by the exciting 
current of the transformer in the period in which the switching elements 9 
and 10 are both in the OFF state. To perform this, it is necessary that 
the total amount of charges of the exciting current in the period (t.sub.3 
-t.sub.4) during which both switching elements 9 and 10 are in the OFF 
state be larger than the amount of charges needed for inverting the 
distributed capacitance voltage. 
The amount of charges received from the exciting current in the period 
(t.sub.3 -t.sub.4) is given by the following equation (1): 
##EQU1## 
Where Q.sub.cur is the amount of charges received from the exciting 
current in the period (t.sub.3 -t.sub.4) and i.sub.Te is the exciting 
current of the transformer. 
Now, regarding the exciting current i.sub.Te in the period (t.sub.3 
-t.sub.4) as equal to its peak value and as constant because of its small 
amount of variation in this period, let it be assumed that the exciting 
current in this period is I.sub.Te which is its peak value. On this 
assumption the amount of charges Q.sub.cur received from the exciting 
current can be expressed by the following equation (2): 
##EQU2## 
Where D is the duty ratio, i.e. the ON-OFF ratio (the rate of the ON 
period to one cycle) and f is the conversion frequency. 
The amount of charges Q.sub.cd needed by the distributed capacitance is 
given by the following equation (3): 
EQU Q.sub.cd =2.multidot.(N.sub.T1 /N.sub.T2).multidot.V.sub.o 
.multidot.C.sub.d (3) 
where N.sub.T1 is the number of turns of the primary winding of the 
transformer, N.sub.T2 is the number of turns of the secondary winding of 
the transformer, Q.sub.cd is the amount of charges needed by the 
distributed capacitance, C.sub.d is the primary conversion value of the 
distributed capacitance, and V.sub.o is an output voltage. 
To operate the converter without incurring the loss by the shorting of the 
exciting current, it is necessary to satisfy the relationship shown by the 
following inequality (4): 
EQU Q.sub.cd .ltoreq.Q.sub.cur (4) 
From expressions (2) to (4) the exciting current needs to satisfy the 
condition of the following inequality (5): 
##EQU3## 
The exciting current of the transformer is determined by the number of 
turns of its windings, the core constant and the voltage to be applied to 
the transformer. 
The maximum magnetomotive force H.sub.m and the maximum magnetic flux 
density B.sub.m of the transformer are given by the following equations 
(6) and (7), respectively: 
##EQU4## 
where l.sub.e is the effective magnetic path length of the core of the 
transformer 
##EQU5## 
where V.sub.T (t) is the voltage to be applied to the primary windings of 
the transformer and A.sub.e is the effective cross-sectional area of the 
core of the transformer. 
Here, a time integration value of voltage for a half cycle thereof, which 
is the numerator on the right side of Eq. (7), can be given by the 
following equation (8): 
##EQU6## 
From Eqs. (7) and (8) the maximum magnetic flux density B.sub.m can 
therefore be expressed as follows: 
##EQU7## 
Further, the maximum magnetomotive force H.sub.m and the maximum magnetic 
flux density B.sub.m bear the relationship given by the following equation 
(10): 
EQU B.sub.m =.mu..sub.o .multidot..mu..multidot.H.sub.m (10) 
where .mu..sub.0 is the space permeability and .mu. is the relative 
magnetic permeability. 
Therefore, the exciting current I.sub.Te which depends on the material and 
the constitution of the transformer can be obtained, from Eqs. (6), (9) 
and (10), as follows: 
##EQU8## 
Based on Eq. (11) there are the following methods for increasing the 
exciting current I.sub.Te, and their merits and demerits are as follows: 
(a) Effective magnetic path length: An increase in the effective magnetic 
path length increases the volume of the core, leading to an increase in 
iron loss. 
(b) Number of turns of the primary winding: A decrease in the number of 
turns of the primary winding increases the maximum magnetic flux density, 
not only causing an increase in iron loss but also incurring the 
possibility of the transformer being saturated. 
(c) Effective cross-sectional area of the core: A decrease in the effective 
cross-sectional area of the core increases the maximum magnetic flux 
density, not only causing an increase in iron loss but also incurring the 
possibility of the transformer being saturated. 
(d) Relative magnetic permeability: The relative magnetic permeability can 
easily be reduced by a suitable selection of the core material, and the 
iron loss depends on the characteristic of the core used. 
Comparison of the above four methods has revealed that the use of a core of 
a low relative magnetic permeability permits arbitrary setting of the 
exciting current without increasing the loss. 
The relationship between the distributed capacitance and the relative 
magnetic permeability for the operation which does not increase the loss, 
based on expressions (5) and (11), is shown by the following inequality 
(12). FIG. 4 shows, by way of example, calculated results by a solid line 
obtainable from Ineq. (12), the experimentally measured results being 
shown by black circles. 
##EQU9## 
The measured results are in good agreement with the results obtained from 
the formula on the right hand side of inequality (12): this indicates the 
adequacy of the formula. Expressing Ineq. (12) in terms of the excitation 
inductance L.sub.T1, the following inequality (13) is obtained: 
##EQU10## 
where L.sub.T1 is the inductance of the primary winding of the transformer 
which is known to be expressed by the following expression: 
##EQU11## 
[Embodiments] 
FIG. 5 is a circuit diagram illustrating a typical embodiment of the 
push-pull current-fed DC-DC converter of the present invention. The 
circuit arrangement of this embodiment is identical with that of FIG. 1 
except that the push-pull transformer 110 is designed so that the relative 
magnetic permeability has such a small value as will satisfy the condition 
of Ineq. (12) as mentioned above, or so that the inductance of the primary 
winding of the transformer will satisfy Ineq. (13). 
FIG. 6 illustrates a specific operative example of the push-pull 
transformer 110. In this example the relative magnetic permeability of the 
transformer 110 is reduced equivalently by forming a gap 20 in a toroidal 
core 100. As a result of this, the excitation inductance of the 
transformer 110 decreases, permitting an increase in the exciting current 
of the transformer in the embodiment shown in FIG. 5. FIG. 7 shows 
waveforms occurring at respective parts of the converter depicted in FIG. 
5. Since the exciting current of the transformer 110 increases, it is 
possible to charge the distributed capacitance 13 in the reverse direction 
and invert its polarity. Accordingly, the primary winding voltage V.sub.T 
is also inverted immediately before time t.sub.4 at which the switching 
element 10 is turned ON. At this time, even if the switching element 10 is 
turned ON, charges stored in the distributed capacitance 13 will not be 
discharged, as a primary current, via the parasitic diode 11 of the 
switching element 9, because it is being supplied with a reverse voltage. 
This eliminates the possibility of the loss attributable to the 
distributed capacitance 13. 
During the time period between t.sub.e and t.sub.4 the exciting current of 
the transformer 110 is supplied as a load current from the secondary side 
of the transformer through the diodes 15 and 16 to the capacitance 18; so 
that even if the exciting current increases, it is mostly used effectively 
though its copper loss somewhat increases. 
The core 100 of the relative magnetic permeability .mu. which satisfies 
Ineq. (12) can be implemented by selecting the length l.sub.g of the gap 
20 as follows: 
##EQU12## 
where .mu.' is the relative magnetic permeability of the core material 
used. 
The reason for which the exciting current is increased by the gap 20 can 
also be explained as follows: Letting the relative magnetic permeability 
of the core 100 including the gap 20, the magnetic permeability of a 
space, the magnetomotive force and the magnetic flux be represented by 
.mu., .mu..sub.0, H and B, respectively, B=.mu..multidot..mu..sub.0 
.multidot.H. The provision of the gap 20 in the core 100 will make the 
relative magnetic permeability .mu. lower than in the case where no such 
gap is provided. Since the provision of the gap 20 does not cause any 
change in the magnetic flux B, the magnetomotive force H 
(=B/.mu./.mu..sub.0) increases, with the result that the exciting current 
increases. With the increased exciting current, the voltage of the 
distributed capacitance 13 falls rapidly in the period (t.sub.3 -t.sub.4) 
during which the main switching elements 9 and 10 are both in the OFF 
state, as referred to previously. 
The gap 20 of the core 100 may also be filled with a non-magnetic substance 
21 as depicted in FIG. 8A. Letting the relative magnetic permeability of 
the non-magnetic substance 21 be represented by .mu.", Ineq. (14) will 
become as follows: 
##EQU13## 
Without the non-magnetic substance 21, there is a risk that a temperature 
change will cause a change in the diameter of the core 100 and 
consequently a change in the gap length which leads to a change in the 
relative magnetic permeability .mu. of the core 100, but the filling of 
the gap 21 with the non-magnetic substance 21 suppresses variations in the 
relative magnetic permeability .mu. which would otherwise result from 
temperature variations. Moreover, the non-magnetic substance 21 is 
effectively utilized also for protecting the transformer from stresses by 
impregnation with an insulator. 
While in the above a toroidal core is employed as the core of the 
transformer, a similar low-loss structure can be achieved also by 
providing a gap in an EI, EE or similar core. It is also possible to 
provide a portion of a small cross-sectional area in the core 100 
constituting a magnetic path, by forming a notch 20' in the core 100 as 
shown in FIG. 8B or drilling a hole in the core 100 though not shown, 
instead of forming the gap in the core. 
It is a matter of course that the same effect as mentioned above would be 
obtainable by using a magnetic substance of low magnetic permeability for 
the core 100 of a high-voltage transformer 110, even if the 
above-mentioned gap is not provided. 
FIG. 9 shows measured values of the loss corresponding to the equivalent 
distributed capacitance which varied with the excitation inductance of the 
transformer. In FIG. 9 the curve (A) shows the relative loss in the case 
where the excitation inductance L.sub.T1 without the gap 20 is represented 
by 1, and curves (B) and (C) show the relative losses in the case where 
the excitation inductance L.sub.T1 was reduced to about 1/3 and about 1/7 
that in the case of the curve (A), by providing gaps of suitable lengths, 
respectively. The measured results proved that the gap would decrease the 
loss, in particular, that an increase in the distributed capacitance would 
further decrease the loss. For obtaining high voltage, a transformer of a 
high turns ratio is used and its distributed capacitance is, for example, 
5 nF or so. It will be seen that the provision of the gap would markedly 
decrease the loss in such an instance. 
FIG. 10 illustrates an example in which the excitation inductance of the 
push-pull transformer 110 is equivalently reduced by using therefor an 
arrangement different from that used in FIG. 5. In this example the 
excitation inductance of the transformer 110 is equivalently reduced by 
connecting an inductor 22 in parallel to the secondary winding of the 
transformer 110. The inductance of the inductor 22 is selected such that 
the value obtained by the parallel connection of its primary-conversion 
inductance and the excitation inductance of the transformer 110 itself 
will satisfy Ineq. (13). 
FIG. 11 shows the waveforms of voltages V.sub.DS1 and V.sub.DS2 of the main 
switching MOSFETs 9 and 10, voltage V.sub.T of the primary winding 3 of 
the transformer 110, current i.sub.L of the inductor 22, and operating 
waveforms occurring at other parts in the circuit depicted in FIG. 10. 
The operation of the circuit shown in FIG. 10 will be described in 
connection with the operation waveforms shown in FIG. 11. 
At first, in the period during which the main switching MOSFET 9 is in the 
ON state (t.sub.0 -t.sub.3 in FIG. 11), the distributed capacitance 13 at 
the secondary side of the transformer 110 is charged by a voltage which is 
negative at the side of the transformer winding marked with the black dot, 
relative to the other side thereof, and at the same time a current i.sub.L 
flowing across the inductor 22 increases. Upon turning OFF the main 
switching MOSFET 9 at time t.sub.3, charges stored in the distributed 
capacitance 13 are decreased by the current i.sub.L, and the energy stored 
in the distributed capacitance 13 is converted into the excitation energy 
of the inductor 22. Accordingly, although the main switching MOSFET 10 is 
turned ON at time t.sub.4, the loss attributable to the distributed 
capacitance can be decreased, because of the decreased amount of charges 
of the distributed capacitance 13. The current i.sub.L flowing through the 
inductor 22 is applied as a load current to a load during a period between 
t.sub.e and time t.sub.4, and hence is not wasted as a loss. 
Thus, even if the distributed capacitance 13 of the transformer 110 is 
large, the loss of the push-pull current-fed DC-DC converter can be held 
low. 
FIG. 12 illustrates another modification of the FIG. 5 embodiment which is 
designed so that the excitation inductance of the transformer 110 is 
equivalently decreased by employing another structure therefor. In this 
example, the inductor 22 is connected in parallel to a tertiary winding 23 
of the transformer 110, thereby reducing the excitation inductance of the 
transformer 110 equivalently. The operation of the converter and the 
effect obtainable in this example are exactly the same as those in the 
example shown in FIG. 10, and hence will not be described. 
Incidentally, the same effect as obtainable in the above example could be 
produced also by connecting the inductor 22 in parallel to either one or 
each of the primary windings 2 and 3 of the transformer 110. 
FIG. 13 shows efficiency characteristics of the converter of the FIG. 18 
embodiment and the conventional converter of the FIG. 1 circuit 
construction by (A) and (B), respectively. The efficiency of the 
conventional converter is below 85%, whereas with the converter of the 
present invention an efficiency above 86% could be obtained, due to 
reduction of the transformer inductance, by the additional provision of 
the inductor 22 despite its inherent copper and iron losses. 
Although the foregoing description has been given of the cases where the 
relative magnetic permeability of the core 100 of the transformer is held 
down and where an inductor is connected in parallel to the transformer 
winding to thereby reduce inductance of the transformer, it will be 
apparent that both methods can be employed in combination with each other. 
[Principle of the Improved Invention] 
It has been described previously in connection with the FIGS. 5 and 7 
embodiments to design the transformer such that Ineq. (13) is satisfied, 
so as to decrease the loss attributable to the distributed capacitance of 
the push-pull transformer 110. In the case where the inductance of the 
primary winding of the transformer is decreased to satisfy Ineq. (13), 
however, the exciting current of the transformer increases and the current 
flowing through the primary side of the transformer is reduced to zero 
before the switching element 9 is turned OFF. The current I.sub.L flowing 
through the choke coil 8, its exciting current component .DELTA.I.sub.Le, 
the exciting current .DELTA.I.sub.Te of the transformer 110, and the 
current I.sub.Dr flowing through either the rectifying diodes 14 and 17 or 
15 and 16 in FIG. 5, in this case, are shown in FIG. 14A together with 
variations of the gate signals V.sub.G1 and V.sub.G2 of the switching 
elements 9 and 10. The difference by subtracting the exciting current 
.DELTA.I.sub.Te of the transformer from the current I.sub.L of the choke 
coil 8 is the current which flows through the primary side of the 
transformer, and this current corresponds to a current I.sub.Dr which 
flows through the rectifying diodes 14 and 17 or 15 and 16. Accordingly, 
as will be seen from FIG. 14A, when the exciting current .DELTA.I.sub.Te 
of the transformer increases, that is, when the amplitude of the current 
.DELTA.I.sub.Te becomes large, the current flowing through the primary 
side of the transformer is reduced to zero (at time t.sub.3 ') before the 
switching element 9 is turned OFF as will be seen from the waveform of 
corresponding diode current I.sub.Dr. consequence, in the period (t.sub.3 
'-t.sub.3) during which the current I.sub.L flows to the choke coil 8 in 
the conventional converter the diode current I.sub.Dr does not flow to the 
load from the secondary side of the transformer; so that the period during 
which the rectifying diodes 14 and 17 are in the ON state is equivalently 
reduced to T.sub.D '. As a result of this, to obtain the same power as in 
the case where the above-said period is not reduced, the effective value 
of the current I.sub.Dr flowing through the rectifying diodes increases, 
causing an increase in the loss during the ON period of the rectifying 
diodes. In addition, output ripples also increase. Now, a description will 
be given of design conditions for decreasing the inductance value of the 
choke coil 8 and reducing the output ripples to the same extent as in the 
prior art so as to obviate the above defects. 
To reduce the output ripples, it is necessary that the current I.sub.Dr 
flowing in either the rectifying diodes 14 and 17 or 15 and 16 at the 
secondary side of the transformer 110 be made to flow for the same period 
during which current flows through either the switching element 9 or 10 at 
the primary side. 
In the following the conditions that are required of the inductance of the 
choke coil 8 and the inductance of the transformer 110 for fulfilling the 
above-mentioned requirement will be described separately under the titles 
"step-down voltage mode", "step-up voltage mode" and "combined mode". 
(A) Step-down voltage mode 
The mode of operation in which the ON-OFF ratio (i.e. the duty ratio) D of 
the switching elements 9 and 10 is selected such that 0.5&gt;D.gtoreq.0 is 
the step-down voltage mode. The relationship between the input/output 
voltage of the converter and the duty ratio, an average value I.sub.Lav of 
the current flowing through the choke coil 8, the amplitude 
.DELTA.I.sub.Le of the exciting current of the choke coil 8, and the 
amplitude .DELTA.I.sub.Te of the exciting current of the transformer 110 
in such a case are expressed by the following equations (15), (16), (17) 
and (18), respectively. 
##EQU14## 
In the above, E.sub.i is input DC voltage, V.sub.c is a primary-conversion 
of output voltage of the transformer, N.sub.L1 and N.sub.L2 are the 
numbers of turns of main and feedback windings of the choke coil, V.sub.L 
is a primary-conversion voltage of the choke coil 8 given in the form of 
V.sub.L =(N.sub.L1 /N.sub.L2)E.sub.i, P.sub.0 is the output power of the 
converter, L.sub.L1 is the inductance of the main winding of the choke 
coil 8, and L.sub.T1 is the primary winding inductance of the transformer 
110. Assume that the current flowing through the transformer 110 
(corresponding to the current I.sub.L flowing through the main winding of 
the choke coil) is positive in the direction of a current flow from the 
choke coil 8 to the primary side of the transformer 110. 
&lt;Condition 1&gt; 
In order to prevent the current flowing through the transformer 110 from 
going negative at the time (t.sub.0) when the switching element 9 is 
turned ON, the following inequality (19) must be satisfied: 
##EQU15## 
From expressions (19), (16), (17) and (18), the inductance of the main 
winding of the choke coil 8 needs to satisfy the following inequality 
(20): 
##EQU16## 
Since the denominator in Ineq. (20) is always positive (D&lt;0.5), there are 
two cases, depending on whether the numerator is positive or negative. 
Case 1: Where the numerator in Ineq. (20) is positive, the following 
inequalities (21) and (22) must be satisfied: 
##EQU17## 
Case 2: The case where the numerator in Ineq. (20) is negative need not be 
considered because the inductance L.sub.T1 of the primary winding of the 
transformer is negative in this case. 
&lt;Condition 2&gt; 
To prevent the current flowing through the transformer 110 from going 
negative at the time (t.sub.3) when the switching element 9 is turned OFF, 
the following inequality (23) must be satisfied: 
##EQU18## 
From expressions (23), (16), (17) and (18), the inductance L.sub.L1 of the 
main winding of the choke coil 8 has to satisfy the following inequality 
(24): 
##EQU19## 
The denominator in Ineq. (24) is always positive (D&lt;0.5). Therefore, there 
are two cases, depending on whether the numerator is positive or negative. 
Case 1: Where the numerator in Ineq. (24) is positive, the following 
inequalities (25) and (26) must be satisfied: 
##EQU20## 
Case 2: Where the numerator in Ineq. (24) is negative, the following 
inequalities (27) and (28) must be satisfied: 
##EQU21## 
Since the numerator in Ineq. (24) is negative, the right side of Ineq. (28) 
is always negative and the inductance L.sub.L1 of the main winding of the 
choke coil may be of an arbitrary value. 
Conditions 1 and 2 in the above-described step-down mode (D&lt;0.5) may be 
summarized as follows: 
The following inequality (29) is obtained from Ineq. (21) in Case 1 of 
Condition 1 and Ineq. (25) in Case 1 of Condition 2, and the following 
inequality (30) is obtained from Ineq. (22) in Case 1 of Condition 1 and 
Ineq. (26) in Case 1 of Condition 2: 
##EQU22## 
The following inequalities (31) and (32) are obtained from Ineqs. (21) and 
(27) and Ineq. (24) in Cases 1 and 2 of Conditions 1 and 2, respectively: 
##EQU23## 
(B) Step-up voltage mode 
The mode of operation in which the ON-OFF ratio of the switching elements 9 
and 10 is selected such that 1&gt;D.ltoreq.0.5 is the step-up voltage mode. 
The relationship between the input/output voltage of the converter and the 
ON-OFF ratio D, the average value I.sub.Lav of the current flowing through 
the choke coil 8, the amplitude .DELTA.I.sub.Le of the exciting current of 
the choke coil 8, and the amplitude .DELTA.I.sub.Te of the exciting 
current of the transformer 110 in this case are expressed by the following 
equations (33), (34), (35) and (36), respectively. 
##EQU24## 
&lt;Condition 1&gt; 
To prevent the current flowing through the transfer 110 from going negative 
at the time (t.sub.0) when the switching element 9 is turned ON, the 
following inequality (37) must be satisfied: 
##EQU25## 
From expressions (37), (34), (35) and (36), the inductance L.sub.L1 of the 
main winding of the choke coil 8 must satisfy the following inequality 
(38): 
##EQU26## 
The denominator in Ineq. (38) is positive because 1&gt;D.gtoreq.0.5. 
Therefore, there are two cases, depending on whether the numerator is 
positive or negative. 
Case 1: Where the numerator in Ineq. (38) is positive, the following 
inequalities (39) and (40) must be satisfied: 
##EQU27## 
Case 2: Where the number in Ineq. (38) is negative, since the right side 
of Ineq. (38) is negative, there is no inductance L.sub.L1 of the main 
winding of the choke coil which satisfies Ineq. (38). 
&lt;Condition 2&gt; 
To prevent the current flowing through the transformer 110 from going 
negative at the time (t.sub.3) when the switching element 9 is turned OFF, 
the following inequality (41) must be satisfied: 
##EQU28## 
Since the currents I.sub.Lav, .DELTA.I.sub.Le and L.sub.Te are all positive 
or zero, Ineq. (41) is always satisfied. 
Conditions 1 and 2 in the above step-up mode (1&gt;D.gtoreq.0.5) may be 
summarized into the following inequalities (42) and (43): 
##EQU29## 
(C) Combined mode 
In the case of operating the converter while arbitrarily changing the 
ON-OFF ratio D of the switching elements 9 and 10 in the range of from 0 
to 1, the inductance L.sub.T1 of the primary winding of the transformer 
110 and the inductance L.sub.L1 of the main winding of the choke coil 8 
need only to be set to a value which satisfies Ineqs. (13), (29), (31) and 
(42) at the same time and a value which satisfies Ineqs. (30), (32) and 
(43) at the same time, respectively. 
[Embodiment of the Improved Invention] 
FIG. 14B shows operating waveforms at respective parts of the converter 
depicted in FIG. 5 in the case where the inductance L.sub.T1 of the 
primary winding of the transformer 110 and the inductance L.sub.L1 of the 
main winding of the choke coil 8 each have a value which satisfies Ineqs. 
(13), (29), (30), (31) and (32) and the converter is operated in the 
step-down voltage mode. 
By decreasing the inductance L.sub.L1 of the choke coil 8 and increasing 
the amplitude .DELTA.I.sub.Le of the exciting current of the choke coil 8, 
it is possible to prevent that the current flowing through the primary 
side of the transformer 110 and consequently the current I.sub.Dr flowing 
through the rectifying diode are reduced to zero before either the 
switching element 9 or 10 is turned OFF. This eliminates the possibility 
of reducing the ON period of either the rectifying diodes 14 and 17 or 15 
and 16 by an increase in the exciting current of the transformer 110, thus 
ensuring prevention of the loss and an increase of the output ripples by 
an increase in the effective value of the current I.sub.Dr flowing through 
either the rectifying diodes 14 and 17 or 15 and 16. 
A description will be given of an example of the range in which to select 
the values of the inductance L.sub.T1 of the transformer 110 and the 
inductance L.sub.L1 of the choke coil 8 in the case of the converter 
operating in the step-down voltage mode alone, for example. 
FIG. 15 shows the relationship between the input voltage E.sub.i and the 
inductance L.sub.T1 of the transformer 110. In FIG. 15 the range of the 
inductance L.sub.T1 in Case 1 satisfies the conditions of Ineqs. (13) and 
(31) at the same time. 
To prevent an increase in the loss by the distributed capacitance under the 
conditions in Case 1, it is necessary that the inductance L.sub.T1 fulfill 
the condition of Ineq. (32), and the range therefor is indicated by the 
hatched region in FIG. 16. To prevent an increase in the loss by the 
distributed capacitance under the conditions in Case 2, the inductance 
L.sub.L1 is required to fulfill the condition of Ineq. (30), and the range 
therefor is indicated by the hatched region in FIG. 17. 
[Effect of the Invention] 
As described above, by designing the inductance of the transformer of the 
push-pull current-fed DC-DC converter within a certain range, charges 
stored in the distributed capacitance are converted into excitation energy 
before they are discharged. This produces the effect of avoiding the loss 
which is attributable to the distributed capacitance of the transformer in 
the prior art. 
Furthermore, the converter of the present invention has the advantage of 
supplying power to a load without reducing the pulse width of the output 
current, by selecting the inductance of the primary winding of the 
transformer 110 and the excitation inductance of the main winding of the 
choke coil 8 such that they satisfy the afore-mentioned inequalities. 
Since the switching elements can be operated without reducing the pulse 
width of the output current as mentioned above and since the period in 
which to supply energy to the load from the smoothing capacitor 18 is 
reduced, the capacity of the smoothing capacitor 18 can be decreased and 
the loss by the distributed capacitance of the transformer 110 can be 
avoided. Accordingly, the present invention can offer a high efficiency, 
small-sized and lightweight push-pull current-fed DC-DC converter. 
It will be apparent that many modifications and variations may be effected 
without departing from the scope of the novel concepts of the present 
invention.