Abstract:
A pulse-width modulated DC-to-DC power converter including a first inductor, i.e. a transformer or an equivalent fixed inductor equal to the inductance of the secondary winding of the transformer, coupled across a source of DC input voltage via a transistor switch which is rendered alternately conductive (ON) and non-conductive (OFF) in accordance with a signal from a feedback control circuit. A first capacitor capacitively couples one side of the first inductor to a second inductor which is connected to a second capacitor which is coupled to the other side of the first inductor. A circuit load shunts the second capacitor. A semi-conductor diode is additionally coupled from a common circuit connection between the first capacitor and the second inductor to the other side of the first inductor. A current sense transformer generating a current feedback signal for the switch control circuit is directly coupled in series with the other side of the first inductor so that the first capacitor, the second inductor and the current sense transformer are connected in series through the first inductor. The inductance values of the first and second inductors, moreover, are made identical. Such a converter topology results in a simultaneous volt-second balance in the first inductance and ampere-second balance in the current sense transformer.

Description:
ORIGIN OF THE INVENTION 
     This invention was made by an employee of the United States Government and therefore may be made and used by the U.S. Government for governmental purposes without the payment of any royalties thereon or therefor. 
    
    
     BACKGROUND OF THE INVENTION 
     This invention relates generally to DC-to-DC. converters and more particularly to a pulse-width modulated switching converter. 
     DC-to-DC power converters utilizing a switching device in a combination of inductors and capacitors to derive power from one source of DC voltage and then deliver that power to a load at the same or a different DC voltage are well known. Many different types of topologies exist for implementing such power converters. The number of different possible combinations using but a relatively few components has resulted in several standard topology types which include, among others, the buck, boost, buck-boost, forward, flyback, and CUK converters. With what initially appears to be only a simple change or a modification in the particular converter implementation, an extremely significant performance variation can result. 
     While many different topologies could be described, each with its own advantages and disadvantages, the configurations shown in FIGS. 1-3 best represent prior art topologies which exhibit the closest similarity to that of the subject invention to be hereinafter described. 
     FIG. 1, for example, discloses what might be termed a forward converter topology and comprises an isolated or transformer version of a buck converter which, without an input filter, is typically characterized by a converter which displays discontinuous input current while providing a continuous output current. Such an arrangement offers an efficient power conversion technique; however, it almost always requires the use of a reset winding on the power transformer in order to reset the transformer core by returning its stored energy to the primary side. This requirement, while not being difficult to implement, creates some additional design considerations associated with the reset circuitry. 
     With respect to the circuitry shown in FIG. 2, it exemplifies what is termed flyback converter topology and comprise what might be referred to as an isolated or transformer version of a boost converter which, without an input filter, is characterized by discontinuous input current while also providing discontinuous output current and where the required inductor is incorporated into the transformer which comprises a flyback transformer. It typically offers the smallest number of components for DC-to-DC power conversion. 
     The third configuration comprises topology which is illustrative of an isolated or transformer version of the CUK converter. An isolated CUK converter utilizes a transformer which is capacitively coupled both on the primary and secondary sides. 
     While each of the above-referenced power converters as well as other known converter topologies have known utility, inherent limitations and certain disadvantages nevertheless exist. 
     SUMMARY 
     Accordingly, it becomes a primary object of this invention to provide an improvement in DC-to-DC power converters. 
     It is another object of the invention to provide an improvement in pulse-width modulated DC-to-DC power converters. 
     It is still another object of the invention to provide a pulse-width modulated DC-to-DC power converter having current mode control. 
     And it is yet another object of the invention to provide a DC-to-DC converter which provides both volt-second balance of the power transformer and ampere-second balance of the current sensing transformer simultaneously. 
     Briefly, the foregoing and other objects of the invention are achieved by a current-mode controlled pulse-width modulated DC-to-DC power converter including both isolated and non-isolated implementations comprised of a first inductor, i.e. a transformer or an equivalent fixed inductor equal to the inductance of the secondary winding of the transformer, coupled across a source of DC input voltage via a controlled switch device, e.g. a transistor, and which is rendered alternately conductive (ON) and non-conductive (OFF) in accordance with a signal from a feedback control circuit which continuously controls the duty cycle of the transistor switch in relation to a complete cycle of operation. A first capacitor capacitively couples one side of the first inductor to an output filter circuit including a second inductor coupled to a second capacitor which in turn is coupled to the other side of the first inductor, with the circuit load being coupled across the second capacitor. A semiconductor diode is additionally coupled from a common circuit connection between the first capacitor and the second inductor to the other side of the first inductor. A current sense transformer generating a current feedback signal for the switch control circuit is directly coupled in series with the other side of the first inductor so that the first capacitor, the second inductor and the current sense transformer are connected in series through the first inductor. This enables the current of the first and second inductors to be alternately sensed during both portions of an operational cycle. The inductance values of the first and second inductors, moreover, are made identical. The location of the current sense transformer and the use of equal valued first and second inductors result in a relatively simple DC-to-DC converter topology wherein volt-second balance in the first inductor and ampere-second balance in the current sense transformer are achieved simultaneously while at the same time reducing undesired stresses on the switching transistor. 
    
    
     BRIEF DESCRIPTION OF THE DRAWING 
     The following detailed description of the invention will be more readily understood when considered together with the accompanying drawings wherein: 
     FIG. 1 is an electrical schematic diagram illustrative of a known prior art forward type of converter topology; 
     FIG. 2 is an electric schematic diagram illustrative of a flyback type converter topology; 
     FIG. 3 is an electrical schematic diagram illustrative of an isolated version of a known prior art CUK type converter topology; 
     FIG. 4 is an electrical schematic diagram illustrative of an isolated or transformer version of the preferred embodiment of the invention; 
     FIG. 5 is an electrical schematic diagram illustrative of a non-isolated version of the preferred embodiment of the invention shown in FIG. 4; 
     FIG. 6 is an electrical schematic diagram illustrative of the topology shown in FIG. 5 during a first portion of a circuit operating time period; 
     FIG. 7 is an electrical circuit diagram illustrative of the circuit shown in FIG. 5 during a second portion of the operational time period; 
     FIG. 8 is a set of time related waveforms illustrative of the current and voltage relationships provided by the non-isolated embodiment shown in FIG. 5; and 
     FIG. 9 is a waveform diagram illustrative of the current flow through the current sensing transformer shown in FIG. 5 during both portions and of the operational time period. 
    
    
     DETAILED DESCRIPTION OF THE INVENTION PRIOR ART 
     Before considering the details of the invention, reference will first be made back to the prior art converter topologies referred to above and illustrated in FIGS. 1-3. 
     As shown in FIG. 1, the isolated forward topology depicted thereat includes a DC voltage input source 10 which applies energy to the primary winding 12 of a power transformer 14 under the control of a transistor switch 16, rendered alternately conductive (ON) and non-conductive (OFF) during each cycle T s  of operation by a feedback control circuit 18 coupled to the primary winding 12 and which controls the ON and OFF time dT s  and dT s , respectively, of the transistor 16, where d designates the duty cycle, and accordingly that of the converter itself. The secondary winding 20 couples energy to an inductor-capacitor output filter including an inductor 22 and capacitor 24, with the load comprising a resistance element shown by reference numeral 26 coupled across or shunting capacitor 24. 
     Furthermore, a diode 28 is connected in series from one (.) polarity end of the secondary winding 20 to the inductor 22, while a second diode 30 shunts both the inductor 22 and the capacitor 24 while being coupled to the other or opposite end of the secondary winding 20 along with the one side of the capacitor 24 and load 26 The primary side of the transformer 14 also includes a reset circuit including a reset winding 32 having its (.) polarity end connected to ground. However, it also requires an additional diode 34 and a capacitor 36 which forms part of an input filter including an inductor 38 connected in series with voltage source 10. The input filter acts to filter out voltage and current noise on the input voltage V in , and primarily to filter converter induced current pulses from the DC power source 10. 
     The forward converter topology illustrated in FIG. 1 offers an efficient power conversion technique; however, it typically requires the use of a reset winding such as the winding 32 to reset the transformer core of the power transformer 14 by returning its stored energy to the primary side. This requirement, although not difficult to implement, causes certain design problems for some applications, such as requiring the additional diode 34 and a relatively large capacitance value for the capacitor 36. 
     With respect to the flyback topology as depicted in FIG. 2, it intentionally stores energy in the inductance of the power transformer 14 during the on-time interval dT s  of the transistor power switch 16 and then releases the energy to the secondary side of the transformer 14 during its off-time dT s  and where for continuous mode operation dT s  +dT s  =T s , the time period for one operational cycle. The energy delivered to the load side of the transformer 14 is out of phase with the reenergizing process of the inductance which is incorporated into the transformer 14. If operated in the continuous inductor current mode, this characteristic produces inherent problems in the stability in the duty cycle control circuit 18 which generally results in compromised dynamic performance and when operated in the discontinuous inductor current mode, the switching transistor 16 and the diode 28 can be subjected to undesirable relatively high peak current stresses. 
     As to the CUK topology illustrated in FIG. 3, in addition to capacitively coupling the primary and secondary windings 12 and 20 of the power transformer 14 to their respective input and output circuit components, the grounded capacitor 36 of the forward and flyback topologies (FIGS. 1 and 2) forming part of the input filter is deleted and the control switch device 16 is no longer directly connected to the primary winding 12, but is now connected to a circuit node 39 common to both the inductor 38 and the coupling capacitor 40. Additionally, damping circuits comprised of respective series circuits including capacitor 44, resistor 46 and capacitor 48, resistor 50 must be utilized and shunt the coupling capacitors 40 and 42. 
     The coupling capacitor arrangement of the CUK topology operates to continuously maintain volt-second balance on the core of the transformer 14 in addition to developing a push-pull driving voltage for improved flux utilization. In so doing, the front end inductor 38 now operates as a current source which drives energy into the transformer 14 and the coupling capacitors 40 and 42. One major disadvantage of the CUK topology, however, is that this current source typically produces voltage spikes across the switching transistor 16, which are often times extremely difficult to reduce. Furthermore, both the switching device 16 and the output diode 30 must carry significantly higher currents than typically encountered in other topologies. The potential voltage and current stresses imposed on both the switching device 16 and the diode 30 force the circuit designer to select components rated for relatively high power levels. 
     In addition to the potential switching component stresses and other additionally required protection circuitry, not shown, the biggest inherent disadvantage of the CUK topology is the necessary presence of relatively large damping components across both the primary and secondary coupling capacitors 40 and 42 which are shown comprising capacitor 44, resistor 46, and capacitor 48, resistor 50. The damping components are required to shape the AC behavior of the control circuitry 18 being generally large in bulk make size and weight an important and undesirable concern for many applications. 
     DESCRIPTION OF THE PREFERRED EMBODIMENTS 
     Considering now the preferred embodiments of the subject invention which are shown in FIGS. 4 and 5, this invention overcomes the inherent deficiencies of the prior art converter topologies shown in FIGS. 1-3 by combining the characteristics of both the forward and flyback topologies shown in FIGS. 1 and 2, while resembling the topology of the CUK topology of FIG. 3. However, subtle differences are now present in the subject invention which at first may not appear apparent but nevertheless are present and necessary for achieving an improved operation. 
     The subject invention does not utilize a capacitively coupled primary winding of the power transformer 14, but instead now employs a driving arrangement similar to that of a forward topology wherein energy is delivered to the output filter and transformer inductance or an equivalent inductor 21 (FIG. 5) thereof during the on-time (dT s ) of the switching transistor 16. The inductor 21 in effect comprises the transformer primary winding 12 reflected to the secondary side by the transformer turns ratio N 1  :N 2 . 
     The energy which is stored in the inductance L 1  of the transformer 14 or the inductor 21, however, is not dumped back to the input side, but instead is released to the secondary coupling capacitor (C 1 ) 42 during the off-time (dT s ) of the transistor 16 and which is similar to the operation of a flyback topology. The topology of the subject invention is therefore termed a &#34;forback&#34; topology converter since it exhibits behavior of both the forward and flyback topologies alternately with dT s  and dT s  of the transistor switching period T s . 
     A current sensing transformer 52 is connected in the secondary circuit as shown in FIGS. 4 and 5 to sense the current I s  flowing in the secondary circuit for controlling the duty cycle (d) of the switching transistor 16 in conjunction with the output voltage V o  across the load 26. The current sensing transformer 52 includes a primary winding 54 directly connected to the end of secondary winding 20 or inductor 21 opposite from the end which is directly connected to the capacitor (C 1 ) 42 so that the inductor currents flowing in the secondary circuit during the respective time intervals of dT s  and dT s  can be detected. The secondary winding 56 of the sensing transformer 52 is connected to the duty cycle control circuit 18 for providing a feedback signal voltage V s  proportional to the secondary current I s . The feedback control circuit 18 controls the duty cycle d of the transistor switch 16. 
     In addition to the specific location of the current sensing transformer 52, the methodology employed in the circuit design and hereinafter described, results in the inductance values of L 1  and L 2  being substantially equal. 
     These two last mentioned features result in a converter topology wherein a volt-second balance of the power transformer 14 and an amp-second balance of the current transformer 52 are achieved simultaneously. This will be more readily appreciated as the following detailed description of operation is considered. 
     DESCRIPTION OF OPERATION 
     Referring now FIGS. 6-9, for the sake of simplicity FIG. 6 is illustrative of the equivalent circuit for the non-isolated converter topology shown in FIG. 5 during the on-time interval dT s  where the transistor switch 16 is conductive. FIG. 7, on the other hand, is the equivalent circuit for FIG. 5 during the off-time interval dT s  where the switch 16 is non-conductive. 
     The following operational conditions exist: ##EQU1## 
     It can be seen with reference to FIG. 6 that during the on-time interval dT s , wherein the semiconductor switch 16 is closed, the diode (D 1 ) 40, becomes reverse biased and is therefore considered an open circuit resulting in the equivalent circuit as shown. During this time, energy flows from V g  i.e. source 10&#39; to inductor (L 1 ) 21, inductor (L 2 ) 22, and capacitor (C 2 ) 24 and from capacitor (C 1 ) 42 to load resistor (R L ) 26. 
     Two currents flow during the dT s  interval, namely, I L1  and I L2 . The energy (E L1 ) stored in the inductance (L 1 ) 21 increases from a minimum value to a maximum value according to the expressions: 
     
         E.sub.L1 (min)=1/2L.sub.1 ×I.sub.L1.sup.2 (min)      (7) 
    
     and, 
     
         E.sub.L1 (max)=1/2L.sub.1 ×I.sub.L1.sup.2 (max)      (8) 
    
     whereupon an increase in energy, ΔE 1 , stored in inductor (L 1 ) 21 which can be expressed as: 
     
         ↑ΔE.sub.1 =1/2L.sub.1 ×[I.sub.L1.sup.2 (max)-I.sub.L1.sup.2 (min)]                               (9) 
    
     Accordingly, the current in inductor (L 1 ) 21 increases linearly from a minimum value to a maximum value as shown in FIG. 8(a) by reference numeral 58. 
     The voltage applied to inductor (L 2 ) 22 is equal to V g  +V C1  -V C2  or simply V g  whereupon the stored energy increases from a minimum value to a maximum value according to the expressions: 
     
         E.sub.L2 (min)=1/2L.sub.2 ×I.sub.L2.sup.2 (min)      (10) 
    
     and 
     
         E.sub.L2 (max)=1/2L.sub.2 ×I.sub.L2.sup.2 (max)      (11) 
    
     causing an increase in energy, ΔE 2 , which can be expressed as: 
     
         ↑E.sub.2 =1/2L.sub.2 ×[I.sub.L2.sup.2 (max)-I.sub.L2.sup.2 (min)]                                                    (12) 
    
     As a consequence, the current I L2  in the inductor 22 increases linearly from a minimum value to a maximum value as shown by reference numeral 60 in FIG. 8(b). 
     With respect to the capacitor currents flowing during dT s , the current out of capacitor (C 1 ) 42 is equal to I L2  and decreases from a maximum value to a minimum value as shown by reference numeral 62 of FIG. 8(c) and is 180° out of phase with I L2  of FIG. 8(b). The energy stored in capacitor (C 1 ) 42 also decreases from a maximum value to a minimum value according to the expressions: 
     
         E.sub.C1 (max)=1/2C.sub.1 ×V.sub.C1.sup.2 (max)      (13) 
    
     and 
     
         E.sub.C1 (min)=1/2C.sub.1 ×V.sub.C1.sup.2 (min)      (14) 
    
     whereupon the energy change, ΔE 3 , stored in capacitor (C 1 ) 42 can be expressed as: 
     
         ↑E.sub.3 =1/2C.sub.1 ×[V.sub.C1.sup.2 (max)-V.sub.C1.sup.2 (min)]                                                    (15) 
    
     The current entering the + terminal of capacitor (C 2 ) 24 is I L2  -I o . An energy change, ΔE 4 , which can be expressed as: 
     
         ↑E.sub.4 =1/2C.sub.2 [V.sub.C2.sup.2 (max)-V.sub.C2.sup.2 (min)](16) 
    
     V C2  appears as the sinusoidal curve portion 64 shown in FIG. 8(d) and changes from a minimum value to a maximum value as shown but is out of phase with I L1  and I L2  by an angle φ which is determined by the relative values of L 2 , C 2  and R L . 
     As a result of these interrelationships, the current I s  flowing through the primary winding 54 of the current sense transformer 52, is equal to I L2  and appears identical to the linear curve portion 60 of FIG. 8(b) as shown in FIG. 9 by reference numeral 66. 
     Turning attention now to the off-time interval dT s , when the transistor switch 16 is non-conductive, the diode (D 1 ) 30 in FIG. 5 becomes forward biased and can be considered a short circuit, resulting in an equivalent circuit as shown in FIG. 7. While two loops are shown, it is done for purposes of illustration only, since the two conductors 68 a  and 68 b  shown thereat are in actuality a single current conducting path. 
     During the dT s  interval, energy flows from the inductor (L 1 ) 21 to the capacitor (C 1 ) 42. Simultaneously, energy is delivered to the load resistance (R L ) 26 from the inductor (L 2 ) 22 and the capacitor (C 2 ) 24. The current I L1  in the inductor (L 1 ) 21 decreases linearly from a maximum value to a minimum value as shown by reference numeral 70 in FIG. 8(a). This results in a decrease in energy, ΔE 1 , stored in inductor 21 (L 1 ) which can be expressed as: ##EQU2## 
     In a like manner, the current I L2  in the inductor (L 2 ) 22 decreases linearly from a maximum value to a minimum value as shown by reference numeral 72 of FIG. 8(b). A decrease in energy, ΔE 2 , stored in inductor 22 (L 2 ) occurs which can be expressed as: ##EQU3## 
     The current flow into capacitor (C 1 ) 42 increases non-linearly as shown by waveform 74 of FIG. 8(c) with an increase in energy storage, ΔE 3 , which can be expressed as: ##EQU4## 
     The current flow out of capacitor (C 2 ) 24 is equal to I o  -I L2  which produces the corresponding voltage waveform as shown in FIG. 8(d). The voltage V C2  lags the current, I o  -I L2 , by the phase angle φ as shown by reference numeral 76 of FIG. 8(d). The corresponding change in energy storage may be expressed as: ##EQU5## 
     With respect to the current I s  in the primary winding 54 of the current sensing transformer 52, it comprises a current -I L1  as indicated by reference numeral 78 of FIG. 9. 
     Design Methodology 
     Regarding a physical implementation of the subject invention, the following method of circuit design would be followed so that among other things, but most importantly, L 1  =L 2 . Typically, a circuit designer would establish or would be provided with a set of initial or desired operational parameters, namely: output voltage V o , switching frequency f s , minimal input voltage V in (min), nominal input voltage V in (nom), maximum input voltage V in (max), minimum output load R L (min), nominal output load R L (nom) and maximum output load R L (max). For purposes of explanation, it should be noted that R L (min), for example, stands for minimum resistance in ohms, whereas R L (max) stands for maximum resistance in ohms. 
     One would then proceed to determine the turns ratio N 1  :N 2  of power transformer 20, including the value of the inductance L 1 , the inductance L 2 , the capacitance C 1  and the capacitance C 2 . This would then be followed by the design of the power transformer if necessary. 
     The first step involved is determining an acceptable duty cycle d, given the output voltage V o , the range of the three input voltages V in  mentioned above, and by selecting the appropriate turns ratio N 1  :N 2  for the transformer. The turns ratio N 1  :N 2  should be selected such that the maximum duty cycle d max  should not exceed a specified upper limit, typically 50% i.e. 0.5 T s  and should typically be in the range between 20% and 40% and from which the duty cycle d can be determined from aforementioned equation (2) as: 
     
         d=N.sub.1 V.sub.o /(N.sub.2 V.sub.in +N.sub.1 ×V.sub.o)(21) 
    
     From this, the average current I L2 (avg) in the output inductor 22, and in the transformer secondary I L1 (avg), as shown in equations (3) and (5), can be calculated from the initial parameters established and equation (21) for minimum, nominal and maximum conditions. 
     Noting that one of the inventive features comprises a DC-to-DC converter where the values of L 1  and L 2  are equal, the value for L 2 , i.e. the inductance value of the inductor 22, is determined first. This is based on three considerations: (1) the filter requirements of the output filter consisting of inductance (L 2 ) 22 and capacitor (C 2 ) 24; (2) the desirability of maintaining a continuous current conduction mode in L 2  ; and (3) the allowable current variation Δi of I L2  in the inductance (L 2 ) 22. 
     As to the output filter requirements, the voltage input to the LC filter comprised of inductor 22 and capacitor 24 is basically a square wave with a magnitude of: 
     
         V.sub.filt =(N.sub.2 /N.sub.1)×V.sub.in +V.sub.C1    (22) 
    
     The worst case scenario exists when the largest peak-to-peak output ripple voltage across the load resistance (R L ) 26 occurs at V in (max), d.sub.(min), and R L (max). Thus, 
     
         V.sub.filt =(N.sub.2 /N.sub.1)×V.sub.in(max) +V.sub.o(23) 
    
     Accordingly, the attenuation in dB necessary to meet the ripple requirement is equal to: 
     
         20×log [V.sub.o(ripple) /V.sub.filt ]                (24) 
    
     The LC filter in this invention will have a --40 dB/dec slope. Knowing this and the required attenuation at the switching frequency f s , the filter corner frequency f c  is determined from the expression: ##EQU6## Rearranging equation (24) yields: 
     
         L.sub.2 =1/[(2πf.sub.c).sup.2 ×C.sub.2 ]          (26) 
    
     Selection of a few trial values for C 2  is now made to allow one to determine one or more candidate values for L 2  which will satisfy the output filter requirements of equation (25). However, the actual value of L 2  will also depend on the other two considerations of maintaining continuous conduction mode and the allowable Δi percentage referred to above. 
     Since it is desirable to maintain a continuous conduction mode, then a critical minimum value of L 2  can be determined for which continuous conduction is maintained under the conditions of lightest load R L (min)  and maximum input voltage V in (max). It can be shown that the minimum value of L 2  necessary to maintain continuous conduction mode under the lightest load and maximum input voltage condition exists where: 
     
         L.sub.2(min) =[d.sub.max ×T.sub.s ×R.sub.L(min) ]÷2(27) 
    
     The value of the inductor (L 2 ) 22 dictates the slope of the current ramp as shown by the waveform segments 60 and 72 of FIG. 8(b). As a general rule, under a nominal input voltage V in (nom) and nominal output load R L (nom), Δi should remain no more than 25% of I L2  (Avg). 
     In solving for L 2 , it can be shown that the voltage across inductor 22 L 2  can be expressed as: 
     
         V.sub.L2 =L.sub.2 ×Δi/Δt                 (28) 
    
     where Δt=d nom  ×T s . Rearranging equation (28) results in L 2  being expressed as: 
     
         L.sub.2 =(V.sub.L2 ×Δt)/Δi               (29) 
    
     or 
     
         L.sub.2 =(N.sub.2 ×V.sub.in(nom ) ×d.sub.nom ×T.sub.s)/(N.sub.1 ×0.25×I.sub.L2)      (30) 
    
     Accordingly, L 2  is selected on the basis of equations (26), equation (27) and equation (30). Having selected a value of L 2 , the value of L 1  is now also determined. The appropriate value of capacitor 24 (C 2 ) is next determined from equation (26). The only component left to be selected is the value for the capacitor 42 (C 1 ). 
     In the determination of the capacitance value for capacitor 42 (C 1 ), the value of C 1  is not as critical as the value of the other components. Preferably, capacitor 24 should be a polycarbonate or polystyrene low ESR capacitor. A 1 μF polycarbonate capacitor, for example, is adequate for 100 kHz designs where load currents are less than one ampere(amp). 
     As a general rule under nominal input voltage V in (nom) and load conditions R L (nom), the change of voltage Δv across C 1  should remain no more than 25% of V o . During the on-time dT s  of the transistor switch 16 where Δv is selected to be 25% of V o , C 1  can be calculated from the expression: 
     
         C.sub.1 =(I.sub.L2(avg) ×d.sub.nom ×T.sub.s)/(0.25×V.sub.o)                      (31) 
    
     With the values for L 1 , L 2 , C 1  and C 2  being selected, it now becomes necessary to calculate the peak currents in both inductors (L 1 ) 21 and (L 2 ) 22 which can be achieved by use of equations (4) and (6), supra. 
     A knowledge of the values of L 1 , I L1 (peak), L 2 , and I L2 (peak) now provides all the information required for an actual design of the power transformer 14 when an embodiment such as shown in FIG. 4 is desired. In designing the power transformer, the designer first selects a trial core, then determines the minimum number of turns on the secondary winding (N 2 ) 20 followed by determining the required air gap. 
     In selecting a trial core, one makes a selection based upon the maximum desired flux density limit (B m ) under the worst case operating conditions, the effective area (A e ), relative permeability (μR) and effective core lengths (l e ). 
     The total reluctance (R T ) of both the core (R c ) and the air gap (R g ) can be determined from the expression: 
     
         R.sub.T =(l.sub.c +l.sub.g ×μ.sub.R)/μ.sub.R A.sub.e(32) 
    
     from which the inductance L 1  in milliHenries can be determined from the expression: 
     
         L.sub.1(mH) =(4π/R.sub.T)×(N.sub.2 /1000).sup.2   (33) 
    
     From equation (33) the total reluctance R T  can be stated as 
     
         R.sub.T =(4π/L.sub.1mH)×(N.sub.2 /1000).sup.2     (34) 
    
     It can be shown that the maximum flux density B m  can be expressed as: 
     
         B.sub.m =I.sub.L1(peak) ×L.sub.1(mH) ×1×10.sup.5 (A.sub.e ×N.sub.2)                                           (35) 
    
     from which N 2  can be obtained by rearranging equation (35)as: 
     
         N.sub.2(min) =I.sub.L1(peak) ×L.sub.1(mH) ×1×10.sup.5 /(A.sub.e ×B.sub.m)                                 (36) 
    
     It is to be noted that N 2 , the secondary winding 20 on the transformer 14, is the inductance L 1  in the equivalent circuit shown in FIG. 5. Thus, equation 36 provides the minimum number of turns needed on the secondary winding 20 of the transformer 14 in order to keep from exceeding B m  at a value of I L1 (peak). When desirable, larger values of N 2  are permissible, which results in a corresponding reduction in B m . 
     Now that both N 2  and L 1  are known, an air gap is determined such that the required relationship between these two parameters N 2  and L 1  for a given core is achieved. Keeping in mind equations (32)-(34), the combined length l g  of the air gap and the length l c  of the core can be expressed as: ##EQU7## At this point, the relationship between the effective length l e , the length of the core l c  and the length of the air gap l g  must be specified according to the geometry of the core. For example, for a torroid, this can be expressed in centimeters(cm) as: 
     
         l.sub.g (cm)=X/Y                                           (38) 
    
     where, 
     X=[4π×μ R  ×A e  ×N 2   2  ]/[10 5  ×L 1  (mH)]-l e , and 
     Y=μ R  -1 
     Following the resolution of an acceptable value of N 2 , the value of N 1  is known from above where the selection of N 1  :N 2  turns ratio is selected to provide an acceptable duty cycle. 
     Due to the flyback characteristic of this topology, it is essential to optimize the coupling between the primary and secondary windings 12 and 20 of the transformer 14 and therefore in addition to minimizing the number of turns for both N 1  and N 2 , the winding should be bifilar wound if possible. 
     Thus what has been shown and described is an improved topology and methodology for the implementation of a current mode control pulse-width modulated DC-to-DC converter which automatically provides simultaneous volt-second balance of the power transformer and amp-second balance of the current sensing transformer simply and expeditiously. 
     Having thus shown and described what is at present considered to be the preferred embodiments of the invention, it should be noted that the same has been made by way of illustration and not limitation. Accordingly, all modifications, alterations and changes coming within the spirit and scope of the invention as defined by the appended claims are herein meant to be included.