Patent Publication Number: US-9413245-B2

Title: Power converter with low ripple output

Description:
RELATED APPLICATION INFORMATION 
     This application is a continuation of U.S. application Ser. No. 12/845,631 filed Jul. 28, 2010, currently pending, and also claims the benefit of U.S. Provisional Application Ser. No. 61/229,217, filed on Jul. 28, 2009, both of which are hereby incorporated by reference as if set forth fully herein. 
    
    
     BACKGROUND OF THE INVENTION 
     1. Field of the Invention 
     The field of the invention generally relates to power supplies and, more specifically, to a versatile DC output power supply. 
     2. Background of the Related Art 
     There are two main classes of power supply or converter: (1) AC to DC, and (2) DC to DC. An AC to DC power supply generally converts AC line voltage as its input to a DC output voltage and is found, for example, in applications such as home audio amplifiers. It can generally be implemented as either a linear or switching power supply. A DC to DC power supply converts from one existing DC voltage to another, for example from a battery, to another higher or lower voltage level. It is typically implemented with a switching power supply. For general use, DC to DC power supplies convert voltages and also provide isolation between input and output. 
     Common components of a conventional power supply include a transformer, rectifier, and smoothing/storage capacitors. Additional components commonly utilized in a switching power supply include a control IC chip, power transistors, filtering and screening to prevent electro-magnetic interference (EMI). The demand for ever smaller equipment has led to a preponderance of switching power supplies. 
     Conventional linear power supplies, used for instance in home audio amplifiers, use a large, heavy, expensive transformer to convert a low frequency, high-voltage AC line supply to a lower voltage suitable for the amplifier or other application. The high-voltage AC line supply is first dropped down to a lower AC voltage, and then the lower AC voltage waveform is rectified to DC. However, the rectified voltage is discontinuous and so large storage capacitors are needed in order to provide a smooth voltage for the amplifier. Even so, the DC supply still has an appreciable irregularity (the ripple voltage) superimposed upon the DC which can manifest as an audible hum and buzz at the amplifier output unless considerable care is taken with the amplifier design and layout. 
     While the design of such a power supply is relatively simple and the EMI emissions relatively low, the transformer is large, heavy and very expensive. The storage capacitors are also large and expensive. Thus the overall bulk of this power supply approach precludes its use on lightweight, low profile designs. The power losses in the power supply are relatively low, with an overall efficiency generally found in the 85-90% range. 
     An alternative to using linear power supplies is to employ a switched-mode power conversion technique. In this technique, the line voltage is first of all rectified and smoothed at full line voltage. This allows the storage capacitor to be smaller as compared to the linear power supply, and also less expensive. The resulting high voltage DC signal is then converted to a lower voltage by chopping it at a very high frequency—several tens of kHz typically—to produce an AC output signal which is transformed down to a lower voltage through a small transformer. Because the operating frequency is much higher than with a linear power supply, the transformer can be much smaller than in a conventional linear power supply. However, the AC signal on the output side of the transformer again has to be rectified to obtain DC and must still be smoothed with storage capacitors, albeit smaller ones than in a linear power supply. An example of such a power supply is an external power supply generally used to power a laptop computer. 
     One penalty to be paid in this approach is that, in order to retain efficiency, the chopping of the DC produces high frequency AC with a discontinuous, square waveshape. Such a waveshape generates high levels of very high frequencies which radiate to cause radio frequency interference (EMI). Careful design, layout and screening are required to reduce these emissions to an acceptable limit. The switching frequency components also need to be removed or isolated from the input and output lines, requiring extra magnetic components that add to the cost and bulk of the supply. The efficiency, although theoretically capable of being very high, typically lies in the 80-90% range. Overall, the size and weight of the switched-mode power supply can be reduced considerably compared to a conventional linear power supply and the basic component cost can also be lower. However, the complexities inherent in the design of a switching power supply can add considerably to the design and certification costs and result in a time to market of many months. 
     In sum, linear power supplies tend to be larger in size and profile, relatively costly, and heavy. They are advantageous in terms of efficiency and low EMI. Switching power supplies tend to be smaller and weigh less. Due to higher frequency operation, the transformers and capacitors of a switching power supply tend to be smaller than with a linear power supply. However, switching power supplies can be less efficient than linear power supplies, and produce significantly more EMI which requires careful filtering and screening. Switching power supplies are also more complex, needing control circuitry and power switching devices. They take longer to design and are generally more expensive than linear power supplies. The trend is towards ever smaller power supplies, requiring higher frequency operation and hence more potential issues relating to EMI. 
     Larger power supplies may utilize three-phase power generation, which is an alternative power supply technique to the ones thus far described. In a three-phase system, three power lines carry three alternating currents of the same frequency but different phases, which reach their instantaneous peak values at different times. The current waveforms are offset by 120 degrees from one another (that is, each current is offset by one-third of a cycle from the other two waveforms). This staggering of waveforms allows energy to be continuously provided to the load(s), with a reduced but nonetheless substantial ripple. As a result, a constant amount of power is transferred over each cycle of the current. Transformers may be used to step-up or step-down the voltage levels at various points in a three-phase power network. A three-phase rectifier bridge commonly includes six diodes, with two diodes used for each branch of the three-phases. 
     While three-phase power supply systems have some benefits, they are also subject to certain drawbacks or limitations. For example, a minimum of three conductors or power lines is generally required, as well as three sets of circuitry for level-shifting (with transformers) and rectifying each branch. Also, while ripple is reduced over a single-phase power supply, the ripple is still substantial and in general requires storage capacitors to bring down to an acceptable level. 
     A need exists for a power supply or converter that can be made small, lightweight and reasonably inexpensive, with minimal EMI. A need further exists for such a power supply that avoids the complexities and complications of a switching power supply. A further need exists for a power supply that can reduce the need for large components and thus be made small in size and profile and lightweight. 
     SUMMARY OF THE INVENTION 
     In one aspect, a power supply is provided in which one or more input waveforms are shaped or otherwise selected so that the output waveform requires minimal smoothing for generation of a DC output waveform. 
     According to one or more embodiments, a power supply is provided having one or more input waveforms are shaped or otherwise selected prior to being provided to an isolating transformer. The nature of the input waveforms is shaped or selected so that the transformed waveform requires no or minimal smoothing for generation of a DC output waveform. 
     The power supply may comprise a waveform generator, a level conversion stage for stepping the voltage level up (or down), a rectification stage, and a signal combiner. The waveform generator may generate complementary waveforms, such that after each of the complementary waveforms is rectified and combined their sum will be constant, thus requiring no or minimal smoothing for generation of a DC output waveform. 
     In one embodiment, a DC output power supply comprises a waveform generator, at least one transformer, a rectification stage, and a signal combiner. The waveform generator may generate complementary waveforms, such that after each of the complementary waveforms is rectified and combined their sum will be constant. The complementary waveforms are preferably identical but are 90-degrees out of phase from one another, although in other embodiments the waveforms may have a different relationship. The complementary waveforms are applied to a pair of transformers or a single transformer with separate windings. The outputs of the transformers are provided to the rectification stage, which outputs a pair of rectified signals. The rectified signals have the property that when added together, their sum is constant. The rectified signals are provided to the signal combiner, which sums the signals and produces a constant DC output signal. 
     In certain embodiments, the output voltage is monitored and fed back to the input side of the power supply, which adjusts the amplitude or other characteristics of the complementary waveform signals prior to being applied to the transformer(s). 
     In other embodiments, a switched-capacitor technique is used to adjust (e.g., step up) the voltage level of the complementary waveforms, instead of transformer(s). In other respects, the power supply operates in a similar fashion. 
     Embodiments as described herein may result in one or more advantages, including being smaller, lighter, thinner and/or less expensive than a conventional power supply, with fewer large components, while retaining high efficiency. The power supply can be designed so as to produce minimal or insignificant EMI. Because the power supply can be simpler to design and manufacture, it can be brought to market more quickly, thus resulting in a faster product design cycle. 
     Further embodiments, alternatives and variations are also described herein or illustrated in the accompanying figures. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is a conceptual block diagram of a DC output power supply as disclosed herein, using one or more transformers for signal level conversion. 
         FIG. 2  is a set of waveform diagrams illustrating operation of the power supply shown in  FIG. 1 , in accordance with one example. 
         FIG. 3  is a set of waveform diagrams illustrating operation of the power supply shown in  FIG. 1 , in accordance with another example. 
         FIG. 4  is a block diagram showing components of an embodiment of a voltage-controlled DC output power supply as disclosed in accordance with the conceptual block diagram of  FIG. 1 . 
         FIG. 5  is a block diagram showing components of an embodiment of a current-controlled DC output power supply as disclosed in accordance with the conceptual block diagram of  FIG. 1 . 
         FIG. 6  is a block diagram illustrating one example of a signal generator as may be used in connection with various embodiments as disclosed herein. 
         FIG. 7  is a schematic diagram showing an embodiment of a power supply using a similar technique to  FIG. 1 , but implemented with switched capacitor circuits. 
         FIG. 8  is a conceptual block diagram of a DC output power supply as disclosed herein. 
         FIG. 9  is a block diagram illustrating a second example of a signal generator as may be used in connection with various embodiments as disclosed herein. 
         FIG. 10  is a waveform diagram illustrating an example of a pair of frequency modulated signals as may be output by a signal generator. 
         FIGS. 11A and 11B  are schematic diagrams of a portion of a DC power supply operating in accordance with the principles of  FIG. 1 , using different input waveforms in each case. 
         FIG. 12  is a schematic diagram of a portion of a DC power supply having amplifiers configured as integrators. 
         FIG. 13  is a diagram of waveforms as may be used in connection with a DC power supply having transconductance amplifiers with an integrator characteristic. 
         FIG. 14  is a schematic diagram of a portion of a DC power supply employing feedforward techniques to linearize the power amplifiers. 
         FIG. 15  is a schematic diagram of a portion of a DC power supply employing both feedforward and feedback techniques. 
         FIG. 16  is a schematic diagram of another embodiment of a DC power supply employing both feedforward and feedback techniques. 
         FIG. 17  is a schematic diagram of an embodiment using switched capacitor circuits to form a multi-stage power converter. 
         FIG. 18  is a schematic diagram showing a switched capacitor power supply having a combination of positive and inverting boosters circuits. 
     
    
    
     DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS 
     According to one or more embodiments, a power supply is provided having one or more input waveforms are shaped or otherwise selected prior to being provided to an isolating transformer. The nature of the input waveforms is shaped, selected or otherwise generated so that the transformed waveform requires minimal rectification and/or smoothing for generation of a DC output waveform. 
       FIG. 8  is a conceptual block diagram of a power supply  800  as disclosed herein. In  FIG. 8 , a signal source (waveform) generator  805  generates a pair of complementary waveform signals  823 ,  824 . The complementary waveform signals  823 ,  824  are selected so as to provide a constant DC output level after being coupled through a level conversion stage  830  to an output (rectification) stage  840  whereupon the level-converted signals are rectified and combined, while minimizing storage/smoothing capacitor requirements in the output stage  840 . The complementary waveform signals  823 ,  824  are preferably of a type as described later herein. The complementary waveform signals  823 ,  824  are respectively stepped up or down via blocks  835 ,  836 , which may be embodied as one or more transformers or switching capacitor networks, for example, as further detailed herein. The level conversion stage  830  provides signals  837 ,  838  to the output stage  840 . Signal  837  from the first level conversion block  835  is provided to a first rectifier block  860  of the output stage  840 . Signal  839  from the second level conversion block  836  is provided to a second rectifier block  861  of the output stage  840 . Each of the rectifier blocks  860 ,  861  may be embodied as, e.g., a full-wave rectifier bridge. The rectified output signals  866 ,  867  of the rectifier blocks  860 ,  861  are waveforms that are complementary in nature such that, when summed together, the result is a constant DC level. To this end, rectified output signals  866 ,  867  are provided to a signal combiner  870 , which sums or otherwise combines the rectified output signals  866 ,  867  and provides a DC output signal  885  that is substantially constant in nature, generally without the need for storage/smoothing capacitors. 
       FIG. 1  is a conceptual block diagram of a DC output power supply  100  as disclosed herein, based on the general principles of  FIG. 8 , and using one or more transformers for signal level conversion. As shown in  FIG. 1 , a signal source (waveform) generator  105  generates a pair of complementary waveform signals V IN1 , V IN2  over signal lines  123 ,  124 . The complementary waveform signals V IN1 , V IN2  are selected so as to provide a constant DC output level after being coupled through a transformer stage  130  to an output stage  140  whereupon they are rectified and combined, while minimizing storage/smoothing capacitor requirements in the output stage  140 . The complementary waveform signals V IN1 , V IN2  are preferably of a type as described later herein. The complementary waveform signals V IN1 , V IN2  are coupled through transformer stage  130  and, more specifically, through respective transformers  135 ,  136  of transformer stage  130  to the output stage  140 . The transformers  135 ,  136  may be step-up or step-down in nature, and are preferably identical in characteristics, assuming that the amplitude of the complementary waveform signals V IN1 , V IN2  is the same. Transformers  135 ,  136  may be physically embodied as a single transformer with separate windings for the input signals  123 ,  124  and for output signals  137 ,  138  but sharing the same magnetic core(s), or else they may be physically embodied as two physically separate transformers. 
     The transformer stage  130  provides signals  137 ,  138  to the output stage  140 . Signal  137  from the secondary output of transformer  135  is provided to a first rectifier block  160  of the output stage  140 . Signal  139  from the secondary output of transformer  136  is provided to a second rectifier block  161  of the output stage  140 . Each of the rectifier blocks  160 ,  161  may be embodied as, e.g., a full-wave rectifier bridge. The rectified output signals  166 ,  167  of the rectifier blocks  160 ,  161  may be periodic waveforms that are complementary in nature such that, when summed together, the result is a constant DC level. To this end, rectified output signals  166 ,  167  are provided to a signal combiner  170 , which sums the rectified output signals  166 ,  167  and provides a DC output signal  185  that is substantially constant in nature, generally without the need for storage/smoothing capacitors. In practice, small amounts of ripple may occur, which can be smoothed out with relatively small smoothing capacitor(s) (not shown) that may be provided in any convenient location, such as at the outputs of rectifier blocks  160 ,  161  and/or after the signal combiner  170 . 
     The characteristics of the generated waveforms V IN1 , V IN2  are selected to be periodic waveforms so that, after the signals are transformed, rectified, and combined (e.g., added), the resulting output signal  185  is a constant DC level. Preferably, waveforms V IN1 , V IN2  are identical in shape but offset from one another by 90 degrees. Also, the waveforms are preferably generally smooth, lacking lack spikes or other features that could be undesirable from an EMI perspective. Examples of suitable waveforms for signals V IN1 , V IN2  are shown in  FIG. 1 , and also illustrated in greater detail in  FIG. 2 . In  FIG. 2 , graphs  2 A and  2 B show waveforms V IN1  and V IN2 , respectively (represented as waveforms  203 ,  204  in  FIG. 2 ), each of which constitutes an alternating non-inverted/inverted raised cosine waveform, but phase offset from one another by 90 degrees. After full-wave rectification, the resulting waveforms  213 ,  214  are illustrated in graphs  2 C and  2 D, which relate to waveforms V IN1 , V IN2  respectively. Waveforms  213 ,  214  are sinusoidal waveforms offset from one another by 90 degrees, i.e., have the relationship of sine and cosine, reflecting the phase offset of original waveforms V IN1 , V IN2 . When added together, rectified waveforms  213 ,  214  result in an output waveform  220  having a constant DC output level, as shown in graph  2 E. In other words, the rectification and summing of waveforms V IN1 , V IN2  results in a constant DC output level, generally without the need for large storage/smoothing capacitors as would normally be required in conventional switching power supplies. 
     Besides the waveforms  203 ,  204  illustrated in graphs  2 A and  2 B of  FIG. 2 , other waveforms can also be used and provide a similar end result.  FIG. 3  illustrates a second example of complementary periodic waveforms selected to provide a constant DC output level after rectification and summing. In  FIG. 3 , graphs  3 A and  3 B depict waveforms V IN1  and V IN2 , respectively (represented as waveforms  303 ,  304  in  FIG. 3 ), each of which constitutes a triangle waveform having alternating non-inverted/inverted triangular waves, but phase offset from one another by 90 degrees. After full-wave rectification, the resulting waveforms  313 ,  314  are shown in graphs  3 C and  3 D, which relate to waveforms V IN1 , V IN2  respectively. Rectified waveforms  313 ,  314  are both positive triangle waveforms having symmetrical shape, offset from one another by 90 degrees, reflecting the phase offset of original waveforms V IN1 , V IN2 . When added together, rectified waveforms  313 ,  314  result in an output waveform  320  having a constant DC output level, as shown in graph  3 E. Because rectified waveforms  313 ,  314  have the same linear slope for the rising and falling portions of the triangular waves, the fall in voltage of the first rectified waveform  313  matches the rise in voltage of the second rectified waveform  314 , and vice versa. Thus, the rectification and summing of waveforms V IN1 , V IN2  results in a constant DC output level, generally without the need for large storage/smoothing capacitors as would normally be required in conventional switching power supplies. 
     Besides the waveforms for V IN1 , V IN2  shown in  FIGS. 2 and 3 , other waveforms can be used as well. Preferably, waveforms V IN1 , V IN2  are selected or generated such that after transformation and full-wave rectification, the rectified waveforms are complementary to one another such that they can be added together to result in a constant DC level. Such waveforms may include periodic waveforms resulting in rectified waveforms that are symmetrical in nature, such that their rising slope and curvature are the same as their falling slope and curvature. Likewise, the rectified waveforms are preferably symmetrical about their midpoint, such that their alternating “positive” and “negative” waves are identical in shape but inverted from one another. The waveform examples shown in  FIGS. 2 and 3  meet the above criteria. Where such rectified waveforms are identical but offset from one another by 90 degrees, the symmetrical nature of the rectified waveforms means that the rise in one rectified waveform will exactly match the fall in the other rectified waveform, thus leading to a constant combined output level. 
     In addition to the above, more complex waveforms can also be used for V IN1 , V IN2 . For example, the waveforms V IN1 , V IN2  may be comprised of a number of different harmonics, and/or may vary over time. 
     The power conversion techniques described above may be applied to either voltage or current based power supplies. More detailed examples are described further herein. 
       FIG. 4  is a block diagram showing components of an embodiment of a voltage-controlled DC output power supply  400  as disclosed in accordance with the conceptual block diagram of  FIG. 1 . The power supply  400  may be supplied by a local power source such as a battery, or by an external power source such as a line source. In  FIG. 4 , a signal generator  405  generates a pair of complementary waveform signals  412 ,  413 , preferably periodic in nature, and which generally have the characteristics previously described for V IN1  and V IN2 —i.e., they are shaped or selected so as to provide a constant DC output after being coupled through a transformer stage, rectified and combined. The complementary waveform signals  412 ,  413  are provided to a voltage controlled amplifier (VCA)  415 , which adjusts the amplitude of the waveforms signals  412 ,  413  based upon feedback received from the DC output signal  485  via feedback sense amplifier  490 . In some embodiments, voltage controlled amplifier  415  may be omitted, as may feedback path  491  and sense amplifier  490 . 
     The voltage controlled amplifier  415  outputs the amplitude-adjusted pair of complementary waveform signals V IN1  and V IN2  to linear amplifiers  430 ,  431 , respectively, as reflected by waveforms  423 ,  424  in the overlay graphs shown in  FIG. 4 , depicting an example similar to the waveforms used in the like example of  FIG. 1  and  FIG. 2 . The power inputs of linear amplifiers  430 ,  431  are connected to power supply rails +V and −V, and they output amplified signals  432 ,  433  that essentially span from rail to rail (subject to minor losses from the amplifiers  430 ,  431 ). The voltage characteristics of signals  432 ,  433  for one waveform example are reflected in overlay graphs  440  and  441  (depicting waveforms Vp1 and Vp2) respectively, illustrated in  FIG. 4 , in the case where the initial generated waveforms appear as in graphs  423 ,  424  for V IN1  and V IN2 . The corresponding current characteristics of Vp1 and Vp2 are reflected in overlay graphs  442  and  443  (depicting waveforms Ip1 and Ip2) respectively. As can be seen from graphs  440 ,  441 ,  442  and  443 , the voltage waveforms Vp1 and Vp2 for this particular example are characterized by alternating inverted and non-inverted raised cosine waves (with Vp1 and Vp2 being identical but offset from one another by 90 degrees), while the corresponding current waveforms Ip1 and Ip2 take the form of square waves having a constant positive current corresponding to the time period of the non-inverted raised cosine waves, and constant negative current corresponding to the time period of the inverted raised cosine waves. Like the voltage waveforms, the current waveforms Ip1 and Ip2 are identical but offset from one another by 90 degrees. 
     The output of the first linear amplifier  430  is coupled to the primary winding of a first transformer  435 . The output of the second linear amplifier  431  is coupled to the primary winding of a second transformer  436 . The secondary windings of transformers  435 ,  436  are coupled to an output stage  450 , which receives the transformer output signals  437 ,  438  from the transformers  435 ,  436 . The transformers  435 ,  436  may be step-up or step-down in nature, and are preferably identical in characteristics, assuming that the amplitude of the complementary waveform signals Vp1 and Vp2 is the same. Transformers  435 ,  436  may be physically embodied as a single transformer with separate windings for the input signals  432 ,  433  and for the output signals  437 ,  438 , but sharing the same magnetic core(s), or else they may be physically embodied as two separate transformers. Transformers  435 ,  436  are preferably designed to have low leakage inductance. 
     The output stage  450  preferably comprises a pair of rectifier blocks  460 ,  461  that may be embodied as, e.g., full-wave rectifier bridges. Signal  437  from the secondary output of transformer  435  is provided to a first rectifier block  460  of the output stage  450 . Signal  439  from the secondary output of transformer  436  is provided to a second rectifier block  461  of the output stage  450 . Each of the rectifier blocks  460 ,  461  may be embodied as, e.g., a full-wave rectifier bridge. The rectified output signals of the rectifier blocks  460 ,  461  are, in this case, periodic waveforms that are complementary in nature such that, when summed together, the result is a constant DC level. To this end, the outputs of rectifier blocks  460 ,  461  are tied together in series so that the rectified output signals therefrom are additively combined, thereby providing a DC output signal  485  that is substantially constant in nature, generally without the need for storage/smoothing capacitors. In practice, small amounts of ripple may occur, which can be smoothed out with relatively small smoothing capacitor(s) (not shown) that may be provided in any convenient location, such as at the outputs of rectifier blocks  460 ,  461  and/or across the load  470 . The load  470  is thus supplied with a constant DC output supply signal. 
     If desired, feedback may be provided via sense amplifier  490 , which samples the DC output signal  485  and provides a voltage feedback signal to voltage-controlled amplifier  415 , which in turn adjusts the amplitude of input waveforms  412 ,  413  so as to be suitable for the linear amplifiers  430 ,  431 . In this manner, the DC output signal  485  may be maintained at a constant voltage level. 
     Operation of the power supply  400  is generally similar to the power supply  100  of  FIG. 1 . For example, where the input waveforms  412 ,  413  take the shape of periodic alternating inverted/non-inverted raised cosine waves such as illustrated in graphs  2 A and  2 B of  FIG. 2 , the resulting rectified and combined waveforms will be similar to those shown in graphs  2 C,  2 D and  2 E of  FIG. 2 , as previously explained. Where the input waveforms  412 ,  413  take the shape of triangular waveforms with alternating inverted/non-inverted triangle waves such as illustrated in graphs  3 A and  3 B of  FIG. 3 , the resulting rectified and combined waveforms will be similar to those shown in graphs  3 C,  3 D and  3 E of  FIG. 3 , as also previously explained. As with  FIG. 1 , any suitable periodic waveforms may be used, including waveforms with multiple harmonics or which alternate over time. With suitable waveforms as described herein, the power supply  400  may result in a constant DC output signal  485  theoretically requiring no storage/smoothing capacitors. 
       FIG. 5  is a block diagram showing components of another embodiment of a power supply  500  in accordance with the general approach of  FIG. 1 . Unlike the power supply of  FIG. 4 , which is a voltage-controlled DC output power supply,  FIG. 5  illustrates a current-controlled DC output power supply  500 . In  FIG. 5 , elements labeled 5xx are generally analogous in function to the similarly labeled elements 4xx in  FIG. 4 . The power supply  500  may, as before, be supplied by a local power source such as a battery, or by an external power source such as a line source. A signal generator  505  generates a pair of complementary waveform signals  512 ,  513 , preferably periodic in nature, and which generally have the characteristics previously described for V IN1  and V IN2 —that is, they are shaped or selected so as to provide a constant DC output after being coupled through a transformer stage, rectified and combined. The complementary waveform signals  512 ,  513  are provided to a voltage controlled amplifier (VCA)  515 , which adjusts the amplitude of the waveforms signals  512 ,  513  based upon feedback received from the DC output signal  585  via feedback sense amplifier  590 . In some embodiments, voltage controlled amplifier  515  may be omitted, as may feedback path  591  and sense amplifier  590 . 
     The voltage controlled amplifier  515  outputs the amplitude-adjusted pair of complementary waveform signals V IN1  and V IN2  to linear transconductance amplifiers  530 ,  531 , respectively, as reflected by waveforms  523 ,  524  in the overlay graphs shown in  FIG. 5 , depicting an example similar to the waveforms used in the like example of  FIG. 1  and  FIG. 2 . Transconductance amplifiers  530 ,  531  output a current proportional to their input voltage, and thus may be viewed as voltage-controlled current sources. The effect of transconductance amplifiers  530 ,  531  is that the waveforms  512 ,  513  generated by the signal generator  505  will be essentially converted to current waveforms of similar shape. As discussed below, this may have advantages for downstream processing and may result in even better EMI characteristics. The transconductance amplifiers  530 ,  531  are connected to power supply rails +V and −V, and output amplified signals  532 ,  533  to transformers  535 ,  536 . The current characteristics for signals  532 ,  533  are reflected in overlay graphs  540  and  541  (depicting waveforms Ip1 and Ip2) respectively, illustrated in  FIG. 5 , in the case where the initial generated waveforms appear as in graphs  523 ,  524  for V IN1  and V IN2 . The corresponding voltage characteristics of signals  532 ,  533  are reflected in overlay graphs  542  and  543  (depicting waveforms Vp1 and Vp2) respectively. As can be seen from graphs  540 ,  541 ,  542  and  543 , the current waveforms Ip1 and Ip2 for this particular example are characterized by alternating inverted and non-inverted raised cosine waves (with Ip1 and Ip2 being identical but offset from one another by 90 degrees), while the corresponding voltage waveforms Vp1 and Vp2 take the form of square waves having a constant positive voltage corresponding to the time period of the non-inverted raised cosine waves, and constant negative voltage corresponding to the time period of the inverted raised cosine waves. Like the current waveforms Ip1 and Ip2, the voltage waveforms Vp1 and Vp2 are identical but offset from one another by 90 degrees. 
     The output of the first transconductance amplifier  530  is coupled to the primary winding of a first transformer  535 . The output of the second transconductance amplifier  531  is coupled to the primary winding of a second transformer  536 . The secondary windings of transformers  535 ,  536  are coupled to an output stage  550 , which receives the transformer output signals  537 ,  538  from the transformers  535 ,  536 . The transformers  535 ,  536  may be step-up or step-down in nature, and are preferably identical in characteristics, assuming that the amplitude of the incoming signals  532 ,  533  is the same. Transformers  535 ,  536  may be physically embodied as a single transformer with separate windings for the input signals  532 ,  533  and for the output signals  537 ,  538 , but sharing the same magnetic core(s), or else they may be physically embodied as two separate transformers. 
     The output stage  550  preferably comprises a pair of rectifier blocks  560 ,  561  that may be embodied as, e.g., full-wave rectifier bridges. Signal  538  from the secondary output of transformer  535  is provided to a first rectifier block  560  of the output stage  550 . Signal  539  from the secondary output of transformer  536  is provided to a second rectifier block  561  of the output stage  550 . Each of the rectifier blocks  560 ,  561  may be embodied as, e.g., a full-wave rectifier bridge. The rectified output signals of the rectifier blocks  560 ,  561  are, in this case, periodic waveforms that are complementary in nature such that, when summed together, the result is a constant DC level. To this end, the outputs of rectifier blocks  560 ,  561  are tied in parallel together so that the rectified output signals therefrom are additively combined, thereby providing a DC output signal  585  that is substantially constant in nature, generally without the need for storage/smoothing capacitors. In practice, small amounts of ripple may occur, which can be smoothed out with relatively small smoothing capacitor(s) (not shown) that may be provided in any convenient location, such as at the outputs of rectifier blocks  560 ,  561  and/or across the load  570 . The load  570  is thus supplied with a constant DC output supply signal. 
     If desired, feedback may be provided via sense amplifier  590 , which samples the DC output signal  585  and provides a voltage feedback signal to voltage-controlled amplifier  515 , which in turn adjusts the amplitude of input waveforms  512 ,  513  so as to be a suitable level for the transconductance amplifiers  530 ,  531 . In this manner, the DC output signal  585  may be maintained at a constant voltage level. The feedback loop is preferably designed so that transconductance amplifiers  530 ,  531  operate close to the rails for maximum efficiency, but far enough so that the amplifiers remain in the linear region of operation and do not clip. The voltage feedback loop is helpful to ensuring that the voltage level remains relatively constant even if the characteristics of the load (e.g., its resistance) fluctuates over time. Voltage feedback can also be used to ensure that, if the input voltage drops (for instance, with a battery as the input source), then the output voltage will remain relatively constant. 
     Operation of the power supply  500  is generally similar to the power supply  100  of  FIG. 1 , treating the output signals  123 ,  124  of waveform generator  105  as relating to current. Where the input waveforms  512 ,  513  take the shape of periodic alternating inverted/non-inverted raised cosine waves such as illustrated in graphs  2 A and  2 B of  FIG. 2 , the resulting rectified and combined waveforms will be similar to those shown in graphs  2 C,  2 D and  2 E of  FIG. 2 , as previously explained. Where the input waveforms  512 ,  513  take the shape of triangular waveforms with alternating inverted/non-inverted triangle waves such as illustrated in graphs  3 A and  3 B of  FIG. 3 , the resulting rectified and combined waveforms will be similar to those shown in graphs  3 C,  3 D and  3 E of  FIG. 3 , as also previously explained. As with  FIG. 1 , any suitable periodic waveforms may be used, including waveforms with multiple harmonics or which alternate over time. With suitable waveforms as described herein, the power supply  500  may result in a constant DC output signal  585  theoretically requiring no storage/smoothing capacitors. 
     Another embodiment of a power supply, using an alternative amplifier arrangement, is shown in  FIGS. 11A and 11B . In these examples, only half of the primary side power supply is shown, for purposes of simplicity; the circuitry in each case would be duplicated to complete the primary side portion of the power supply. Thus, the transformer  1148  shown in  FIG. 11A  would correspond conceptually to transformer  135  (T1) in  FIG. 1 , while a second set of circuitry and second transformer corresponding to transformer  136  (T2) would be utilized to complete the primary side portion of the power supply. Likewise, because only the power supply circuitry  1102  on the primary side is depicted in  FIGS. 11A and 11B , the circuitry on the secondary side would generally be formed of half the bridge circuitry as shown, for example, in  FIG. 1  as rectifier  160  (R1) or in  FIG. 5  (i.e., diodes D1-D4 of output stage  550 ). 
     The general approach in  FIGS. 11A and 11B  is to employ a push-pull amplifier design; hence, transformer  1148  has a single secondary winding  1146  but two primary windings  1147 . 
     Looking first at the example of  FIG. 11A , voltage sources  1105 ,  1106  generate output waveforms  1112  and  1113 , respectively, depicted in the accompanying superposed graphs proximate the voltage sources  1105 ,  1106 . Waveforms  1112  and  1113  generally equate to the positive and negative half-cycles, respectively, of the periodic waveform shown in  FIG. 2A . The first voltage source  1105  generates a waveform  1112  corresponding to the non-inverted raised cosine waves in  FIG. 2A , while the second voltage source  1106  generates a waveform corresponding the inverted raised cosine waves in  FIG. 2A ; but these waves are shown as positive instead of negative because they are applied to the inverted side of the dual-primary transformer  1148 . For the second transformer (not shown) generating the complementary waveform, two similar voltage sources would be provided to generate waveforms corresponding to the positive and negative half-cycles, respectively, of the periodic waveform shown in  FIG. 2B , and are similarly phase-offset from the waveforms of voltage generators  1105 ,  1106  just like the waveforms of  FIGS. 2A and 2B . 
     Each of waveforms  1112 ,  1113  constitutes a series of non-inverted raised cosine waves, which in this example are phase offset from one another by 180 degrees. Voltage sources  1105 ,  1106  are provided as inputs to linear amplifiers  1120 ,  1121  respectively, which in turn feed field-effect transistors (FETs)  1130 ,  1131 . Each of the transistors  1130 ,  1131  is connected to one of the primary windings  1147  of the transformer  1148 , and the source of each is also connected to the non-inverting input of the respective signal amplifier  1120 ,  1121  and to respective current sense resistors  1116  and  1117 . Also, the centertap  1149  of the transformer  1149  and power supply inputs of amplifiers  1120 ,  1121  are connected to a separate power supply  1107 , which may comprise, e.g., a series of batteries or other DC power source. 
     Amplifier  1120  and transistor  1130  (Q1) along with amplifier  1121  and transistor  1131  (Q2) together form a push-pull amplifier providing a defined current output defined by the voltage waveforms  1112 ,  1113  applied by sources  1105  and  1106 . The current waveforms are fed to transformer  1149 , and then appear on the secondary winding  1146  for rectification by the output stage (not shown in  FIG. 11A ). 
     In some configurations, the device of  FIG. 11A  may provide an advantage in that single-polarity power transistor devices can be utilized, and the drive voltages can be unipolar and ground-referenced. 
     For optimal performance, the transistors  1130 ,  1131  might be configured according to conventional methods to conduct a permanent quiescent current in order to improve linearity and speed of response at lower output current levels. However, such a quiescent current may decrease the overall efficiency of the power supply. The slightly modified operational arrangement shown in  FIG. 11B  may reduce the amount of quiescent current. The basic structure of  FIG. 11B  is similar to  FIG. 11A , but the waveforms supplied by the signal generators  1105 ,  1106  are modified to improve linearity and speed of response at low output current levels while minimizing any decrease in overall efficiency. The additional periodic waveforms  1197 ,  1198  shown beneath the main driving waveforms  1112 ,  1113  are amplitude-magnified views in each case of a common-mode waveform added to both halves of the push-pull amplifier simultaneously. This common-mode waveform causes the transistors  1130 ,  1131  to conduct quiescent current only around the region where the respective main waveform  1112 ,  1113  approaches zero; at all other periods outside of the conduction period the transistors  1130 ,  1131  are biased OFF. The common-mode current causes the transistors  1130 ,  1131  to enter their conduction region shortly in advance of when they are required to operate, thus reducing turn-on distortion. The common mode current in each half of the output stage (on the secondary side) cancels out in the transformer  1148  and so does not appear in the output from the transformer secondary windings  1146 . 
     The period during which the common mode waveform causes the transistors  1130 ,  1131  to conduct can be varied from the example shown. In this manner, the average power loss due to the quiescent current can be significantly reduced compared to the continuous conduction case. 
     The power amplifier arrangements depicted in  FIG. 5  and  FIGS. 11A and 11B  generally may be characterized as linear transconductance amplifiers with a nominally flat frequency response, such that they accurately reproduce the complementary waveforms fed to their inputs. The complementary waveforms are non-sinusoidal and so typically require a high gain-bandwidth product from the amplifiers for optimum performance. 
     In the case of the particular complementary waveforms shown in  FIGS. 2A and 2B , this constraint can be relaxed by appropriate modification of the complementary waveforms such that the amplifiers may be configured as integrators. The closed loop response of an integrator generally falls at 6 dB/octave with increasing frequency, allowing an amplifier with a lower open-loop bandwidth to be employed. 
     One example of an amplifier configuration that may be used with this approach is shown in  FIG. 12 . In this embodiment, as with the design in  FIGS. 11A and 11B , only half of the primary side power supply is illustrated corresponding to the circuitry associated with one of two transformers. As with the earlier designs, the transformer  1248  in this example has a single secondary winding  1246  but two primary windings  1247 . As before, only the power supply circuitry  1202  on the primary side is depicted, while the circuitry on the secondary side for this half of the primary side circuitry would generally comprise bridge circuitry similar to that of half the output stage of  FIG. 1  or  FIG. 5 , for instance. In this example, a pair of voltage sources  1205 ,  1206  generate output waveforms  1212  and  1213 , respectively, depicted in the accompanying graphs proximate the voltage sources  1205 ,  1206 . The outputs of voltage sources  1205 ,  1206  are provided to linear amplifiers  1220 ,  1221  respectively, via resistors  1270  (R3) and  1271  (R4), while amplifiers  1220 ,  1221  in turn feed field-effect transistors (FETs)  1230 ,  1231 . Each of the transistors  1230 ,  1231  is connected to one of the primary windings  1247  of the transformer  1248 , and the source of each is also connected respectively to current sense resistors  1216  and  1217  and to respective integrating capacitors  1272  (C1) and  1274  (C2), each of which is straddled by a resistor  1273  (R5) and  1275  (R6) respectively. The centertap  1249  of the transformer  1249  and power supply inputs of amplifiers  1220 ,  1221  are connected to a separate power supply  1207 , which may comprise, e.g., a series of batteries or other DC power source. 
     In operation, feedback from the current sensing resistors  1216  (R1) and  1217  (R2) is accomplished by means of capacitors  1272  (C1) and  1274  (C2), with resistors  1273  (R5) and  1275  (R6) included to provide DC stability. The integrator action of capacitors  1272  and  1274  forces the voltage across resistors  1216  (R1) and  1217  (R2) and hence the current through transistors  1230  (Q1) and  1231  (Q2) to be the integral of the voltages output by signal generators  1205  and  1206 , i.e., of voltages  1212  and  1213 . In order for that current to match the desired shape, the voltage waveforms  1212  and  1213  are selected to be the differentials of waveform  203  depicted in  FIG. 2A  (or waveform  204  for the complementary section of the primary side power supply circuitry), again (similar to  FIG. 11A ) only taking every other half-cycle from waveform  203  for waveform  1212  and for waveform  1213 . Because waveform  1213  is applied to the negative winding of the dual-primary transformer  1248 , the waves are shown as positive in nature. 
     In alternative integrator configuration may be constructed by dispensing with capacitors  1272  and  1274  (C1 and C2) and replacing current sensing resistors  1216  and  1217  (R1 and R2) with inductors. The current through the inductors in this case would be the integral of the voltage across them. 
     The use of an integrator for the power amplifier sections is not restricted to these particular examples. In the more generalized version of the power supply circuit of  FIG. 5 , amplifiers  530  and  531  may be configured as transconductance amplifiers with an integrator characteristic, fed with modified voltage waveforms in place of waveforms  523  and  524  shown in  FIG. 5 . The modified waveforms for this purpose are shown as waveforms  1312 ,  1313  in  FIG. 13 , while the solid lines show the waveforms  1303 ,  1304  resulting after integration. The modified waveforms  1312 ,  1313  may be described as a sequence of sine or cosine waves, with the sine or cosine waveform being inverted at the end of each cycle. As with  FIGS. 2A and 2B , the waveforms  1312 ,  1313  and the resulting integrated waveforms  1303 ,  1304  are identical in shape but phase offset from one another. 
     The goal of low quiescent power drain could also be fulfilled in other ways, for example by employing feedforward techniques to linearize the power amplifiers. This approach is illustrated in  FIG. 14 . For simplicity, the circuitry  1402  shown in FIG.  14  corresponds to one side of the power amplifier of  FIG. 11A ; a second set of similar components would be provided corresponding to the other half of the power amplifier of  FIG. 11A  in order to make a complete amplifier; and then, in turn, the entire set of circuitry would again be duplicated to provide the complementary signal for rectification and combination on the other side of the power supply. In  FIG. 14 , amplifier  1420 , transistor  1430  (Q1) and resistor  1416  (R1) form an amplifier A1 which performs as in  FIG. 11A , but with low to zero quiescent current. The output  1432  of transistor  1430  (Q1) is connected to one of the primary windings of a dual-primary transformer (similar to transformer  1148  shown in  FIG. 11A ). A DC power source  1407  supplies power to amplifiers  1420  and  1421 , and is also connected to a center tap of the transformer (similar to the DC source signal connected to the centertap of transformer  1148  of  FIG. 11A ). 
     Amplifier  1421 , transistor  1431  (Q2) and resistor  1417  (R2) form a low power error correction amplifier A2 which amplifies and scales the difference between the input voltage to A1 (output from signal generator  1405 ) and the output voltage across resistor  1416  (R1). A scaled version of this difference voltage is converted to a current through transistor  1431  (Q2) to add to the current from transistor  1430  (Q1). This is accomplished in part using differencer  1418 , which receives the voltage signal from voltage source  1405  (V1) and subtracts the voltage signal at the node between the source of transistor  1430  (Q1) and the sense resistor  1416  (R1). Amplifier A2 therefore adds a correction current to the output that compensates for errors in A1. The correction current required from amplifier A2 is generally considerably smaller than the current output from amplifier A1, and therefore amplifier A2 can be a lower power amplifier than amplifier A1 and can also have a much smaller quiescent power dissipation. 
     The output  1432  of transistor pair  1430 ,  1431  may be fed to one of the primary windings of a transformer, similar to  FIG. 11A . Another similarly configured feedforward amplifier, would be connected to the other primary winding of the transformer, as in  FIG. 11A . The signal generators ( 1405  and its counterpart) may be configured to generate signals similar to  FIG. 11A  or other embodiments as disclosed herein. 
     An alternative to using feedforward correction as illustrated in  FIG. 14  is to apply both feedforward and feedback techniques as in the arrangement shown in the embodiment of  FIG. 15 . As with  FIG. 14 , the circuitry  1502  in  FIG. 15  corresponds to one side of the power amplifier of  FIG. 11A ; a second set of similar components would correspond to the other half of the power amplifier of  FIG. 11A  in order to make a complete amplifier; and then, in turn, the entire set of circuitry would again be duplicated to provide the complementary signal for rectification and combination on the other side of the power supply. In  FIG. 15 , amplifier  1520 , transistor  1530  (Q1) and impedance element  1516  (Z4) form an amplifier A1 which performs as in  FIG. 11A , but with low to zero quiescent current. Amplifier  1521 , transistor  1531  (Q2) and impedance element  1517  (Z3) form a low power correction amplifier. Another impedance element  1572  (Z2) forms a feedback path from the output of amplifier  1520  to its inverting input, and impedance element  1571  (Z1) connects the inverting input of amplifier  1520  to the node between transistor  1530  (Q1) and impedance element  1516  (Z4). If the relationship Z2·Z4=Z1·Z3 is satisfied, then distortion in transistor  1530  (Q1) may be cancelled from the output current formed by the sum of the currents through transistors  1530  (Q1) and  1531  (Q2). Thus, amplifier stage A1 can be operated at low to zero quiescent current for maximum efficiency. 
     Furthermore, if impedance element  1572  (Z2) is chosen as a capacitor, impedance element  1516  (Z4) chosen to be an inductor, and impedance elements  1571  (Z1) and  1517  (Z3) are resistors, then the balance equation can be satisfied whilst the output current is the integral of the input voltage V1 from signal generator  1505 , allowing the waveforms shown in  FIG. 12  to be used. 
     Other combinations of impedance elements Z1-Z4 may also be used to achieve similar results, and the impedance elements need not be unitary circuit elements but may be networks of elements. For instance, impedance element  1572  (Z2) may be a capacitor, impedance element  1571  (Z1) a series combination of resistor and capacitor, impedance element  1516  (Z4) a resistor, and impedance element  1517  (Z3) a parallel combination of resistor and capacitor. This could also use the waveforms shown in  FIG. 12  as inputs. As another example, impedance element  1572  (Z2) may be a capacitor, impedance element  1571  (Z1) a resistor, impedance element  1516  (Z4) may also be a resistor, and impedance element  1517  (Z3) may be a capacitor. In this case, the device could use the input waveforms shown in  FIG. 11A , or other suitable waveforms. 
     A further alternative is to combine an impedance element for Z3 with a filter on the input to the non-inverting input terminal of amplifier  1521 . The transfer function of the correction amplifier A2 could also be altered by the addition of feedback elements  1675  (Z5) and  1676  (Z6) as shown in  FIG. 16 . For example, impedance element  1675  (Z5) may be a resistor, and impedance element  1676  (Z6) may be a capacitor. The transfer function of amplifier A2 may be modified to make impedance element  1617  (Z3) appear like a different type of impedance element; for example, it may be desired to implement impedance element  1617  (Z3) as a resistor, thus avoiding use of a reactive element as impedance element  1617 . In other respects,  FIG. 16  is identical to  FIG. 15 , and components 16xx in  FIG. 16  generally correspond to their counterpart components 15xx in  FIG. 15 . 
     Although the feedforward error correction and feedforward plus feedback correction techniques have been described and illustrated with respect to a particular power amplifier configuration, they are applicable to other power amplifier and related designs as well. 
       FIG. 7  is a block diagram showing an embodiment of a power supply  700  in general accordance with the principles of the conceptual diagram of  FIG. 8 , implemented with switched-capacitors. The power supply  700  may, as with the other examples described herein, be supplied by a local power source such as a battery, or by an external power source such as a line source. In  FIG. 7 , a waveform generator comprising, in this example, a pair of signal generators  705 ,  715 , generates a pair of complementary waveform signals  706 ,  716 , which are preferably periodic in nature, and generally have the characteristics previously described for V IN1  and V IN2 —that is, they are shaped or selected so as to provide a constant DC output after being level-shifted, rectified and combined. Examples of such waveforms are shown as periodic alternating inverted/non-inverted raised cosine signal waveforms  707  and  717  (corresponding to waveform signals  706  and  716  respectively, according to one example). The complementary periodic waveform signals  706 ,  716  may optionally be provided to a voltage controlled amplifier (VCA) (not shown) for adjusting the amplitude of the waveforms signals  706 ,  716 , based upon a feedback signal (also not shown) received from the DC output signal  785 . 
     Waveform signal  706  is provided to transconductance amplifiers  731  and  751 , while waveform signal  716  is provided to transconductance amplifiers  741  and  761 . Transconductance amplifiers  731 ,  741 ,  751  and  761  output a current proportional to their input voltage, and thus may be viewed as voltage-controlled current sources. The effect of transconductance amplifiers  731  and  741  is that waveform signals  706 ,  716  will be essentially converted to current waveforms  735 ,  745  of similar shape. The effect of transconductance amplifiers  751  and  761  is that waveform signals  706 ,  716  will be essentially converted to current waveforms  755 ,  765  of similar shape but inverted in nature, due to the fact that waveform signals  706 ,  716  are coupled to the inverting inputs of transconductance amplifiers  751  and  761 . As with the  FIG. 5  embodiment, converting to a current-driven waveform may have advantages for downstream processing and may result in improved EMI characteristics. The transconductance amplifiers  731 ,  741 ,  751 , and  761  may be of similar configuration to those previously described. 
     For the example illustrated in  FIG. 7 , the current characteristics of signals  735  and  745  may be characterized by alternating inverted/non-inverted raised cosine waves (with the current waveforms of signals  735  and  745  being identical but offset from one another by 90 degrees), while the corresponding voltage waveforms relating to signals  735  and  745  generally are square waves having a constant positive voltage corresponding to the time period of the non-inverted raised cosine waves, and constant negative voltage corresponding to the time period of the inverted raised cosine waves. Like the current waveforms for signals  735  and  745 , the voltage waveforms are identical but offset from one another by 90 degrees. Similarly, the current and voltage characteristics of signals  755  and  765  are inverted from signals  735  and  745 . Thus, the current characteristics of signals  755  and  765  for this example may be characterized by alternating non-inverted/inverted raised cosine waves (with the current waveforms of signals  755  and  765  being identical but offset from one another by 90 degrees), while the corresponding voltage waveforms relating to signals  755  and  765  generally are square waves having a constant positive voltage corresponding to the time period of the non-inverted raised cosine waves, and constant negative voltage corresponding to the time period of the inverted raised cosine waves. Like the current waveforms for signals  755  and  765 , the voltage waveforms are identical but offset from one another by 90 degrees. 
     The outputs of transconductance amplifiers  731 ,  741 ,  751  and  761  are each coupled to a similar network of components that operate to step up (or down) the input voltage level and provide a level-converted output to the load  770  as a constant DC source signal  785 , using principles of, e.g., a charge-boost switched capacitor circuit. The output of the first transconductive amplifier  731  is coupled to a capacitor  732  whose other end is coupled to the input power supply rail  789 . The transconductance amplifier  731  serves to periodically charge capacitor  732  in a manner causing the level of applied signal to be stepped up (approximately doubled), thus resulting in a level-converted signal  737 . Diode  734  serves to rectify the stepped up (or down) signal  737 . In a similar manner, transconductance amplifiers  741 ,  751  and  761  are coupled to capacitors  742 ,  752  and  762 , respectively, each of which is coupled to the input power supply rail  789  via diodes  743 ,  753  and  763 , respectively. The capacitors  732 ,  742 ,  752  and  762  and associated diodes  733 ,  743 ,  753  and  763  form switched capacitor circuits that step up (or down) the input signal level, thus resulting in level-converted signals  735 ,  745 ,  755  and  767 . Rectifying diodes  744 ,  754  and  764  serve to rectify the stepped up (or down) signals  747 ,  757  and  767 , respectively, in the same manner as rectifying diode  734  relative to stepped up (or down) signal  737 . The additive combination of the rectified signals derived from level-converted signals  737  and  757  is, for the example illustrated in  FIG. 7 , similar to waveform  213  in  FIG. 2 . The additive combination of the rectified signals derived from level-converted signals  747  and  767  is, for this same example, similar to waveform  214  in  FIG. 2 —that is, a 90-degree offset version of the same waveform as generated by the additive combination of rectified signals derived from level-converted signals  737  and  757 . As noted earlier, the additive combination of waveforms  213  and  214  is a constant DC signal level. 
     Thus, by combining all four of the rectified signals derived from level-converted signals  737 ,  747 ,  757  and  767  together, the end result is a stepped-up (or down) DC signal  785  that is substantially constant in nature, generally without the need for storage/smoothing capacitors. In practice, small amounts of ripple may occur, which can be smoothed out with relatively small smoothing capacitor(s)  772  that may be provided in any convenient location, such as across the load  770 . The load  770  is thereby supplied with a constant DC output supply signal. The four-phase design also ensures that the current taken from the supply  789  is substantially ripple free. The example of  FIG. 7  illustrates a single stage of voltage step-up, but the same principle can be applied to a multi-stage step-up converter. 
     In one aspect,  FIG. 7  shows a voltage booster using capacitors that provides a single stage of boost, approximately doubling the supply voltage Vsupply. This approach can be extended by the addition of further rectifiers and capacitors as shown, for example, in the embodiment of  FIG. 17  to produce a further stage of boost. In  FIG. 17 , voltage waveforms V1 and V2 may be identical to those of  FIG. 7  (i.e., similar to waveforms  707  and  717 ). The components labeled 17xx in  FIG. 17  generally correspond to their counterparts labeled 7xx in  FIG. 7 . In addition, a second stepped-up (or stepped-down) DC signal  1795  is provided in  FIG. 17 . Using the same principles of  FIG. 7 , an additional output capacitor  1772 ′ has been added to the circuit, and charge capacitors  1732 ′,  1742 ′,  1752 ′ and  1762 ′ are periodically charged via diodes  1733 ′,  1734 ′,  1743 ′,  1744 ′,  1753 ′,  1754 ′,  1763 ′, and  1764 ′ in a similar manner as the other charge capacitors ( 1732 ,  1742 ,  1752 , and  1762 ) via similar diode/capacitor configurations shown in  FIG. 7 . No further power amplifier stages are required, although such may optionally be used, and the output and input ripple of the device is still very low. The voltage across the transconductance amplifier outputs remains a square wave, as with  FIG. 7 , so the overall amplifier of  FIG. 17  still can be operated with high efficiency. 
     The technique used for positive boosting as illustrated in  FIGS. 7 and 17  can also be used to produce an inverted power supply by changing the polarity of the rectifiers and referencing the charging rectifiers to ground instead of a positive voltage. In the same way that the dual boost supply approach can combine a two-stage boost onto one set of power amplifiers, the same can be done with positive and inverting boosters.  FIG. 18  is a schematic diagram showing a power supply with a combination of positive and inverting boosters circuits. Here, the top half of the circuit, i.e., a non-inverting power section  1802 , is generally equivalent to the circuit of  FIG. 17 , while an inverting power supply section  1803  has been added. Thus, in  FIG. 18 , components labeled 18xx generally correspond to their counterparts labeled 7xx in  FIG. 7 . In inverting power supply section  1803 , additional charge capacitors  1836 ,  1846 ,  1856  and  1866  are periodically charged via diodes  1837 ,  1838 ,  1847 ,  1848 ,  1857 ,  1858 ,  1867 , and  1868  in a similar manner to the charging capacitors  1832 ,  1842 ,  1852  and  1862 , but with opposite polarity although using the same input waveforms, so the result is a negative power supply output voltage  1896  across output capacitor  1876 . In this manner, the power supply may provide both a positive output voltage  1885  and a negative output voltage  1896  in the same device. 
       FIG. 6  is a simplified block diagram illustrating one example of a signal generator  600  as may be used in connection with various embodiments as disclosed herein, for generating a waveform having alternating inverted/non-inverted raised cosine waves. As shown in  FIG. 6 , the signal generator  600  may comprise a first sinusoidal waveform generator  602  having an output  603  in the form of a sine wave having peaks at ±Vs. The sine wave signal  603  is coupled as an input to a summer  610 . The other input of the summer  610  is a DC input signal  608  that is at a fixed level of +Vs. The resulting signal  607  is a DC offset version of sine wave signal  603 , having peaks between ground and +Vs. The DC offset sine wave signal  607  is split into two paths, with one path being provided to an analog inverter  604 , which outputs a phase-inverted version of DC offset sine wave signal  607  with peaks between ground and −Vs. The DC offset sine wave signal  607  and inverted DC offset sine wave signal  609  may optionally be provided to a pair of amplifiers  605 ,  606  for gain adjustment, if desired, with the gain of both amplifiers  605 ,  606  being the same. The outputs  612 ,  613  from the amplifiers  605 ,  606  are DC offset sine waves, phase-shifted with respect to one another, similar to the input signals  607 ,  609 . Switch  620  alternates between outputs  612  and  613 , switching between them each time the sine wave from the lower amplifier  606  reaches its top peak, which is the same time that the sine wave from the upper amplifier  605  reaches its lower peak. The result is an output signal  621  that alternates between a “non-inverted” raised cosine wave and an “inverted” raised cosine wave every half-cycle, with a smooth transition between non-inverted and inverted raised cosine waves, as illustrated by the output V 1  in  FIG. 6 . 
     A similar technique may be used to generate a 90 degree phase-shifted version of output signal  621 . The signal generator  600  may comprise a second sinusoidal waveform generator  622  having an output  623  in the form of a sine wave having peaks at ±Vs. Signal  623  is an inverted version of signal  603 ; thus, signal  623  may also be generated by merely inverting signal  603 . The sine wave signal  623  is coupled as an input to a summer  630 . The other input of the summer  630  is a DC input signal  608  that is at a fixed level of −Vs. The resulting signal  627  is a DC offset version of sine wave signal  623 , having peaks between ground and −Vs. The DC offset sine wave signal  627  is split into two paths, with one path being provided to an analog inverter  624 , which outputs a phase-inverted version of DC offset sine wave signal  627  with peaks between ground and +Vs. The DC offset sine wave signal  627  and inverted DC offset sine wave signal  629  may optionally be provided to a pair of amplifiers  625 ,  626  for gain adjustment, if desired, with the gain of both amplifiers  625 ,  626  being the same. The outputs  632 ,  633  from the amplifiers  625 ,  626  are DC offset sine waves, phase-shifted with respect to one another, similar to the input signals  627 ,  629 . Switch  640  alternates between outputs  632  and  633 , switching between them each time the sine wave from the lower amplifier  626  reaches its top peak, which is the same time that the sine wave from the upper amplifier  625  reaches its lower peak. The result is an output signal  641  that alternates between a “non-inverted” raised cosine wave and an “inverted” raised cosine wave every half-cycle, with a smooth transition between non-inverted and inverted raised cosine waves, as illustrated by the output V 2  in  FIG. 6 . 
     Together, outputs  621  and  641  may be used as input signals V IN1  and V IN2  in the transformer-based power supply embodiments disclosed herein. 
     In practical applications, the output signal(s) from the signal generator  600  may be run through a small capacitor or high-frequency filter to remove any residual DC component that may be inadvertently created in the signal generator  600 . In addition, various bias current adjustments and other implementation details may be added according to techniques well known in the art. 
     Other techniques may alternatively be used to generate periodic alternating waveforms. For example, digital synthesis can be used to generate similar waveforms to those described above. According to one such implementation illustrated in  FIG. 9 , a waveform generator  900  stores waveform data in digital form in a lookup table  905  (e.g., a read-only memory (ROM) or other non-volatile memory storage), and reads it out in appropriate sequence under control of a micro-controller, micro-sequencer, finite state machine, or other controller. The digital data may be provided to a pair of digital-to-analog converters (DACs)  910 ,  911 , one for each waveform. That is, the first DAC  910  outputs a first converted waveform  914 , and the second DAC  911  outputs a second converted waveform  915  that is identical to but 90 degrees offset from the first converted waveform  914 , as previously described. The converted waveforms  914 ,  915  are provided to filters  920 ,  921  for smoothing. Together, outputs  930  and  931  may be used as input signals V IN1  and V IN2  in the transformer-based power supply embodiments disclosed herein. 
     In other embodiments, a rotorized mechanical generator similar in principle to a hub dynamo may be used to generate a waveform having the characteristics of alternating inverted and non-inverted raised cosine waves that have been previously described, and illustrated in  FIG. 2 . Such a waveform generator may be particularly suitable for larger-wattage applications of the inventive power supply designs disclosed herein. A hub dynamo generator generally operates by the rotation of a permanent magnet on an axle, with the magnet disposed within a coil of wires. The output of a hub dynamo generator has been observed to be a waveform that has alternating inverted and non-inverted raised cosine waves. Complementary waveforms may be generated, for example, by the addition of a second permanent magnet oriented perpendicularly with respect to the first magnet, on the same axle therewith, but within a second coil of wires separate from the first coil of wires. Two permanent magnets preferably have the same size and physical characteristics, as do the two coils of wires, which may be laterally offset from one another along the length of the axle. Rotation of the axle may be accomplished by any suitable means, including motorized techniques, wind power, or other means. More generally, appropriate waveforms can be generated using a rotary AC power generator having a coil of wires in relative rotational motion with respect to one or more magnetic fields. 
     Where the power supply is used to convert a relatively high DC voltage to a lower DC voltage, the high-frequency AC waveform produced from a relatively high voltage DC source is, in one aspect, transformed to a lower voltage through one or more small transformers such as illustrated in the various embodiments described herein. The design of power supply may make it possible to avoid the need for large storage capacitors to smooth the output voltage from the transformers after the transformed signals are rectified. Both the input and the output of the power converter can theoretically be made free from ripple at all output levels, so that no extra magnetic components are required for filtering. The elimination of the output storage requirement and elimination of comprehensive filtering may reduce size and cost as compared to, e.g., a conventional switching supply. 
     As noted previously, in practice some small output capacitance may be required to reduce any residual ripple from the transformer stage or otherwise. Such slight ripple may be caused by inductance inherent in the amplifier stages. It is expected that a capacitance of approximately 300 to 600 nF would be adequate for a 50 Watt power supply operating with periodic waveforms of 25 Kilohertz. This size capacitance is significantly smaller than that needed for a conventional switched power supply. 
     Another technique that may be employed for reducing any residual ripple at the output is to use a low dropout (LDO) linear regulator. An LDO linear regulator generally may include a power FET disposed in series with the output signal. A differential amplifier controls the power FET in such a way as to maintain a small DC voltage difference between the input and output of the LDO linear regulator. The voltage difference is maintained at a value higher than the peak to peak ripple voltage at the output of the rectifying circuit. The LDO linear regulator is configured to reject the ripple voltage and prevent it appearing at its output, by means of a filter. Since the residual ripple voltage is generally expected to be quite small in the embodiments described and illustrated herein, an LDO linear regulator is one option for reducing or eliminating the residual ripple—thus mitigating or eliminating the need for the small smoothing capacitor that may otherwise be desirable to have at the output, without significantly compromising the efficiency. 
     Some power supply embodiments as disclosed herein may be built using two transformers. These transformers may be made low profile and thus not significantly impact the overall size of the power supply electronics. For example, for a 200 Watt power supply for an audio system, a pair of toroidal transformers may be used, each approximately 1″ in size. The result is power supply that is more compact than a conventional switched power supply of similar wattage. 
     The power supply designs described herein are not limited to power ranges of a few hundred Watts, but may also be used for much larger DC-to-DC conversion applications, in the Kilowatts or larger. 
     Embodiments of a power supply as disclosed herein may have significantly reduced EMI as compared with a conventional switched power supply. Where the voltage waveforms appear as in  FIG. 2 , i.e., periodic inverted/non-inverted raised cosine waves, the corresponding current waveform is a square-wave, which is less desirable from an EMI standpoint. The embodiment of  FIG. 5  overcomes those issues by transforming the inverted/non-inverted raised cosine waves to current waveforms before being sent to the transformer stage. The relatively smooth current waveform in this embodiment mitigates EMI concerns. While the corresponding voltage waveform becomes a square-wave, the electrostatic emissions created by the voltage square wave are easier to shield and deal with than the electromagnetic emissions that would be created from a current square-wave. 
     Although the EMI generated by the described method of DC-DC conversion can be very low due to the low ripple nature of the preferred input and output voltage and current waveforms, it is possible to further reduce the effective EMI emissions by modulating the frequency of the complementary waveforms with respect to time. This type of modulation would cause the spectral components of the residual interference to be spread over a wider spectral bandwidth, thus reducing the average amplitude of the interference at any given frequency. The modulating waveform can be either periodic or random (including pseudo-random) in nature. An example of an illustration of a set of frequency-modulated complementary waveforms  1030 ,  1031  is shown in  FIG. 10 . This particular example is based on chirp modulation, with the deviation over time in the wavelengths of waveforms  1030 ,  1031  exaggerated in  FIG. 10  merely for purposes of illustration. 
     A variety of different transformer designs and techniques may be used in connection with the transformer stage ( 130 ,  430  or  530 ) of the various power supply embodiments described herein. The particular transformer design may be chosen according to the desired application. For example, the transformers may employ bifilar windings, in which the primary and secondary wires are twisted together before being wound around the magnetic core, which may have the effect of reducing leakage inductance. Alternatively, coaxial windings may be used, in which the primary and secondary wires are coaxially combined, which may also reduce leakage inductance significantly. 
     In terms of transformer shapes and configurations, the transformer(s) may be toroidal, or else may be planar (with spiral windings) to achieve a particularly low profile as well as potentially simpler manufacturing. Another option is to use a winding through a series of hollow cube-shaped magnetic cores, as generally described for example in U.S. Pat. No. 4,665,357 to Herbert, incorporated herein by reference as if set forth fully herein. Yet another possibility is to embed one of the transformer primary/secondary windings (as a twisted pair or coaxial pair) in a hollowed out groove in the sidewall of a toroidally-shaped magnetic core with squared-off edges, as generally described for example in U.S. Pat. No. 4,210,859 to Meretsky et al, incorporated herein by reference as if set forth fully herein. In this example, the other transformer primary/secondary winding is repeatedly wrapped around the magnetic core, similar to a conventional toroidal transformer, but with the primary/secondary winding being a twisted pair or coaxial pair. Doing this provides magnetic field that are orthogonal and do not interact, and provides increased energy density. This design allows two independent transformers to share the same magnetic core. 
     Of course, other transformer designs may also be utilized. 
     The power supply designs and techniques described herein may be used with different types of power inputs, including a local battery power supply or else a line supply that is first converted to an input DC level before being converted to a DC output level. Where an AC line power supply is used, the line AC voltage is first rectified to produce a high voltage DC. While the DC-DC conversion process may then be carried out at relatively high frequencies, unlike the switched-mode power converter, the AC waveform used for this process has very low levels of radio frequency components and so electromagnetic interference is not an issue. The AC waveform, although smooth and with very low EMI, is used in such a way that the supply still retains very high efficiency, typically as good as, or better than, a conventional switched-mode supply. 
     According to certain embodiments as described herein, the high frequency AC waveform produced from the high voltage DC is again transformed to a lower voltage through one or more small transformers. However, the particular design potentially avoids the need for storage capacitors to smooth the output voltage after rectification. Both the input and the output of the converter can theoretically be made free from ripple at all output levels and so no extra magnetic components are required for filtering. The elimination of the output storage requirement and elimination of comprehensive filtering generally reduces size and cost compared to a switching supply. 
     The elimination of the output storage capacitors brings a further benefit. A power supply according to embodiments as disclosed herein can respond rapidly to a control signal and so can be employed as a fast tracking power supply for efficient, high quality, low noise and low EMI audio power amplifiers. Where a DC supply is already available, either from batteries or from an external power supply, then the input rectification and storage can be dispensed with and the power supply can then be made with an extremely low profile due to the elimination of the output storage capacitors. 
     The approach leads to an efficient supply, as there are no or minimal losses associated with EMI reduction and no power device dynamic switching losses to contend with, and so the efficiency in practice can exceed 90%. 
     The mode of driving the transformers, the elimination of switching artifacts and the simplicity of the control architecture may significantly simplify the design process and shorten the time to market compared to a switched-mode supply. 
     The inventive power supply designs as described and illustrated herein may find use in a wide variety of applications, including audio devices, portable electronic equipment (e.g., laptops, cellular phones or wireless devices, etc.), military, avionics, medical equipment, solar power conversion, power distribution, and so on. 
     In various embodiments, a power supply built according to the embodiments described above may find particular utility, for example, in the automobile industry as an on-vehicle power supply for an audio amplifier. Embodiments as described herein may result in a smaller, lighter and/or thinner power supply, that can be less expensive, highly efficient, and with fewer major components, while being relatively benign from the standpoint of EMI. Because the power supply can be simpler to design and produce, it can be brought to market more quickly, thus resulting in a faster product design cycle. Among other things, the low emissions reduce the time and cost for certification. The simple design process, low component costs and low certifications costs result in a considerable cost saving over existing power supply approaches. Also, the low profile, low cost and weight, and very low emissions allow the use of the inventive power supply in locations within a vehicle that presently are very difficult to fulfill with switched-mode power supply designs. 
     For portable battery operated products, the low profile capability offers form factors that are presently difficult to achieve. 
     For more generalized, heavy duty power distribution applications, the ability to produce a ripple free output without the use of large energy storage components has distinct advantages over conventional approaches. 
     In various embodiments, a low cost, lightweight, efficient, isolated, fast responding DC output power converter is provided having a very low input and output ripple and very low EMI emissions. The power converter generally requires very little output storage capacity and so can be implemented in very low profile configurations. The design process is also simpler than a conventional switched-mode converter resulting in a quicker design process. Although it may have beneficial use for audio amplifiers, the general principles embodied in the concept allow it to be applied in a wide variety of power conversion applications. 
     Certain embodiments described herein generate a DC output signal by the combination of two rectified signals having certain characteristics. However, the same principles may be extended to configurations having three or more signals that are rectified and additively combined, provided that adequate waveforms are selected. 
     While preferred embodiments of the invention have been described herein, many variations are possible which remain within the concept and scope of the invention. Such variations would become clear to one of ordinary skill in the art after inspection of the specification and the drawings. The invention therefore is not to be restricted except within the spirit and scope of any appended claims.