Voltage regulation is commonly required to prevent variation in the supply voltage powering various microelectronic components such as digital ICs, semiconductor memories, display modules, hard disk drives, RF circuitry, microprocessors, digital signal processors and analog ICs, especially in battery powered applications like cell phones, notebook computers and consumer products.
Since the battery or DC input voltage of a product often must be stepped-up to a higher DC voltage, or stepped-down to a lower DC voltage, such regulators are referred to as DC-to-DC converters. Step-down converters are used whenever a battery's voltage is greater than the desired load voltage. Step-down converters may comprise inductive switching regulators, capacitive charge pumps, and linear regulators. Conversely, step-up converters, commonly referred to boost converters, are needed whenever a battery's voltage is lower than the voltage needed to power the load. Step-up converters may comprise inductive switching regulators or capacitive charge pumps.
Of the aforementioned voltage regulators, the inductive switching converter can achieve superior performance over the widest range of currents, input voltages and output voltages. The operation of a DC/DC inductive switching converter is based on the prinicple that the current in an inductor (coil or transformer) cannot be changed instantly and that an inductor will produce an opposing voltage to resist any change in its current.
The basic principle of an inductor-based DC/DC switching converter is to switch or “chop” a DC supply voltage into pulses or bursts, and to filter those bursts using a low-pass  filter comprising and inductor and capacitor to produce a well behaved time-varying voltage, i.e. to change a DC voltage into an AC voltage. By using one or more transistors switching at a high frequency to repeatedly magnetize and de-magnetize an inductor, the inductor can be used to step-up or step-down the converter's input voltage, producing an output voltage different from its input voltage. After changing the AC voltage up or down using magnetics, the output is then rectified back into a DC voltage and filtered to remove any ripple.
The transistors are typically implemented using MOSFETs with a low on-state resistance, commonly referred to as “power MOSFETs”. Using feedback from the converter's output voltage to control the switching conditions, a constant, well-regulated output voltage can be maintained despite rapid changes in the converter's input voltage or output current.
To remove any AC noise or ripple generated by switching action of the transistors, an output capacitor is placed across the output terminal of the switching regulator. Together, the inductor and the output capacitor form a “low-pass” filter able to remove most of the transistors' switching noise before it reaches the load. The switching frequency, typically 1 MHz or more, must be “high” relative to the resonant frequency of the filter's “LC” tank. Averaged across multiple switching cycles, the switched inductor behaves like a programmable current source with a slow-changing average current.
Since the average inductor current is controlled by transistors that are either biased as “on” or “off” switches, power dissipation in the transistors is theoretically small and high converter efficiencies, in the 80% to 90% range, can be realized. Specifically, when a power MOSFET is biased as an on-state switch using a “high” gate bias, it exhibits a linear I-V drain characteristic with a low RDS(on) resistance, typically 200 milliohms or less. At 0.5A for example, such a device will exhibit a maximum voltage drop ID·RDS(on) of only 100 mV despite its high drain current. Its power dissipation during its on-state conduction time is ID2·RDS(on). In the example given, the power dissipated while the transistor is conducting is (0.5A)2·(0.2Ω)=50 mW.
In its off state, a power MOSFET has its gate biased to its source, i.e. so that VGS=0. Even with an applied drain voltage VDS equal to a converter's battery input voltage Vbatt, a power MOSFET's drain current IDSS is very small, generally well below one  microampere and typically in the range of nanoamperes. The current IDSS primarily comprises junction leakage.
Thus a power MOSFET used as a switch in a DC/DC converter is efficient, since in its off condition it exhibits low currents at high voltages, and in its on state it exhibits high currents at a low voltage drop. Excepting switching transients, the ID·VDS product in the power MOSFET remains small, and power dissipation in the switch remains low.
A critical component in switching regulation is the rectifier function needed to convert, or “rectify”, the synthesized AC output of the chopper back into DC. To ensure that the load never sees a reversal of polarity in voltage, a rectifier diode is placed in the series path of the switched inductor and the load, thereby blocking large AC signals from the load. The rectifier may be located topologically either in the high-side path somewhere between the positive terminal of the power or battery input and the positive terminal of the output, or on the low-side, i.e., in the “ground” return path. Another function of the rectifier is to control the direction of energy flow so that current only flows from the converter to the load and doesn't reverse direction.
In one class of switching regulators, the rectifier function employs a P-N junction diode or a Schottky diode. The Schottky diode is preferred over the P-N junction because it exhibits a lower forward voltage drop than P-N junctions, typically 400 mV instead of 700 mV, and therefore dissipates less power. During forward conduction, a P-N diode stores charge in the form of minority carriers. These minority carriers must be removed, i.e. extracted, or recombine naturally before the diode is able to block current in its reverse-biased polarity.
Because a Schottky diode uses a metal-semiconductor interface rather than a P-N junction, ideally it does not utilize minority carriers to conduct and therefore stores less charge than a P-N junction diode. With less stored charge, a Schottky diode is able to respond more quickly to changes in the polarity of the voltage across its terminals and to operate at higher frequencies. Unfortunately, Schottky diodes have several major disadvantages, one of which is that they exhibit a significant and unwanted off-state leakage current, especially at high temperatures. Unfortunately, there is a fundamental tradeoff between a Schottky diode's off-state leakage and its forward-biased voltage drop. 
The lower its voltage drop during conduction, the leakier it becomes in its off state. Moreover, this leakage exhibits a positive voltage coefficient of current, so that as leakage increases, power dissipation also increases causing the Schottky diode to leak more and dissipate more power causing even more heating. With such positive feedback, localized heating can cause a hot spot to get hotter and “hog” more of the leakage till the spot reaches such a high current density that the device fails, a process known as thermal runaway.
Another disadvantage of Schottky diodes is the difficulty of integrating them into an IC using conventional wafer fabrication processes and manufacturing. Metals with the best properties for forming Schottky diodes are not commonly available in IC processes. Commonly available metals exhibit an excessively high voltage barrier, i.e. they produce a voltage drop that is too high. Conversely, other commonly available metals exhibit a barrier potential that is too low, i.e. they produce too much leakage when used in a Schottky diode.
Despite these limitations, many switching regulators today rely on P-N diodes or Schottky diodes for rectification. As a two-terminal device, a rectifier doesn't require a gate signal to tell it when to conduct or not. Aside from the transient charge storage issue, the rectifier naturally prevents reverse current, so energy cannot flow from the output capacitor and electrical load back into the converter and its inductor.
To reduce voltage drops and improve conduction losses, power MOSFETs are sometimes used to replace the Schottky rectifier diodes in switching regulators. Operation of a MOSFET as a rectifier is often accomplished by placing the MOSFET in parallel with a Schottky diode and turning on the MOSFET whenever the diode conducts, i.e. synchronous to the diode's conduction. In such an application, the MOSFET is therefore referred to as a synchronous rectifier.
Since a synchronous rectifier MOSFET can be sized to have a low on-resistance and a lower voltage drop than a Schottky diode, current is diverted from the diode to the MOSFET channel, and the overall power dissipation in the “rectifier” is reduced. Most power MOSFETs include a parasitic source-to-drain diode. In a switching regulator, the orientation of this intrinsic P-N diode must have the same polarity as the Schottky diode, i.e. cathode to cathode, anode to anode. Since the parallel combination of this silicon P-N  diode and the Schottky diode only carry current for brief intervals, known as “break-before-make” intervals, before the synchronous rectifier MOSFET turns on, the average power dissipation in the diodes is low and the Schottky diode is often eliminated altogether.
Assuming that transistor switching events are relatively fast compared to the oscillating period of the regulator, the power loss during switching can in circuit analysis be considered negligible or alternatively treated as a fixed power loss. Overall, then, the power lost in a low-voltage switching regulator can be estimated by considering the conduction and gate drive losses. At multi-megahertz switching frequencies, however, the switching waveform analysis becomes more significant and must be considered by analyzing a device's drain voltage, drain current, and gate bias voltage drive versus time.
The synchronous rectifier MOSFET, unlike a Schottky or junction diode, allows current to flow bi-directionally and the timing of its gate signal must be precise to prevent reverse current flow, an unwanted type of conduction that lowers efficiency, increase power dissipation and heating, and may damage the device. By slowing down switching rates and increasing turn-on delays, efficiency can oftentimes be traded for improved robustness in DC/DC switching regulators.
Based on the above principles, present day inductor-based DC/DC switching regulators are implemented using a wide range of circuits, inductors, and converter topologies. Broadly they are divided into two major types of topologies, non-isolated and isolated converters.
The most common isolated converters include the flyback and the forward converter, and require a transformer or coupled inductor. At higher power, full bridge converters are also used. Isolated converters are able to step up or step down their input voltages, depending on the primary-to-secondary winding ratio of the transformer. Transformers with multiple windings can produce multiple outputs simultaneously, including voltages that are both higher and lower than the input. The disadvantage of transformers is they are large compared to single-winding inductors and suffer from unwanted stray inductances.
Non-isolated power supplies include the step-down Buck converter, the step-up boost converter, and the Buck-boost converter. Buck and boost converters are especially  efficient and compact in size, particularly when operating in the megahertz frequency range where inductors of 2.2 μH or less may be used. Such topologies produce a single regulated output voltage per coil, and require a dedicated control loop and separate PWM controller for each output to constantly adjust switch on-times to regulate voltage.
In portable and battery-powered applications, synchronous rectification is commonly employed to improve efficiency. A step-up boost converter employing synchronous rectification is known as a synchronous boost converter. A step-down Buck converter-employing synchronous rectification is known as a synchronous Buck regulator.
Non-Synchronous versus Synchronous Boost Converter Operation: As illustrated in FIG. 1A, prior art boost converter 1 includes an N-channel power MOSFET 7, an inductor 4, a capacitor 3, a Schottky rectifier 2, and a pulse-width modulation (PWM) controller 6. Inductor 4, MOSFET 7 and rectifier 2 share a common node referred to here as the “Vx” node, sometimes referred as the Lx node. Diode 5 is parasitic to MOSFET 7 and remains reverse-biased and off throughout regular operation of boost converter 1. Converter 1 is powered by an input voltage Vbatt.
Through the switching action of power MOSFET 7, the voltage Vx at the Vx node switches over a range larger than the supply rail, exhibiting potentials alternating between approximately ground when MOSFET 7 is on and conducting current IL(on) and to slightly above VOUT when MOSFET 7 is off and a current IL(off) flows through rectifier 2. The waveform of Vx for a conventional boost converter is illustrated by curve segments 31, 32, 38, 34, 35, 36 and 37 in graph 30 of FIG. 1D where Vx while MOSFET 7 is conducting (segment 31) is given by the expression I·RDS(on) and Vx while MOSFET 7 is off (segment 38) is given by (VOUT+Vf). The output voltage VOUT is greater the input voltage Vbatt. Without feedback and closed-loop control, converter 1 would drive VOUT to an increasingly higher level until diode 5 goes into avalanche breakdown, an unwanted and potentially damaging condition.
At time t1, after duration ton, inductor 4 drives the voltage Vx positive, and depending on the design and layout of converter 1, some voltage overshoot and unwanted oscillations or ringing may result (segment 32). After an interval toff, at time t2, MOSFET 7 turns on, and after any stored charge is removed from diode 2, Vx exhibits a negative transition and ringing (segment 35). The entire cycle  repeats with a cycle time T=(ton+toff), which remains constant in fixed-frequency PWM converters and may vary in variable-frequency converters.
In a synchronous boost converter, the rectifier diode is replaced by a second power MOSFET. Synchronous boost converter 10, shown in FIG. 1B, includes a floating synchronous rectifier MOSFET 13 with an intrinsic parallel diode 15, an inductor 12, an output capacitor 14, and a low-side power MOSFET 11 with an intrinsic parallel diode 16. The gates of MOSFETs 11 and 13 are driven by break-before-make (BBM) circuitry 17 and controlled by a PWM controller 18 in response to a feedback voltage VFB from the output terminal of converter 10, present across filter capacitor 24. BBM operation is needed to prevent shorting out output capacitor 14.
The switching waveform at the Vx node of synchronous converter 10, illustrated in graph 30 of FIG. 1D, is similar to that of non-synchronous boost converter 1 except for portion 33, where the voltage decreases during the time the synchronous rectifier MOSFET 13 is conducting. The waveform of graph 30 illustrates that the voltage while MOSFET 11 is conducting (portion 31) is given by the expression (I·RDS1(on)).
At time t1, after duration ton, inductor 12 drives the voltage Vx positive, and depending on the design and layout of converter 10, the waveform may include some voltage overshoot and unwanted oscillations or ringing (portion 32), then settle to a voltage (VOUT+Vf), where Vf equals the forward voltage drop across diode 15. After a break-before-make time interval tBBM as determined by BBM circuit 17, Vx is reduced by conducting synchronous rectifier MOSFET 13 to a magnitude (VOUT+I·RDS2(on))(portion 33), reducing the power loss compared to dissipation in P-N diode 15.
Just before low-side MOSFET 11 is turned on at time t2, synchronous rectifier MOSFET 13 is shut off, as shown by line segment 34, and Vx returns to (VOUT+Vf). After an interval toff, MOSFET 11 turns on, and after diode 15 recovers from any stored charge, Vx exhibits a negative transition and depending on diode-recovery of P-N junction in diode 15, may exhibit an over-voltage spike 35. After that spike and subsequent ringing (portion 36), Vx stabilizes at (I·RDS1(on)) (portion 37). The entire cycle repeats with a cycle time T=(ton+toff), which remains constant in fixed frequency PWM converters and may vary in variable frequency converters. 
Floating synchronous rectifier MOSFET 13 may be N-channel or P-channel, while grounded low-side power MOSFET 11 is more conveniently implemented using an N-channel device. Diode 16 which remains off and reverse-biased during normal operation of converter 10, is a P-N diode intrinsic to low-side MOSFET 11. Since diode 16 does not conduct under normal boost operation, it is shown in dotted lines. Diode 15, intrinsic to synchronous rectifier MOSFET 13, becomes forward-biased whenever low-side MOSFET 11 is off, but carries substantial current only when synchronous rectifier MOSFET 13 is also off. A Schottky diode may be included in parallel with MOSFET 13 but with series inductance may not operate fast enough to divert current from the forward-biased intrinsic diode 15.
Defining the duty factor D of DC/DC converter 10 as the time that energy flows from the battery or power source into converter 10, i.e. the time when low-side MOSFET switch 11 is on and inductor 12 is being magnetized, then the output-to-input voltage ratio of a boost converter 10 is inversely proportionate to one minus the duty factor, i.e.
            V      out              V              i        ⁢                                  ⁢        n              =                    1                  1          -          D                    ≡              1                  1          -                                    t              on                        T                                =          T              T        -                  t          on                    
This output-to-input voltage transfer characteristic as a function of the duty factor D is illustrated graphically in FIG. 1C by curve 23. While this equation describes a wide range of conversion ratios, a boost converter cannot smoothly approach a unity transfer characteristic without requiring extremely fast devices and circuit response times. Considering finite break-before-make intervals and non-zero MOSFET rise and fall times, the discontinuity 22 to a unity transfer 21 occurs because there is inadequate time at very low duty factors to react. Instead the converter jumps from some minimum duty factor to 0% and loses its ability to regulate.
Moreover, at high duty factors and high load currents, the time available for inductor 12 to deliver its energy to capacitor 14 and the load is limited and MOSFET 13 must carry high-currents for short durations. These high current spikes degrade performance and lower converter efficiency. Considering these factors, the duty factor of a boost converter is in practice limited to the range of 5% to 75%.
Current Dependence of Synclironous Boost Converters: 
To better understand the limitations imposed by current and by duty factor on the conversion ratio and efficiency of a boost converter, the energy flow from input to output must be considered in detail. As shown in FIG. 2A, an inductor 52 is magnetized with a current IL while low-side MOSFET 51 is on, and the node Vx is biased near ground at a voltage 71 as illustrated in graph 70 shown in FIG. 2C.
Also as shown in graph 75 of FIG. 2C, during the time ton the inductor current Iramps from point 76 to 77 linearly as inductor 52 stores energy in a magnetic field of magnitudeEL=½·L·IL2 
During this interval, synchronous rectifier MOSFET 53 is off and diode 54 is reverse-biased, so no energy flows from the battery or the inductor to load 56 or capacitor 55. Instead, capacitor 55 must supply load 56 with the necessary current as its voltage drops from 79 to 80, as shown in graph 78. During the same interval ton, capacitor 55 loses energy and charge of magnitude
      Δ    ⁢                  ⁢    Q    =                    C        ·        Δ            ⁢                          ⁢      V        =                  ∫        0                  t          on                    ⁢                        I          OUT                ·                  ⅆ          t                    
To maintain steady state operation, this charge must be replenished in the charge transfer cycle when MOSFET 51 is off. As shown in FIG. 2B, during the time toff, the voltage Vx flies up, forward-biasing diode 54 and transferring charge and energy to capacitor 55 and load 56. This condition is illustrated in graph 70 between times t1 and T, where Vx is equal to (VOUT+Vf), i.e. voltage 73, when synchronous rectifier MOSFET 53 is not conducting. When synchronous rectifier MOSFET 53 is conducting, Vx shown by line 72 is equal to (VOUT+I·RDS(HS)), reducing the power losses in diode 54 and reducing the amount of energy removed from inductor 52. The energy transferred to capacitor 55, however, remains the same.
During this toff interval from t1 to T, the inductor current decays from its peak 77 towards a minimum value 76, while the output voltage VOUT grows from its minimum value 80 toward its peak voltage 79 as illustrated in graphs 75 and 78, respectively.
Using the principle of charge conservation
      Δ    ⁢                  ⁢    Q    =                    C        ·        Δ            ⁢                          ⁢      V        =                            ∫                      t            1                    T                ⁢                              I            L                    ·                      ⅆ            t                              =                                    I            Lave                    ·                      t            off                          2            
So if in the ripple ΔV is kept small and the output well regulated, the shorter the time toff, the higher ILave must be. In other words, with increasingly high duty factors, MOSFET 54 must carry increasing higher currents.
Current Dependence of Synchronous Boost Converter Frequency
In the event that the load current decreases, the pulse width during ton when MOSFET 51 is on decreases and at some specific current it reaches a minimum pulse width. For any current decline beyond this minimum pulse width, to maintain regulation the off-time of MOSFET 51 must increase either by decreasing the oscillator frequency or by skipping pulses, i.e. by not turning on synchronous rectifier MOSFET 51.
In the event that the time toff increases, then for fixed on-time operation the converter's frequency drops. As shown by graph 88 in FIG. 2D, the inductor current ranges from a minimum value of zero at points 89 and 91 to a peak value at point 90. Specifically, whenever the synchronous rectifier MOSFET 51 is on, the inductor current equals the load current. Unavoidably, as shown in graph 88 the average value of IL drops to a much lower value than in normal operation shown in previously in graph 75.
Except for the break-before-make interval when both low-side and synchronous rectifier MOSFETs 51 and 53 are briefly off, a synchronous boost converter operating within the range of currents shown by FIGS. 2C and 2D has only two modes of operation—magnetizing the inductor or transferring energy to its output. These modes are illustrated in Table 1.
TABLE 1Boost ConverterLow-SideHigh-SideConductionInductorOutputEnergy Flow (Normal)MOSFETMOSFETModeCurrentVoltageMagnetizingOnOffContinuousILmax > ILminDecliningInductorTransferring toOffOnContinuousILmin ≧ 0IncreasingOutput
As described, in a conventional synchronous boost converter energy is either flowing into the inductor from the battery input or from the inductor to the load. Below some threshold of current corresponding to the onset of light load operation, the boost  converter's operating frequency necessarily varies with load current. One major problem arises when this oscillating frequency corresponds to a frequency approaching 20 kHz or below.
Under such conditions, the converter begins to oscillate within the audio frequency range and can be heard audibly through any sound amplification circuitry and even by listening to the printed-circuit board itself. Unfortunately, without being able to vary the lowest frequency, the output capacitor will over charge and its voltage will exceed the specified tolerance range for the output voltage.
Current Reversal in Synchronous Boost Converters
Aside from audio susceptibility and audible noise, other problems occur at very low current load conditions. Specifically, at lower currents than those depicted in FIG. 2D, a new and problematic condition occurs, as shown in FIG. 2E. Assuming ton is already at its minimum duration, the inductor current ramps (line 117) to its peak value at point 118, then if the current ramps down (line 119) to point 120 it actually reaches zero. Leaving the synchronous rectifier MOSFET 53 on beyond this point actually allows the inductor current to reverse direction, flowing from output capacitor 55 back into inductor 52. The current is negative in this condition as shown by line segment 121 and may reach a peak reverse value 122 before changing direction again. Current flowing the wrong direction in inductor 52 wastes energy and lowers overall efficiency. Corresponding to this current reversal, the voltage VX=(VOUT+I·RDS) drops below VOUT at point 107 or anytime IL is negative, as shown by dashed line segment 108 in graph 100.
In order to prevent reverse current in the synchronous rectifier, the only option in the prior art synchronous boost converter is to turn it off. This action involves detecting the onset of current reversal and shutting off synchronous rectifier MOSFET 53 at time t2. Because P-N diode 54 cannot normally conduct in the reverse direction, the inductor current at point 120 reaches zero and stays at zero shown by line 122 for the remaining duration of polarity reversal, i.e. until time T. This type of converter operation is known as discontinuous conduction, identical to the operation of a non-synchronous boost converter operating under light load conditions. Table 1 above is then modified to reflect that the converter operates in three states, as shown in Table 2.
TABLE 2Converter EnergyLow-SideHighSideInductorOutputFlow (Light Load)MOSFETMOSFETConductionModeCurrentVoltageMagnetizingOnOffContinuousILmax > ILminDecliningInductorTransferring toOffOnContinuousILmin ≧ 0IncreasingOutputCurrent ReversalOffOffDiscontinuous0Declining
By shutting off the synchronous rectifier MOSFET and entering discontinuous conduction, the converter efficiency in light load operation is improved. The onset of discontinuous conduction is not without problems. Referring again to graph 100 in FIG. 2E, shutting off the synchronous rectifier MOSFET 53 at time t2 results in an unwanted oscillation in Vx (curve 109) before Vx finally settles down to the voltage (VOUT+Vf), as shown by line 110.
The cause for this instability is residual energy stored in inductor 52 and in the diffusion and junction capacitance of forward-biased P-N diode 54 at the time synchronous rectifier MOSFET 52 is shut off. At that moment IL, while close to zero, may be slightly positive or negative because synchronous rectifier MOSFET 53 cannot be shut off perfectly at its zero-current crossing. The energy stored in these passive elements forms a tuned circuit or RLC tank circuit with output capacitor 55 and load 56. The oscillation frequency of this tuned circuit and its damping is therefore load dependent. Moreover, the converter's overall loop stability also changes when it enters discontinuous conduction. Unwanted instability and poor dynamic response can result, depending on the selection of the converter's passive elements.
Another major problem with operating the inductor under starved current conditions is its inability to react to rapid load transients. Since the inductor current is so low, reacting to a sudden change in load current requires finite time to reestablish current in the inductor. This time could exceed several switching cycles, during which capacitor 55 must satisfy the current demands of load 56. Unless capacitor 55 is intentionally oversized for step response conditions, a conventional boost converter operating in light  load near or in discontinuous conduction will exhibit extremely poor regulation during a step load transient.
Unfortunately no means exist in a boost or synchronous boost converter to maintain a higher inductor current and limit the converter's operating frequency range during light load conditions.
P-N Rectifier Imposed Limitations in Prior-Art Synchronous Boost Converters
Another set of limitations in the operation of prior-art synchronous boost converters derive from the presence of the P-N rectifier diode in parallel with the synchronous rectifier MOSFET. While it may at first glance appear this diode is an unavoidable consequence of the design and fabrication of the power MOSFET structure used as the synchronous rectifier, it is in fact an unavoidable and necessary element for synchronous boost converter operation.
Referring again to the conventional synchronous boost converter 10 shown in FIG. 1B, P-N diode 15 is electrically in parallel to synchronous rectifier MOSFET 13, regardless of whether MOSFET 13 is a P-channel or an N-channel device. The polarity of diode 15 in a positive output boost converter is extremely important, having its cathode connected to the output and its anode connected to the Vx node, so that it remains off and reverse-biased whenever low-side MOSFET 11 is on, Vx is near ground and inductor 12 is magnetizing, a condition with an equivalent electrical circuit shown in circuit 50 of FIG. 2A. If its polarity were reversed, turning on the low-side MOSFET would forward bias the diode and undesirably pull down the output voltage.
FIG. 2B illustrates that the P-N rectifier diode 54 is forward-biased whenever low-side MOSFET 51 is off and therefore Vx>VOUT, regardless of whether synchronous rectifier MOSFET 53 is on or off. MOSFET 53 may shunt current around diode 54, but it is nonetheless forward-biased whenever low-side MOSFET 51 is off. At first inspection this feature appears fortuitous since it limits the maximum voltage of node Vx to a magnitude of (VOUT+Vf) during the break before make interval, when both MOSFETs 51 and 53 are off.
Unfortunately, the presence of rectifier diode 54 limits the output to a voltage greater than Vbatt, making it difficult to regulate an output voltage near the input voltage whenever VOUT≈Vbatt. This issue arises from the moment when power is first applied to  the converter 50 and both MOSFETs 51 and 53 are momentarily off and non-conducting. Because initially Vout is near ground and capacitor 55 is discharged, the application of power Vbatt to the converter's input instantly forward biases diode 54 and charges VOUT to a voltage approximately equal to Vbatt.
Since VOUT≈Vbatt before MOSFETs 51 and 53 have even started switching, then further operation can only further increase the output voltage. There is no lossless means by which to charge capacitor 55 only to a voltage part-way up, i.e. to a voltage smaller than the input voltage Vbatt. Accordingly, as shown in FIG. 1C, the minimum (VOUT/VIN) transfer ratio is unity, as illustrated by line 21. The discontinuous jump 22 represents the minimum duty factor to regulate the output voltage under closed loop conditions, above which converter 50 behaves predictably according to curve 23.
The height of discontinuity 22 can be interpreted as a quantum of energy or charge corresponding to the minimum possible pulse duration. If that minimum duration stores energy EL in the inductor 52 corresponding to a current IL, then that same energy dumped into the output capacitor 55 charges capacitor 55 with a finite number of coulombs ΔQ of charge, resulting in a finite increment or step in voltage ΔV=(ΔQ/C) in one switching cycle. Since this voltage is added atop of the charge already present on capacitor 55 resulting from unavoidable pre-charging when power was first applied, then it follows that VOUT>(VIN+ΔV) and therefore
            V      OUT              V      IN        =                              V          IN                +                  Δ          ⁢                                          ⁢          V                            V        IN              =                  (                  1          +                                    Δ              ⁢                                                          ⁢              V                                      V              IN                                      )            >      1      
In other words, with a conventional synchronous boost converter it is impossible to regulate VOUT within a quantum ΔV above VIN, let alone produce an output voltage less than the input voltage.
Another major problem with the conventional boost or synchronous boost converter occurs at startup. Referring again to FIG. 2B, after the application of power pre-charges capacitor 55 to the input voltage, the very first switching cycle where Vx exceeds Vbatt, diode 54 becomes forward-biased and removes the little energy stored in inductor 52 to charge capacitor 55. If load 56 consumes all the charge on capacitor 55 before the boost circuit magnetizes inductor 52, then in the next cycle inductor 52 again charges a  capacitor with no added charge above it pre-charge condition, i.e. the net ΔV=0 after one cycle.
As a result of this circuit loading, VOUT remains at Vbatt and the boost circuit never starts up. The boost converter loaded by electrical load 56 is stuck in a permanent condition, unable to boost the output voltage to the desired higher voltage. This problem is especially severe when Vbatt is at its minimum condition when the resistance of MOSFET 51 is higher and unable to establish adequate current in inductor 52. For example in a one-cell NiMH or dry-cell battery, only 0.9V may be available to turn on the MOSFETs and achieve startup.
One possible remedy to the loaded startup problem may appear to be to leave MOSFET 51 on for a longer duration during startup, but then inductor 52 may conduct too much current, store too much energy, and cause VOUT to overshoot. Overshoot can cause instability, oscillations and possibly damage load 56.
In the event that too much energy is stored in inductor 52, no remedy exists in a conventional boost or synchronous converter to remove or siphon off the extra energy. If synchronous rectifier MOSFET 53 is turned on, the output voltage VOUT will continue to rise to an unwanted value as inductor 52 transfers its energy into capacitor 55. If MOSFET 51 is turned on, even more energy is stored in inductor 52, worsening the problem. Even if both MOSFETs 51 and 53 are left off, diode 54 is still forward-biased and inductor 52 will continue to overcharge capacitor 55. And since the load current of load 56 is not known and may vary, there is no way to insure reliable startup without the risk of an output voltage that is too high.
Since rectifier diode 54 is the cause of the problem, one choice may be to eliminate it, as shown in circuit 130 of FIG. 3A. In this circuit synchronous rectifier MOSFET 133 is off and no forward-biased rectifier is present across it. Instead two back to back diodes 136a and 136b are included to represent the lack of the rectifier in the circuit. After MOSFET 131 is turned on for some duration to magnetize inductor 132 and current 150 ramps, as shown in FIG. 3B, switching off MOSFET 131 causes a major problem.
At the time the current in inductor 132 is interrupted at point 151 and time t1, the voltage Vx jumps without limit. Without a forward-biased rectifier across MOSFET 133,  Vx is no longer limited to (VOUT+Vf) and Vx continues to increase until diode 137 goes into avalanche breakdown, oscillating (curve 156) and settling to a voltage BVDSS (curve 157), while the current in inductor 132 ramps back down (curve 152). The energy is then removed from inductor 132 in a fast and very noisy manner known as unclamped inductive switching or UIS. After the energy is removed, at time t2 the voltage returns to Vbatt (curve 158), the circuit's input condition. In addition to the fact that the energy was lost, dissipated as heat in diode 137, there is a good chance that MOSFET 131 may be damaged or destroyed from the high currents, voltages, and temperature present simultaneously during the UIS transient.
In other words, despite the limitations imposed by the rectifier diode in a synchronous boost converter, there is no simple way to remove it from prior art circuit topologies without causing UIS related problems and efficiency loss.
Summary of Problems in Conventional Boost Converters
Prior art boost and synchronous boost switching regulators both suffer from numerous limitations intrinsic to their circuit topology adversely affecting efficiency, noise, stability, transient capability and more. These problems include undesirable variable frequency operation, audio noise, the need for current reversal detection circuitry, unwanted oscillations when turning off the synchronous rectifier MOSFET to prevent current reversal, poor transient regulation in light load operation, and the inability to regulate at low-duty-factor and unity voltage conversion ratios.
Especially problematic is the fact that the inductor current, operating frequency, and converter stability are particularly sensitive to the load current and the complex equivalent impedance of the load being powered by the boost converter. Achieving reliable start-up into a full load current from a low input voltage greatly limits prior art step-up converters. Over-magnetizing the inductor creates a problem of overvoltage conditions on the output that may damage the converter's load. Eliminating the rectifier diode to achieve step-down operation or to improve startup by unloading the circuit creates additional and even greater problems due to unclamped inductive switching, noise, efficiency loss and potential device damage. 
What is needed is an alternative step-up topology that ameliorates or eliminates these aforementioned problems without adding undue complexity, cost, or creating new problems achieving converter instability or reliable operation.
An even more ambitious goal of such an improved converter and regulator is not only to regulate at or above unity voltage conversion ratios, i.e. when VOUT≧Vbatt, but to be able to step-down or step-up an input to regulate a desired output voltage from a changing input source without utilizing complex and inefficient Buck-boost converter circuitry and techniques and without the need to change operating modes whenever VOUT≈Vbatt.