Patent Publication Number: US-2011075457-A1

Title: Capacitor startup apparatus and method with failsafe short circuit protection

Description:
RELATED APPLICATIONS 
     This application is a divisional of application Ser. No. 11/670,802; filed 2007-02-02 (pending) which is a divisional of application Ser. No. 10/821,415 filed 2004-04-09 and now issued as U.S. Pat. No. 7,180,277 on 2007-02-20, all of the above applications are hereby incorporated by reference for all purposes. 
    
    
     FIELD OF THE INVENTION 
     The present invention relates generally to circuits for filtering voltages and enhancing power supply ride-through performance, and, more particularly, to current limiting circuits for controlling large capacitor charging currents. 
     BACKGROUND 
     Power supplies are ubiquitous devices present in electrical and electronic equipment. Typically, a power supply converts alternating current (AC) power into direct current (DC) power for use within the equipment. The AC power is generally delivered to the power supply at a relatively high voltage, for example, 120 VAC, while the DC power is generated within the power supply at one or more relatively low voltages, for example, 5 and 12 VDC. In some applications, the power converted by a power supply is received from a DC source, but at a voltage that cannot be used directly by the equipment. For example, the input power may come from a source of voltage that is too high or too low for direct use within the equipment. The power supply then regulates the voltage down to the needed level, or performs DC-to-DC transformation, either stepping the DC voltage up or down, as needed. 
     Ideally, the DC voltage delivered by a power supply is stable and does not have any AC components. In practice, however, the DC voltage has some AC components. The most common source of the AC components is feed through of the AC voltage, such as the 60 Hz spectral components in North America or the 50 Hz frequency common in Europe. Another source of AC noise is the equipment using the DC power. Still another source of the noise is radio frequency interference. But whatever the source of the AC noise on the power supply output, it is desirable to reduce its magnitude. A power supply&#39;s ability to suppress the AC noise on its output is an important performance characteristic of the supply. 
     Another important measure of power supply performance is the capability to continue delivering stable DC power during disturbances on the AC power line that feeds the power supply. This capability is sometimes descriptively called “ride-through” capability, because it allows the equipment to perform as expected during AC power interruptions of short duration, or to power down in a controlled manner during such interruptions. 
     Large capacitors are often connected across DC power supply outputs to improve both AC noise suppression and ride-through capability. Capacitors perform these functions because they are reservoirs of electrical charges, and can absorb or supply the charges as required. The larger the capacitance of a given capacitor, the better it will suppress AC noise and the longer it will be able to supplement or replace DC power normally provided by the power supply. One type of capacitor that can provide large capacitance is that known to those skilled in the art as a double-layer capacitor. Double layer capacitors can provide previously unattainable large capacitance values in small form factor housings. For example, a 500 Farad double-layer capacitor can now be made to fit within a battery sized housing, including D-cell sized housings and the like. 
     Connecting a capacitor across a power supply output is not without its own set of problems. In the present context, we focus on three such problems. First, a capacitor may draw a large amount of electrical current on power-up, until the capacitor is sufficiently charged. This is problematic because the capacitor may keep The voltage of the power supply from reaching its nominal level for an excessive period of time. Power monitoring and power-on reset circuits, common in electronic equipment, may time-out before the voltage stabilizes at the nominal level, keeping the equipment in the reset mode or initiating another start-up sequence of the equipment. Even when the equipment can tolerate a prolonged start-up period, many users find additional waiting annoying. These problems become worse as capacitance is increased, because higher capacitance allows a capacitor to receive more charge and, therefore, more current from a power supply. Thus, when using high capacitance capacitors, for example, double-layer capacitors, high current draw needs to be considered during the design-in phase even more than before. It would also be preferable to avoid extensive start-up delays that use of high capacitance capacitors may cause. 
     Second, in some applications excessive current draw may disable the power supply. For example, large current drawn from a power supply can blow a fuse, trip an overload protection circuit, or cause permanent damage to internal components of the power supply. Excessive current draw may also damage the capacitor, causing it to leak, catch fire, or even explode, presenting a safety hazard. Therefore, it would be desirable to prevent excessive current draw and avoid such possibilities. 
     Third, a typical capacitor failure mode is a short circuit between capacitor terminals. With the capacitor installed across power supply output terminals, the failure would not only affect the AC noise suppression and ride-through capability of the power supply, but would also cause a catastrophic failure because the voltage level output by the power supply would likely fall precipitously, leaving the equipment powered by the supply without adequate power. It would be beneficial to prevent such catastrophic failures due to capacitor failures. 
     A need thus exists for methods and apparatus to prevent excessive start-up delays caused by charging output capacitors of power supplies. Another need exists to prevent excessive current draw that can disable power supplies during equipment start-up. Yet another need exists to prevent capacitor failures from causing catastrophic equipment failures. A further need exists to implement such solutions with high capacitance capacitors such as double-layer capacitors. 
     SUMMARY 
     The present invention is directed to circuits for coupling an energy storage device to an output of a power supply. One circuit in accordance with the invention includes a current-sensing resistor, and a switch with a pair of outputs and an input. The outputs of the switch are coupled in series with the energy storage device and with the current-sensing resistor, forming a series combination. The combination series is in turn coupled across the output of the power supply. In one embodiment, the energy storage device comprises high capacitance capacitors such as double-layer capacitors. 
     The input of the switch receives a switching signal that controls the state of the switch. When the switching signal is at a first level, the switch assumes a conducting (on) state with low resistance between the switch&#39;s outputs; when the switching signal is at a second level, the switch assumes a non-conducting (off) state with high resistance between the outputs of the switch. 
     The circuit further includes a differential high-gain device, such as a comparator or an operational amplifier. An output of the differential high-gain device is coupled to the input of the switch, so as to control the state of the switch and the charging current flowing through the switch and other components of the series combination. A non-inverting input of the differential high-gain device is biased by a control voltage generated, for example, by a voltage divider coupled across the outputs of the power supply. An inverting input of the differential high-gain device receives a feedback voltage generated by the charging current flowing through the current-sensing resistor. 
     The output of the differential high-gain device drives the input of the switch with the switching signal at the first level when the control voltage exceeds the feedback voltage by an input offset voltage of the differential high-gain device. The differential high-gain device drives the input of the switch with the switching signal at the second level when the feedback voltage exceeds the control voltage by the input offset voltage. In this way, the charging current that the energy storage device can draw from the power supply is limited to a level determined by the values of the current-sensing resistor, the resistors of the voltage divider, and the voltage level at the output of the power supply. 
     Another circuit in accordance with the invention includes a switch with a pair of outputs and an input. The switch&#39;s outputs are coupled in series with an energy storage device to form a first series combination, which combination is coupled across the output of the power supply. A switching signal at the input of the switch controls the state of the switch. The switch is turned on (assumes a conductive state) when the switching signal is at a first level; the switch is turned off (assumes a non-conducting state) when the switching signal is at a second level. 
     The circuit also includes a reference voltage source, for example, a temperature-compensated voltage reference, and first and second resistors coupled in series to form a second series combination. The second series combination is also coupled across the output of the power supply. 
     The circuit further includes a differential high-gain device, such as a comparator or an operational amplifier, providing the switching signal at its output. A non-inverting input of the differential high-gain device is coupled to the junction of the first and second resistors, while its inverting input receives a voltage reference signal from the reference voltage source. To add hysteresis to the circuit, a positive feedback resistor is coupled between the output and the non-inverting input of the differential high-gain device. With this arrangement of components, the circuit does not allow a charging current to flow into the energy storage device until the voltage at the output of the power supply reaches a voltage level determined by the voltage reference signal and the values of the first resistor, the second resistor, and the feedback resistor. 
     In one embodiment, a system for use with a power supply comprises two double-layer capacitors, the two double-layer capacitors operatively coupled to output terminals of the power supply, wherein each double-layer capacitor comprises a capacitance of greater than or equal to 1 Farad; a voltage balancing circuit; the voltage balancing circuit operatively coupled to the two double-layer capacitors to balance a voltage applied to the two capacitors by the power supply; and a current control device, the current control device including a feedback portion, the current control device coupled to output terminals of the power supply, wherein the current control device controls current flowing through the two double-layer capacitors according to a signal provided by the feedback portion. In one embodiment, the feedback portion provides a positive feedback signal. In one embodiment, the feedback portion provides a negative feedback signal. 
     In one embodiment, a circuit for coupling an energy storage device to an output of a first power supply comprises a current-sensing resistor; a switch comprising a pair of outputs coupled in series with the energy storage device and with the current-sensing resistor, and an input receiving a switching signal, the switch assuming a conducting state when the switching signal is at a first level, the switch assuming a non-conducting state when the switching signal is at a second level; a differential high-gain device comprising an output coupled to the input of the switch, a first input biased by a control voltage, and a second input receiving feedback voltage generated by a charging current flowing through the current-sensing resistor; wherein the output of the differential high-gain device drives the input of the switch with the switching signal at the first level when the control voltage exceeds the feedback voltage by an input offset voltage of the differential high-gain device, and the differential high-gain device drives the input of the switch with the switching signal at the second level when the feedback voltage exceeds the control voltage by the input offset voltage; and the current-sensing resistor, the switch, and the energy storage device are coupled across the output of the first power supply. 
     In one embodiment, a circuit for coupling an energy storage device to an output of a first power supply comprises a switch comprising a pair of outputs coupled in series with the energy storage device to form a series combination, the series combination being coupled across the output of the first power supply, and an input receiving a switching signal, the switch assuming a conducting state when the switching signal is at a first level, the switch assuming a non-conducting state when the switching signal is at a second level; a connection receiving a voltage reference signal; and a differential high-gain device comprising an output coupled to the input of the switch, a first input biased by a control voltage, and a second input receiving the voltage reference signal; wherein: the control voltage is monotonically related to a voltage appearing at the output of the first power supply so that the differential high-gain device drives the input of the switch with the switching signal at the first level when the control voltage exceeds the voltage reference signal by an input offset voltage of the differential high-gain device, and the differential high-gain device drives the input of the switch with the switching signal at the second level when the voltage reference signal exceeds the control voltage signal by the input offset voltage. 
     In one embodiment, a circuit for coupling an energy storage device to an output of a first power supply comprises a switch comprising a pair of outputs coupled in series with the energy storage device to form a first series combination, the first series combination being coupled across the output of the first power supply, and an input receiving a switching signal, the switch assuming a conducting state when the switching signal is at a first level, the switch assuming a non-conducting state when the switching signal is at a second level; a connection receiving a voltage reference signal; a first resistor and a second resistor coupled in series to form a second series combination comprising a junction of the first and second resistors, the second series combination being coupled across the output of the first power supply; a differential high-gain device comprising an output coupled to the input of the switch, a non-inverting input coupled to the junction of the first and second resistors, and an inverting input receiving the voltage reference signal; and a positive feedback resistor coupled between the output of the differential high-gain device and the non-inverting input of the differential high-gain device. 
     In one embodiment, a method for coupling an energy storage device to an output of a power supply comprises steps of: coupling the energy storage device in series with a switch controllable by a switching signal; generating a feedback signal representing current flowing into the energy storage device; comparing the feedback signal to a predetermined control signal; and generating the switching signal to turn off the switch when the comparing step indicates that the current is not lower than a predetermined level. 
     These and other embodiments, features, advantages, and aspects of the present invention will be better understood with reference to the following description, drawings, and appended claims. 
    
    
     
       BRIEF DESCRIPTION OF THE FIGURES 
         FIG. 1  is a high-level illustration of a circuit for limiting current flowing into a device coupled across a power supply output, in accordance with the present invention; 
         FIG. 2  is a high-level illustration of a circuit of  FIG. 1  using a cell balancer and a pair of double layer capacitors; 
         FIG. 3  is a high-level illustration of a circuit for connecting an energy storage element in parallel with a power supply, in accordance with the present invention; 
         FIG. 4  is a high-level illustration of another circuit for connecting an energy storage element in parallel with a power supply, in accordance with the present invention; 
         FIG. 5  is a high-level illustration of a current-limiting circuit capable of enhancing power supply ride-through performance, in accordance with the present invention; and 
         FIG. 6  is a high-level schematic diagram of a generalized current-limiting circuit capable of enhancing power supply ride-through performance, in accordance with the present invention. 
     
    
    
     DETAILED DESCRIPTION 
     Reference will now be made in detail to several embodiments of the invention that are illustrated in the accompanying drawings. Wherever possible, same or similar reference numerals are used in the drawings and the description to refer to the same or like parts. The drawings are in a simplified form and not to precise scale. For purposes of convenience and clarity only, directional terms, such as top, bottom, left, right, up, down, over, above, below, beneath, rear, and front may be used with respect to the accompanying drawings. These and similar directional terms should not be construed to limit the scope of the invention in any manner. In addition, the words couple, connect, and similar terms with their inflectional morphemes are used interchangeably, unless the difference is noted or made otherwise clear from the context. These words and expressions do not necessarily signify direct connections, but include connections through mediate components and devices. 
       FIG. 1  is a high-level illustration of a circuit  100  in accordance with the present invention. The circuit  100  includes terminals  171  and  172  that couple the circuit  100  to a power supply  160 , and terminals  114  and  116  that connect to an energy storage device  110 . In one variant of the circuit  100 , the energy storage device  110  is a double layer capacitor (also known as ultracapacitors and super capacitors). Double-layer capacitors store electrostatic energy in a polarized electrode/electrolyte interface layer. Double-layer capacitors include two electrodes, which are separated from contact by a porous separator. The separator prevents an electronic (as opposed to an ionic) current from shorting the two electrodes. Both the electrodes and the porous separator are immersed in an electrolyte, which allows flow of the ionic current between the electrodes and through the separator. At the electrode/electrolyte interface, a first layer of solvent dipole and a second layer of charged species is formed (hence, the name “double-layer” capacitor). Double-capacitors enable that individual capacitor cells may be designed with capacitance on the order of thousands of Farads. In one embodiment, individual double-layer capacitor cells can be connected in parallel to further increase capacitance. Present double-layer capacitor technology limits nominal operating voltages of double-layer capacitors to below about 3.0 volts. Higher operating voltages are possible, but at such voltages undesirable destructive breakdown may begin to appear. Those skilled in the art will identify that increased operating voltage at a given high capacitance, as can be provided by a double-layer capacitor, can be achieved by connecting two or more double-layer capacitors in series. 
     Resistors  130  and  135  form a voltage divider between positive and negative power supply rails that connect to the terminals  171  and  172 . The voltage divider sets a control voltage (V.sub.c) at the junction of the two resistors, which voltage is monotonically related to the voltage difference between the terminals  171  and  172 . The divider is also coupled to a non-inverting input  122  of a differential high-gain device  120 , biasing the input  122  with the control voltage. Output  121  of the device  120  drives, through a current-limiting resistor  140 , an input  183  of a switching device  180 . The switching device  180 —a transistor switch in the illustrated embodiment—assumes a conductive state when the voltage at its input  183  exceeds a certain threshold. For example, the device  180  assumes a conductive state when the output  121  of the differential high-gain device  120  is at a high voltage level. The differential high-gain device  120  drives its output  121  to a high voltage level when the voltage at the inverting input  123  is lower than the control voltage V.sub.c at the non-inverting input  122 . When the voltage, at the input  123  is higher than the voltage at the input  122 , the output  121  is driven to a low voltage level. 
     The control voltage V.sub.c at the input  122  is equal to the voltage V.sub.cc of the supply  160  (5 volts, for example) multiplied by resistance value R.sub. 135  of the resistor  135 , and divided by the combined resistance values R.sub. 130  and R.sub. 135  of the resistors  130  and  135 : V c=V cc*R  135  (R  130 +R  135 ). (Note that here and elsewhere in this document; R.sub.N designates resistance value of a resistor designated by numeral N.) 
     As long as the control voltage V.sub.c exceeds the voltage at the inverting input  123  of the device  120 , the output  121  drives the input  183  of the switching device  180  with a voltage sufficient to turn on or saturate the switching device  180 . Current I.sub.c through the switching device  180  charges the energy storage device  110 , and returns to ground through a current-sensing resistor  150 . The voltage drop across the resistor  150  (referred to as V.sub.f or feedback voltage) is equal to the resistance value of the resistor  150  (R.sub. 250 ) multiplied by the charging current I.sub.c. Thus, V.sub.f=I.sub.c*R.sub. 150 . Note that the voltage V.sub.f is fed back to the inverting input  123  of the differential high-gain device  120 . The discussion below explains how generation of the voltage V.sub.f and feeding this voltage back to the input  123  provide a feedback mechanism that allows the circuit  100  to control and limit the charging current I.sub.c flowing into the energy storage device  110 . 
     As the current I.sub.c increases, the feedback voltage, V.sub.f also increases. At a point where V.sub.f is approximately equal to V.sub.c, the differential high-gain device  120  begins to drive its output  121  to a low voltage state, gradually turning the switching device  180  off and reducing or cutting off the charging current I.sub.c. The charging current I.sub.c will thus be limited to a value I.sub. 1 , which can be determined from formula (1) below: 
         I 1= Vcc*R 135 R 150*( R 130+ R 135).  (1)
 
     As a person skilled in the art would recognize, equation (1) immediately above ignores certain second- and higher-order effects, such as the effect of the input offset voltages of the differential high-gain device  120 . The equation may also not apply during a brief settling period immediately after the power supply  160  is turned on. 
     If the power supply  160  fails and becomes incapable of providing a current I.sub.supply to a load  199  connected to it, the energy storage-device  110  takes over the function of providing I.sub.supply to the load. While the energy storage device  110  discharges, the control voltage V.sub.c exceeds the feedback voltage V.sub.f, so that the switching device  180  remains in the conductive state and the circuit  100  continues to function as expected. This document will refer to operation during periods when the power supply  160  fails as operation during discharge cycles. 
     In the circuit  100  illustrated in  FIG. 1 , the differential high-gain device  120  is a CMOS operational amplifier (op amp). CMOS technology enables the op amp to provide high input impedances at its inputs  122  and  123 , minimizing the distortion of the control voltage V.sub.c and the negative feedback voltage V.sub.f due to input leakage currents. In this way, relatively large values of the resistors  130  and  135  can be selected to lower the stand-by current draw. In other variants of the circuit  100 , the device  120  is implemented as a bipolar operational amplifier, a comparator, a switch, a discrete transistor circuit, or another electronic circuit. In the illustrated embodiment, the switching device  180  is a power metal oxide semiconductor field-effect transistor (MOSFET) capable of switching on and off the relatively large charging current I.sub.c. In other embodiments, the switching device  180  is implemented as a bipolar transistor, an analog semiconductor switch, or an equivalent or similar device. 
     Source resistance seen by the load  199  during the discharge cycles includes (and is approximated by) the resistance of the resistor  150 . It is generally desirable to minimize this resistance. For a given, design with predetermined I.sub. 1  (the maximum value of the charging current) and V.sub.cc the value of the resistor  150  can be determined by re-writing formula (1) as follows: 
         R 150= VccI 1*( R 135 R 130+ R 135).  (2)
 
     Formula (2) indicates that in order to minimize the source resistance of the circuit  100 , the ratio (R  135  R  130 +R  135 ) of the resistive voltage divider should be minimized. The ratio, however, cannot be made arbitrarily small: it is limited by the magnitude and variability of the input offset voltage of the differential high-gain device  120 . The offset voltage ideally should be much smaller (e.g., by a factor of about 10) than the control voltage V.sub.c. Practically, the control voltage V.sub.c can be set to about 10 mV for a conventional comparator or op amp used as the device  120 , and to about 1 mV for a low offset device. To allow further decreases in the control voltage V.sub.c, precision, temperature stable components can be used for resistors  130  and  135 . 
     The energy storage device  110  need not be limited to a single capacitor or cell. For example, several cells can be connected in series to boost the voltage capability of the device. In the case of double layer capacitors that can be provided with a high capacitance (for example, in range of 1-5000 Farads) and small form factor, the typical nominal operating voltage is on the order of about 3 volts or less. For double layer capacitors to be used in higher voltage applications, one or more capacitor can be connected in series. In some applications, the voltages across series connected capacitors may need to balanced. Several capacitor cell voltage balancing circuits are known to those skilled in the art, and others of a novel nature are described in a commonly-assigned U.S. application Ser. Nos. 10/423,708, 10/498,197, and 60/518,052, which are hereby incorporated by reference in their entirety. To illustrate this concept,  FIG. 2  shows a circuit  200  that includes two series connected double-layer capacitors  111  and  112 , and a cell balancer  113 . Although circuit  200 , as well as others described further herein, are described as utilizing capacitor technology, it is understood that the present invention should not limited thereby, as it is envisioned that other energy storage devices could be utilized, for example, secondary batteries and other types of rechargeable cells. 
       FIG. 3  is a high-level illustration of a circuit  300  for connecting an energy storage element  310  in parallel with a power supply  360 . In one embodiment, the energy storage element  310  comprises voltage balancer  313  and a series combination of capacitors  311  and  312 . 
     In the circuit  300 , the energy storage element  310  is coupled in series with a switching device  380 ; the series combination of the device  380  and the element  310  is coupled across the power supply  360 , so that the charging current of the energy storage element  310  flows through and is controlled by the switching device  380 . The switching device  380  is, in turn, controlled by a voltage at its input  383 , driven by output  321  of a differential high-gain device  320 . Inverting input  323  of the device  320  is biased by a reference voltage V.sub.ref provided by a reference voltage source  397 , for example, a temperature-compensated precision voltage reference. Non-inverting input  322  of the comparator  320  receives a control voltage V.sub.c, which is monotonically related to the voltage across the terminals  371 / 372 . In this embodiment, the control voltage V.sub.c is generated by a voltages divider formed by resistors  330  and  335 . The control voltage V.sub.c is equal to (V cc.times. R  335  R  330 +R  335 ). (V.sub.cc denotes the power supply voltage across terminals  371  and  372 .) Thus, the comparator  320  keeps the switching device  380  in the off or non-conducting state until (Vcc*R  335  R  330 +R  335 ) exceeds V.sub.ref. At approximately that point, the differential high-gain device  320  begins to turn on the switching device  380 , and allows some charging current to flow into and charge the energy storage element  310 . The values of V.sub.ref, R.sub. 330 , and R.sub. 335  are chosen so that the turn-on point (V.sub.on) is set below the normal operating range of the power supply  360 , but above the minimum voltage level required by load  399  powered by the supply  360 . In a 5 volt design, for example, V.sub.on can be set to about 4.75 volts. The relationship of V.sub.on, V.sub.ref, R.sub. 330 , and R.sub. 335  is governed by the following equation: 
         V on= Vref *( R 330+ R 335) R 335.  (3)
 
     After the voltage level of the power supply  360  reaches V.sub.on, the circuit  300  allows the energy storage element  310  to draw enough current to keep the voltage level of the supply  360  substantially at V.sub.on, in effect charging the energy storage element  310  with a current that is close to the excess current available from the power supply  360  after providing the I.sub.supply current to the load  399 . Thus, on power-up the energy storage element  310  remains substantially discharged until the power supply voltage reaches the operating level required by the load  399 ; from that point on, the energy storage element  310  is charged at substantially the highest rate that the power supply can deliver. Eventually, the energy storage element  310  becomes fully charged, and only leakage current flows through the series combination of the element  310  and the switching device  380 . 
     Let us next turn to the description of the specific components used in the circuit  300 . The switching device  380  and the comparator  320  are similar to the devices  180  and  120 , respectively, of the previously-described embodiments. In some variants of the circuit  300 , the reference voltage source  397  is provided on the same integrated circuit (IC) as the device  320 . A simple voltage divider can also be used as the source  397 . As regards the resistors  330  and  335 , in some variants of the circuit  300  they are high-precision, temperature stable resistors. 
     Note that a jumper can be substituted for the resistor  330  (0 ohm resistance), while the resistor  335  can be removed altogether (open circuit with infinite resistance). 
       FIG. 4  is a high-level illustration of a circuit  400  in accordance with the present invention. The circuit  400  is similar to the circuit  300  of  FIG. 3 , but also includes a resistor  337  coupled between the noninverting input  322  and the output  321  of the comparator  320 . This resistor portion of the circuit provides positive feedback within the circuit, resulting in hysteresis in turning the switching device  380  on and off. The hysteresis allows the circuit  400  to begin charging the energy storage element  310  when the voltage of the power supply ramps-up to a turn-on voltage value V.sub.on, which is higher than a voltage V.sub.off at which the circuit  400  disconnects the energy storage element  310  during discharge cycles. 
     Two simplifying assumptions help in analyzing the performance of the circuit  400 . First, we assume that the output  321  of the comparator  320  is driven between substantially ground potential and the potential of the voltage across the power supply terminals  371 / 372 . Second, we assume that the resistance of the switching device  380  in a conductive state is substantially zero. Next, we define C.sub.on and C.sub.off as the ratios of V.sub.on and V off.times. .times. to .times. .times. V ref, .times. C on=V on V ref, .times. C off=V off V ref. With these assumptions and definitions, we can choose a value for one of the resistors  330 ,  335 , or  337 , and solve a set of two simultaneous non-linear equations to express the values of the remaining two resistors in terms of (1) the chosen resistor value, (2) C.sub.on, and (3) C.sub.off. Here, we simply present expressions for R.sub. 335  and R.sub. 337  in terms of R.sub. 330 , omitting their derivation for brevity: 
         R 335= C off *R 330 C on*( C off−1),.times.and  (4)
 
         R 337= C off* R 330 C on− C off.  (5)
 
     Let us go through a numerical example to clarify the above results. Suppose the circuit is to be designed using a voltage reference generating V.sub.ref of 4.0 volts (V.sub.ref=4.0), so that the energy storage device  360  begins to charge when the power supply voltage reaches 4.8 volts (V.sub.on=4.8), and the energy storage element  360  is cutoff from the load when the voltage reaches 4.4 volts (V.sub.off=4.4) Given these values we calculate C.sub.on and C.sub.off. C on=V on V ref=4.8 4.0=1.2, .times. and C off=V off V ref=4.4 4.0=1.0. After choosing 10 K.OMEGA. for R.sub. 330 , we can calculate R.sub. 335  and R.sub. 337  as follows: R  335 =C off*R  330  C on*(C off−1)=1.1*10.times. .times. K .times. .times. .OMEGA. 1.2*(1.1−1)=91.67.times. .times. K .times. .times. .OMEGA., .times. and R  337 =C off*R  330  C on−C off=1.1*10.times. .times. K .times. .times. .OMEGA. 1.2−1.1=110.times. .times. K .times. .times. .OMEGA.. 
     It can be easily verified that, using the above values, the voltage at the input  322  will be 4.0 volts when (1) V.sub.cc=4.8 volts on ramp-up, and (2) V.sub.cc=4.4 volts during discharge. 
     The circuits described above can be coupled with a voltage regulator or a DC-to-DC converter to provide longer ride-through periods.  FIG. 5  illustrates a circuit  500  implementing one such arrangement. 
     Most components of the circuit  500  are similar or identical to components of the circuit  100  of  FIG. 1 , and are interconnected in the same fashion. In one variation, circuit  500  does not have an optional current limiting resistor between an output  521  of a differential high-gain device  520  and control input  583  of a switching device  580 , such as the resistor  140  in  FIG. 1 . Second, power supply  560  of the circuit  500  does not power the load directly, but through a second power supply  590 . In the illustrated embodiment, the power supply  590  is a 5 volt regulator, while the power supply  560  is a 12 volt supply. In other variants, the supply  590  is a high-efficiency DC-to-DC voltage converter. 
     Operation of the circuit  590  is predictable from the discussion relating to the circuit  100 . On power-up, the circuit  500  prevents the current charging the energy storage device  510  from exceeding a limit current I.sub. 1 , which can be determined from this equation: 
         I 1 =Vcc*R 535 R 550*( R 530+ R 535).  (6)
 
     The last equation is the same as equation (1), with reference numerals of  FIG. 5  substituted for those of  FIG. 1 . Once voltage of the 12 volt supply  560  exceeds the operating voltage of the supply  590  by a specified regulator drop-off voltage, the supply  590  provides its nominal output voltage to a load  599 . A regulator&#39;s drop-off voltage is typically of the order of 0.5 volts, with low drop-off regulators offering even lower drop-off voltages. 
     If the output voltage of the supply  560  drops fails, the energy storage element  510  begins to provide power to the supply  590 , which continues to power the load  599 . As the energy storage element  510  discharges, its voltage also drops, but remains sufficient for the supply  590  to function normally for a period of time. The length of the period of time is of course a measure of the ride-through capability offered by the circuit  500 . 
     The ride-through period provided by the circuit  500  is extended because of the relatively large difference between the operating voltages of the power supplies  560  and  590 . The voltage difference is 7 volts in this example, but need not be limited to any particular number. When the energy storage element  510  is a capacitor (or a combination of several capacitors), the ride-through period is extended even more effectively than when the energy storage is provided by a battery. The reason for this enhanced ride-through capability is that the discharge curve for a capacitor under a constant current load is a straight line. In contrast, a battery&#39;s voltage remains relatively constant until late in the discharge cycle, and then drops abruptly. Because the circuit  500  allows a capacitor used as the energy storage element  500  to discharge more deeply, it uses a higher proportion of the energy stored in the capacitor for ride-through enhancement. 
     The principles underlying enhanced ride-through protection provided by the circuit  500  are not limited to the use of a variant of the basic current limiting circuit  100  in combination with dual power supplies. In fact, dual power supplies can be used with any of the other circuits described in this document, and with other equivalent or similar circuits.  FIG. 6  illustrates, in a high-level manner, such generalized arrangement of a current limiting circuit  601 , high voltage power supply  660 , low voltage power supply  690 , and energy storage element  610 . 
     This document describes in considerable detail the inventive circuits and methods for limiting charging currents drawn from power supplies, and for enhancing power supply ride-through capability. This was done for illustration purposes only. Neither the specific embodiments of the invention as a whole, nor those of its features limit the general principles underlying the invention. In particular, the invention is not limited to the specific components and component values described, or to particular applications. The specific features described herein may be used in some embodiments, but not in others, without departure from the spirit and scope of the invention as set forth. Many additional modifications are intended in the foregoing disclosure, and it will be appreciated by those of ordinary skill in the art that in some instances some features of the invention will be employed in the absence of a corresponding use of other features. The illustrative examples therefore do not define the metes and bounds of the invention and the legal protections afforded the invention, which function is served by the claims and their equivalents.