Abstract:
A capacitor array circuit having at least two capacitors, switching circuitry coupled to the capacitors and to input, output and common nodes and control circuitry. The control circuitry operates to sequentially switch the array through three different states so that a voltage is developed across each of the capacitors which is at a fixed value proportional to a voltage present at the input node. The fixed and thus determinate voltage drop across each of the capacitors operates to define voltages at any nodes intermediate the capacitors thereby, among other things, insuring reliable operation of the capacitor array circuit.

Description:
BACKGROUND OF THE INVENTION 
     1. Field of the Invention 
     The present invention relates generally to electrical circuits and in particular to switched capacitor circuits for use in DC-DC converters and the like. 
     2. Related Art 
     DC-DC converters are frequently used when a DC power source, such as a battery, is used to power an electrical device, such as a cellular telephone, designed to operate at a DC voltage level different than that of the DC power source. One typical DC-DC converter utilizes a switched capacitor array circuit which includes a plurality of capacitors and electronic switching circuitry for switching the capacitors into various configurations. An exemplary DC-DC converter which utilizes such a switched capacitor array is disclosed in U.S. Pat. No. 4,451,743 entitled “DC-DC Voltage Converter”. 
     DC-DC voltage converters having switched capacitor arrays usually have fairly high conversion efficiency and can be implemented in integrated circuit form. However, there is an increasing demand for DC-DC converters capable of even high efficiency operation. The present invention is advantageous in that high efficiency operation is achieved. This and other advantages of the present invention will become apparent to those skilled in the art upon a reading of the following Detailed Description of the Invention together with the drawings. 
     SUMMARY OF THE INVENTION 
     A capacitor array circuit for use in a DC-DC converter and the like is disclosed. The array circuit includes at least two capacitors and typically three capacitors. Switching circuitry, such as transistor switches, is coupled to the capacitors and to the input and output nodes of the array together with a third node, typically the circuit common. 
     The array circuit further includes control circuitry coupled to the switching circuitry for sequentially switching the array through first, second and third differing states. The capacitor configurations produced in each of the states will be such that a voltage is developed across each of the capacitors that will be fixed relative to voltages present at the input, output and third nodes. Stated in other terms, the voltage across the capacitors is forced to a fixed proportion of the voltage at the input node. Thus, for example, should the input voltage be at voltage Vin, the voltage across the capacitors will be approximately K(Vin) where K is a constant. 
     One aspect of the subject invention is that the three differing states provides a large number of potential gain configurations using a reduced number of capacitors and transistor switches. The large number of high gain configurations enables higher operating efficiency. The fixed voltages across each of the capacitors permits, for example, the capacitors to be connected in series in one or more of the states, with the high impedance node intermediate the capacitors being at a known and controllable voltage to ensure proper operation. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS. 
     FIG. 1 is a simplified diagram of a prior art DC-DC converter which utilizes a switched capacitor array. 
     FIG. 2 is a schematic diagram of an exemplary prior art switched capacitor array of the type which can be used in the FIG. 1 DC-DC converter. 
     FIGS. 3A and 3B are equivalent circuits of the FIG. 2 switched capacitor array when the array is switched to a first mode and a second mode, respectively. 
     FIG. 4 is a first embodiment of a switched capacitor array in accordance with the present invention. 
     FIGS. 5A,  5 B and  5 C are equivalent circuits of the FIG. 4 array when switched to first, second and third modes (states) of operation, respectively. 
     FIGS. 6A,  6 B and  6 C are waveforms for three non-overlapping clocks which control switching of the FIG. 4 array to the first, second and third operating states, respectively. 
     FIG. 7 is a second embodiment of a switched capacitor array in accordance with the present invention. 
     FIGS. 8A,  8 B,  8 C and  8 D are waveforms for four non-overlapping clocks used to control switching of the FIG.  7  and FIG. 10 arrays to first, second, third and fourth operating states, respectively. 
     FIGS. 9A,  9 B,  9 C and  9 D are equivalent circuits of the FIG. 4 array when switched to first, second, third and fourth modes or states of operation, respectively. 
     FIG. 10 is a third embodiment of a switched capacitor array in accordance with the present invention. 
     FIGS. 11A,  11 B and  11 C are equivalent circuits of the FIG. 10 array when switched to first, second and third states of operation, respectively, and which produce a gain Gsc of −3. 
     FIGS. 12A and 12B are equivalent circuits of the FIG. 10 array when switched to first and second states of operation, respectively, and which produce a gain Gsc of −2. 
     FIGS. 13A,  13 B,  13 C and  13 D are equivalent circuits of the FIG. 10 array when switched to first, second, third and fourth states of operation, respectively, and which produce a gain Gsc of −3/2. 
     FIGS. 14A and 14B are equivalent circuits of the FIG. 10 array when switched to first and second states of operation, respectively, and which produce a gain Gsc of −1. 
     FIGS. 15A,  15 B,  15 C and  15 D are equivalent circuits of the FIG. 10 array when switched to first, second, third and fourth states of operation, respectively, and which produce a gain Gsc of −2/3. 
     FIGS. 16A,  16 B and  16 C are equivalent circuits of the FIG. 10 array when switched to first, second and third states of operation, respectively, and which produce a gain Gsc of −1/2. 
     FIGS. 17A,  17 B,  17 C and  17 D are equivalent circuits of the FIG. 10 array when switched to first, second, third and fourth states of operation, respectively, and which produce a gain Gsc of −1/3. 
     FIGS. 18A,  18 B,  18 C and  18 D are equivalent circuits of the FIG. 10 array when switched to first, second, third and fourth states of operation, respectively, and which produce a gain Gsc of 1/4. 
     FIGS. 19A,  19 B,  19 C and  19 D are equivalent circuits of the FIG. 10 array when switched to first, second, third and fourth states of operation, respectively, and which produce a gain Gsc of 1/3. 
     FIGS. 20A,  20 B,  20 C and  20 D are equivalent circuits of the FIG. 10 array when switched to first, second, third and fourth states of operation, respectively, and which also produce a gain Gsc of 1/3. 
     FIGS. 21A,  21 B,  21 C and  21 D are equivalent circuits of the FIG. 10 array when switched to first, second, third and fourth states of operation, respectively, and which produce a gain Gsc of 2/5. 
     FIGS. 22A,  22 B,  22 C and  22 D are equivalent circuits of the FIG. 10 array when switched to first, second, third and fourth states of operation, respectively, and which also produce a gain Gsc of 2/5. 
     FIGS. 23A,  23 B and  23 C are equivalent circuits of the FIG. 10 array when switched to first, second and third states of operation, respectively, and which produce a gain Gsc of 1/2. 
     FIGS. 24A,  24 B and  24 C are equivalent circuits of the FIG. 10 array when switched to first, second and third states of operation, respectively, and which also produce a gain Gsc of 1/2. 
     FIGS. 25A,  25 B,  25 C and  25 D are equivalent circuits of the FIG. 10 array when switched to first, second, third and fourth states of operation, respectively, and which also produce a gain Gsc of 3/5. 
     FIGS. 26A,  26 B and  26 C are equivalent circuits of the FIG. 10 array when switched to first, second and third states of operation, respectively, and which also produce a gain Gsc of 2/3. 
     FIGS. 27A,  27 B,  27 C and  27 D are equivalent circuits of the FIG. 10 array when switched to first, second and third states of operation, respectively, and which also produce a gain Gsc of 3/4. 
     FIGS. 28A and 28B are equivalent circuits of the FIG. 10 array when switched to first and second states of operation, respectively, and which produce a gain Gsc of 1. 
     FIG. 29 is an equivalent circuit of the FIG. 10 array which also produces a gain Gsc of 1. 
     FIGS. 30A,  30 B,  30 C and  30 D are equivalent circuits of the FIG. 10 array when switched to first, second, third and fourth states of operation, respectively, and which also produce a gain Gsc of 4/3. 
     FIGS. 31A,  31 B and  31 C are equivalent circuits of the FIG. 10 array when switched to first, second and third states of operation, respectively, and which produce a gain Gsc of 3/2. 
     FIGS. 32A,  32 B,  32 C and  32 D are equivalent circuits of the FIG. 10 array when switched to first, second, third and fourth states of operation, respectively, and which produce a gain Gsc of 5/3. 
     FIGS. 33A and 33B are equivalent circuits of the FIG. 10 array when switched to first and second states of operation, respectively, and which produce a gain Gsc of 2. 
     FIGS. 34A,  34 B,  34 C and  34 D are equivalent circuits of the FIG. 10 array when switched to first, second, third and fourth states of operation, respectively, and which produce a gain Gsc of 5/2. 
     FIGS. 35A,  35 B,  35 C and  35 D are equivalent circuits of the FIG. 10 array when switched to first, second, third and fourth states of operation, respectively, and which also produce a gain Gsc=5/2. 
     FIGS. 36A and 36B are equivalent circuits of the FIG. 10 array when switched to first and second states of operation, respectively, and which produce a gain Gsc of 3. 
     FIGS. 37A,  37 B and  37 C are equivalent circuits of the FIG. 10 array when switched to first, second and third states of operation, respectively, and which produce a gain Gsc of 3. 
     FIGS. 38A,  38 B, and  38 C are equivalent circuits of the FIG. 10 array when switched to first, second, third and fourth states of operation, respectively, and which produce a gain Gsc of 4. 
     FIGS. 39A,  39 B,  39 C and  39 D are tables showing the various switch positions of the FIG. 10 array and the corresponding gains Gsc which result. 
     FIGS. 40A,  40 B,  40 C and  40 D are waveforms for alternative non-overlapping clocks including first and second clock phases, each having two states, used to control switching of the FIG.  7  and FIG. 10 arrays to first, second and third operating states, respectively. 
     FIGS. 41 A-C show three states of another array. 
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
     Referring to the drawings, FIG. 1 is a block diagram of a typical prior art DC-DC voltage converter  20 . Converter  20  includes a switched capacitor array circuit  22 , the details of which are shown in FIG.  2 . Array circuit  22  includes a pair of capacitors A and B which are connected into one of two operating modes by way of transistor switches T 1 A, T 2 A and T 3 A together with transistor switches T 1 B, T 2 B, T 3 B and T 4 B. The transistor switches are preferably implemented using P or N type MOS depending upon the polarity and magnitudes of the voltages being switched. In some circumstances it is preferred that both P and N type transistors be used if the voltages vary over a relatively wide range. In that case, the two transistors are connected in parallel and are driven by complementary polarity drive signals. 
     The drive signals for driving the transistor switches in the array  22  are generated by a switch driver circuit  24 . Driver circuit  24  provides a set of drive signals to the seven transistor switches of array  22 . During a first phase, switches T 1 A, T 2 A and T 3 A are turned on, with the remaining switches being turned off. The resultant equivalent circuit is shown in FIG.  3 A. Switch T 1 A operates to connect the “+” terminal of capacitor A to node In, switch T 3 A operates to connect the remaining terminal of capacitor A to the “+” terminal of capacitor B and switch T 2 A connects the remaining terminal of capacitor B to ground. Note that a capacitor terminal is considered to be “facing” a node (or circuit common or ground) if the capacitor terminal is connected directly to the node or connected indirectly through one or more additional capacitors. Thus, the “+” terminal of capacitor A is facing node In whereas the other terminal of capacitor A is facing ground. Further, the “+” terminal of capacitor B is also facing node In, with the remaining capacitor B terminal facing ground. 
     During the second phase, transistors T 1 A, T 2 A and T 3 A are turned off, followed by switches T 1 B, T 2 B, T 3 B and T 4 B being turned on. The resultant equivalent circuit is shown in FIG.  3 B. The four conductive switches operate to connect capacitor A and B in parallel between nodes In and Out, with the “+” terminals facing the Out node. At the end of the second phase, driver circuit  24  switches the transistors back to the first phase shown in FIG. 3A, with the array alternating between the two phases. 
     The capacitor array provides a gain Gsc which can be determined by inspecting the equivalent circuits of FIGS. 3A and 3B. In the first phase, the total voltage drop across capacitors A and B is equal to the voltage present at node In, voltage Vin (FIG.  1 ). Voltage Vin is produced by a power source such as a battery or the like. Thus, the voltage across the capacitors can be expressed by the following equation: 
     
       
           V in =V   A   +V   B   (1) 
       
     
     where V A and V B  are the voltages across capacitors A and B, respectively. 
     In the second phase, the capacitors are connected in parallel between nodes In and Out, with the “+” terminals facing node Out. As can be seen in FIG. 1, output voltage Vout is produced at node Out. Assuming that the charge on the capacitors has been conserved, the voltages across the capacitors can be expressed by the following equation: 
     
       
           V   A   =V   B   =V out− V in  (2) 
       
     
     Solving equations (1) and (2) simultaneously, it can be seen the Vout=3/2Vin, with the gain Gsc (Vout/Vin) thus being 3/2. 
     Referring again to FIG. 1, the output of the array  22  is connected to a holding capacitor CH and to a load (not shown). The holding capacitor CH is periodically charged by the array to compensate for the charge removed by virtue of current flow to the load. If the rate at which the array is switched between the two phases is relatively low, the array will not have sufficient time to replace the charge removed from the holding capacitor CH. Thus, charge will not be conserved between the two phases so that voltage Vout will be less than Vin times the gain of the array Gsc. As will be explained, the regulation circuitry of the FIG. 1 converter relies upon this aspect of the switched capacitor array to accomplish regulation. 
     The FIG. 1 converter includes a comparator circuit  26  which compares the magnitude of voltage Vout to a reference voltage produced by a reference circuit  28 , with the reference voltage magnitude being equal to the desired output voltage magnitude. The comparator circuit output drives a voltage to frequency converter  30  which in turn controls the rate at which the switch driver circuit  24  switches the array  22  between the two phases. If Vout is too large, the output of comparator circuit  26  will drop thereby causing the frequency of the converter  30  output to drop. Assuming that a load is connected to the converter output, the reduction in clock rate will cause voltage Vout to drop. Conversely, if Vout is too small, the clock rate is increased thereby increasing Vout. 
     In order for regulation to occur, the desired value of Vout must be smaller than input Vin times the gain of the array Gsc. Assuming, for example, that Vin is +3.5 volts, the array gain Gsc of 3/2 requires that the target value of Vout be less than +5.25 volts (3.5 volts×3/2). If the target value is exactly +5.25 volts, the converter will have essentially no output current capability, with the output current capability increasing if the desired Vout, set by the reference voltage generator, is set lower than +5.25 volts if the input is higher than +3.5 volts. 
     The overall efficiency of the converter  22  is reduced by an amount proportional to the extent that the actual output voltage magnitude exceeds the product of Gsc times the input voltage Vin. Thus, it is desirable from an efficiency point of view, that the array operate with as small a gain Gsc, for given values of Vout and Vin, needed to provide the required minimum output current drive capability. Prior to the present invention, switched capacitor array architectures capable of providing differing values of Gsc have been relatively complex to implement. A relatively large number of transistor switches have been required which results in a large die area. If the switches are made small to conserve die area, the on resistance of the switches becomes large thereby decreasing efficiency. Even if die area is sacrificed and the switches are made large, the charge current required to turn the switches on and off becomes significant and contributes directly to the inefficiency of the converter. The prior art approaches have also typically required a relatively large number of capacitors and a relatively large number of pins thereby increasing costs and hampering miniaturization. 
     FIG. 4 depicts a switched capacitor array  32  for use in a converter in accordance with one embodiment of the invention. As will be explained in greater detail, array  32  is capable of being switched to a large number of gain. (Gsc) configurations, particularly in view of the relatively low number of capacitors and transistor switches utilized in the array. If less than all of the gain configurations are needed for a particular converter application, those switches and capacitors that are not utilized can be eliminated thereby further reducing the part count. 
     Array  32  includes two capacitors C 2  and C 3  which are typically of the same value. However, as will be explained, accurate gain values (Gsc) will not depend upon matching of the capacitor values. FIGS. 6A,  6 B and  6 C depict non-overlapping clock waveforms for controlling the timing of the switching of array  32 . The waveforms can be characterized as providing first and second phases. The first phase (clock P 1  of FIG. 6A) has a single state, with the second phase clocks (FIGS. 6B and 6C) having a first state P 2 A and a second state P 2 B. Each of the three clock states P 1 , P 2 A and P 2 B will cause the array  32  to switch to one of three array modes or states for a given array gain configuration, a given value of Gsc. For some gain configurations, less than the three clock states may be used, as will be explained. 
     As can be seen from FIGS. 6A,  6 B and  6 C, the array is switched to a the first state by clock P 1  and then to the second state by clock P 2 A. The array is then switched back to the first state, again by clock P 1 , and then to the third state by clock P 2 B. Finally, the array is switched from the third state back to the first state by clock P 1 , with this sequence being repeated. Thus, it can be seen that the array is switched to the first state intermediate switching to the second and third states. In a typical application, a state machine (not depicted) that is part of the switch driver circuit  24  (FIG. 1) is used to provide a particular gain state configuration by turning on and turning off selected ones of the transistor switches S 3  through S 7  and S 9 . 
     FIGS. 5A,  5 B and  5 C are equivalent circuits of the FIG. 4 array  32  configured to produce a gain Gsc of 3/2. When clock P 1  goes active at time T 0  (FIG.  6 A), all of the transistor switches of array  32  are first turned off due to the non-overlapping aspect of clocks P 1 , P 2 A and P 2 B. Selected transistor switches S 3  and S 9  are then turned on as indicated by the FIG. 5A circuit so as to connect capacitors C 2  and C 3  in series between the input node Vin and ground, with the polarity of the capacitors being as depicted. The transistor switches are then turned off and, when P 2 A goes active at time T 1  (FIG.  6 B), switches S 7  and S 6  are turned on thereby connecting capacitor C 3  between the input node Vin and the output node Vout. Array  32  is then in the second state. One terminal capacitor C 2  remains connected, with the remaining terminal being left open so that capacitor C 2  is effectively out of the FIG. 5B equivalent circuit. Array  32  is then switched back to the first state when P 1  again goes active at time T 2  so that the array is back to the FIG. 5A configuration. Then, at time T 3 , clock P 2 A goes active switching the array to the third state shown in FIG. 5C with capacitor C 2  connected between the input node Vin and the output node Vout. Only one terminal of capacitor C 3  remains connected to that the capacitor is not part of the FIG. 5C equivalent circuit. At time T 4 , clock P 1  again goes active, with the sequence being repeated. 
     An important aspect of the subject invention is to force the voltages across each of the capacitors to a value which is fixed in terms of the voltages present at the input and output nodes relative to the common node. When the voltages are forced to a known value, the voltages that appear on the nodes intermediate the capacitors, the voltages present on the transistor switches, to a known values. In most cases, the voltages across each of the capacitors is set to the same value in terms of the input and output nodes Vin and Vout. 
     In the first state of FIG. 5A, it can be seen by inspection that the total voltage drop across capacitors C 2  and C 3  is equal to the input voltage Vin. However, the node intermediate capacitors C 2  and C 3  is a high impedance node which could otherwise assume any one of a wide range of voltages other than a voltage equal to Vin/2. This would be true regardless of the relative sizes of the two capacitors. However, the second and third states of FIGS. 5B and 5C connect the two capacitors between the same two nodes thereby insuring that the voltage drop across the capacitors are nominally equal and which are at a fixed value relative to the input voltage Vin. Since, as will be described below, there is a fixed relationship between the voltage Vin and output voltage Vout (Gsc), the voltage across the two capacitors can be also be considered to be fixed relative to the output voltage Vout. Thus, the high impedance node intermediate the two capacitors in the first state will not be at some indeterminate voltage, but rather, will be at a voltage which remains substantially equal to Vin/2, ignoring the change in voltage due to discharge to a load during the second and third states. 
     Assuming that the voltage drop across each capacitor is the same, inspection of FIG. 5A shows that the voltage across capacitor C 2  (or C 3 ) is Vin/2. It can then be seen by inspection of FIG. 5B (or FIG. 5C) that the output voltage Vout can be expressed as the sum of Vin and Vin/2 so that the gain is as follows: 
     
       
         Gsc= V out/ V in=3/2  (3) 
       
     
     It would appear that the second and third states could be combined to a single state where capacitors C 2  and C 3  are both connected in parallel between nodes Vin and Vout at the same time as shown in prior art FIG.  3 B. However, an examination of array  32  indicates that there are an insufficient number of transistor switches to provide this combined state. This illustrates an important feature of the present invention, which is to maximize the number of potential gains Gsc while minimizing the number of capacitors and transistor switches. As will become apparent, the basic structure of the array of FIG. 32 together with the switch control circuitry can be modified, depending upon the needed gain Gsc, by adding capacitors and switches and by eliminating switches. 
     The array  34  of FIG. 7 is an expansion of array  32  of FIG. 4. A third capacitor C 1  is added to capacitors C 2  and C 3  of array  32  along with transistor switches S 1 , S 2  and S 14 . In addition, switch S 3  of the FIG. 4 array  32  has been eliminated. Array  34  can be clocked so that the array will have up to four states. For example, a first phase clock P 1  as shown in FIG. 8A can be used having a single state together with a second phase clock P 2  having three states, including P 2 A (FIG.  8 B), P 2 B (FIG. 8C) and P 2 C (FIG.  8 D). Again, the second phase clock is interleaved with the first phase clock so that, for example, after an active clock P 1 , clock P 2 A goes active, followed by clock P 1  again, followed by clock P 2 B, followed by clock P 1  and then followed by clock P 2 C. 
     FIGS. 9A,  9 B,  9 C and  9 D are equivalent circuits based upon the FIG. 7 array for the first, second, third and fourth states, respectively, which produces a gain Gsc of 5/3. During the first phase, when P 1  is active, the transistor switches are controlled to connect capacitors C 1 , C 2  and C 3  in series between the input node Vin and ground with the polarity shown in FIG.  9 A. This is accomplished by turning on transistor switches S 1 , S 13  and S 9  of the FIG. 7 array  34 . During the second phase, first state, when clock P 2 A is active, FIG. 9B shows that switches S 7 , S 4  and S 13  are turned on so that capacitors C 3  and C 2  are connected in series between Vin and Vout with the positive terminal of the capacitors facing node Vout. 
     When clock P 2 A goes inactive, clock P 1  again goes active thereby returning array  34  back to the configuration of FIG.  9 A. Next, clock P 2 B goes active producing the configuration of FIG. 9C, with switches  5 , S 13  and S 2  being conductive. In this configuration, capacitors C 2  and C 1  are connected in series between nodes Vin and Vout. Array  34  returns to the FIG. 9A configuration when P 1  goes active and then switches to the FIG. 9D configuration when P 2 C goes active (FIG.  8 D). Switches S 7 , S 14  and S 2  are turned on thereby connecting capacitors C 3  and C 1  in series between nodes Vin and Vout. 
     It can be seen that by switching the three capacitors C 1 , C 2  and C 3  in three pairs (C 3 /C 2 , C 2 /C 1  and C 3 /C 1 ) in series between the input node Vin and the output node Vout as shown in FIGS. 9B,  9 C and  9 D, a voltage will be produced across each of the capacitors that is fixed in terms of the voltages present at the input and output nodes. These voltages, VC 1 , VC 2  and VC 3 , the voltage drops across capacitors C 1 , C 2  and C 3 , respectively, and can be expressed as follows: 
      ( V out− V in)= V C 2 + V C 3 = V C 2 + V C 1 = V C 3 + V C 1   (4) 
     or 
     
       
           V C 1 = V C 2 = V C 3 =( V out− V in)/2  (5) 
       
     
     By inspection of FIG. 9A, it can be seen that the following applies: 
     
       
           V in= V C 1 + V C 2 + V C 3   (6) 
       
     
     Combining equations (5) and (6) establishes that the gain Gsc=Vout/Vin=5/3. Since a known voltage is produced across each of the three capacitors, the voltages at the various nodes intermediate the capacitors, such as the voltages at switches S 13  of FIG. 9A, will be at a relatively fixed value to ensure proper operation of the array circuit. Note also that other gains Gsc can be obtained using array  34  of FIG. 7 as will become more apparent. 
     FIG. 10 is an array  36  which is a further expansion of array  34  (FIG.  7 ), which itself is an expansion of array  32  (FIG.  4 ). Array  36  is similar to array  34  with the addition of more transistor switches so as to provide a greater number of potential gains Gsc. Array  36  is controlled by the FIG. 8A,  8 B,  8 C and  8 D clocks or modification of the clocks. 
     FIGS. 39A through 39D are tables setting forth the large number of gains Gsc that can be obtained using array  36 . Many of the entries will also be applicable to the more basic arrays  32  and  34 . The left-most column contains the switch numbers S 1  through S 14  of the array, with the remaining columns each corresponding to a particular gain Gsc. The row adjacent a particular switch shows that state of the switch for each of the gains Gsc. The symbol P 1  indicates that the switch is conductive when clock P 1  (FIG. 8A) is active, the symbol P 2 A indicates that the switch is conductive when clock P 2 A (FIG. 8B) is active and symbols P 2 B and P 2 C indicate that the switch is conductive when clocks P 2 B and P 2 C (FIGS. 8C and 8D) are active, respectively. As will be described, certain gains will use less than four states created by the four clocks P 1 , P 2 A, P 2 B and P 2 C. In that event, the clocks shown in FIGS. 6A,  6 B and  6 C may be used and possibly other clocks. 
     Some exemplary gain configurations will now be discussed. Assume that array  36  is to operate with a gain Gsc of −3. The table of FIG. 39A shows for Gsc=−3 that the switches are controlled by clocks P 1 , P 2 A and P 2 B as shown in FIGS. 6A,  6 B and  6 C so that there are three array states. When clock P 1  is active, FIG. 39A indicates that switches S 8 , S 12  and S 13  are turned on, with the remaining switches being off. This produces the equivalent circuit of FIG. 11A with capacitors C 1 , C 2  and C 3  being connected in series between the output node Vout and ground, with the “+” capacitor terminals facing the ground connection. When clock P 2 A is active, FIG. 39A indicates that switches S 1 , S 5 , S 9  and S 11  are on, with the remaining switches being off. This produces the equivalent circuit of FIG. 11B where capacitors C 1  and C 3  are connected in parallel between the input node Vin and ground, with the “+” terminals facing the input node. Finally, when clock P 2 B is active, capacitor C 2  is connected between the input node Vin and ground, with the “+” terminal facing the input node. This is accomplished turning on switches S 3 , S 10  and S 13  with the remaining switches being off. Thus, switches S 2 , S 4 , S 6 , S 7  and S 14  are not used in this configuration and can be deleted from array  36  in the event a gain Gsc of −3 is the only desired gain. 
     The circuits of FIGS. 11B and 11C operate to set the voltage drop across all three capacitors C 1 , C 2  and C 3  to be equal to Vin. The capacitors are reversed when connected as shown in FIG. 11A so that inspection reveals that Vout is equal to −3Vin thereby providing a gain Gsc=Vout/Vin=−3. Note that one of the states could be eliminated by combining the circuits of FIGS. 11B and 11C so that all three capacitors are connected in parallel between the input node Vin and ground in a single state. However, this would require that the “+” terminal of capacitor C 3  be capable of being disconnected from the non “+” terminal of capacitor C 2  so that C 2  and C 3  can both be connected in parallel with “+” terminals connected to the input node. Thus, an additional switch would be required to provide this disconnect function. 
     FIGS. 12A and 12B are equivalent circuits of array  36  which utilizes only two of the three capacitors and two clocks P 1  and P 2  to produce a Gsc=−2. This can be seen in FIG. 39A table. Clock P 1  is shown in FIG.  8 A. Clock P 2  can readily be produced from the circuitry that produces clocks P 2 A, P 2 B and P 2 C since P 2  is simply all three of these clocks “ORed” together. The parallel connection of FIG. 12B establishes that the voltage across capacitors C 1  and C 3  is Vin so that the two capacitors, when connected in series, with the polarity shown in FIG. 12A, produces and output voltage Vout equal to −2(Vin) so that Gsc=−2. 
     It should be noted that the use of two capacitors connected electrically as shown in FIGS. 12A and 12B to provide a gain Gsc=−2 is conventional since only two states are used. However, it is not conventional to produce that gain as shown in FIGS. 12A and 12B using an array such as array  36 . 
     The FIG. 39A table also shows the switch closures necessary to provide a gain Gsc=−3/2. The first and second phase clocks each have two states so that non-overlapping clocks P 1 A, P 1 B, P 2 A and P 2 B are utilized as shown in FIGS. 40A,  40 B,  40 C and  40 D, respectively. Note that these clocks can be readily produced from the clocks of FIGS. 8A,  8 B,  8 C and  8 D. 
     As shown in the FIG. 13A, and as indicated by the table of FIG. 39A, switches S 1 , S 10  and S 13  are turned on when clock P 1 A, the first state of the first clock phase, is active. This causes capacitors C 1  and C 2  to be connected in series between the input node Vin and ground. During the second state of the first clock phase, when clock P 1 B is active, switches S 5  and S 9  are turned on thereby connecting the third capacitor C 3  between the input node and ground. During the first state of the second clock phase, when clock P 2 A is active, switches S 8 , S 11  and S 13  are turned on so that capacitors C 2  and C 3  are connected in series between the output node Vout and ground as shown in FIG.  13 C. Finally, during the second state of the second phase, when clock P 2 B is active, the appropriate switches are turned on to connect capacitors C 1  and C 3  in series between the output node Vout and ground as shown in FIG.  13 D. 
     The gain configuration of FIGS. 13A-13D differ from the previously described configurations in that the voltages across capacitors C 1 , C 2  and C 3  are not equalized. However, as was the case of the previously described embodiments, the voltage across each of the capacitors is forced to a predetermined value related to Vin and Vout since there is a fixed relationship between Vin and Vout. Stated in different terms, the voltage across the capacitors is set to a fixed proportion of the input voltage Vin. 
     It can be seen by inspection of FIGS. 13A-13D that the voltage across each capacitors is fixed in terms of Vin and Vout therefore the voltage at the high impedance nodes intermediate the capacitors in FIGS. 13A,  13 C and  13 D will be at a known value which is a function of Vin and Vout. Since voltage VC 3 , the voltage across capacitor C 3 , is fixed at Vin (FIG.  13 B), the magnitude of voltage VC 2 , the voltage across capacitor C 2 , will be fixed at the sum of Vin and Vout (FIG.  13 C). Further, since voltage VC 3  is fixed at Vin, the magnitude of VC 1 , the voltage across capacitor C 1 , will also be fixed at the sum of Vin and Vout (FIG.  13 D). Thus, the voltage drop across capacitors C 1  and C 2  will both be equal in magnitude to Vin plus Vout and also to Vin/2 as indicated by FIG.  13 A. Taking the polarities of the voltages into account, the following represents the input voltage Vin as indicated by FIG.  13 A: 
     
       
           V in =VC   1 + VC   2   (7) 
       
     
     or 
     
       
           V in=(− V in− V out)+(− V in− V out)  (8) 
       
     
     Thus, Gsc=Vout/Vin=−3/2 as confirmed by the table of FIG.  39 A. 
     FIGS. 14A and 14B show the equivalent circuits for providing a gain Gsc=−1. As indicated by the FIG. 39A table, clock phases P 1  and P 2  are used. Typically, clocks P 2 A and P 2 B will be produced from a single state clock P 2 . In any event, the single state clock phase P 2  can be produced by “ORing” clocks P 2 A and P 2 B of FIGS. 6B and 6C together. During the first phase, when array  36  is in the first state, the voltage across capacitor C 1  is at Vin and during the second phase, when the array is in the second state, the voltage across capacitor C 1  is Vout so that Vin=Vout. A gain Gsc of −2/3 is produced by the gain configurations of FIGS. 15A,  15 B,  15 C and  15 D. The FIG. 15A equivalent circuit occurs during clock P 1  (FIG.  8 A), as indicated by the table of FIG. 39A, with the equivalent circuits of FIGS. 15B,  15 C and  15 D occurring during clocks P 2 A (FIG.  8 B), P 2 B (FIG. 8C) and P 2 C (FIG.  8 D), respectively. During the three states of the second clock P 2 , the three capacitors C 1 , C 2  and C 3  are connected in series, two at a time, between the input Vin and ground. As previously described in connection with FIGS. 9A,  9 B and  9 C, this forces the voltages across each of the three capacitors to a set value. The voltage across the three capacitors of FIGS. 15A,  15 B and  15 C can be expressed as follows: 
     
       
         − V out =VC   1 + VC   2 = VC   2 + VC   3 = VC   3 + VC   1   (9) 
       
     
     or 
     
       
           VC   1 = VC   2 = VC   3 =− V out/2  (10) 
       
     
     Thus, the voltages at all of the high impedance nodes intermediate the capacitors are known. By inspection of FIG. 15A, the input voltage Vin is as follows: 
     
       
           V in=−( VC   1 + VC   2 + VC   3 )=−3/2 V out  (11) 
       
     
     Thus, it can be seen from equation (11) that the gain Gsc=Vout/Vin=−2/3. 
     A similar analysis can be readily applied to the remaining configurations set forth in the tables of FIGS. 39A,  39 B,  39 D and  39 E and the corresponding equivalent circuits shown in the drawings. FIGS. 16A,  16 B and  16 C are the equivalent circuits for producing a gain Gsc=−1/2. Note that the voltages across capacitors C 1  and C 2  are equalized in the second and third states as shown in FIGS. 16B and 16C by first connecting capacitor C 1  between Vout and ground and then connecting capacitor C 2  between Vout and ground. 
     FIGS. 17A,  17 B,  17 C and  17 D are equivalent circuits of array  36  in first, second, third and fourth states, respectively, so as to provide a gain Gsc 1/3. The voltages are equalized to −Vout in the second, third and fourth states so that Vin is, based upon the first state, equal to −3(Vout) to provide the gain Gsc=Vout/Vin=−1/3. 
     FIGS. 18A,  18 B,  18 C and  18 D are equivalent circuits of array  36  in four states for producing a gain Gsc=1/4. As shown by the table of FIG. 39B, the circuit of FIG. 18A is produced when clock P 1  (FIG. 8A) is active, with the remaining three states being produced when clocks P 2 A, P 2 B and P 2 C (FIGS. 8B,  8 C and  8 D) are active. The voltages across the capacitors are equalized in the last three states to Vout. The circuit of FIG. 18A shows that Vout is equal to Vin −3(Vout) to achieve the gain of Gsc=1/4. 
     A gain Gsc of 1/3 is achieved by the four states represented by FIGS. 19A,  19 B,  19 C and  19 D. The capacitor voltages are equalized to Vout during the last three states (FIGS. 19B,  19 C and  19 D), with Vin set equal to 3(Vout) in the first state to provide the gain of 1/3. 
     An alternative configuration for providing a gain Gsc of 1/3 is shown in FIGS. 20A,  20 B,  20 C and  20 D. The capacitor voltages are equalized in the last three states (FIGS. 20B,  20 C and  20 D) to be equal to (Vin−Vout)/2. Inspection of FIG. 20A indicates that Vin is equal to 3(Vin−Vout)/2so that Gsc=Vout/Vin=1/3. 
     A gain Gsc of 2/5 is produced using the four states shown in FIGS. 21A,  21 B,  21 C and  21 D. By inspecting FIGS. 21B,  21 C and  21 D, it can be determined that the voltages across the capacitors are equalized to Vout/2. Inspection of FIG. 21A shows that Vout=Vin −3(Vout)/2 to provide the gain Gsc=Vout/Vin=2/5. 
     An alternative configuration for producing a gain Gsc of 2/5 is shown in FIGS. 22A,  22 B,  22 C and  22 D. As was the case for the gain of −3/2 previously described in connection with FIGS. 13A,  13 B,  13 C and  13 D, the voltages across the capacitors are not equalized, but the voltages are nevertheless forced to a known value. As indicated by FIG. 22B, the voltage across capacitor C 3  is forced to Vout during the second state of array  36 . This occurs during the second state of the first phase, clock P 1 B (FIG.  40 B), as indicated by the table of FIG.  39 B. During the third state, when clock P 2 A is active, capacitor C 3  is connected in series with capacitor C 2  between Vin and Vout thereby forcing the voltage across capacitor C 2  to a known value (VC 2 =Vin−2Vout). During the fourth state, when clock P 2 B is active, capacitor C 3  is connected in series with capacitor C 1  between Vin and Vout thereby forcing the voltage across capacitor C 1  to the same value as capacitor C 2  (VC 1 =Vin −2 Vout). During the first state when capacitors C 1  and C 2  are connected in series between Vout and ground (FIG.  22 A), the value of Vout is  2 (Vin−2 Vout) so that Gsc=Vout/Vin=2/5. 
     FIGS. 23A,  23 B and  23 C show the first, second and third states, respectively, of array  36  to produce a gain Gsc=1/2. The voltage across capacitors C 1  and C 3  are both set to (Vin−Vout) during the second state when clock P 2 A is active and during the third state when clock P 2 B is active. Thus, during the first state, when clock P 1  is active, the input voltage Vin=2(Vin−Vout) so that Gsc=Vout/Vin=1/2. 
     FIGS. 24A,  24 B and  24 C show the first, second and third states, respectively, of array  36  as an alternative method of producing a gain Gsc=1/2. The voltage across capacitors C 1  and C 3  are both set to Vout during the second state when clock P 2 A is active and during the third state when clock P 2 B is active. Thus, during the first state, when clock P 1  is active, the input voltage Vin=2Vout so that Gsc=Vout/Vin=1/2. 
     A gain Gsc=3/5 is provided by the four array states of FIGS. 25A,  25 B,  25 C and  25 D. As indicated by the table of FIG. 39B, the first state occurs when clock P 1  (FIG. 8A) is active, The last three states (FIGS. 25B,  25 C and  25 D) occur when clocks P 2 A (FIG.  8 B), P 2 B (FIG. 8C) and clock P 2 D (FIG. 8D) are active and function to equalize the three capacitor voltages to (Vin−Vout)/2. Thus, by inspection of FIG. 25A, it can be seen that Vout=3(Vin−Vout)/2. Thus Gsc=Vout/Vin=3/5. 
     A gain Gsc=2/3 is produced by switching array  36  to the three states shown in FIGS. 26A,  26 B and  26 C. 
     As indicated by the FIG. 39C table, the first, second and third states are produced when clock P 1  (FIG.  6 A), P 2 A (FIG. 6B) and P 2 B (FIG. 6C) are active. During the last two states, the voltages across capacitors C 1  and C 3  are equalized to (Vin−Vout). Thus, by inspection of the FIG. 26A state, it can be seen that Vout=2(Vin−Vout) so that Gsc=Vout/Vin=2/3. 
     FIGS. 27A,  27 B,  27 C and  27 D show the four states of array  36  that are active during clocks P 1 , P 2 A, P 2 B and P 2 C, respectively, to produce a gain Gsc=3/4. During the last three states, the voltage across each of the capacitors is set to (Vin−Vout). During the first state, inspection of FIG. 27A indicates that Vout=3(Vin−Vout) so that Gsc=Vout/Vin=3/4. 
     Two configurations of array  36  can be used to provide a gain Gsc of one. As indicated by FIGS.  28 A and  28 B, one approach is to set the voltage across capacitor C 1  to Vin during the first state and then the connect capacitor C 1  between the output node Vout and ground so that Vout is equal to Vin during the second state. The second approach is shown in FIG. 29 where switches S 1  and S 2  are closed when clock P 1  is active thereby connecting the input and output nodes Vin and Vout directly together. The holding capacitor (not depicted) will maintain the output voltage when clock P 2  is active. 
     FIGS. 30A,  30 B,  30 C and  30 D show four states of array  36  which will produce a gain Gsc=4/3. The voltages across the three capacitors are forced during the last three states to Vout−Vin. Thus, examination of the first state shown in FIG. 38A shows that Vin=3(Vout−Vin) so Gsc=Vout/Vin=4/3. 
     A gain Gsc of 3/2 is produced as shown by the three states of array  36  of FIGS. 31A,  31 B and  31 C. The voltages across capacitors C 1  and C 3  are set to Vin−Vout during the second and third states. The first state shown in FIG. 31A has the two capacitors connected in series between the input Vin and ground so that Vin=2(Vin−Vout) so that Vout/Vin is 3/2. 
     A gain Gsc of 5/3 is produced when array  36  is set to the four states shown in FIGS. 32A,  32 B,  32 C and  32 D. As indicated by the table of FIG. 39D, the last three states are produced when clocks P 2 A, P 2 B and P 2 C are active. This causes the voltage across each of the three capacitors to be equal to (Vout−Vin)/2. When the three capacitors are connected in series between input Vin and ground (FIG.  32 A), Vin=3(Vout−Vin)/2. Thus, Gsc=Vout/Vin=5/3. 
     FIGS. 33A and 33B depict the two states of array  36  for producing a gain Gsc of 2. As shown in the table of FIG. 39D, the first and second states are entered when single state clocks P 1  and P 2  are active, respectively. As previously noted, clock P 2  can be readily produced by “ORing” clocks P 2 A (FIG. 6B) and P 2 B (FIG. 6C) together. During either state, the capacitor voltage are equalized. In the second state the capacitor voltage are equal to (Vout−Vin) and in the first state, Vin=(Vout−Vin) so that Gsc=Vout/Vin 2. 
     Two approaches can be used to provide a gain Gsc of 5/2. FIGS. 34A,  34 B,  34 C and  34 D show one approach using four states of array  36  where the voltages across the three capacitors are not equalized but nevertheless are forced to a known value in terms of Vin and Vout. Clocks P 1 A (FIG. 40A) and P 1 B (FIG. 40C) are active during the first and second states of FIGS. 34A and 34B, respectively. The voltage across capacitor C 3  is set to Vin in the second state shown in FIG.  34 B. The voltage across C 2  and the voltage across C 1  will be equal to one another as can be seen by inspecting the states of FIGS. 34C and 34D and thus will each be equal to Vin/2 as can be seen by inspecting the state of FIG.  34 A. Thus, Vout=Vin+Vin/2+Vin, as indicated by either FIG. 34C or FIG. 34D, so as to produce a gain Gsc=Vout/Vin=5/2. 
     The second approach for providing a gain Gsc=5/2 is shown in FIGS. 35A,  35 B,  35 C and  35 D. The states of FIGS. 35B,  35 C and  35 D force the voltages across the three capacitors to all be equal to Vin/2. Inspection of FIG. 35A shows that Vout=Vin+3(Vin/2) so that Gsc=Vout/Vin=5/2. 
     FIGS. 36A and 36B show the two states of array  36  for providing a gain Gsc of  3 . The voltage across the two capacitors are equalized to Vin in the first state of FIG.  36 A. Inspection of FIG. 36B shows that Vout=Vin+2Vin so that Gsc=Vout/Vin=3. 
     Another technique for providing a gain Gsc of 3 is shown in FIGS. 37A,  37 B and  37 C. The first two states of FIGS. 37A and 37B force the voltage drop across each capacitor to be equal to Vin. Inspection of FIG. 37C shows that Vout=3Vin so that Gsc=Vout/Vin=3. 
     A gain Gsc of 4 is shown in FIGS. 38A,  38 B and  38 C. The first two states shown in FIGS. 38A and 38B cause the voltage drop across each of the three capacitors to be equal to Vin. Inspection of FIG. 38C shows that Vout=Vin+3Vin so that Gsc=Vout/Vin=4. 
     The subject invention is not limited to the particular capacitor arrays  32 ,  34  and  36 . Other arrays can be used which are switchable to more that two states and which operate to control the voltage across each capacitor to a known value in terms of voltages that appear on the array external nodes such as the input and output node voltages Vin and Vout and the ground node. This will cause any internal nodes, such as high impedance nodes intermediate series-connected capacitors, to be at a known voltage. One approach previously described is to connect the individual capacitor directly between two nodes to set the voltage across each capacitor as shown in FIGS. 38A and 38B, for example. Another approach previously described is to connect the three capacitors in series, two at a time, between two nodes, as shown in FIGS. 9B,  9 C and  9 D. A still further approach is to connect a first one of the capacitors directly between two external nodes as shown in FIG. 13B so that the first capacitor has a known voltage and to then connect the first capacitor in series with a second one of the remaining capacitors as shown in FIG. 13C to force the second capacitor to a known voltage. The first capacitor can then be connected in series with a third capacitor as shown in FIG. 13D so that the voltage across the third capacitor is a known voltage. 
     As a further example, FIGS. 41A,  41 B and  41 C show three states of another array, with the switches not being depicted, connected between external nodes X and Y. Nodes X and Y could, by way of example, be an input node Vin, output node Vout or ground. The array could, for example, be switched to the three states by clocks P 2 A, P 2 B and P 2 C of FIGS. 8B,  8 C and  8 D. Since all three of the capacitors are eventually connected in parallel with each other, the voltages across the three capacitors are made to be equal to one another. Inspection of any of FIGS. 41A,  41 B and  41 C shows that the voltage across each of the capacitors is a fixed value in terms of the voltages at the external nodes X and Y as follows: 
     
       
           VC   1 = VC   2 = VC   3 =( Vy−Vx )/2  (12) 
       
     
     Thus, when the capacitors are connected in a fourth state (not depicted), the voltage across each capacitor will be fixed even when the capacitors are connected in series with one another. 
     Thus, several embodiments of a switched capacitor array circuit and related method have been disclosed. Although these embodiments have been described in some detail, it is to be understood that certain changes can be made by those skilled in the art with out departing from the spirit and scope of the invention as defined by the appended claims.