Abstract:
The present invention introduces an integrated analog multiplier-divider circuit. The multiplier-divider block according to the present invention is ideal for use in the power factor correction (PFC) controllers of many switch-mode power supplies. The analog multiplier-divider according to the present invention is built with CMOS devices. Because of this, it has many advantages over prior-art multiplier-dividers. One important advantage is that the die-size and the cost can be reduced. Another important advantage of the multiplier-divider according to the present invention is substantially reduced temperature dependence.

Description:
BACKGROUND OF THE INVENTION 
   1. Field of the Invention 
   The present invention relates to the art of power supplies, and in particular to an analog multiplier-divider for a power factor correction (PFC) circuit. 
   2. Description of the Prior Art 
   There are many uses for analog multiplier-dividers in modern electronics. Multiplier-dividers produce an output signal that is proportional to a ratio of two or more input signals. The input and output signals can either be voltages or currents. 
   One common use of multiplier-dividers is in power factor correction (PFC) circuits. PFC circuits commonly use multiplier-dividers to generate a control signal based on the input current, the feedback signal, and the input voltage.  FIG. 1  demonstrates the use of an analog multiplier-divider in a PFC circuit. 
   There are many known ways of constructing analog multiplier-dividers, such as logarithmic amplifiers and antilog amplifiers. The implementation of a logarithmic amplifier normally uses the p-n junction volt-ampere characteristic; it is given by
 
 I   D   =I   0 ×[exp( V   D   /ηV   T )−1]  (1)
 
   where I 0  is the reverse saturation current; V D  is the forward bias voltage; η is the constant; V T =T/11,600 and T is the temperature ° K. Since the output current I D  is the exponential function of the forward bias voltage V D , the linear operating region is small. The book “Analog Integrated Circuit Design” by David A. Johns and Ken Martin (1997, pg. 366–367) teaches a known analog multiplier-divider. This particular multiplier-divider is also referred to as a four-quadrant multiplier. It is shown in  FIG. 2 . 
   The prior-art analog multiplier-divider shown in  FIG. 2  supplies an output current with an amplitude that is proportional to the product of a first input current and a current ratio. The current ratio is equal to the amplitude of a second input current divided by the amplitude of a bias current. The prior-art multiplier-divider shown in  FIG. 2  is built using bipolar transistor devices. 
   Many other known prior-art multiplier-dividers exist that are based on the principles of the prior-art multiplier-divider shown in  FIG. 2 . They all share the same disadvantages, to the extent that they are built using bipolar transistor devices. 
   One disadvantage of the prior-art multiplier-divider shown in  FIG. 2  is that it is a bipolar device. For many present-day applications, such as PFC circuits, integrated circuits manufactured using a bipolar process are not suitable, because their die-size are too large and the cost is too high. 
   Another disadvantage of the prior-art multiplier-divider shown in  FIG. 2  is that the output of the circuit varies significantly with temperature. The characteristic equations of bipolar transistors have high temperature coefficients. Thus, the output of the circuit is highly susceptible to temperature changes. 
   Another disadvantage of the prior-art multiplier-divider shown in  FIG. 2  is high power consumption. The prior-art multiplier-divider requires a constant non-zero biasing current to bias bipolar transistors in linear mode. This results in significant power consumption. 
   Another disadvantage of the prior-art multiplier-divider shown in  FIG. 2  is poor noise immunity. The prior-art multiplier-divider uses high-gain bipolar transistor devices. With such devices, even relatively small input signal distortion can result in significant output signal distortion. 
   Another disadvantage of the prior-art multiplier-divider shown in  FIG. 2  is that it has a narrow input range, limited to the linear operating region of bipolar transistors. Outside of this narrow input range, the multiplier-divider shown in  FIG. 2  is highly susceptible to distortion. 
   Therefore, there is a need for an improved analog multiplier-divider. In particular, there is a need for an improved analog multiplier-divider that has a smaller die size while being suitable for a wider range of operating temperatures. 
   SUMMARY OF THE INVENTION 
   The multiplier-divider according to the present invention produces an output signal in response to a first multiplier signal, a second multiplier signal and a divisor signal. The output signal is proportional to a product of the first multiplier signal and the second multiplier signal divided by a square of the divisor signal. 
   The multiplier-divider according to the present invention itself consists of two multiplier-divider stages cascaded together. A pulse generator is used to regulate the operation of the cascaded multiplier-divider stages. Each multiplier-divider stage consists of a charge-time control circuit, a linear charging block, and a sample-and-hold circuit. 
   The charge-time control circuit of each multiplier-divider stage produces a charge-time for the linear charging block. To perform division, the charge-time is modulated by a sawtooth signal, with a peak value proportional to the divisor signal. The length of the charge-time and a magnitude of a charge current are respectively determined in response to the first multiplier signal and the second multiplier signal of the multiplier-divider. The linear charging block of each multiplier-divider stage will be charged so that when sampled, it will output a voltage signal proportional to an appropriate ratio of the input signals. 
   Briefly, the multiplier-divider according to the present invention is built according to the principles of capacitor charge theory. The voltage across the capacitor is proportional to the product of the charge current and the charge time interval, and is divided by the capacitance of the capacitor. By using a modulated charge current and a programmable charge time to switch the capacitor, the voltage across the capacitor can be controlled. This capacitor voltage is also the output voltage of the multiplier-divider. 
   A general objective of the present invention is to provide an analog multiplier-divider for a power factor correction circuit of a switch-mode power supply. The multiplier-divider according to the present invention is intended for low speed applications that generally operate at internal clock rates of less than 100 kHz. 
   Another objective of the present invention is to provide an analog multiplier-divider that is manufactured using CMOS fabrication. The multiplier-divider according to the present invention exclusively uses MOSFET-based devices. Therefore, the multiplier-divider according to the present invention can be manufactured at a significantly smaller die-size, and at a lower cost, than the prior-art multiplier-dividers. 
   Another objective of the present invention is to provide an analog multiplier-divider having a characteristic equation that is substantially temperature-independent, compared to the prior-art multiplier-divider. The multiplier-divider according to the present invention is constructed with MOSFET-devices. Thus, the temperature coefficient of the multiplier-divider according to the present invention is low. The multiplier-divider according to the present invention can operate successfully over a very wide temperature range. 
   Another objective of the present invention is to provide an analog multiplier-divider with reduced power consumption. The multiplier-divider according to the present invention does not require a constant biasing current. 
   Another objective of the present invention is to provide an analog multiplier-divider with improved noise immunity. The accuracy of the output signal of the multiplier-divider according to the present invention is not significantly affected by small noise components from the input signals. 
   Still further objects and advantages will become apparent from a consideration of the ensuing description and drawings. 

   
     BRIEF DESCRIPTION OF THE DRAWINGS 
     The accompanying drawings are included to provide a further understanding of the invention, and are incorporated in and constitute a part of this specification. The drawings illustrate embodiments of the invention and, together with the description, serve to explain the principles of the invention. 
       FIG. 1  shows a schematic diagram of a switch mode power supply with a power factor correction circuit including a multiplier-divider. 
       FIG. 2  shows a block diagram of a prior-art multiplier-divider. 
       FIG. 3  shows a block diagram of a multiplier-divider according to the present invention. 
       FIG. 4  shows a pulse generator of the multiplier-divider according to the present invention. 
       FIG. 5  shows a detailed block diagram of a sawtooth-signal generator of the pulse generator according to the present invention. 
       FIG. 6  shows a detailed block diagram of a variable current sink of the sawtooth-signal generator according to the present invention. 
       FIG. 7  shows a detailed block diagram of a first multiplier-divider stage of the multiplier-divider according to the present invention. 
       FIG. 8  shows a detailed block diagram of a second multiplier-divider stage of the multiplier-divider according to the present invention. 
       FIG. 9  shows a timing diagram of the pulse generator according to the present invention. 
   

   DESCRIPTION OF THE PREFERRED EMBODIMENTS 
   Referring now to the drawings wherein the contents are for purposes of illustrating the preferred embodiment of the invention only and not for purposes of limiting same,  FIG. 2  shows a prior-art multiplier-divider. 
   The prior-art multiplier-divider is constructed with an array of six bipolar transistors. The multiplier-divider includes six transistors  10 ,  11 ,  12 ,  13 ,  14  and  15 . A base of each of the transistors  10 ,  11 ,  12 ,  13 ,  14  and  15  are tied together. 
   A collector of the transistor  10  is connected to the base of the transistor  10 . An emitter of the transistor  10  is connected to a ground reference. The collector of the transistor  10  is connected to a first positive input terminal I 1 . A collector of the transistor  11  is connected to a negative output terminal I′ O . A collector of the transistor  12  is connected to a positive output terminal I O . A collector of the transistor  13  is connected to the negative output terminal I′ O . An emitter of the transistor  12  and an emitter of the transistor  13  are connected to a second positive input terminal I 2 . A collector of the transistor  14  is connected to the positive output terminal I O . An emitter of the transistor  11  and an emitter of the transistor  14  are connected to a second negative input terminal I′ 2 . A collector of the transistor  15  is connected to a first negative input terminal I′ 1.  The collector of the transistor  15  is connected to the base of the transistor  15 . An emitter of the transistor  15  is connected to the ground reference. Operation of this circuit will be well known to those skilled in the art and therefore detailed description thereof is omitted herein. 
   As discussed above, one major drawback of this prior-art multiplier-divider is that it is constructed using bipolar devices. This results in a large die-size, and introduces a high degree of temperature dependence into the characteristic of the multiplier-divider. For these reasons, the prior-art multiplier-divider shown in  FIG. 2  is not suitable for use in a power converter with power factor correction (PFC).  FIG. 1  shows a power converter. The power converter having power factor correction comprises an AC-power source  50 , a rectifier  51 , an inductor  52 , a diode  53 , two capacitors  54  and  61 , a switch  55 , four resistors  56 ,  57 ,  58  and  60 , two comparators  59  and  62 , a gate-driver  63  and a PFC circuit. The PFC circuit of  FIG. 1  includes six resistors  64 ,  65 ,  67 ,  101 ,  102  and  103 , a comparator  66 , two capacitors  68  and  104 , and a V-to-I converter  69 . The PFC circuit further includes a multiplier-divider  100 . 
   The power converter shown in  FIG. 1  is a standard power supply known in the art. An input of the power supply is the AC-power source  50 . The AC-power source  50  is coupled to a first input and to a second input of the rectifier  51 . A first output of the rectifier  51  is connected to a first terminal of the inductor  52 . A second terminal of the inductor  52  is connected to an anode of a diode  53 . A cathode of the diode  53  is connected to an output voltage terminal V OUT . The capacitor  54  is connected between the output voltage terminal V OUT  and the ground reference. The switch  55  is connected between the second terminal of the inductor  52  and the ground reference. 
   To provide a feedback signal to the PFC circuit, the output voltage terminal V OUT  is also connected to the ground reference via a resistor-divider network. The resistor-divider network consists of two resistors  64  and  65  connected in series. A junction of the resistor  64  and the resistor  65  is connected to a negative input of the comparator  66 . A positive input of the comparator  66  is supplied with a reference voltage V R . The negative input of the comparator  66  is connected to an output of the comparator  66  via a resistor  67  and a capacitor  68 . 
   The output of the comparator  66  supplies a first multiplier signal V E  to a first multiplier-input terminal VE of the multiplier-divider  100 . A divisor-input terminal VAC of the multiplier-divider  100  is supplied with a divisor signal V AC . The divisor-input terminal VAC of the multiplier-divider  100  is also connected to the ground reference via the resistor  103 . The capacitor  104  is connected in parallel with the resistor  103 . An input voltage V IN  is supplied to the divisor-input terminal VAC via the resistor  102 . A second multiplier-input terminal IAC of the multiplier-divider  100  is supplied with the input voltage V IN  via the resistor  101 . The resistor  101  transfers the input voltage V IN  into a second multiplier signal I AC . An output terminal OUT of the multiplier-divider  100  supplies an output signal V O  to an input of the V-to-I converter  69 . 
   An output of the V-to-I converter  69  generates a voltage V M . The voltage V M  is supplied to a second output of the rectifier  51  via the resistor  57 . A positive input of the comparator  59  is also supplied with the voltage V M . A negative input of the comparator  59  is connected to the ground reference via the resistor  58 . The negative input of the comparator  59  is also connected to an output of the comparator  59 , via the resistor  60  and the capacitor  61 . The resistor  56  is connected between the second output of the rectifier  51  and the ground reference. The output of the comparator  59  is connected to a positive input of the comparator  62 . A negative input of the comparator  62  is supplied with a sawtooth-signal V SAW . An output of the comparator  62  drives the switch  55  via the gate-driver  63 . The operation of this circuit will be well known to those skilled in the art and therefore detailed description thereof will be omitted herein. 
   To overcome the problems of the prior-art multiplier-divider, the present invention proposes an analog multiplier-divider constructed with MOSFET devices.  FIG. 3  shows a block diagram of the multiplier-divider  100  according to the present invention. The multiplier-divider  100  has a first multiplier-input terminal VE for receiving a first multiplier signal V E , a second multiplier-input terminal IAC for receiving a second multiplier signal I AC , and a divisor-input terminal VAC for receiving a divisor signal V AC . The multiplier-divider  100  also has an output terminal OUT, which provides an output signal V O . The magnitude of the output signal V O  is proportional to the magnitude of the first multiplier signal V E  multiplied by the magnitude of the second multiplier signal I AC , divided by the square of the magnitude of the divisor signal V AC . The output signal V O  of the multiplier-divider  100  can be expressed as, 
   
     
       
         
           
             
               
                 
                   V 
                   O 
                 
                 ∝ 
                 
                   
                     I 
                     R 
                   
                   × 
                   
                     ( 
                     
                       
                         
                           I 
                           AC 
                         
                         × 
                         
                           V 
                           E 
                         
                       
                       
                         V 
                         AC 
                         2 
                       
                     
                     ) 
                   
                 
               
             
             
               
                 ( 
                 2 
                 ) 
               
             
           
         
       
     
   
   where the current I R  is constant. 
   According to the present invention, the second multiplier signal I AC  and the constant current I R  are current signals while the first multiplier signal V E , the divisor signal V AC  and the output signal V O  are voltage signals. 
   The multiplier-divider  100  consists of a first multiplier-divider stage  130 , a second multiplier-divider stage  150 , and a pulse generator  200 . The first multiplier-divider stage  130  and the second multiplier-divider stage  150  are both multiplier-dividers. Each multiplier-divider has three inputs and an output. In the multiplier-divider  100 , the first multiplier-divider stage  130  and the second multiplier-divider stage  150  are cascaded to obtain the desired output signal V O . 
   The pulse generator  200  generates signals including a pulse-signal PLS, an inverse pulse signal /PLS, a clear signal CLR, a sawtooth signal V SAW , and a sample signal SMP. Above signals are respectively supplied to the first multiplier-divider stage  130  and the second multiplier-divider stage  150  to control the operation of the multiplier-divider  100 . 
   The first multiplier-divider stage  130  has a first input connected to the first multiplier-input terminal VE of the multiplier-divider  100 . The first multiplier-divider stage  130  further has a second input driven by a constant current source  135 , which provides a constant current I R . The first multiplier-divider stage  130  further has a third input coupled to the divisor signal. 
   The second multiplier-divider stage  150  has a first input supplied with an output signal V 1  of the first multiplier-divider stage  130 . The second multiplier-divider stage  150  further has a second input connected to the second multiplier-input terminal IAC of the multiplier-divider  100 . The second multiplier-divider stage  150  further has a third input coupled to the divisor signal. 
     FIG. 4  shows the pulse generator  200 . The pulse generator  200  includes a sawtooth-signal generator  110 , a current source  210 , a switch  211 , a switch  212 , and a current sink  213 . The pulse generator  200  further includes a capacitor  220 , a hysteresis comparator  221  and two NOT-gates  222  and  223 . The pulse generator  200  further includes a comparator  230 , three NOT-gates  231   232  and  242 , and two NAND-gates  240  and  241 . The pulse generator  200  further includes three NOT-gates  250 ,  251  and  252 , and an AND-gate  253 . The pulse generator  200  further includes four NOT-gates  260 ,  261 ,  262  and  271 , an AND-gate  263  and a NAND-gate  270 . 
   An input of the current source  210  is connected to a voltage source V DD . The switch  211  is connected between an output of the current source  210  and an input junction. The switch  212  is connected between the input junction and an input of the current sink  213 . An output of the current sink  213  is connected to the ground reference. An input of the hysteresis comparator  221  is connected to the input junction. The capacitor  220  is connected between the input of the hysteresis comparator  221  and the ground reference. An output of the hysteresis comparator  221  is connected to an input of the NOT-gate  222 . An output of the NOT-gate  222  is connected to an input of the NOT-gate  223 . An output of the NOT-gate  223  provides a signal V R . 
   A positive input of the comparator  230  is connected to an output terminal of the sawtooth-signal generator  110 . A negative input of the comparator  230  is supplied with a reference voltage V REF . An output of the comparator  230  is connected to an input of the NOT-gate  231 . An output of the NOT-gate  231  is connected to an input of the NOT-gate  232 . An output of the NOT-gate  232  provides a signal V S . 
   A first input of the NAND-gate  240  is driven by the signal V R . A second input of the NAND-gate  240  is connected to an output of the NOT-gate  241 . A first input of the NAND-gate  241  is connected to an output of the NAND-gate  240 . A second input of the NAND-gate  241  is driven by the signal V S . The output of the NAND-gate  240  supplies a signal CK 1  to drive a control terminal of the switch  211  via the NOT-gate  242 . Further, a control terminal of the switch  212  is also supplied with the signal CK 1 . 
   An input of the NOT-gate  250  is driven by the signal CK 1 . An input of the NOT-gate  251  is connected to an output of the NOT-gate  250 . An input of the NOT-gate  252  is connected to an output of the NOT-gate  251 . An output of the NOT-gate  252  is connected to an input of the AND-gate  253 . An inverted input of the AND-gate  253  is supplied with the signal CK 1 . An output of the AND-gate  253  supplies the sample signal SMP of the pulse generator  200 . An input of the NOT-gate  260  is supplied with the signal V R . An input of the NOT-gate  261  is connected to an output of the NOT-gate  260 . An input of the NOT-gate  262  is connected to an output of the NOT-gate  261 . An output of the NOT-gate  262  is connected to an input of the AND-gate  263 . An inverted input of the AND-gate  263  is supplied with the signal V R . An output of the AND-gate  263  supplies the clear-signal CLR. 
   A first input of the NAND-gate  270  is supplied with the signal CK 1 . A second input of the NAND-gate  270  is supplied with the signal V R . An output of the NAND-gate  270  supplies the pulse signal PLS and supplies the inverse pulse signal /PLS via the NOT-gate  271 . The operation of the pulse generator  200  will be well known to those skilled in the art and therefore is discussed detail herein. 
     FIG. 5  shows the sawtooth-signal generator  110  according to a preferred embodiment of the present invention. The sawtooth-signal generator  110  comprises a switch  111 , a switch  112 , a capacitor  113 , and a variable current sink  120 . A control terminal of the switch  111  is supplied with the pulse-signal PLS. A control terminal of the switch  112  is supplied with the inverse pulse signal /PLS. An input terminal of the switch  111  is connected to the divisor-input terminal VAC. An output terminal of the switch  111  is connected to an input terminal of the switch  112 . The capacitor  113 , generates the sawtooth signal V SAW , is connected between the output terminal of the switch  111  and the ground reference. An output terminal of the switch  112  is connected to the ground reference via the variable current sink  120 . A control terminal of the variable current sink  120  is connected to the divisor-input terminal VAC. 
   When the pulse generator  200  supplies a logic-high pulse signal PLS, the switch  111  will close. This will cause the capacitor  113  to be promptly charged to a voltage level of the divisor signal V AC . When the pulse signal PLS goes low, the switch  112  will close, and the switch  111  will open. At this point, the capacitor  113  will begin to discharge. The variable current sink  120  will discharge the capacitor  113 . To ensure that the discharge time will be independent of the divisor signal V AC , the dynamic current sink  120  generates a sink current I 1  that is proportional to the magnitude of the divisor signal V AC . 
     FIG. 6  shows the variable current sink  120  according to a preferred embodiment of the present invention. The variable current sink  120  generates the sink current I 1  that is proportional to the magnitude of the divisor signal V AC . This property is used to regulate the discharge time of the capacitor  113 , so that the length of the sawtooth period will be independent of the magnitude of the divisor signal of the multiplier-divider  100 . 
   The variable current sink  120  comprises an operation amplifier  121 , a resistor  122 , and a MOSFET  123 . A positive terminal of the operation amplifier  121  is connected to the control terminal of the variable current sink  120 . A negative terminal of the amplifier  121  is connected to a source of the MOSFET  123 . The source of the MOSFET  123  is connected to an output terminal of the variable current sink  120  via the resistor  122 . An output terminal of the operation amplifier  121  is connected to a gate of the MOSFET  123 . A drain of the MOSFET  123  is connected to an input terminal of the variable current sink  120 . The variable current sink  120  will sink the sink current I 1  that is proportional to the magnitude of the divisor-input signal V AC , divided by the resistance of the resistor  122 . Operation of this circuit will be well known to those skilled in the art and therefore a detailed description thereof is omitted herein. 
     FIG. 7  shows the first multiplier-divider stage  130  of the multiplier-divider  100  according to a preferred embodiment of the present invention. The first multiplier-divider stage  130  comprises of a charge-time control circuit, a linear charging block, and a sample-and-hold circuit. 
   The charge-time control circuit of the first multiplier-divider stage  130  includes a comparator  131  and an AND-gate  132 . A negative input of the comparator  131  is supplied with the sawtooth signal V SAW . A positive input of the comparator  131  is connected to the first multiplier-input terminal VE. An output of the comparator  131  is connected to a first input of the AND-gate  132 . A second input of the AND-gate  132  is supplied with the inverse pulse signal /PLS. An output of the AND-gate  132  generates a charge-time control signal. The charge-time control signal determines the length of an on-time t CHG  of the switch  133 . 
   When the pulse signal PLS supplied by the pulse generator  200  goes low, the AND-gate  132  will output the charge-time control signal in response to the magnitude of the first multiplier signal V E . 
   The charge-time control signal is supplied to the linear charging block. The linear charging block includes a capacitor  135  and two switches  133  and  134 . An input terminal of the switch  133  is supplied with the constant current I R . An output of the switch  133  is connected to an input terminal of the switch  134 . A control terminal of the switch  133  is connected to an output of the AND-gate  132 . An output terminal of the switch  134  is connected to the ground reference. A control terminal of the switch  134  is supplied with the clear signal CLR. The capacitor  135  is connected in parallel with the switch  134 . The on-time t CHG  of the switch  133  will be proportional to the first multiplier signal V E  and will be inversely proportional to the magnitude of the divisor signal V AC . 
   When the switch  133  is closed by the charge-time control signal supplied by the AND-gate  132 , the capacitor  135  will begin to be charged by the constant current I R . When the pulse generator  200  generates a clear signal CLR, the switch  134  will close, and the charge stored in the capacitor  135  will be discharged. 
   The capacitor  135  generates a charge signal V CHG1 , which is supplied to the sample-and-hold circuit. The sample-and-hold circuit includes an OPA  136 , a switch  137 , and a capacitor  138 . A positive input of the OPA  136  is connected to the output terminal of the switch  133 . A negative input of the OPA  136  is connected to an output terminal of the OPA  136 . An input terminal of the switch  137  is connected to the output terminal of the OPA  136 . A control terminal of the switch  137  is supplied with the sample signal SMP of the pulse generator  200 . The capacitor  138 , which is connected between an output terminal of the switch  137  and the ground reference, generates an output signal V 1 . 
   The OPA  136  is a buffer for the charge of the capacitor  135 . When a logic-high sample signal SMP from the pulse generator  200  closes the switch  137 , the voltage at the output terminal of the OPA  136  will be equal to the potential of the capacitor  135 . The maximum voltage of the capacitor  135  will determine the output signal V 1  of the first multiplier-divider stage  130 . The magnitude of the output signal V 1  will be proportional to the magnitude of the first multiplier signal V E  multiplied by the magnitude of the constant current I R , divided by the magnitude of the divisor signal V AC . The capacitor  138  is included as a holding capacitor. 
   The output signal V 1  of the first multiplier-divider stage  130  of the multiplier-divider  100  is coupled to the second multiplier-divider stage  150  of the multiplier-divider  100 . The second multiplier-divider stage  150  of the multiplier-divider  100  also has a charge-time control circuit, a linear charging block, and a sample-and-hold circuit with the same components as the first multiplier-divider stage  130 . 
   The first multiplier-divider stage  130  of the switched-charge multiplier-divider  100  is implemented according to the principles of capacitor charge theory. An important equation describing the behavior of capacitors is:
 
 Q=C×V=I×T   (3)
 
   where Q is the charge stored in the capacitor, C is the capacitance of the capacitor, V is the voltage across the capacitor, I is the charge current, and T is the charge time. 
   According to equation (3), the voltage across the capacitor C 135  can be expressed as: 
   
     
       
         
           
             
               
                 
                   V 
                   CHG1 
                 
                 = 
                 
                   
                     
                       I 
                       R 
                     
                     × 
                     
                       t 
                       CHG 
                     
                   
                   
                     C 
                     135 
                   
                 
               
             
             
               
                 ( 
                 4 
                 ) 
               
             
           
         
       
     
   
   where the constant current I R  is used to charge the capacitor  135 . 
   t CHG  refers to the length of time that the charge current I R  is applied to the capacitor  135 . This can be expressed as: 
   
     
       
         
           
             
               
                 
                   t 
                   CHG 
                 
                 = 
                 
                   
                     Δ 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     t 
                     × 
                     
                       V 
                       E 
                     
                   
                   
                     V 
                     AC 
                   
                 
               
             
             
               
                 ( 
                 5 
                 ) 
               
             
           
         
       
     
   
   Here, V E  is the first multiplier signal of the first multiplier-divider stage  130  of the multiplier-divider  100 . V AC  is input into the sawtooth-signal generator  110 . Δt is the off-period of the pulse-signal PLS generated by the pulse generator  200 . The off-period Δt of the pulse signal PLS is constant for the purposes of this operation (see  FIG. 9 ). Thus, equation (4) can be rewritten as: 
   
     
       
         
           
             
               
                 
                   V 
                   CHG1 
                 
                 = 
                 
                   
                     
                       I 
                       R 
                     
                     
                       C 
                       135 
                     
                   
                   × 
                   
                     
                       V 
                       E 
                     
                     
                       V 
                       AC 
                     
                   
                   × 
                   Δ 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   t 
                 
               
             
             
               
                 ( 
                 6 
                 ) 
               
             
           
         
       
     
   
   Since I R , C 135 , and Δt are constants, equation (6) can be simplified to: 
   
     
       
         
           
             
               
                 
                   V 
                   CHG1 
                 
                 ∝ 
                 
                   
                     V 
                     E 
                   
                   
                     V 
                     AC 
                   
                 
               
             
             
               
                 ( 
                 7 
                 ) 
               
             
           
         
       
     
   
   After the charging of the capacitor  135  is completed, the sample-and-hold circuit of the first multiplier-divider stage  130  will buffer the charge signal V CHG1 . The magnitude of the output signal V 1  of the first multiplier-divider stage  130  will be equal to V CHG1 . 
   Thus, the basic principles of the first multiplier-divider stage  130  of the multiplier-divider  100  according to the present invention are described above. The second multiplier-divider stage  150  of the multiplier-divider  100  is built according to the same principles as the first multiplier-divider stage  130 . 
   Thus, according the equation (6), the output V O  of the second multiplier-divider stage  150  can be expressed as: 
   
     
       
         
           
             
               
                 
                   V 
                   O 
                 
                 = 
                 
                   
                     
                       I 
                       AC 
                     
                     
                       C 
                       155 
                     
                   
                   × 
                   
                     
                       V 
                       1 
                     
                     
                       V 
                       AC 
                     
                   
                   × 
                   Δ 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   t 
                 
               
             
             
               
                 ( 
                 8 
                 ) 
               
             
           
         
       
     
   
   C 155  and Δt are constants. Combining equation (7) and (8), the output signal V O  of the multiplier-divider  100  can be expressed as: 
   
     
       
         
           
             
               
                 
                   V 
                   O 
                 
                 ∝ 
                 
                   
                     
                       I 
                       AC 
                     
                     × 
                     
                       V 
                       E 
                     
                   
                   
                     V 
                     AC 
                     2 
                   
                 
               
             
             
               
                 ( 
                 9 
                 ) 
               
             
           
         
       
     
   
     FIG. 8  shows the second multiplier-divider stage  150  according to a preferred embodiment of the present invention. The second multiplier-divider stage  150  includes a comparator  151 , an AND-gate  152 , three switches  153 ,  154  and  157 , two capacitors  155  and  158 , and an op amplifier (OPA)  156 . A positive input of the comparator  151  is supplied with the output signal V 1  of the first multiplier-divider stage  130 . A negative input of the comparator  151  is supplied with the sawtooth signal V SAW . A first input of the AND-gate  152  is connected to an output of the comparator  151 . A second input of the AND-gate  152  is supplied with the inverse pulse signal /PLS of the pulse generator  200 . A control terminal of the switch  153  is driven by an output of the AND-gate  152 . An input terminal of the switch  153  is connected to the second multiplier-input terminal IAC. An output terminal of the switch  153  is connected to an input terminal of the switch  154 . An output terminal of the switch  154  is connected to the ground reference. The capacitor  155  is connected in parallel with the switch  154 . A positive input of the OPA  156  is connected to the output terminal of the switch  153 . A negative input of the OPA  156  is connected to an output of the OPA  156 . The switch  157  is connected between an output terminal of the OPA  156  and the output terminal OUT of the multiplier-divider  100 . The capacitor  158  is connected between the output terminal OUT of the multiplier-divider  100  and the ground reference. 
     FIG. 9  is a timing diagram illustrating the operation of the pulse generator  200 . The pulse generator  200  supplies the pulse signal PLS, and the inverse pulse signal /PLS, the sample signal SMP, and the clear signal CLR. The sample signal SMP follows the pulse signal PLS after a delay time t D1 . The clear signal CLR follows the sample-signal SMP after a delay time t D2 . 
   When the pulse generator  200  generates the pulse signal PLS, the sawtooth-signal generator  110  will create the sawtooth signal V SAW  in response to the divisor signal VAC. After the pulse signal PLS goes low, the charge-time control circuit will compare the sawtooth signal V SAW  with the first multiplier signal V E  to produce the on-time of the switch  133 . The length of the on-time t CHG  will be proportional to the magnitude of the first multiplier-signal V E  divided by the magnitude of the divisor-signal V AC . The linear charging block will charge the capacitor  135  for the duration of the on-time t CHG . The constant current I R  will charge the capacitor  135 . At this point, the charge of the capacitor  135  will determine the magnitude of the output signal V 1  of the first multiplier-divider stage  130  of the multiplier-divider  100 . When the pulse generator  200  supplies a logic-high sample signal SMP, the sample-and-hold circuit will hold the output signal V O  of the multiplier-divider  100  across the capacitor  158 . The pulse generator  200  will generate the clear-signal CLR following the sample signal SMP, to reset the multiplier-divider  100 . 
   It will be apparent to those skilled in the art that various modifications and variations can be made to the structure of the present invention without departing from the scope or spirit of the invention. In view of the foregoing, it is intended that the present invention cover modifications and variations of this invention provided they fall within the scope of the following claims or their equivalents.