Charge-scaling multiplier circuit with digital-to-analog converter
A multiplier circuit can be fabricated within an integrated circuit and can draw a product output node to a voltage proportional to a product of first and second binary numbers received at two sets of inputs. The multiplier circuit includes a set of scaled capacitors, each capacitor of the set connected to an output of a multiplexor and to a local product output node. Each multiplexor is connected to the output of a multiplexor configured to generate an analog voltage in proportion to the value of the first binary number. Each scaled capacitor has a capacitance proportional to a significance of a respective bit of the second binary number. The multiplier circuit includes a reference capacitor connected to ground and the product output node, and a reset circuit configured to draw, in response to a RESET signal, the product output node to ground.
1. A multiplier circuit fabricated within an integrated circuit (IC), the multiplier circuit configured to draw a product output node to a voltage proportional to a product of two received N-bit binary numbers, the multiplier circuit comprising:
a first set of N inputs configured to receive a first N-bit binary number, each input of the first set of N inputs indexed by an integer bit number “n” corresponding to each input's respective significance, where n is in a range between and including 0 and N−1;
a second set of N inputs configured to receive a second N-bit binary number, each input of the second set of N inputs indexed by the integer bit number “n” corresponding to each input's respective significance;
a local reset device configured to draw, in response to receiving a reset signal, a local product node to ground;
a unity gain amplifier configured to drive a product output node to a voltage equivalent to a voltage on the local product node;
a digital-to-analog converter (DAC) configured to drive, to a DAC output node, an analog voltage that represents a value of the first N-bit binary number, the DAC including:
a voltage divider circuit configured to generate a set of 2 N analog voltages; and
a first analog multiplexer (mux) configured to:
receive, through 2 N analog inputs electrically connected to the voltage divider circuit, the set of 2 N analog voltages;
receive, through a set of N select inputs, the first N-bit binary number; and
drive, to the DAC output node, a DAC output voltage that represents the value of the first N-bit binary number, the DAC output voltage selected, in response to the value of the first N-bit binary number, from the set of 2 N analog voltages; and
a set of N analog muxes, each analog mux of the set of N analog muxes configured to drive, in response to a respective input of the second set of N inputs, to a corresponding analog mux output node, the DAC output voltage;
a set of N scaled capacitors, each capacitor of the set of N scaled capacitors electrically connected to a respective analog mux output node and further electrically connected to the local product node, each capacitor of the set of N scaled capacitors having a capacitance value equal to 2 n * a unit capacitance value (C UNIT ); and
a reference capacitor electrically connected to GND and further electrically connected to the local product node, a value of the reference capacitor equal to C UNIT .
2. The multiplier circuit of claim 1 , wherein the voltage divider circuit includes a set of resistors of equal value configured to provide the set of 2 N analog voltages, wherein the set of 2 N analog voltages are evenly distributed in a range including and between VDD and GND.
3. The multiplier circuit of claim 1 , wherein a voltage of the product output node is in a range between ground (GND) and a supply voltage (Vdd).
4. The multiplier circuit of claim 1 , wherein the local reset device is an N-channel field-effect transistor (NFET).
5. The multiplier circuit of claim 1 , wherein the multiplier circuit receives binary numbers from digital logic circuits within the IC and outputs an analog voltage representing the product of the binary numbers to an analog-to-digital converter (ADC) within the IC.
6. The multiplier circuit of claim 5 , wherein the ADC is selected from the group consisting of: a flash ADC, a resistor ladder ADC, a parallel comparator ADC, a successive-approximation ADC, and a counter type ADC.
7. The multiplier circuit of claim 1 , wherein a supply voltage of the multiplier circuit is in a range between 0.9 V and 1.1 V.
8. The multiplier circuit of claim 1 , wherein the voltage proportional to a product of received N-bit binary numbers is within a voltage range corresponding to +/−1 least significant bit (LSB) of the received N-bit binary numbers.
9. The multiplier circuit of claim 1 , wherein an IC technology is selected from the group consisting of: complementary metal-oxide semiconductor (CMOS) and silicon on insulator (SOI).
10. A multiplier circuit fabricated within an integrated circuit (IC), the multiplier circuit configured to draw a product output node to a voltage proportional to a product of two received N-bit binary numbers, the multiplier circuit comprising:
a first set of N inputs configured to receive a first N-bit binary number, each input of the first set of N inputs indexed by an integer bit number “n” corresponding to each input's respective significance, where n is in a range between and including 0 and N−1;
a second set of N inputs configured to receive a second N-bit binary number, each input of the second set of N inputs indexed by the integer bit number “n” corresponding to each input's respective significance;
a local reset device configured to draw, in response to receiving a reset signal, a local product node to ground;
a digital-to-analog converter (DAC) configured to drive, to a DAC output node, an analog voltage that represents a value of the first N-bit binary number, the DAC including:
a first set of N scaled capacitors, each capacitor of the first set of N scaled capacitors electrically connected to a respective input of the first set of N inputs, and further electrically connected to a scaled node, each capacitor of the first set of N scaled capacitors having a capacitance value equal to 2 n *a unit capacitance value (C UNIT );
a first reference capacitor electrically connected to GND and further electrically connected to the scaled node, a value of the reference capacitor equal to C UNIT *a scaling factor (S); and
a first unity gain amplifier configured to drive the DAC output node to a voltage equivalent to a voltage on the scaled node; and
a set of N analog muxes, each analog mux of the set of N analog muxes configured to drive, in response to a respective input of the second set of N inputs, the DAC output voltage to a corresponding analog mux output node;
a second set of N scaled capacitors, each capacitor of the second set of N scaled capacitors electrically connected to a respective analog mux output node and further electrically connected to the local product node, each capacitor of the second set of N scaled capacitors having a capacitance value equal to 2 n *C UNIT ;
a second reference capacitor electrically connected to GND and further electrically connected to the local product node, a value of the reference capacitor equal to C UNIT ; and
a second unity gain amplifier configured to drive the product output node to a voltage equivalent to a voltage on the local product node.
11. The multiplier circuit of claim 10 , wherein an IC technology is selected from the group consisting of: complementary metal-oxide semiconductor (CMOS) and silicon on insulator (SOI).
12. The multiplier circuit of claim 10 , wherein a value of C UNIT is in a range between 2× and 10× an input capacitance of an analog-to-digital converter (ADC) connected to the product output node.
13. The multiplier circuit of claim 10 , wherein the scaled capacitors and the reference capacitor are selected from the group consisting of: Metal-Insulator-Metal (MIM) capacitors, metal-oxide semiconductor (MOS) capacitors, and trench capacitors.
14. The multiplier circuit of claim 10 , wherein a smallest voltage increment of the voltage, proportional to a product of the received N-bit binary numbers, at the product output node, is greater than an operating voltage of an analog-to-digital converter (ADC) divided by 250.
15. The multiplier circuit of claim 10 , wherein a supply voltage of the multiplier circuit is in a range between 0.9 V and 1.1 V.
16. A method of operating a multiplier circuit that uses charge-scaling to multiply a first N-bit binary number by a second N-bit binary number, the multiplier circuit fabricated within an integrated circuit (IC), the method comprising:
resetting the multiplier circuit by drawing to ground, with a local reset device of the multiplier circuit, a local product node of the multiplier circuit;
receiving, with a first set of N inputs of the multiplier circuit, a first N-bit binary number;
receiving, with a second set of N inputs of the multiplier circuit, a second N-bit binary number;
driving, with a digital-to-analog converter (DAC) and in response to a value of first N-bit binary number, at a DAC output node, a DAC output voltage that represents the value of the first N-bit binary number;
selecting, in accordance with a respective input of the second set of N inputs applied to each analog mux of a set of N analog muxes, the DAC output voltage to be applied to respective scaling capacitors electrically connected to respective analog mux output nodes;
scaling, with the respective scaling capacitors, the DAC output voltage to produce, on the local product node of the multiplier circuit, a product output voltage representing a product of the first N-bit binary number and the second N-bit binary number; and
driving, with a unity gain amplifier electrically connected to the local product node, a product output node to the product output voltage.
17. The method of claim 16 , wherein the DAC includes:
a voltage divider circuit having a set of resistors of equal value that are configured to provide a set of 2 N analog voltages that are evenly distributed in a range including and between VDD and GND; and
an analog mux configured to drive, to the DAC output node, a DAC output voltage that represents the value of the first N-bit binary number, the DAC output voltage selected, in response to the value of the first N-bit binary number, from the set of 2 N analog voltages.
18. The method of claim 16 , wherein the DAC includes:
an additional set of scaled capacitors electrically connected to the first set of N inputs, the additional set of scaled capacitors configured to provide, on a scaled node, a voltage representing the first N-bit binary number; and
an additional unity gain amplifier configured to drive the DAC output node to a voltage equivalent to a voltage on the scaled node.
19. The method of claim 16 , further comprising converting, with an analog-to-digital converter (ADC) within the IC, the product output voltage to a binary number representing the product of the first and second N-bit binary numbers.
20. The method of claim 16 , wherein a supply voltage of the multiplier circuit is in a range between 0.9 V and 1.1 V.