Multiplying digital-to-analog converters and methods that selectively connect unit and feedback capacitors to reference voltages and feedback voltages

[0002] This invention relates to digital-to-analog converters and converting methods, and more particularly to multiplying digital-to-analog converters and methods and pipelined analog-to-digital converters and methods using the same.

[0003] Multiplying Digital-to-Analog Converters (MDAC) and converting methods are widely used in electronic systems to multiply an analog input signal at an analog input terminal and a digital input signal at a digital input terminal, to produce an analog output signal at an analog output terminal. For example, MDACs are widely used as a component of a pipelined analog-to-digital converter (ADC). As is well known to those having skill in the art, a pipelined ADC employs a plurality of MDACs that are serially connected, such that the analog output terminal of a preceding MDAC is connected to the analog input terminal of a succeeding MDAC. A pipelined ADC also uses a plurality of ADCs, a respective one of which is connected between the analog input terminal and the digital input terminal of a respective one of the MDACs. Pipelined ADCs are widely used, for example for high-speed data processing in high definition television, image recognition, radar and medical instrument systems.

[0004] Unfortunately, it may be difficult to match the various elements of a pipelined ADC in order to maintain a high degree of linearity. In order to match these elements, self-calibration, error averaging and laser trimming techniques have been employed in the design and manufacture of pipelined ADCs. Notwithstanding these developments, linearity may continue to be a problem in pipelined ADCs.

[0005] Referring now to FIG. 1, a pipelined ADC 100 comprises MDACs 110, 130 and 150, ADCs 120, 140, 160 and 180, and a correction and data output circuit 190 that corrects the data output from the ADCs 120, 140, 160, 180 to generate the corrected digital output data DO. An external analog signal AI1 is input to the first ADC 120 and to the first MDAC 110. The first ADC 120 converts the external analog signal AI1 into first digital data DDI1 that is applied to the first input d1 of the correction and data output circuit 190 and to the first MDAC 110. The first MDAC 110 amplifies the difference between the external analog signal AI1 and the first digital data DDI1 to generate a first multiplied analog signal AI2.

[0006] Similarly, the multiplied analog signal AI2 is input to the second ADC 140 and to the second MDAC 130. The second ADC 140 converts the first multiplied analog signal AI2 into second digital data DDI2 that is applied to the second input d2 of the correction and data output circuit 190 and to the second MDAC 130. The second MDAC 130 amplifies the difference between the first multiplied analog signal AI2 and the second digital data DDI2 to generate a second multiplied analog signal AI3.

[0007] Likewise, the second multiplied signal AI3 is input to the third ADC 160 and to the third MDAC 150. The third ADC 160 converts the second multiplied analog signal AI3 into third digital data DDI3 that is applied to the third input d3 of the correction and data output circuit 190 and to the third MDAC 150. This third MDAC 130 amplifies the difference between the second multiplied analog signal AI3 and the third digital data DDI3 to generate a third multiplied analog signal AI4 that is applied to the fourth ADC 180. The fourth ADC 180 converts the third multiplied analog signal AI4 into fourth digital data that is applied to the fourth input d4 of the correction and data output circuit 190. Finally, the correction and data output circuit 190 corrects the second to fourth digital data received through the second to fourth inputs d2 to d4 based on the first digital data received through the first input d1, to generate the digital output data DO.

[0008] Referring to FIG. 2, an N-bit MDAC 120-180 that can be used in a pipelined ADC as shown in FIG. 1, comprises a plurality of switches, a capacitor array and an operational amplifier. When a first clock pulse is generated, the MDAC samples the analog input signal to the capacitors. When a second clock pulse is generated, the switches are selectively connected to the reference voltage Vref, the feedback line F/B or ground GND according to the digital data obtained from the input analog signal, to amplify the residue voltage which is the difference between the values of the analog signal and the digital data. The MDAC may employ a fixed feedback capacitor and/or a rearrangement feedback capacitor. The MDAC shown in FIG. 2 employs both fixed feedback capacitors and rearrangement feedback capacitors. Such a pipelined ADC is disclosed in an article entitled “Pipelined A-D Conversion Technique with Near-Inherent Monotonicity”, IEEE Vol. 42, pp. 500-502, July 1995, the disclosure of which is hereby incorporated herein by reference.

[0009] The conventional MDAC uses two fixed feedback capacitors C₇and C₈. Reference symbol C represents a unit capacitor. Vref represents a first reference voltage and GND represents a second reference voltage such as ground voltage. The analog input signal corresponds to digital data from 000 to 111. This MDAC structure establishes a code pattern, as shown in FIGS. 3 and 4, which includes 4 nominal ranges and 4 error correction ranges (2 add ranges and 2 subtract ranges) to correct the errors occurring in the other flash ADC blocks. Hence, it is possible to correct the errors with over 4 bits precision in the flash blocks.

[0010] In such an MDAC, the overall errors that may occur due to the capacitor error are expressed by means of Vdrop (generally 1-2 V_ref), and the linearity difference is expressed by DNL (Differential Non-Linearity) in the following Equations, which represent the values of the Vdrops in the transition from 000 to 111. In the Equations, V₁represents a residue peak voltage, and V₂represents a residue bottom voltage. Vdrop represents the difference between V₁and V₂, i.e., the residue drop.

[0011] C_T={fraction (1/9)}(C₀+C₁+C₂+C₃+C₄+C₅+C₆+C₇+C₈)  (1)

[0012] C_i=C(1+ε_i), I=0, 1, 2, . . . , 8  (2)

[0013] $\begin{array}{cc}{V}_1=8\frac{C}{C\left(2+{ϵ}_7+{ϵ}_8\right)}\times \frac{\mathrm{Vref}}{8}=\frac{\mathrm{Vref}}{2+{ϵ}_7+{ϵ}_8}& \left(3\right)\\ V_2=8\frac{C}{2+{ϵ}_8+{ϵ}_7}\times \frac{\mathrm{Vref}}{8}-\frac{1+{ϵ}_0}{2+{ϵ}_8+{ϵ}_7}\mathrm{Vref}=-{ϵ}_0\frac{\mathrm{Vref}}{2+{ϵ}_8+{ϵ}_7}& \left(4\right)\\ V_{\mathrm{drop}}=\mathrm{V1}-\mathrm{V2}=\frac{\mathrm{Vref}}{2+{ϵ}_8+{ϵ}_7}-\frac{-{ϵ}_0\mathrm{Vref}}{2+{ϵ}_8+{ϵ}_7}=\frac{\left(1+{ϵ}_0\right)\mathrm{Vref}}{2+{ϵ}_8+{ϵ}_7}=\frac{1}{2}\left(1+{ϵ}_0-\frac{1}{2}{ϵ}_8-\frac{1}{2}{ϵ}_7\right)\mathrm{Vref}& \left(5\right)\end{array}$

[0014] This MDAC can also employ a rearrangement feedback capacitor without using a fixed feedback capacitor, to produce a code pattern as shown in FIG. 5. The error Vdrop of such structure may be obtained by the following Equations: $\begin{array}{cc}{V}_1=8\frac{C}{C\left(1+{ϵ}_1\right)}\times \frac{1}{8}\mathrm{Vref}=\frac{1}{1+{ϵ}_2}\mathrm{Vref}& \left(6\right)\\ V_2=\frac{\mathrm{Vref}}{C\left(1+{ϵ}_2\right)}-\frac{C\left(1+{ϵ}_1\right)}{C\left(1+{ϵ}_2\right)}\mathrm{Vref}=-\frac{{ϵ}_1}{1+{ϵ}_2}\mathrm{Vref}& \left(7\right)\\ V_{\mathrm{drop}}=V_1-V_2=\frac{\mathrm{Vref}}{1+{ϵ}_1}+\frac{{ϵ}_1}{1+{ϵ}_2}\mathrm{Vref}=\mathrm{Vrefx}\frac{1+{ϵ}_2+{ϵ}_1+{ϵ}_1^2}{1+{ϵ}_1+{ϵ}_2+{ϵ}_1{ϵ}_2}=\mathrm{Vref}\left(1+{ϵ}_1^2-{ϵ}_1{ϵ}_2\right)& \left(8\right)\end{array}$

[0015] According to Eq. 5, the primary error factor ε₀is eliminated but the secondary error factor may not be eliminated. Constructing a pipelined ADC by using such MDAC structure, the code pattern proceeds as shown in FIG. 6. This results in 8 nominal ranges with 2 error correction ranges (1 add and 1 subtract range), thereby reducing the error correction region. However, the precision may be limited to 6 bits for the ADC blocks. In this case, while the capacitor array of the MDAC with the fixed feedback does not limit the precision over 4 bits, the value of the capacitor array may inherently have an error in the divisor as shown in Eq. 5. The third and fourth terms of the divisor may be minimized in designing the MDAC, but the second term ε₀inherently belongs to all the capacitors, and may be difficult to eliminate. Alternatively, in the capacitor array of the MDAC only with the unit capacitors, the precision may not be limited over 6 bits. As shown by Eq. 8, the primary error factor may be eliminated, but the secondary error factors may remain.

[0016] It is therefore an object of the present invention to provide multiplying digital-to-analog converters and converting methods that can include reduced capacitor errors.

[0017] It is another object of the present invention to provide pipelined analog-to-digital converters and converting methods that can include reduced capacitor errors.

[0018] These and other objects are provided according to the present invention by Multiplying Digital-to-Analog Converters (MDAC) that multiply an analog input signal at an analog input terminal and a digital input signal at a digital input terminal to produce an analog output signal at an output terminal. The MDACs comprise a plurality of unit capacitors and a feedback capacitor. The unit capacitors are connected to the analog input terminal during a first time interval and the unit capacitors are selectively connected to one of a first reference voltage, a second reference voltage and the output terminal during a second time interval in response to the digital input signal at the digital input terminal. The feedback capacitor is connected to the second reference voltage during the first time interval and to the output terminal during the second time interval.

[0019] Preferred embodiments of MDACs and methods according to the invention include a plurality of first switches, a respective one of which connects a respective unit capacitor to the analog input terminal during the first time interval. A plurality of second switches is also provided. A respective one of the first switches connects a respective one of the unit capacitors to a respective one of the second switches during the second time interval. The second switches are selectively connected to one of the first reference voltage, the second reference voltage and the output terminal during the second time interval in response to the digital input signal at the digital input terminal. More preferably, one of the second switches is connected to the output terminal and remaining ones of the second switches are connected to one of the first reference voltage and the second reference voltage during the second time interval in response to the digital input signal at the digital input terminal.

[0020] Most preferably, the second switches are arranged from a most significant bit to a least significant bit. The second reference voltage is ground voltage and a selected one of the second switches that corresponds to the digital input signal is connected to the output terminal. More significant second switches than the selected switch are connected to ground voltage and less significant second switches than the selected switch are connected to the first reference voltage. Specifically, for an N bit digital input signal, 2^Ncapacitors, 2^Nfirst switches and 2^Nsecond switches are provided. The 2^Nsecond switches are arranged from a most significant bit to a least significant bit. A selected one of the 2^Nsecond switches that corresponds to the value of the N bit digital input signal is connected to the output terminal. The second switches that are more significant than the selected one of the 2^Nsecond switches are connected to ground voltage and the second switches that are less significant than the selected one of the 2^Nsecond switches are connected to the first reference voltage during a second time interval.

[0021] An operational amplifier may also be provided in MDACs according to the invention. The operational amplifier connects the plurality of unit capacitors and the feedback capacitor to the output terminal. The feedback capacitor is preferably connected between the operational amplifier and the second reference voltage during a first time interval and is connected between the operational amplifier and the output terminal during the second time interval.

[0022] Pipelined Analog-to-Digital Converter (ADC) systems and methods according to the present invention include a plurality of MDACs, each of which multiplies an analog input signal at an analog input terminal thereof at a digital input signal at a digital input terminal thereof to produce an analog output signal at an output terminal thereof. The MDACs are serially connected such as the analog output terminal of a preceding MDAC is connected to the analog input terminal of a succeeding MDAC. A plurality of ADCs are also provided, a respective one of which is connected between the analog input terminal and the digital input terminal of a respective one of the MDACs. Each of the MDACs may include the elements and perform the steps as described above.

[0023] According to another aspect of the present invention, MDAC systems and methods include 2^Ncapacitors that are arranged from a most significant bit to a least significant bit of the N bit digital input signal. The 2^Ncapacitors are connected to the analog input terminal during a first time interval. One of the 2^N/2 most significant capacitors is selectively connected to the output terminal during a second time interval in response to the N bit digital input signal at the digital input terminal. The more significant capacitors are connected to a first reference voltage and the less significant capacitors are connected to a second reference voltage, or the more significant capacitors are connected to the second reference voltage and the less significant capacitors are connected to the first reference voltage, during the second time interval in response to the N bit digital input signal at the digital input terminal.

[0024] Preferably, the more significant capacitors are connected to the first reference voltage and the less significant capacitors are connected to a second reference voltage, or the more significant capacitors are connected to the second reference voltage and the less significant capacitors are connected to the first reference voltage, in response to the most significant bit of the N bit digital input signal. These connections may be implemented by 2^Nfirst switches, 2^Nsecond switches and controlling circuits and methods. Improved MDAC systems and methods and ADC systems and methods having reduced capacitor errors may therefore be provided.

[0025] FIG. 1 is a block diagram illustrating a conventional pipelined ADC;

[0026] FIG. 2 is a diagram illustrating a circuit of an MDAC shown in FIG. 1;

[0027] FIG. 3 is a table illustrating connection of the capacitor array shown in FIG. 2;

[0028] FIG. 4 is a diagram illustrating an expansion of FIG. 3;

[0029] FIG. 5 is a table illustrating a connection of the capacitor array used in a conventional 3-bit MDAC;

[0030] FIG. 6 is a diagram illustrating an expansion of FIG. 5;

[0031] FIG. 7 is a diagram illustrating MDAC systems and methods according to a first embodiment of the present invention;

[0032] FIG. 8 is a table illustrating a connection of a capacitor array of 2-bit MDACs according to the present invention;

[0033] FIG. 9 is a table illustrating a connection of a capacitor array of 3-bit MDACs according to the present invention;

[0034] FIG. 10 is a diagram illustrating MDAC systems and methods according to a second embodiment of the present invention;

[0035] FIG. 11 is a table illustrating a connection of a unit capacitor array of 2-bit MDACs according to the present invention;

[0036] FIG. 12 is a table illustrating a connection of a unit capacitor array of 3-bit MDACs shown in FIG. 10; and

[0037] FIGS. 13A and 13B are graphs illustrating a comparison of characteristics of a conventional pipelined ADC and a pipelined ADC according to the invention.

[0038] The present invention now will be described more fully hereinafter with reference to the accompanying drawings, in which preferred embodiments of the invention are shown. This invention may, however, be embodied in many different forms and should not be construed as limited to the embodiments set forth herein; rather, these embodiments are provided so that this disclosure will be thorough and complete, and will fully convey the scope of the invention to those skilled in the art. Like numbers refer to like elements throughout.

[0039] Referring now to FIG. 7, a first embodiment of Multiplying Digital-to-Analog Converters (MDACs) and methods according to the present invention is illustrated. As shown in FIG. 7, the MDAC multiplies an analog input signal at an analog input terminal AI1 and a digital input signal at a digital input terminal DDI1 to produce an analog output signal at an output terminal AI2. MDACs according to FIG. 7 may be used in pipelined Analog-to-Digital Converters (ADCs) of FIG. 1.

[0040] Still referring to FIG. 7, MDACs according to the present invention include a plurality of unit capacitors. In FIG. 7, eight unit capacitors C₈-C₁are included. A feedback capacitor C₀is also included. A circuit is also included that connects the unit capacitors C₁-C₈to the analog input terminal AI1 during the first time interval and then selectively connects the unit capacitors C₁-C₈to one of a first reference voltage the V_ref, a second reference voltage such as ground voltage GND and the analog output terminal AI2 during a second time interval in response to the digital input signal at the digital input terminal DDI1. A circuit also connects the feedback capacitor C₀to the second reference voltage GND during the first time interval and to the output terminal AI2 during the second time interval.

[0041] As shown in FIG. 7, the circuit includes a plurality of first switches S₂₁-S₂₈, a respective one of which connects a respective unit capacitor C₁-C₈to the analog input terminal AI1 during the first time interval. A plurality of second switches S_{31 -S38}is also included. A respective one of the first switches S₂₀-S₂₈connects a respective one of the unit capacitors C₀-C₈to a respective one of the second switches S_{31 -S38}during the second time interval. A switch control circuit 210 selectively connects the second switches S₃₁-S₃₈to one of the first reference voltage V_ref, the second reference voltage GND and the output terminal AI2 during the second time interval in response to the digital input signal at the digital input terminal DDI1. More specifically, as will be described below, the switch control circuit 210 connects one of the second switches S₂₀-S₂₈to the output terminal and connects remaining ones of the second switches to one of the first reference voltage V_refand the second reference voltage GND during the second time interval. Even more specifically, the switch control circuit connects a selected one of the second switches that corresponds to the digital input signal to the output terminal. Those second switches that are more significant than the selected switch are connected to ground voltage and those second switches that are less significant than the selected second switch are connected to the reference voltage during the second time interval.

[0042] Still continuing with the description of FIG. 7, an operational amplifier 220 is also included. The operational amplifier connects the plurality of unit capacitors C₁-C₈and the feedback capacitor C₀to the analog output terminal AI2. Thus, the feedback capacitor C₂₀is connected between the operational amplifier 220 and the output terminal AI2 during the second time interval.

[0043] Thus, an MDAC according to FIG. 7 comprises an operational amplifier 220 with an inverting input terminal and a non-inverting input terminal, a capacitor array consisting of 2^Nunit capacitors C₈-C₁with one end connected to the inverting input terminal, and a first selection circuit comprising a plurality of first switches S₂₈-S₂₁respectively connected to the capacitors C₈-C₁. A feedback terminal 3/b,also referred to as an output terminal AI2, feeds back the signals of the capacitors to the operational amplifier 220. A second selection circuit comprising a plurality of second switches S₃₈-S₃₁selectively connects to the reference voltage terminal 4/c,ground terminal 5/dor the feedback terminal 3/b.A switch control circuit 210 generates control signals to control the operation of the switches S₂₀-S₂₈and S₃₁-S₃₈. The switch control circuit 210 controls the switches to selectively connect the unit capacitors with the terminal lines 3, 4, 5 in response to the digital signal received from the previous stage. The operational amplifier 220 amplifies the difference between the digitalized sampled analog signal and the analog signal to generate a first multiplied analog output signal at the analog output terminal AI2, that is applied to the next stage.

[0044] Operation of a simplified embodiment of FIG. 7 is illustrated in FIG. 8. FIG. 8 illustrates the connection of the unit capacitors in a 2-bit MDAC according to the control signal from the switch control circuit. The unit capacitors C₄-C₁and the fixed feedback capacitor C₀make different connections according to the digital data applied to the switch control circuit 210. When the data 11, 10, 01, 00 is input, the fixed capacitor C₀is connected to the feedback line 3. When the data 11 is input to the switch control circuit 210, the corresponding capacitor C₄is connected to the feedback line 3 and less significant capacitors to the right of the capacitor C₄are connected to the reference voltage line 4. When data 10 is input, the corresponding capacitor C₃is connected to the feedback line 3 while the less significant capacitors C₂, C₁to the right thereof are connected with the reference voltage line 4, and the more significant capacitor C₄to the left thereof is grounded. When data 01 is input to the switch control circuit 210, the capacitor C₂is connected with the feedback line 3 while the less significant capacitor C₁to the right thereof is connected with the reference voltage line 4, and the more significant capacitors C₄, C₃to the left thereof are grounded. Finally, when the data 00 is input to the switch control circuit 210, the capacitor C₁is connected with the feedback line 3, and the more significant capacitors C₄-C₂to the left thereof are all grounded.

[0045] Referring now to FIG. 9, a 3-bit MDAC may include the eight unit capacitors C₈-C₁and a fixed feedback capacitor C₀connected to the inverting input terminal of the operational amplifier 220, as shown in FIG. 7. The unit capacitors C₈-C₁are sequentially arranged from the Most Significant Bit (MSB) to the Least Significant Bit (LSB). The first MDAC of a pipelined ADC will now be described. It will be understood that the other MDACs are constructed and operated in the same manner.

[0046] In operation, the switch control circuit 210 controls the switches S₂₁-S₂₈to connect the unit capacitors C₁-C₈with the first switch terminals 1 during the first time interval of a first clock pulse, so that the unit capacitors perform sampling of the input analog signal. During the second time interval of a second clock pulse, the switch control circuit 210 controls the switches S₂₈-S₂₁to connect the unit capacitors with the second switch terminals 2 while selectively connecting the capacitors C₁-C₈with the feedback line 3, reference voltage line 4 or ground line 5 in response to the first digital data DDI of the first ADC 120. Consequently, the first MDAC amplifies the difference between the values of the first digital data DDI1 and the analog signal AI1 to generate the first multiplied analog signal AI2. The capacitors are connected as shown in FIG. 9.

[0047] For example, if the digital input data of the digital input terminal DDI1 is 100, the switch control circuit 210 controls the switches S₂₁-S₂₈to connect the capacitors to the second switch terminals 2 at the second interval while connecting the capacitor C₅with the feedback terminal 3/a.Then, the less significant capacitors C₄-C₁to the right of the capacitor C₅are connected through the switches S₂₄-S₂₁, S₃₄-S₃₁to the reference voltage terminal 4/cwhile the more significant capacitors C₈-C₆to the left thereof are connected through the switches S₂₈-S₂₆, S₃₈-S₃₆to the ground terminal 5/d.Such an MDAC employs a feedback capacitor structure including a fixed feedback capacitor C₀and a unit feedback capacitor selected from the unit capacitors. In the present embodiment, the relationship between V₁, V₂and Vdrop may be expressed by the following Equations. $\begin{array}{cc}{V}_1=4\frac{C}{C\left(1+{ϵ}_1\right)+C\left(1+{ϵ}_0\right)}\times \frac{\mathrm{Vref}}{4}=\frac{\mathrm{Vref}}{2+{ϵ}_1+{ϵ}_2}& \left(9\right)\\ V_2=4\frac{C}{2+{ϵ}_2+{ϵ}_0}\times \frac{\mathrm{Vref}}{4}-\frac{\left(1+{ϵ}_1\right)}{2+{ϵ}_{20}+{ϵ}_0}\mathrm{Vref}=\frac{-{ϵ}_1\mathrm{Vref}}{2+{ϵ}_0+{ϵ}_2}& \left(10\right)\\ {\hspace{0.17em}}_{\mathrm{drop}}=V_1-V_2=\frac{\mathrm{Vref}}{2+{ϵ}_1+{ϵ}_0}-\frac{-{ϵ}_1\mathrm{Vref}}{2+{ϵ}_2+{ϵ}_0}=\frac{2+{ϵ}_2+{ϵ}_0+2{ϵ}_1+{ϵ}_1^2+{ϵ}_1{ϵ}_0}{4+2{ϵ}_2+4{ϵ}_0+2{ϵ}_1+{ϵ}_1{ϵ}_2+{ϵ}_1{ϵ}_0+{ϵ}_2ϵ+{ϵ}_0^2}\mathrm{Vref}=\frac{1}{2}\left[1-\frac{1}{2}{ϵ}_0+\frac{1}{2}{ϵ}_1\right]\times \mathrm{Vref}.& \left(11\right)\end{array}$

[0048] As shown by the above Equations, it will be noted that the capacitor error may be reduced to ε₂, 3ε₀compared to a conventional MDAC. In addition, if the value of ε₀is minimized, the value of the overall capacitor error may be reduced to about ½.

[0049] A second embodiment of an MDAC as shown in FIG. 10 has the same construction as the first embodiment except that the fixed feedback capacitor shown in FIG. 7 may be omitted. Operation of a 2-bit MDAC according to this embodiment has the capacitor connection as shown in FIG. 11. The unit capacitors constituting the capacitor array are selectively connected to the feedback terminal b, reference voltage terminal c and ground terminal d, as shown in FIG. 10. When the switch control circuit 210 receives the four digital input data 11, 10, 01, 00, the capacitors C₄-C₁make different connections with the upper data 11, 10 and the lower data 01, 00. The more significant capacitors C₄, C₃corresponding to the upper data 11, 10 are connected with the feedback line 3. Thus, when applying data 11, the less significant capacitors C₃-C₁to the right of the capacitor C₄are connected with the reference voltage line 4. Applying data 10, the less significant capacitors C₂, C₁to the right of the capacitor C₃are connected with the reference terminal line 4 while the capacitor C₄to the left thereof is grounded.

[0050] When the lower data 01, 00 is applied to the switch control circuit 210, the capacitor C₃is again connected with the feedback terminal line 3 as in the previous case. However, the less significant capacitors C₂, C₁to the right of the capacitor C₃are grounded, which is reversed compared to the upper data application. The capacitor C₄to the left thereof is connected to the reference terminal line 4. When applying data 00, the capacitor C₄is connected to the feedback line 3 while the less significant capacitors C₃-C₁to the right thereof are all connected to the ground line 5. Thus, the switch control circuit is responsive to the most significant bit of the digital input signal to connect the more significant capacitors to a first reference voltage and connect the less significant capacitors to a second reference voltage, or to connect the more significant capacitors to the second reference voltage and connect the less significant capacitors to the first reference voltage during the second time interval.

[0051] Describing the operation of the 3-bit MDAC with reference to FIGS. 10 and 12, the capacitors C₈, C₇, C₆, C₅diagonally arranged in the negative slope line corresponding to the upper four digital data 111, 110, 101, 100 of the eight digital data are connected to the feedback terminal line 3 as in the case of the 2-bit MDAC. Sequentially applying the four upper digital data 111, 110, 101, 100 to the switch control circuit 210, the less significant capacitors to the right of the capacitor connected to the feedback terminal line 3, are connected to the reference voltage line 4. The more significant capacitors to the left thereof are connected to the ground line 5.

[0052] Further, applying the four lower digital data 011 to 000 of the eight digital data 111 to 000 to the switch control circuit 210, the capacitors 011/C₅, 010/C₆, 001/C₇, 000/C₈diagonally arranged in a positive slope line, are connected to the feedback terminal line 3. Sequentially applying the four lower digital data 011 to 000 to the switch control circuit 210, the less significant capacitors to the right of the capacitor connected to the feedback terminal line 3, are connected to the ground line 5. The more significant capacitors to the left thereof are connected to the reference voltage line 4. Thus, when applying N bits (2^Nvalues of digital data) to the switch control circuit 210, the arrangement of the capacitors corresponding to the upper 2^N/2 digital data values is different from that corresponding to the lower 2^N/2 digital data, on both sides of the capacitor that is connected to the feedback terminal line 3.

[0053] Referring to FIGS. 13A and 13B, the maximum standard deviation of DNL occurs at the center I=8 of a conventional MDAC based on the unit capacitor array. The standard deviation of DNL of an MDAC according to the invention may be 0.38LSB as shown in FIG. 13B. This can provide about 30% reduced error compared to the standard deviation 0.56LSB of DNL of a conventional MDAC.

[0054] In the drawings and specification, there have been disclosed typical preferred embodiments of the invention and, although specific terms are employed, they are used in a generic and descriptive sense only and not for purposes of limitation, the scope of the invention being set forth in the following claims.