Architecture for an algorithmic analog-to-digital converter

[0001] This application is related to the patent application entitled “Clocking Scheme for an Algorithmic Analog-to-Digital Converter” by Mikko Waltari, filed on even date herewith and having common assignee.

[0002] The present invention relates to analog-to-digital converters and, in particular, relates to an area-efficient analog-to-digital converter having an improved algorithmic architecture.

[0003] Analog-to-digital converters (ADCs) are in widespread use. Essentially, the ADC converts a continuous analog signal into discrete bits by sampling the continuous analog signal and quantizing it into a set of discrete levels. There are various types of ADCs, each having different cost and performance characteristics. Algorithmic ADCs (also known as “cyclic” or “recirculating” ADCs) operate by amplifying a signal to be converted and comparing the amplified signal to a reference voltage. If the amplified signal is greater than the reference voltage, then the most significant bit (MSB) of the output code is set to one, and the reference is subtracted from the amplified signal. If the amplified signal is less than the reference voltage, the MSB is set to zero and there is no subtraction operation. The remaining part of the amplified signal is called the “residue voltage”. The residue voltage undergoes the same operation: it is amplified and compared to determine the next bit in the output code, and another residue voltage is developed. This process continues until the least significant bit (LSB) is obtained.

[0004] Because algorithmic ADCs perform a heavily serial operation using a simple circuit, they are area efficient and consume a low amount of power. The main disadvantage of algorithmic ADCs is their relatively long conversion cycle occasioned by its serial nature of operation. For applications such as video analog-to-digital conversion, having resolutions in the range of 7–14 bits and clock frequencies in the range of 20–50 MHz, this conversion cycle is too slow. Hence, algorithmic topologies have not been suitable for applications such as video ADCs having this speed and resolution range. Instead, other topologies such as pipeline topologies have been used. Additionally, known algorithmic ADCs comprise at least two single-bit processing units sharing a common operational amplifier.

[0005] The present invention provides an algorithmic ADC having an improved area efficiency and a conversion rate suitably high for high speed and bit resolution applications such as video ADC.

[0006] One embodiment of the invention is an algorithmic analog-to-digital converter (ADC). The ADC comprises a sample-and-hold circuit, and one ADC processing unit. The sample-and-hold circuit and the ADC processing unit operate in parallel and share a single operational amplifier.

[0007] Another embodiment of the invention is a method for converting an input analog signal to an output digital bit stream. An input analog signals is sampled and held during a sample-and-hold clock period. N sets of bits are generated during the sample-and-hold clock period by an ADC unit comprising one MDAC and one sub-ADC. The N sets of bits are generated by alternately applying a residue or sampled voltage and a reference voltage to switched capacitors in the MDAC. Finally, the output digital bit stream is generated by adding the N sets of bits.

[0008] Another embodiment of the invention is a method for converting an input analog signal to an output digital bit stream. The method comprises a step for sampling and holding the input analog signal during a sample-and-hold clock period; a step for generating an ADC clock having N cycles per sample-and-hold clock period; a step for generating an intermediate analog voltage per cycle using the sampled analog signal and residue voltages derived from the sampled analog signal; a step for generating a set of data bits per cycle from the intermediate analog voltage; a step for generating feedback signals for generating the intermediate analog voltage in the next cycle; and a step for generating the output digital bit stream using the N sets of data bits.

[0009] Another embodiment of the present invention is a system for conversion of an analog input signal to an output digital bit stream. The system comprises means for sampling and holding an input analog signal; means for applying the sampled and held signal to a switched capacitor circuit; means for generating a residue voltage with the switched capacitor circuit; means for generating N sets of data bits from the residue voltage per sampled and held signal; and means for generating feedback signals corresponding to the data bits to control reference voltages applied to the switched capacitor circuit.

[0010] Other systems, methods, features and advantages of the invention will be or will become apparent to one with skill in the art upon examination of the following figures and detailed description. It is intended that all such additional systems, methods, features and advantages be included within this description, be within the scope of the invention, and be protected by the accompanying claims.

[0036] The present invention provides an algorithmic analog-to-digital converter (ADC) having an improved area efficiency and a conversion rate suitably high for high speed and bit resolution applications such as video ADC. It is area efficient because it contains only one processing unit and has a heavily serial operation principle. By contrast, existing algorithmic ADCs have at least two processing units. The higher conversion rate is achieved by processing multiple bits in each cycle. The processing unit, which employs a switched capacitor topology, resembles a multi-bit stage in a pipelined ADC.

[0037] Overview

[0038] The architecture comprises a sample-and-hold circuit and a multi-bit serial ADC processing unit (the processing unit, in turn, comprises a multiplying digital-to-analog converter (MDAC) and a sub-ADC). These two circuits work in parallel and share a single operational amplifier. As depicted in FIG. 1, the sample-and-hold circuit works at the sampling rate with uneven duty cycle (S/H clock 10), while the processing unit (MDAC and sub-ADC) operates at a faster rate: N (an integer) times the sampling rate (ADC clock 12). In one period of S/H clock 10, analog-to-digital conversion is carried out in N cycles, each cycle yielding k effective bits plus one redundant bit. The redundant bit is used to correct comparator errors using a digital algorithm. In one implementation, the redundant sign digit (RSD) algorithm is used. After the N cycles, the N*K+1 bit analog-to-digital conversion result is formed using the sub-conversion results in a process analogous to the process used in pipelined analog-to-digital converters.

[0039] N clock cycles 1-N are depicted in FIG. 1. Each clock cycle, in turn, is divided into two phases. Hence, cycle 1 consists of phases 1A and 1B, and so on. FIG. 1 depicts generally the events that occur in the sample-and-hold circuit (S/H phases 18) and the processing unit (MDAC phases 14 and sub-ADC phases 16) with respect to the cycles and phases defined by S/H clock 10 and ADC clock 12. The operation of the sample-and-hold circuit consists of two phases: a hold phase 20 and a sample phase 22. Operation of sample-and-hold circuits for sample phase 22 and hold phase 20 are depicted in FIGS. 2a and 2b. During the input sampling phase 2B-NB, FIG. 2a, sample-and-hold circuit 30 takes a sample of the input voltage Vin, continually charging capacitor Cs to the sample voltage during that phase. In the hold phase 1B-2A, FIG. 2b, sample-and-hold circuit 30 buffers this sample voltage and loads it to the switched capacitors of the MDAC.

[0040] As noted above, the ADC processing unit comprises an MDAC and a sub-ADC. MDAC 40 (FIGS. 3a–b) is typically a switched capacitor (SC) circuit comprising an operational amplifier (op amp) 44, N (=2^k) nominally equal capacitors C1 . . . CN, and a number of switches 46 that are controlled by the ADC result from the previous cycle. For clarity, many of the switches are not shown. Sub-ADC 42 can be any type of low latency ADC, such as a flash ADC. Connection of the capacitors of MDAC 40 and the sub-ADC 42 in the residue generation phases 2B, 3B . . . NB is depicted in FIG. 3a, and connection of the MDAC capacitors in the sample phases 2A, 3A . . . NA is depicted in FIG. 3b.

[0041] When the residue generation phase begins (FIG. 3a), all capacitors are charged to the same voltage Vin, which is either the previous residue voltage or, in the case of phase 2B, the new sample voltage provided by the sample-and-hold circuit. The conversion result generated by sub-ADC 42 in the previous B phase is used to control the switches 46 on the left side of capacitors C1, . . . ,CN. By means of switches 46, each of capacitors C1, . . . ,CN is connected to one of three reference voltages (Vr+, 0 or Vr−) according to the control code provided by sub-ADC 42. The resulting charge redistribution forms a residue voltage

[0042] $\mathrm{Vout}=2^k·\mathrm{Vin}-\sum _{n=1}^{2^k-1}\mathrm{Vrn}$
at the output of op amp 44. Sub-ADC 42 then samples the new residue voltage and begins ADC, which provides the switch control signals for the next cycle as well as the sub-conversion result later used to form the ADC output code.

[0043] Residue sampling phase 40, depicted in FIG. 3b, loads all capacitors to the new residue voltage which is still memorized in capacitor C0.

[0044] FIG. 4 is a block diagram of an 11-bit advanced video ADC 100 implementing an algorithmic architecture and using switched capacitor techniques, as described above. It should be understood that ADC 100 is just one implementation example of the principles of the present invention; many other implementations are possible and envisioned.

[0045] ADC 100 comprises an MDAC 102; a 2.5-bit parallel ADC 104; reference buffers (3) 106; digital error correction logic 108; and delay-locked loop (DLL) 110. BGR (bandgap reference) 112 is also provided for generating the on-chip reference currents for the reference buffers, the OTA, the 2.5-bit ADC and the DLL. Alternatively, reference voltages could be used. ADC 100 may be implemented in, for example, a video encoder or decoder, a set-top box, a television tuner, a computer, or in any other environment in which conversion of analog to digital signals is required. In one implementation, video ADC receives analog input from an anti-aliasing filter (not shown), and provides a digital output stream for further processing.

[0046] ADC 100 uses an internal clock that is five (or some other integer N) times faster than the sampling XTAL clock. In one implementation, the maximum frequency of the XTAL clock is 29.5 MHz. One period of a sampling XTAL clock signal 130 is depicted in FIG. 6. DLL 110 multiplies the input XTAL clock frequency (xtal_ck) by five to result in the ADC clock output ck_—5×, having a maximum frequency of 147.5 MHz. FIG. 6 depicts an ADC clock output signal 132. As can be seen, one period of sampling clock 130 corresponds to five periods or cycles of ADC clock 132. Moreover, as described below, each period of ADC clock 132 is divided into two phases for a total of ten phases (see, e.g., signal 134 comprising ten phases). One conversion is completed in one sampling clock period, or in five ADC clock cycles, or in ten phases.

[0047] MDAC 102 is illustrated in more detail in FIG. 5. MDAC 102 comprises a high-performance fully-differential operational transconductance amplifer (OTA) 120, sampling capacitor C_s, capacitors C_{0,1,2,3}p, a plurality of switches and two buffers 122 and 124. In one implementation, op amp 120 has a folded-cascoded topology. This topology is preferable because it is suitable for driving capacitive loads and allows large input common-mode range, wide output swing, high output impedance and high unity-gain frequency. In order to simplify the description, a single-ended version of MDAC 102 is illustrated. It should be understood, however, that fully differential operation is envisioned. FIG. 4, for example, depict differential inputs to MDAC 102 and sub-ADC 104.

[0048] Now, the various switches and their configurations will be described. The purpose of this configuration will become more apparent during the description of FIGS. 7a–j. Capacitors C_{1,2,3}p are connected on their left ends to the output of op amp 120 if switch s2 is closed, or to a reference voltage ref_{p,m,z} if one of switches q_{{1,2,3}{p,z,m}} is closed. Capacitors C_{1,2,3}p are connected on their right ends to ground if switch s_2p is closed, or to the right end of capacitor C_0p if switch h₂ is closed. Capacitor C_0p is connected on its left end to the output of op amp 120. On its right end, capacitor C_0p is connected to the right ends of capacitors C_{1,2,3}p if switch h₂ is closed; to ground if switch s_1p is closed, or to the negative input of op amp 120 if switch h₁ is closed.

[0049] The sampling capacitor C_s is connected at its bottom end to the negative input of op amp 120 if switch sh is closed, or to ground if switch sp_sh is closed. The top end of capacitor C_s is connected to the output of op amp 120 if switch shd is closed, or to the signal in if switch sa_sh is closed. Sampling circuit Cs and its associated switches forms the “sample-and-hold” circuit portion described above in the overview, and operates in parallel with MDAC 102 and sub-ADC 104 as dictated by the positions of the adjacent switches.

[0050] The positive input to op amp 120 is connected to ground and couples the ground signal to the negative input as well if the reset switch is closed. The negative input to op amp 120 is connected to ground if the reset switch is closed, to the right end of capacitor C_0p if switch h₁ is closed, or to the bottom end of capacitor C_s if switch sh is closed. The output of op amp 120 is connected to the left ends of capacitors C_{1,2,3}p if switches s₂ are closed, to sampling capacitor C_s if switch shd is closed, or to ground if the reset switch is closed.

[0051] MDAC 102 is the most critical block of video ADC 100. It performs digital-to-analog conversion of the output of the sub-ADC, subtracts the resulting analog signal from the sampled and held input signal, and amplifies the residue. MDAC 102 is implemented using the switched capacitor (SC) technique; its core is essentially a SC integrator formed around an operational amplifier. Using the conservation of charge at the input node of op amp 120, the output voltage can be computed as:

[0052] $V_{\mathrm{out}}=\left(1+\frac{k}{1+\frac{k}{A_0}}\right)·v_{\mathrm{in}}-\frac{k}{1+\frac{k}{A_0}}·v_{\mathrm{dac}}$

[0053] where

[0054] $k=\frac{C_1+C_2+C_3}{C_0},$
A₀ is the DC gain of op amp 120, v_dac is the output of MDAC 102:

[0055] $v_{\mathrm{dac}}=\frac{1}{C_0}·\sum _{i=1}^3{C}_i{v}_i$

[0056] and v_i is equal to either the positive-, negative- or zero-reference voltage according to table 10 (applied to capacitors C_{1,2,3}p via the input switches). As will be described below, these quantities are available to MDAC 102 at the ends of phases four, six and eight. It is also available at the end of phase ten, but is discarded when a new sample begins processing.

[0057] The output of MDAC 102 is provided to sub-ADC 104 which, in turn, generates five triplets of output bits d_{0,1,2} over one sampling period (i.e. over five cycles or ten phases) and corresponding sets of control signals q_{{1,2,3}{p,z,m}}. The five triplets of output bits d_{0,1,2} are added as will be described to generate the 11-bit digital output stream b_{0-10} of ADC 100, while the control signals q_{{1,2,3}{p,z,m}} are fed back to MDAC 102 to control the operation of the corresponding switches on the left ends of capacitors C_{1,2,3}p to couple the capacitors to the appropriate reference voltages at the appropriate time.

[0058] In one implementation, sub-ADC 104 is a flash ADC. The details of its operation will be described in detail below. First, with reference to FIGS. 7a–7j, the operational state of MDAC 102 during each of the ten phases (corresponding to the ten phases of signal 134 in FIG. 6) will be described. In the descriptions of FIGS. 7a–7j, where a switch and a circuit component are not depicted, this means that the switch is in an open state and adjacent (non-depicted) components have been removed from the circuit.

[0059] FIG. 7a depicts cycle one, phase one. During phase one, the input and output nodes of op amp 120 are reset by closing the reset switches. Phase one cancels any memory effects due to the input parasitic capacitance of op amp 120. Capacitors C_{0,1,2,3}p are also coupled to ground by the closures of switches s₂, s_2p and s_1p. Switches shd, sa_sh, sp_sh and sh are open to remove capacitor C_s, which remains charged to the sample voltage obtained during phases 5–9 of the previous resolution cycle, from the circuit. At the end of phase one, the fifth output triplet of digital bits d_{0,1,2}^v is generated by sub-ADC 104 and, accordingly, the final 11-bit output digital stream b[10:0] of the conversion cycle can be generated by ADC 100. As will be described in more detail with reference to the description of sub-ADC 104, the output digital stream b[10:0] is ready during the middle of phase two. The feedback signals q_{{1,2,3}{p,z,m}} are also available from sub-ADC 104, but are not needed and are discarded.

[0060] FIG. 7b depicts cycle one, phase two. During phase two, the sampled input voltage held by capacitor C_s is buffered via the closure of switches sh and shd, causing capacitors C_{0,1,2,3}p to be charged to the sampled voltage. Sub-ADC 104 is coupled to and samples the output of MDAC 102.

[0061] FIG. 7c depicts cycle two, phase three. The configuration of MDAC 102 during phase two is the same as it was during phase three. The output of the sub-ADC comparators is latched at the beginning of phase three, and sub-ADC 104 generates the first output triplet of digital bits d_{0,1,2}^I as well as feedback signals q_{{1,2,3}{p,z,m}} at the end of phase three.

[0062] FIG. 7d depicts cycle two, phase four. Switches s₂ are opened to remove the sampled voltage from capacitors C_{1,2,3}p, and the right ends of capacitors C_{1,2,3}p are coupled to the negative input of op amp 120 via the closure of switches h_{2 and h1} (and opening of switches s_2p and s_1p). The sampled voltage carried by capacitor C_s is removed from the circuit by the opening of switches shd and sh, and capacitor C₀ is coupled between the output and input of op amp 120 by the closure of switch h₁ and opening of switch h₂.

[0063] Also in phase four, according to feedback signals q, the appropriate reference buffers are coupled to capacitors C_{1,2,3}p. In this regard, it should be understood that capacitors C_{1,2,3}p are not necessarily coupled to the three reference buffers by three separate switches (e.g., switches q_1{p,z,m} as depicted). For instance, the control signals q could control the operation of just one switch coupled to the inputs of each of capacitors C_{1,2,3}p to couple the capacitors to the appropriate reference buffer (as determined by the control signals q). In one implementation, the reference buffer voltages ref_p, ref_z, and ref_m are created by sending a reference current (25 μA) through a resistor ladder. At the end of phase four, in one implementation, the MDAC output settles to the final value within an accuracy of 1.6 mV (1LSB).

[0064] FIG. 7e depicts cycle three, phase five. In phase five, switches s2 are closed, and switches q_{{1,2,3}{p,z,m}} opened to remove capacitors C_{1,2,3}p from the reference voltages applied in the previous phase and couple capacitors C_{1,2,3}p to the new residue voltage at the output of MDAC 102. Capacitor C_0p is also coupled in the feedback loop around op amp 120 during phase five by the closure of switch h₁. Sampling capacitor C_s begins to sample the input analog signal in via the closures of switches sa_sh and sp_sh. This operation occurs in the middle of phase five when switching activity is at its minimum so that the sample is free of any disturbances from the power rails. At the end of phase five, the second triplet of output bits d_{0,1,2}^II are ready at the output of sub-ADC 104, as are feedback signals q_{{1,2,3}{p,z,m}}.

[0065] FIG. 7f depicts cycle three, phase six. Phase six is very similar to phase four, with the exception that the sampling capacitor C_s is now actively sampling the input analog signal. The appropriate reference buffers ref_{p,z,m} are coupled to capacitors C_{1,2,3}p according to the feedback signals q_{{1,2,3}{p,z,m}} generated in phase five. At the end of phase six, the MDAC output settles to the final value within an accuracy of 6.4 mV.

[0066] FIG. 7g depicts cycle four, phase seven. This phase is identical in operation to phase five. Sampling capacitor C_s continues to sample the input analog signal. Switches S₂ are closed, and switches q_{{1,2,3}{p,z,m}} are opened, to remove capacitors C_{1,2,3}p from the reference voltages applied in the previous phase and couple capacitors C_{1,2,3}p to the new residue voltage at the output of MDAC 102. At the end of phase seven, the third triplet of output bits d_{0,1,2}^III are ready at the output of sub-ADC 104, as are feedback signals q_{{1,2,3}{p,z,m}}.

[0067] FIG. 7h depicts cycle four, phase eight. This phase is identical in operation to phase six. Sampling capacitor C_s continues to sample the input analog signal, and the appropriate reference buffers ref_{p,z,m} are coupled to capacitors C_{1,2,3}p according to the feedback signals q_{{1,2,3}{p,z,m}} generated in phase seven. At the end of phase eight, the MDAC output settles to the final value within an accuracy of 25.6 mV.

[0068] FIG. 7i depicts cycle five, phase nine. This phase is identical in operation to phase seven. Sampling capacitor C_s continues to sample the input analog signal. Switches S₂ are closed, and switches q_{{1,2,3}{p,z,m}} are opened, to remove capacitors C_{1,2,3}p from the reference voltages applied in the previous phase and couple capacitors C_{1,2,3}p to the new residue voltage at the output of MDAC 102. At the end of phase seven, the fourth triplet of output bits d_{0,1,2}^IV are ready at the output of sub-ADC 104, as are feedback signals q_{{1,2,3}{p,z,m}}.

[0069] FIG. 7j depicts cycle five, phase ten. The input signal is sampled onto C_s: the sp_sh switch closes, followed by the sa_sh switch. This operation occurs in the middle of phase ten when the switching activity is at its minimum so that the sample is free of any disturbances from the power rails. At the sampling instant, the sp_sh switch opens, leaving the top plate of C_s floating (shd is also open). As the sp_sh switch is always connected to ground, the charge injected into C_s is constant. When the sa_sh switch opens, C_s is disconnected from the input. The charge injection and the input voltage variation cause distortion to the voltage on C_s, but this distortion is not dangerous, as the sampled voltage is in the form of a charge and cannot be changed as there is no DC path to ground. In phase ten, the MDAC output must settle to the final value within an accuracy of 102.4 mV.

[0070] Sub-ADC 104 may be any type of low latency ADC. In one implementation, depicted in FIG. 8, the sub-ADC is a 2.5 bit sub-ADC 130 having a full-flash architecture to maximize the settling time of the MDAC output. As the operation of a full flash ADC is well known to those of skill in the art; it will be only briefly described herein. In order to relax the quantization accuracy specification for the sub-ADC, a digital correction algorithm is used. In one implementation, redundant sign digit coding (RSD) is used. Using one bit of redundancy in each cycle, only six comparators 132 and digital logic 134 are required. In one implementation, digital logic 134 comprises 3.3V digital logic. The effect of the RDS coding on the sub-ADC transfer function 140 is shown in FIG. 9.

[0071] The performance of flash ADC 130 is limited primarily by the accuracy of comparators 132 and secondarily by the accuracy of the reference voltage. Each of these can be modeled as an offset in the comparator threshold level. The amount of offset voltage that can be tolerated for each cycle when the RSD coding is employed is, in general:

[0072] $V_{\mathrm{offset}}=\pm \frac{r}{2^{n+R}}·V_{\mathrm{ref}},$

[0073] where r is the number of redundancy bits per cycle, n is the effective cycle resolution and V_ref is the reference voltage.

[0074] In one implementation, comparators 132 are implemented using an input sensing pre-amplifier followed by a regenerative latch. The offset voltage, generated by component mismatch and process parameter variations, is reduced by the pre-amplification and is further reduced by applying auto-zeroing techniques. The different reference voltage levels needed are implemented with a resistor string 136, which relies on the relative matching of the resistors. When RDS coding is applied, the matching requirements can easily be achieved without use of any high-precision components.

[0075] The thermometer code at the output of the comparators is converted into the binary output bits d_{0,1,2}, needed by the digital decoder, and the feedback signals q_{{1,2,3}{p,z,m}}, needed by MDAC 102, according to the table set forth in FIG. 10. The feedback signals are enabled during phases two, four, six and eight by a DAC_EN signal generated by a clock generator. Five triplets of output bits are level-shifted down and fed to decoder logic that builds the 11-bit output code, as described below. In one implementation, the three output bits are level-shifted down to 1.2V. The five triplets of output bits are added by the decoder logic according to the digital reconstruction algorithm set forth in FIG. 11, generating the final output bits b[10:0] of algorithmic ADC 100.

[0076] Digital reconstruction logic or decoder 150 is illustrated in FIG. 12, and the timing for logic 150 is illustrated in FIG. 13 with reference to the DLL clock and ADC clock (five cycles per DLL clock period). Logic 150 comprises a finite state machine, synchronous with the DLL clock, that generates latch signals DD[5:1] to produce triplets of data x[2:0], y[4:2], x[6:4], y[8:6] and x[10:8] from elements 152, 154, 156, 158 and 160, wherein x[3], x[7], y[0], y[1], y[5], y[9] and y[10]=0. Ripple-carry full-adder 162 sums the five triplets of data (now in the form x[10:0] and y[10:0]) to produce the 11-bit digital output stream b[10:0].

[0077] The present invention provides numerous advantages and differences relative to previous algorithmic ADCs. The use of a single MDAC-based processing unit, rather than two units as in known algorithmic ADCs, makes the area very small. An extra clock phase is used to load the capacitors. In conventional algorithmic ADCs, by contrast, two MDACs operate in opposite phases—one generates a residue, which is sampled by the other one, and vice-versa. While the elimination of the other MDAC has a slight cost in increased conversion time, this penalty is offset by a faster settling time because the elimination of extra load capacitors (in the eliminated MDAC) makes the MDAC load smaller. Additionally, in the present invention, there is no immediate need for the result from the sub-ADC, because of the half clock cycle additional time from the moment when the sub-ADC is triggered and the moment that the result is needed by the MDAC.

[0078] Resolving multiple bits per conversion cycle yields a certain number of bits in fewer conversion cycles resulting in a higher conversion rate.

[0079] Integration of the sample-and-hold circuit with the MDAC (they share the same op amp) is another novelty of the present invention. Having a slower rate sample-and-hold circuit working in parallel with a faster rate ADC alleviates the task of a circuit driving the ADC, since the time that can be used to charge the sampling capacitor is not set by the internal clock rate of the ADC: it is set by the slower sample-and-hold clock rate. Furthermore, the sampling capacitor can be sized independently of the MDAC capacitors leading to a more optimal solution.

[0080] While various embodiments of the invention have been described, it will be apparent to those of ordinary skill in the art that many more embodiments and implementations are possible that are within the scope of this invention.