Patent Publication Number: US-2022239311-A1

Title: Techniques for linearizing digital-to-analog converters in sigma-delta analog-to-digital converters

Description:
BACKGROUND 
     Sigma-delta modulation is a useful technique for encoding analog signals into digital signals for an analog-to-digital converter (ADC). A sigma-delta ADC may be configured with a multibit quantizer to support data encoding for various applications, such as cellular telecommunications (e.g., fourth generation (4G) systems, fifth generation (5G) systems). These applications may require wide-bandwidth high-resolution high-linearity power-efficient ADCs. 
     Some sigma-delta ADC designs employ a multi-bit digital-to-analog converter (DAC) in a feedback loop of the ADC. However, a mismatch between elements of a multibit DAC can cause non-linearities in DAC performance, limiting the accuracy of the ADC. Furthermore, existing linearization techniques often increase the delay in the feedback loop, which can negatively impact overall ADC performance. 
     SUMMARY 
     A sigma-delta modulator is described. The sigma-delta modulator may include a multibit quantizer configured with a mapping engine to perform one or more of a sorting, a mapping, and switching operating within the multibit quantizer. In some embodiments, the mapping engine is embedded within the multibit quantizer. 
     The sigma-delta modulator may further include a first summing node configured to subtract a feedback analog signal from a received input analog signal and generate a first analog output signal; a loop filter configured to receive and filter the first analog output signal from the first summing node; and a second summing node configured to subtract the feedback analog signal from the first filtered analog output signal and generate a second analog output signal, wherein the multibit quantizer is configured to receive the second analog output signal and a reference signal from the mapping engine to produce a digital output signal. 
     In some embodiments, the mapping engine is coupled between the reference signal and the multibit quantizer. 
     In some embodiments, the sigma-delta modulator may further include an excess loop delay (ELD) DAC configured to: receive the digital output signal via a feedback loop; covert the digital output signal to the feedback analog signal; and provide the feedback analog signal to the second summing node. In some embodiments, the ELD DAC is further configured to convert the digital output signal to the feedback analog signal. 
     In some embodiments, the sigma-delta modulator may further include a main DAC configured to receive the digital output signal via a feedback loop; covert the digital output signal to the feedback analog signal; and provide the feedback analog signal to the first summing node. 
     In some embodiments, the main DAC is further configured to provide the feedback analog signal as an input to a mismatch sensor via a direct signaling path between the main DAC and the mismatch sensor. 
     In some embodiments, the mismatch sensor is further configured to measure a static mismatch between unit elements of the main DAC; and provide measurement information including the measured static mismatch to a logic associated with the multi-bit continuous-time sigma-delta modulator. 
     In some embodiments, the mismatch sensor is further configured to measure a dynamic mismatch between unit elements of the main DAC; and provide measurement information including the measured dynamic mismatch to a logic associated with the multi-bit continuous-time sigma-delta modulator. 
     In some embodiments, the logic is further configured with a sorting algorithm, a mapping algorithm, or a switching algorithm, or any combination thereof. 
     In some embodiments, the mapping engine is further configured to apply one or more of the sorting algorithm, the mapping algorithm, or the switching algorithm, or any combination thereof, to the reference. 
     In some embodiments, the mapping engine is external to a feedback loop of the multi-bit continuous-time sigma-delta modulator and is further configured to provide a linearization of the multi-bit continuous-time sigma-delta modulator without an output from the multibit quantizer. 
     In some embodiments, a feedback loop of the multi-bit continuous-time sigma-delta modulator comprises a set of per-bit parallel loops, each loop configured to provide a per-bit signal summation of the filtered analog output signal such that an output of the multiple per-bit parallel loops is a multi-bit quantization digital output signal. 
     A device is described. The device includes a first summing node configured to subtract a feedback analog signal from a received input analog signal and generate a first analog output signal; a loop filter configured to receive and filter the first analog output signal from the first summing node; a multilevel quantizer including a plurality of slices coupled to the loop filter to receive the filtered signal and output a digital output signal, each slice of the plurality of slices includes an amplifier coupled to a second summing node, a latch coupled to the second summing node, an ELD DAC coupled to the second summing, and a reference DAC coupled to the second summing node, wherein the reference DAC is configured to receive from a mapping engine a set of output reference codes. 
     In some embodiments, the mapping engine is further configured to receive the digital output signal as feedback via a feedback loop plus the set of input codes to provide the set of output codes to the reference DAC. 
     In some embodiments, the digital output signal comprises a multibit quantization digital output signal. 
     In some embodiments, a feedback loop of the device comprises a set of per-bit parallel loops, each loop configured to provide a per-bit signal summation of the filtered analog output signal such that an output of the multiple per-bit parallel loops is a multi-bit quantization digital output signal. 
     In some embodiments, the device may further include a set of respective latches configured to provide an output of the multiple per-bit parallel loops to provide a multi-bit quantization digital output signal. 
     In some embodiments, the multibit quantizer is a multilevel quantizer including a number of slices of 1-bit comparator latches and a number of duplicate ELD summation nodes. 
     In some embodiments, the reference DAC is configured to convert a number of reference codes into a reference current, wherein the mapping engine further comprises a number of switches to connect a set of input codes to the set of output reference codes based on a selected order. 
     A method may be described. The method may include filtering, via a filter of a sigma-delta modulator, a first analog output signal; subtracting, via a summing node of the sigma-delta modulator, a feedback analog signal from the filtered analog output signal; generating, via an output of the summing node of the sigma-delta modulator, a second analog output signal; and receiving, via a multibit quantizer of the sigma-delta modulator, the second analog output signal and a reference signal from a mapping engine to produce a digital output signal, wherein the mapping engine is coupled between the reference signal and the multibit quantizer. 
     In some embodiments, the mapping engine is further configured to receive the digital output signal as feedback via a feedback loop plus a set of input codes to provide a set of output codes to a reference DAC. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The present disclosure may be better understood, and its numerous features and advantages made apparent to those skilled in the art by referencing the accompanying drawings. The use of the same reference symbols in different drawings indicates similar or identical items. 
         FIG. 1  is a block diagram of a continuous-time sigma-delta ADC in accordance with some embodiments. 
         FIG. 2  is a block diagram of a continuous-time sigma-delta ADC in accordance with some embodiments. 
         FIG. 3  is a block diagram of a continuous-time sigma-delta ADC in accordance with some embodiments. 
         FIG. 4  is a block diagram of a continuous-time sigma-delta ADC in accordance with some embodiments. 
         FIG. 5  is a block diagram of a continuous-time sigma-delta ADC in accordance with some embodiments. 
     
    
    
     DETAILED DESCRIPTION 
     Various aspects of the present disclosure relate to techniques for linearizing a DAC in a continuous-time sigma-delta ADC. In an ADC, an analog signal may be sampled with a sampling frequency and subsequently quantized into a digital signal. In some embodiments, this may introduce a quantization error noise. The continuous-time sigma-delta ADC may perform delta modulation, which may encode the change in the signal (i.e., delta), rather than the absolute value. The result is a stream of pulses, as opposed to a stream of numbers, as is the case with pulse code modulation. In sigma-delta modulation, the accuracy of the modulation is improved by passing the digital output through a DAC and adding (sigma) the resulting analog signal, to the input signal (i.e., the signal before delta modulation), thereby reducing the error introduced by the delta-modulation. 
     Continuous-time sigma-delta ADCs include one or multiple sigma-delta modulators (SDMs). An SDM is a feedback loop containing a loop filter, a quantizer, and a feedback DAC(s). The function of the quantizer is sampling and quantization. Its input signal is continuous in time domain and continuous in voltage (or current) domain, (i.e., a continuous-time, continuous-value (analog signal)). Its output signal may be discrete in time domain and discrete in voltage domain (i.e., discrete-time discrete-value (digital signal)). The function of the main feedback DAC is a zero-order hold, which converts the digital signal to analog signal. 
     Sigma-delta ADCs with multi-bit quantization are popular for a lot of applications which need wide-bandwidth high-resolution high linearity power-efficient ADCs. To achieve high linearity, the mismatch of the multibit DAC is often a bottleneck. There are some linearization techniques for high-linearity DACs, such as sorting, data weighted averaging, randomization, etc. However in the highspeed sigma-delta ADCs, the DAC is in a feedback loop. In some embodiments, the DAC linearization techniques may increase the delay in the feedback loop, which is not desired. Various aspects of the present disclosure provide improvement to linearization techniques by changing the references of the multibit quantizer. As a result, this reduces delay in the feedback loop of the sigma-delta modulator, which is beneficial for high-speed sigma-delta ADCs. 
     For example, a mapping engine is typically in the main feedback loop of the SDM, and more specifically the mapping engine is between the quantizer and the main DAC. In the present disclosure, the mapping engine is not part of the main feedback loop of the SDM. By sorting, mapping, and switching of the reference code of the reference DAC, a corresponding sorting, mapping, and switching of the unit element of the main DAC is achieved. If the mapping engine needs the quantizer output as an input, the mapping engine is between the quantizer and the reference DAC, but out of the main feedback loop. Because the mapping engine is not in the main feedback loop, the delay of the mapping engine also does not contribute to the total loop delay of the SDM main feedback loop. In the case that the mapping engine needs the quantizer output information, the SDM main feedback loop and the DAC linearization loop are partially decoupled, and hence can be separately optimized. 
       FIG. 1  is a block diagram of a continuous-time sigma-delta ADC  100  in accordance with some embodiments. The continuous-time sigma-delta ADC  100  may implement a feedforward, or feedback, or a hybrid feedforward-feedback SDM architecture. In the following description of the continuous-time sigma-delta ADC  100 , certain components may be added or omitted from the continuous-time sigma-delta ADC  100 . The continuous-time sigma-delta ADC  100  may support analog-to-digital conversion of signals by processing a signal over one or more components of the continuous-time sigma-delta ADC  100 . The continuous-time sigma-delta ADC  100  may include a loop filter  104 , a multibit quantizer  106 , a DAC  112 , a mismatch sensor  114 , and a logic  116 . In the example of  FIG. 1 , the multibit quantizer  106  is embedded with a mapping engine  108 . The multibit quantizer  106  thereby includes the mapping engine  108  and a quantizer  110 . 
     One or more of the components of the continuous-time sigma-delta ADC  100  may be coupled (e.g., operatively, communicatively, functionally, electronically) to each other. One or more of the components of the continuous-time sigma-delta ADC  100  may include one or more inputs and one or more outputs. In some embodiments, the loop filter  104  may include multiple inputs. For example, the loop filter  104  may include a first input configured to receive an input signal  102  (e.g., an analog signal) and a second input coupled to an output of the DAC  112  to receiver another signal (e.g., a feedback signal  118 ). The loop filter  104  may also include an output that is coupled to a first input of the multibit quantizer  106 . For example, the output of the loop filter  104  may be coupled to an input of the quantizer  110 . 
     The multibit quantizer  106  may include an output configured to output a signal  120  (e.g., a digital signal). In some embodiments, the output of the multibit quantizer  106  may be coupled to an input of the DAC  112 . In some embodiments, the DAC  112  may include a second output coupled to an input of the mismatch sensor  114 . An output of the mismatch sensor  114  may be coupled to an input of the logic  116 . In some embodiments, the mismatch sensor  114  may measure a static mismatch or a dynamic mismatch, or both, between elements of the DAC  112  as described herein. The logic  116  may be configured with various algorithms including: a sorting algorithm, a mapping algorithm, or a switching algorithm, and the like to support linearization for the continuous-time sigma-delta ADC  100 . In some embodiments, an output of the logic  116  may be coupled to a second input of the multibit quantizer  106 . For example, the output of the logic  116  may be coupled to an input of the mapping engine  108  embedded within the multibit quantizer  106 . The mapping engine  108  may be coupled to the quantizer  110  within the multibit quantizer  106 . The mapping engine  108  may be configured with one or more circuit elements, such as switches to support linearization techniques as described herein. 
       FIG. 2  is a block diagram of a continuous-time sigma-delta ADC  200  in accordance with some embodiments. The continuous-time sigma-delta ADC  200  may implement a feedforward SDM architecture. In the following description of the continuous-time sigma-delta ADC  200 , certain components may be added or omitted from the continuous-time sigma-delta ADC  200 . The continuous-time sigma-delta ADC  200  may support analog-to-digital conversion of signals by processing a signal over one or more components of the continuous-time sigma-delta ADC  200 . The continuous-time sigma-delta ADC  200  may include a set of summing nodes (e.g., a summing node  204  and a summing node  208 ), a loop filter  206 , a quantizer  210  associated with a corresponding delay  214 , an excess loop delay (ELD) compensation DAC  220 , a main DAC  224 , a mismatch sensor  230 , a logic  232 , and a mapping engine  236 . In some embodiments, the continuous-time sigma-delta ADC  200  may provide a feedback loop, which may include one or more of the components (e.g., the second input of the summing node  204 , both the input and the output of the loop filter  206 , all of the inputs of the summing node  208 , the first input of the quantizer  210 , both the input and the output of the ELD DAC  220 , both the input and the output of the main DAC  224 , and the first input of the mapping engine  236 ) of the continuous-time sigma-delta ADC  200 , as described herein. 
     One or more of the components of the continuous-time sigma-delta ADC  200  may be coupled (e.g., operatively, communicatively, functionally, electronically) to each other. One or more of the components of the continuous-time sigma-delta ADC  200  may include one or more inputs and one or more outputs. The summing node  204  may include one or more inputs, such as a first input to receive a signal and a second input coupled to a first output of the main DAC  224  to receive another signal. The summing node  204  may also include an output coupled to an input of the loop filter  206  to output a signal to the loop filter  206 . The loop filter  206  may also include an output that is coupled to a first input of the summing node  208  to receive a signal from the loop filter  206 . The summing node  208  may also include a second input coupled to an output of the ELD DAC  220  to receive a signal from the ELD DAC  220 . The quantizer  210  may include one or more inputs, for example, a first input coupled to an output of the summing node  208  to receive a signal from the summing node  208 , and a second input coupled to an output of the mapping engine  236  to receive a signal from the mapping engine  236 . 
     The quantizer  210  may also include an output that is coupled to an input of the delay  214  to output a signal to the delay  214 , which may include one or more outputs including a first output to provide an output signal  216 , a second output coupled to a first input of the mapping engine  236  to output a signal to the mapping engine  236 , and a third output coupled to an input of the ELD DAC  220  to output a signal to the ELD DAC  220  and an input to the main DAC  224  to output a signal to the main DAC  224 . The main DAC  224  may also include a second output coupled to an input of the mismatch sensor  230  to output signal to the mismatch sensor  230 , which may include an output coupled to an input of the logic  232  to output a signal to the logic  232 . The logic  232  may include an output that is coupled to a second input of the mapping engine  236  to output a signal to the mapping engine  236 . Additionally, the mapping engine  236  may include a third input to receive a reference signal  234 . 
     In the example of  FIG. 2 , the summing node  204  may receive, via the first input, an input signal  202 , which may be an analog signal. The summing node  204  may also receive, via the second input, a main feedback signal  226  from the output of the main DAC  224 . The summing node  204  may be configured to add or subtract signals, for example, add or subtract the input signal  202  from the main feedback signal  226  to produce a resultant signal. The summing node  204  may provide, via the output of the summing node  204 , the resultant signal to the input of the loop filter  206 . The loop filter  206  may be made up of one or more circuit elements. For example, the loop filter  206  may be made up of one or more resistors and capacitors. The loop filter  206  may also be associated with a respective transfer function that models the continuous-time sigma-delta ADC  200 . 
     The loop filter  206  may provide, via the output of the loop filter  206 , a filtered signal to the first input of the summing node  208 . The summing node  208  may also receive, via the second input, a feedback ELD compensation signal  222  from the output of the ELD DAC  220 . The summing node  208  may be configured to add or subtract signals, for example, add or subtract the filtered signal from the feedback ELD compensation signal  222  to produce a resultant signal. The summing node  208  may provide, via the output of the summing node  208 , the resultant signal to the first input of the quantizer  210 , which may also receive a resultant signal  212  at the second input of the quantizer from the output of the mapping engine  236 . The quantizer  210  may convert the analog output of the summing node  208  into digital code. 
     The mapping engine  236  may be configured to receive, via the third input, a reference signal  234 . The mapping engine  236  may also be configured to receive, via the second input, a resultant signal from the output of the logic  232 . Additionally, or alternatively, the mapping engine  236  may also be configured to receive, via the first input, a feedback signal  216  from the output of the delay  214 . In some embodiments, the mismatch sensor  230  may measure a static mismatch or a dynamic mismatch, or both, between elements of the main DAC  224 . The mapping engine  236  may be configured with one or more circuit elements, such as switches to support linearization techniques. 
     The logic  232  may be configured with various algorithms including: a sorting algorithm, a mapping algorithm, or a switching algorithm, and the like to support linearization for the continuous-time sigma-delta ADC  200 . As illustrated in the example of  FIG. 2 , instead of configuring the mapping engine  236  to be between the quantizer  210  and the main DAC  224 , the mapping engine  236  is configured between the reference  234  and the quantizer  210  (e.g., a multibit quantizer). The analog signal output from the summing node  208  and the resultant signal  212  from the mapping engine  236  may be input to the quantizer  210  (e.g., a multibit quantizer) and an input to a delay  214  associated with the quantizer  210  (τ 1  is the delay  214  of the quantizer  210 ). The output of the delay  214  may be the output signal  216  of the continuous-time sigma-delta ADC  200 . 
     In the example of  FIG. 2  the DACs (e.g., the main DAC  224 , the ELD DAC  220 ) have non-linearities, and these non-linearities are the result of mismatches in elements of the DAC (e.g., the main DAC  224 , the ELD DAC  220 ), the mismatch sensor  230  detects the mismatches in the DAC elements (e.g., the main DAC  224 , the ELD DAC  220 ), based on the information received from the logic  232  or the output signal  216 , or both, the mapping engine  236  may be configured to adjust (e.g., change) an order of how the reference is connected to the quantizer  210 . Additionally, the mapping engine  236  may generate a map of the non-linearities, and to generate a correction signal for the quantizer  210  based on the identified non-linearities. 
     In some embodiments, the quantizer  210  (e.g., a multibit quantizer) may be implemented as a flash sub-ADC. This flash sub-ADC may be configured to compare the input signal of the quantizer  210  (which may be the output signal of the summing node  208 ) with a series of reference (e.g., reference voltages or reference currents). The unit 1-bit comparator in the flash sub-ADC (e.g., multibit quantizer  210 ) and unit element of the main DAC  224  may be one-to-one connected through a connection circuitry (e.g., samplers, buffers, D-flipflops, etc.). By sorting, mapping, or switching, or any combination thereof, the reference among the unit 1-bit comparators, an effective sorting, mapping, or switching, or any combination thereof of the unit elements of the main DAC  224  may be achieved. Therefore, as illustrated in  FIG. 2 , the mapping engine  236  is not in the main feedback loop between the quantizer  210  and the DACs  220  and  224 , reducing the loop delay and improving the performance of the continuous-time sigma-delta ADC  200 . 
       FIG. 3  is a block diagram of a continuous-time sigma-delta ADC  300  in accordance with some embodiments. In the following description of the continuous-time sigma-delta ADC  300 , certain components may be added or omitted from the continuous-time sigma-delta ADC  300 . The continuous-time sigma-delta ADC  300  may implement aspects of the continuous-time sigma-delta ADC  100  as described in  FIG. 1 . For example, the continuous-time sigma-delta ADC  300  may implement a feedforward SDM architecture. The continuous-time sigma-delta ADC  300  may include summing nodes, such as a summing node  304  and a summing node  312 , which may be configured to add or subtract signals. The continuous-time sigma-delta ADC  300  may include a loop filter  308 , which may be made up of one or more circuit elements (e.g., one or more resistors, capacitors, inductors, etc.). The continuous-time sigma-delta ADC  300  may also include an amplifier  310 , an ELD DAC  314 , a reference (REF) DAC  318 , a latch  316 , a main DAC  324 , a mismatch sensor  330 , a logic  332 , and a mapping engine  334 . One or more of the components of the continuous-time sigma-delta ADC  300  may be coupled (e.g., operatively, communicatively, functionally, electronically) to each other. In some embodiments, the continuous-time sigma-delta ADC  300  may provide a feedback loop, which may include one or more of the components of the continuous-time sigma-delta ADC  300 , as described herein. 
     The summing node  304  may include one or more inputs, such as a first input to receive a signal and a second input coupled to a first output of the main DAC  324  to receive another signal. The summing node  304  may also include an output coupled to an input of the loop filter  308  to output a signal to the loop filter  308 . The loop filter  308  may also include an output that is coupled to an input of the amplifier  310  to receive a signal from the loop filter  308 . The summing node  312  may include one or more inputs, including a first input coupled to an output of the amplifier  310 , a second input coupled to an output of the REF DAC  318  to receive a signal from the REF DAC  318 , and a third input coupled to an output of the ELD DAC  314  to receive a signal from the ELD DAC  314 . The amplifier  310  (e.g., a Gm cell also referred to as a transconductance amplifier) may convert a voltage signal into a current signal. 
     The summing node  312  may include an output coupled to an input of the latch  316 . The latch  316  may include an output to provide an output signal (e.g., output signal  320 ). The output of the latch  316  may be coupled to an input of the ELD DAC  314  and an input to the main DAC  324 . The main DAC  324  may include a second output coupled to an input of the mismatch sensor  330 , which may include an output coupled to an input of the logic  332 . The logic  332  may include an output coupled to a first input of the mapping engine  334 . The mapping engine  334  may include a set of second inputs to receive a set of codes, and a set of outputs to provide reference codes to an input of the REF DAC  318 . 
     In the example of  FIG. 3 , the continuous-time sigma-delta ADC  300  may support a linearization technique (e.g., a DAC linearization technique) that may not involve a quantizer  320  output. In some embodiments, the DACs (e.g., the main DAC  324 , the ELD DAC  314 , etc.) may include non-linearities that need to be corrected, and these non-linearities may be the result of mismatches in elements of the DAC (e.g., the main DAC  324 , the ELD DAC  314 ). The mismatch sensor  330  may detect the mismatches in the DAC elements (e.g., the main DAC  324 , the ELD DAC  314 ), and provide these as input to the mapping engine  334 , which may change the order of how the one or more codes (e.g. Codes 1, . . . , Code N) are connected to one or more reference codes (e.g., a ref code 1, . . . , a ref code N). 
     In some embodiments, the mapping engine  334  may be positioned external to the feedback loop of the continuous-time sigma-delta ADC  300 . One or more operations including sorting, mapping, or switching, or any combination thereof of unit elements of the main DAC  324  may be achieved by sorting, mapping, or switching, or any combination thereof of the current reference of a multi-bit quantizer  320 . As illustrated in  FIG. 3 , an n+1 level quantizer  320  is shown. The n+1 level quantizer  320  may include n slices of 1-bit comparators (i.e., latches  316 ) and a duplicated current-mode excess loop delay (e.g., the ELD DAC  314 ) at summation nodes  312 . In some embodiments, the REF DAC  318  converts the reference code (referred to as ref code) into a reference current. 
     The n+1 level quantizer  320  may haven reference codes, which may be, for example, code 1, code 2, . . . , code n. In some embodiments, the mapping engine  334  may be configured with one or more switches to connect the input code 1, code 2, . . . , code n to the output ref code 1, ref code 2, . . . , ref code n. In some other embodiments, the mapping engine  334  may be configured with one or more switches to connect the input code 1, code 2, . . . , code n to the output ref code 1, ref code 2, . . . , ref code n based on a selected order. Thus, a particular operation, for example, sorting, mapping, or switching, or any combination thereof can be implemented through the connection from the input code to the output code of the mapping engine  334 . The 1-bit comparator (e.g., the latch  316 ) and the 1-bit unit DAC  318  may be one-to-one connected. By sorting, mapping, or switching, or any combination thereof of the reference code of the quantizer  320 , an equivalent sorting, mapping, or switching, or any combination thereof of unit elements of a DAC (e.g., the ELD DAC  314 , the main DAC  324 ) may be effectively achieved. 
     The continuous-time sigma-delta ADC  300  may support linearization techniques that might not need information from a quantizer  320  output. In some examples, the continuous-time sigma-delta ADC  300  may perform a sorting linearization technique or a mapping linearization technique, or both. In these examples, with the measured information on a static and a dynamic mismatch of unit elements of a DAC (e.g., the ELD DAC  314 , the REF DAC  318 , the main DAC  324 ), a certain order of the unit elements of the DAC (e.g., the ELD DAC  314 , the REF DAC  318 , the main DAC  324 ) may be calculated by the logic  332 . This order may be fixed in the operation of the DAC. In some embodiments, the mapping engine  334  may be configured to implement a fixed connection with a certain optimal order between the input code and the output code. In this case, as the mapping engine  334  is not switched during the operation of the continuous-time sigma-delta ADC  300 , its delay is not harmful. 
     Some linearization techniques, such as switching linearization techniques might not need information from a quantizer  320  output, for example, a randomization linearization technique. In this example, the order of unit elements of a DAC (e.g., the ELD DAC  314 , the REF DAC  318 , the main DAC  324 ) is randomly switched. In this case, after the switching, for example, the REF DAC  318  output current and the comparator input may be settled before the next sampling moment of the comparator. Thus, in this case, the delay of the mapping engine  334  when a switching happens may be less than one sampling clock period of the continuous-time sigma-delta ADC  300 . As illustrated in  FIG. 3 , the main feedback loop and ELD feedback loop of the continuous-time sigma-delta ADC  300  are speed critical and sensitive to extra delay. The REF DAC  318  and the mapping engine  334  are configured for the DAC linearization technique. For the case that the mapping engine  334  is switching during the operation of the continuous-time sigma-delta ADC  300 , in some embodiments, the REF DAC  318  and the mapping engine  334  have maximally one sampling clock period to settle when the switching happens. 
       FIG. 4  is a block diagram of a continuous-time sigma-delta ADC  400  in accordance with some embodiments. In the following description of the continuous-time sigma-delta ADC  400 , certain components may be added or omitted from the continuous-time sigma-delta ADC  400 . The continuous-time sigma-delta ADC  400  may implement aspects of the continuous-time sigma-delta ADC  100  as described in  FIG. 1 . For example, the continuous-time sigma-delta ADC  400  may implement a feedforward SDM architecture. The continuous-time sigma-delta ADC  400  may include summing nodes, such as a summing node  404  and a summing node  412 , which may be configured to add or subtract signals. The continuous-time sigma-delta ADC  400  may include a loop filter  408 , which may be made up of one or more circuit elements (e.g., one or more resistors, capacitors, inductors, etc.). The continuous-time sigma-delta ADC  400  may also include an amplifier  410 , an ELD DAC  414 , a REF DAC  418 , a latch  416 , a main DAC  424 , a mismatch sensor  430 , a logic  432 , and a mapping engine  434 . One or more of the components of the continuous-time sigma-delta ADC  400  may be coupled (e.g., operatively, communicatively, functionally, electronically) to each other. In some embodiments, the continuous-time sigma-delta ADC  400  may provide a feedback loop, which may include one or more of the components of the continuous-time sigma-delta ADC  400 , as described herein. 
     The summing node  404  may include one or more inputs, such as a first input to receive a signal and a second input coupled to a first output of the main DAC  424  to receive another signal. The summing node  404  may also include an output coupled to an input of the loop filter  408  to output a signal to the loop filter  408 . The loop filter  408  may also include an output that is coupled to an input of the amplifier  410  to receive a signal from the loop filter  408 . The summing node  412  may include one or more inputs, including a first input coupled to an output of the amplifier  410  to receive an amplified signal, a second input coupled to an output of the REF DAC  418  to receive a signal from the REF DAC  418 , and a third input coupled to an output of the ELD DAC  414  to receive a signal from the ELD DAC  214 . 
     The summing node  412  may include an output coupled to an input of the latch  416 . The latch  416  may include an output to provide an output signal (e.g., output signal  420 ). The output of the latch  416  may be coupled to an input of the ELD DAC  414  and an input to the main DAC  424 . The main DAC  424  may include a second output coupled to an input of the mismatch sensor  430 , which may include an output coupled to an input of the logic  432 . The logic  432  may include an output coupled to a first input of the mapping engine  434 . The mapping engine  434  may include a set of second inputs to receive a set of codes, and a set of outputs to provide reference codes to an input of the REF DAC  418 . Additionally, the mapping engine  434  may include third input coupled to the output of the latch  416  to receive the output signal  420 . 
     Thus, in the example of  FIG. 4 , the output signal  420  is also an input of the mapping engine  434 . Some examples of these type of DAC linearization techniques are dynamic weighted averaging linearization techniques and randomized dynamic weighted averaging linearization techniques. In the example of  FIG. 4 , the main feedback loop of the sigma-delta modulator and the DAC linearization loop are (partially) decoupled. The DAC linearization loop may include the comparator (i.e., the latch  416 ), the mapping engine  434 , the REF DAC  418 , and the ELD summation node  412 . The SDM main feedback loop may include the comparator (i.e., the latch  416 ), the main DAC  424 , the loop filter  408 , the Gm-cell (i.e., the amplifier  410 ) and the ELD summation node  412 . Thus, the SDM main feedback loop and the DAC linearization loop can be optimized separately for their different requirements. 
     In some embodiments, for example, the main DAC  424  may have a noise and matching requirement. Thus, unit elements of the main DAC  424  may be within relatively large current (e.g., for lower thermal noise) and relatively large area (for better matching and lower flicker noise). In some embodiments, the REF DAC  418  in the multi-bit quantizer may have a relaxed noise and matching requirement than the main DAC  424 , as the noise and non-linearity contributed by the REF DAC  418  is noise-shaped by the SDM. Thus, it may be beneficial to configure the mapping engine  434  to be between the comparator and the REF DAC  418 , compared to some approaches where the mapping engine may be configured between the comparator and the main DAC  424 . 
     As illustrated in  FIG. 4 , the continuous-time sigma-delta ADC  400  may include the main feedback loop, the ELD feedback loop and the DAC linearization loop of the SDM. In some embodiments, the total delay of the DAC linearization loop may be maximally one sampling clock period. In some embodiments, the total delay of the main feedback loop may also be maximally one sampling clock period. In some embodiments, unit elements of the main DAC  424  may not be selected based on the current sample of the quantizer output. Rather, an order of the unit element of the main DAC  424  may be selected to be used based on the previous sample of the quantizer output. 
       FIG. 5  is a block diagram of a transistor-level implementation of a continuous-time sigma-delta ADC  500  in accordance with some embodiments. In the following description of the continuous-time sigma-delta ADC  500 , certain components may be added or omitted from the continuous-time sigma-delta ADC  500 . The continuous-time sigma-delta ADC  500  may support one or more linearization techniques, for example DAC linearization techniques. In some embodiments, the continuous-time sigma-delta ADC  500  may support a linearization technique that does not need a quantizer output. 
     In the example transistor-level implementation, a Gm cell, an ELD DAC  510 , an associated reference current  528 , a latch  530 , a sample and hold (S&amp;H) circuit  538  and buffers  540  compose a slice of an ELD-compensated quantizer. The transistor-level circuit implementation of the proposed continuous-time sigma-delta ADC  500  shows the m th  slice of the duplicated summation node and 1-bit comparator in detail. In the example of  FIG. 5 , the SDM uses (n+1)-level quantization. So the SDM has n total slices of duplicated summation node and 1-bit comparator. 
     In some embodiments, the loop filter  506  has differential voltage outputs Vi +  and Vi − . These differential voltage signals are converted to differential current signals with a source-degenerated transconductance (Gm) stage  516 . In some embodiments, the Gm cell may be implemented as a source degenerated PMOS transconductance amplifier, which is composed of current sources Is  506 , source-degeneration resistor R s    508 , a capacitor Cs  510 , and thin-oxide PMOS transistors M 1 , M 2    518 . In some embodiments, source degeneration may be employed to improve the linearity of the Gm cell for a large input swing of ±250 mV. The capacitor Cs may be added at the source of M 1 , M 2    518  to generate a zero in the transfer function of the Gm stage  516  (V/I converter), and to compensate its phase shift/delay. The current source I s    506  may be, for example, implemented as a cascaded PMOS current source. 
     The bandwidth of the Gm cell may, in some embodiments, affect the stability of the outer feedback loop, but not the fast feedback loop. The ELD DAC  510  may be implemented as a current steering DAC. The NMOS switches M 3 , M 4    514  and the current source I dac,u    512  may compose a unit ELD DAC. The NMOS transistors M 5 , M 6    522  and the current source I ref,u    524  may construct the unit reference DAC (Ref DAC). In some embodiments, for n+1-level quantization, n reference levels may need to be created, and thus n−1 reference current units may be required for every slice. The reference DAC converts a digital input code—reference code, into an output current. The n+1-level quantizer shown in  FIG. 5  has n reference codes—ref code 1, ref code 2, . . . , ref code n. These n reference codes may be a permutation of the n input codes {code 1, code 2, . . . , code n}. The mapping engine  550  applies a certain sorting operation, mapping operation, and/or a switching operation on the connection from the input code {code 1, code 2, . . . , code n} to its output code {ref code 1, ref code 2, . . . , ref code n}. 
     The ELD DAC may be an n+l-level current steering DAC, which is composed by NMOS transistors M 3 -M 4    514  and current sources I dac,u    512 . The ELD DACs are implemented similarly as the reference DACs, but their switches are controlled by the digital output of the n+1-level quantizer. The current sources in the reference DACs and ELD DACs can be for example implemented as cascaded NMOS current sources. 
     After the latch block, a transmission gate (M 7 , M 8    534 ) with complementary sampling clocks (clkp SH    536  and clkn SH    532 ) is employed to sample the latch output at the end of the latch  530 . In some embodiments, two buffers  540  are inserted between the sampled latch output and the input of the ELD DACs. The choice of a number of buffers is a trade-off between minimizing the load capacitance of the latch, and reducing the delay of the buffers. The first buffer (M 9 , M 10    542 - 1 ) is a NMOS buffer with PMOS load, while the second buffer (M 11 , M 12    542 - 2 ) is a CMOS buffer. In some embodiments, the NMOS buffer may have lower input capacitance than the CMOS buffer, but it consumes more power. The CMOS buffer offers rail-to-rail driving ability. For the n+1-level quantization, one sampled latch output node should drive n unit ELD DACs after two buffers. As such, the latch output is sampled by the S&amp;H circuit (pass gate M 7 -M 8 ) with the sampling clock clk SH . After that, the sampled quantizer output goes through two buffers composed by the M 9 -M 12 . The first buffer composed by M 9 -M 10  is a NMOS buffer with PMOS load. The second buffer composed by M 11 -M 12  is a CMOS buffer (a CMOS inverter). The second buffer output D + , D −  are the digital output V of the SDM, and they also drive the main DAC and ELD DACs. Since the 1-bit latch is one-to-one connected to the DAC unit element through the S&amp;H circuit and buffers, by sorting, mapping, switching of the reference code of the reference DAC, a corresponding sorting, mapping, switching of the DAC unit elements is effectively achieved. 
     In some embodiments, the reference current may be designed to have the same common-mode current for every slice (i.e., I refp,1 +I refn,1 =I refp,2 ±I refn,2 = . . . = refpn +I refn,n ). The differential reference current signal I refp,m −I refn,m  may be different for every slice. In some embodiments, the source-degenerated Gm stages, the connection circuit, the latches, and the samplers are exactly the same for these n slices. The m th  ELD DAC may be an n+1-level current steering DAC. 
     In some embodiments, certain aspects of the techniques described above may implemented by one or more processors of a processing system executing software. The software comprises one or more sets of executable instructions stored or otherwise tangibly embodied on a non-transitory computer readable storage medium. The software can include the instructions and certain data that, when executed by the one or more processors, manipulate the one or more processors to perform one or more aspects of the techniques described above. The non-transitory computer readable storage medium can include, for example, a magnetic or optical disk storage device, solid state storage devices such as Flash memory, a cache, random access memory (RAM) or other non-volatile memory device or devices, and the like. The executable instructions stored on the non-transitory computer readable storage medium may be in source code, assembly language code, object code, or other instruction format that is interpreted or otherwise executable by one or more processors. 
     A computer readable storage medium may include any storage medium, or combination of storage media, accessible by a computer system during use to provide instructions and/or data to the computer system. Such storage media can include, but is not limited to, optical media (e.g., compact disc (CD), digital versatile disc (DVD), Blu-Ray disc), magnetic media (e.g., floppy disc, magnetic tape, or magnetic hard drive), volatile memory (e.g., random access memory (RAM) or cache), non-volatile memory (e.g., read-only memory (ROM) or Flash memory), or microelectromechanical systems (MEMS)-based storage media. The computer readable storage medium may be embedded in the computing system (e.g., system RAM or ROM), fixedly attached to the computing system (e.g., a magnetic hard drive), removably attached to the computing system (e.g., an optical disc or Universal Serial Bus (USB)-based Flash memory), or coupled to the computer system via a wired or wireless network (e.g., network accessible storage (NAS)). 
     Note that not all of the activities or elements described above in the general description are required, that a portion of a specific activity or device may not be required, and that one or more further activities may be performed, or elements included, in addition to those described. For example, for some DAC linearization techniques, such as randomization, the information on the DAC unit element mismatch is not required. In such cases, the mismatch sensor  114 ,  230 ,  330 ,  430 ,  546  is not required. Still further, the order in which activities are listed are not necessarily the order in which they are performed. Also, the concepts have been described with reference to specific embodiments. However, one of ordinary skill in the art appreciates that various modifications and changes can be made without departing from the scope of the present disclosure as set forth in the claims below. Although a feedforward SDM architecture is shown as an example in  FIGS. 1-5 , the present disclosure can also be used in other SDM architectures, such as feedback architectures, and hybrid feedforward-feedback architectures. Although a single-loop SDM architecture is shown as an example in  FIGS. 1-5 , the present disclosure can also be used in other SDM architectures, such as Multi-stAge noise SHaping (MASH) architectures. Accordingly, the specification and figures are to be regarded in an illustrative rather than a restrictive sense, and all such modifications are intended to be included within the scope of the present disclosure. 
     Benefits, other advantages, and solutions to problems have been described above with regard to specific embodiments. However, the benefits, advantages, solutions to problems, and any feature(s) that may cause any benefit, advantage, or solution to occur or become more pronounced are not to be construed as a critical, required, or essential feature of any or all the claims. Moreover, the particular embodiments disclosed above are illustrative only, as the disclosed subject matter may be modified and practiced in different but equivalent manners apparent to those skilled in the art having the benefit of the teachings herein. No limitations are intended to the details of construction or design herein shown, other than as described in the claims below. It is therefore evident that the particular embodiments disclosed above may be altered or modified and all such variations are considered within the scope of the disclosed subject matter. Accordingly, the protection sought herein is as set forth in the claims below.