The present invention relates to analog-to-digital conversion.
There are many analog-to-digital converter (ADC) architectures to choose from, each with its own merits and shortcomings. The successive approximation register (SAR) ADC and pipeline ADC are often combined to form a high speed ADC with 10 or more effective number of bits (ENOB). A SAR-ADC can be implemented using so called charge redistribution with a capacitive array using a switched-capacitor technique. Examples are provided e.g. in Hurrell, C. P.; Lyden, C.; Laing, D.; Hummerston, D.; Vickery, M., “An 18 b 12.5 MS/s ADC With 93 dB SNR,” Solid-State Circuits, IEEE Journal of, vol. 45, no. 12, pp. 2647, 2654, December 2010, and Dai Zhang; Alvandpour, A., “Analysis and Calibration of Nonbinary-Weighted Capacitive DAC for High-Resolution SAR ADCs,” Circuits and Systems II: Express Briefs, IEEE Transactions on, vol. 61, no. 9, pp. 666, 670, September 2014. This scheme also generates the residue, i.e. the analog remainder part after conversion to a given number of bits, that in turn can be used in a pipeline structure to be further processed in a second or more conversion stages.
In high-performance SAR-ADC architectures a merged capacitor switching (MCS) technique is often used. The MCS operation, which is illustrated in
Various sources of inaccuracies in a SAR-ADC cause the output signal from the SAR-ADC to deviate from the ideal output signal.
An object of the present invention is to provide for corrections of imperfections in a SAR-ADC. In particular, the inventors have realized how leakage, or signal decay, within a SAR-ADC can impact the accuracy of the output signal of the SAR-ADC, and proposed a signal processing approach to counteract this.
According to a first aspect, there is provided an analog-to-digital conversion circuit. The analog-to-digital conversion circuit comprises a switched-capacitor SAR-ADC arranged to receive an analog input signal and a clock signal, to sample the analog input signal, and to generate a sequence of digital output words corresponding to samples of the analog input signal. The SAR-ADC is arranged to generate a bit of the digital output word per cycle of the clock signal. The analog-to-digital conversion circuit comprises a clock-signal generator arranged to supply the clock signal to the SAR-ADC, and a control unit arranged to control a rate of the clock signal. The analog-to-digital conversion circuit comprises a post-processing unit adapted to receive the sequence of digital output words and generate a sequence of digital output numbers, corresponding to the digital output words, based on bit weights assigned to the bits of the digital output words. The bit weights depend on the rate of the clock signal.
The post-processing unit may be adapted to gather statistics of samples of the sequence of digital output words of the SAR-ADC and determine the bit weights based on the statistics of samples of the sequence of digital output words.
The analog-to-digital conversion circuit may comprise an auxiliary ADC arranged to convert an analog residue of the SAR-ADC to a sequence, in the following referred to as residue sequence, of digital words corresponding to samples of said analog residue. The post-processing unit may be adapted to gather statistics of samples of the residue sequence, and determine the bit weights based on the statistics of samples of the residue sequence. The SAR-ADC may be a stage in a pipeline ADC, and the auxiliary ADC may be a subsequent stage in the pipeline ADC.
The post-processing unit may be adapted to determine a parameter representative of a time constant for a decay of a signal level in the SAR-ADC, and determine the bit weights based on said parameter.
According to a second aspect, there is provided an analog-to-digital conversion circuit. The analog-to-digital conversion circuit comprises a switched-capacitor SAR-ADC arranged to receive an analog input signal and a clock signal, to sample the analog input signal, and to generate a sequence of digital output words corresponding to samples of the analog input signal. The SAR-ADC is arranged to generate a bit of the digital output word per cycle of the clock signal. The analog-to-digital conversion circuit comprises a clock-signal generator arranged to supply the clock signal to the SAR-ADC. The analog-to-digital conversion circuit comprises a post-processing unit adapted to receive the sequence of digital output words and generate a sequence of digital output numbers, corresponding to the digital output words, based on bit weights assigned to the bits of the digital output words. The post-processing unit is adapted to determine a parameter representative of a time constant for a decay of a signal level in the SAR-ADC, and determine the bit weights based on said parameter.
The post-processing unit may be adapted to gather statistics of samples of the sequence of digital output word of the SAR-ADC and determine the parameter based on the statistics of samples of the sequence of digital output word.
The analog-to-digital conversion circuit may comprise an auxiliary ADC arranged to convert an analog residue of the SAR-ADC to a sequence, in the following referred to as residue sequence, of digital words corresponding to samples of said analog residue. The post-processing unit may be adapted to gather statistics of samples of the residue sequence, and determine the parameter based on the statistics of samples of the residue sequence.
The analog-to-digital conversion circuit may comprise a control unit arranged to control a rate of the clock signal. The bit weights may depend on the rate of the clock signal.
According to a third aspect, there is provided a receiver circuit comprising the analog-to-digital conversion circuit according to the first or the second aspect.
According to a fourth aspect, there is provided a communication apparatus comprising the receiver circuit according to the third aspect. The communication apparatus may e.g. be a wireless terminal or a network node.
According to a fifth aspect, there is provided a method of post processing data from a switched-capacitor SAR-ADC arranged to receive an analog input signal and a clock signal, to sample the analog input signal, and to generate a sequence of digital output words corresponding to samples of the analog input signal, wherein the SAR-ADC is arranged to generate a bit of the digital output word per cycle of the clock signal. The method comprises generating a sequence of digital output numbers, corresponding to the digital output words, based on bit weights assigned to the bits of the digital output words, wherein the bit weights depend on the rate of the clock signal.
According to a sixth aspect, there is provided a method of post processing data from a switched-capacitor SAR-ADC arranged to receive an analog input signal and a clock signal, to sample the analog input signal, and to generate a sequence of digital output words corresponding to samples of the analog input signal, wherein the SAR-ADC is arranged to generate a bit of the digital output word per cycle of the clock signal. The method comprises determining a parameter representative of a time constant for a decay of a signal level in the SAR-ADC. The method further comprises determining bit weights assigned to the bits of the digital output words based on said parameter. Moreover, the method comprises generating a sequence of digital output numbers, corresponding to the digital output words, based on the bit weights assigned to the bits of the digital output words.
According to a seventh aspect, there is provided a computer program product comprising computer program code for executing the method according to the fifth or sixth aspect when said computer program code is executed by a programmable post-processing unit of an analog-to-digital conversion circuit comprising the switched-capacitor SAR-ADC.
According to an eighth aspect, there is provided a computer readable medium having stored thereon a computer program product comprising computer program code for executing the method according to the fifth or sixth aspect when said computer program code is executed by a programmable post-processing unit of an analog-to-digital conversion circuit comprising the switched-capacitor SAR-ADC.
Further embodiments are defined in the dependent claims. It should be emphasized that the term “comprises/comprising” when used in this specification is taken to specify the presence of stated features, integers, steps, or components, but does not preclude the presence or addition of one or more other features, integers, steps, components, or groups thereof.
Further objects, features and advantages of embodiments of the invention will appear from the following detailed description, reference being made to the accompanying drawings, in which:
In this disclosure, the MCS SAR-ADC shown in
The inventors have realized that switches S1p and S1n in the capacitive SAR architecture (
The inventors have realized that such a discharge gives rise to an error that manifests itself as incorrect bit weights of the SAR-ADC. The inventors have further realized that, for a given clock frequency, the resulting error is static. That is, it does not depend on the history of the input signal at previous sample instants, but only on the signal level at the current sampling instant. As is further elaborated on below, the inventors have also realized that the error can be compensated for by recombining the bits from the SAR-ADC output word into a number using modified (compared with the ideal) bit weights assigned to the different bits. Furthermore, the inventors have realized that the error depends on the clock frequency, such that in order to enable compensation in a SAR-ADC that can be operated at multiple clock frequencies, the values of the modified bit weights should depend on the clock frequency, or clock rate.
Now, the impact of discharge is discussed in some more detail. After the capacitor array has been charged to hold the voltage of the input signal, switches S1p and S1n are set to an OFF state and stick to that state throughout the SAR iteration process. The switches facing the other side of the capacitors will only alternate between the common mode (CM) level, reference voltage (Vref) and signal ground as a result of the SAR iteration process. Thus, for all practical purposes, the terminals of this side of the capacitors show low impedance and can be viewed as grounded. This means that the capacitor array will experience an exponential discharge proportional to e−t/τ where t is time and τ=RoffCSAR. Here Roff is the resistance of S1p and S1n respectively in OFF state and CSAR is the total capacitance of the capacitor array connected to each input of differential comparator. The parameter τ is a time constant for signal decay internally in the SAR-ADC.
Also, the capacitor array is linear and thus superposition applies. This can be used to understand how the discharge impacts the operation. S1p and S1n switch from track to hold state at a first time instant t=0. From there on the input signal decays as e−t/τ until all bits have been determined. At subsequent clock cycles, t=(n+1)Tclk, (Tclk being the clock period of SAR operation), of the SAR iteration process a charge is applied to yield a voltage offset from the previous voltage of either Vref/2n+1 or −Vref/2n+1 depending on the comparator output from previous clock cycle. This voltage too will decay as e−t/τ but starting from t=(n+1)Tclk. In other words, when referenced to the time instant at which all bits and the residue voltage have been determined, the steps taken and thus the bits generated will not be binary weighted. Rather, the weight ratio between two consecutive bits n and n−1 becomes
or slightly less than 2. Hence, if the weight of the LSB b0 is set to w0=20=1, the actual weights of the other bits are given by
wk=2ke−kT
If not corrected for, this will lead to performance degradation.
The Vcomp trajectories in
At the end of the SAR iteration process, the residue is given by
The first term is the sampled input voltage Vinput subject to a decay during the SAR iteration process. The second term, which we refer to below as the “output voltage”, is the contribution provided during the SAR iteration process via charge redistribution, also subject to decay as captured by the wk factors. An observation that the inventors have made is that is that for the non-binary weights wk, the output voltage range covered will not be uniform. If N=6 bits and Tclk/τ=0.1 (exaggerated discharge for illustration purposes), then for each bit pattern of respective digital input code, which we label [0, 1 . . . , 63], where 0 corresponds to the binary code 000000, 1 corresponds to the binary code 000001, . . . , and 63 corresponds to the binary code 111111, to the capacitive array we get the distribution of sum of weighted bits as shown in
where bk=[0,1] The plotted values in
The fact that the input signal sample is established in the circuit at a first time instant before a second time instant at which a SAR iteration k is performed to determine bit bk means that the input signal will discharge over a longer time than any of the voltage offsets introduced in the iteration process. We then can conclude that the voltage offsets will always be able to represent a larger range than the input signal at the time instant when the residue voltage is determined.
Some examples on how the decay affects the results are described below with reference to
The SAR iteration process will be affected by this as the decisions taken are based on the comparator input voltage which in turn is a sum of decaying voltages where the input voltage part thus becomes a moving target. If N=6 bits and a discharge given by Tclk/τ=0.01 (note, a factor 10 less than the previously used examples for more realistic data) it will be clearly visible by looking at the distribution of digital output, see
The same behavior can be seen for other signals as well and for much less discharge. With a Gaussian-distributed noise input of 100,000 samples and Tclk/τ=0.002, the corresponding results are as shown in
Finally, the distortion caused by the discharge can be investigated. The spectrum in
We now proceed with describing procedures for compensating the errors caused by the leakage. As the real weight ratio of two subsequent bits can be written as
it is proposed that the weights bits bk (k=0, . . . , N−1) of the digital output be compensated by e−kT
In other embodiments, approximations may be used for the compensation factor. For example, in case NTclk<<τ, the discharge becomes almost linear e−kT
which has a fairly low computational complexity. The compensated digital output, in the following denoted y(n), where n is a sequence index indicating the sampling instant, can now be calculated as
Note that the word length for representing y(n) can be different from the number N of bits bk in the output from the SAR-ADC. For example, the word length used for representing y(n) may be higher than N, e.g. to overlap with the bits generated by a subsequent ADC in a pipeline structure.
Some embodiments concern circuits where the rate of the clock signal is variable. For example, the analog-to-digital conversion circuit 100 may be used in a radio receiver circuit for sampling a received signal. The radio receiver circuit may be employed in a radio environment where the signals to be received may have a variable frequency bandwidth, and the selected sampling frequency of the analog-to-digital conversion circuit 100 may depend on the current bandwidth. The above-mentioned clock signal is not a sampling clock signal, but it is related to the sampling clock signal in that, for each period of the sampling clock signal, the clock signal needs to complete a certain number of periods in order for all the bits of W(n) to be generated before the next sample is sampled. Hence, also the rate of the clock signal might be varied, e.g. in accordance with a selected bandwidth. In view of the analysis provided above, the inventors have realized that by allowing the bit weights to depend on the rate of the clock signal, compensation of the leakage errors described above is enabled in variable clock-rate scenarios. Hence, in accordance with some embodiments, the control unit 130 is arranged to control the rate of the clock signal, wherein the bit weights applied by the post-processing unit 140 depend on the rate of the clock signal.
It should be noted though that the approaches and methods described herein for generating bit weights and compensating for signal decay internally in the SAR-ADC 110 are applicable also in implementations where the rate of the clock signal is fixed.
As indicated in
In line with what has been described above, the post-processing unit 140 is, in some embodiments, adapted to gather statistics of samples of the sequence W(n) of digital output words of the SAR-ADC 110 and determine the bit weights wk based on the statistics of samples of the sequence W(n) of digital output words. For example, as has been described above, it can be foreseen, in the presence of leakage, that certain codes are expected to be less frequently occurring than other codes in the sequence W(n). That is, these certain codes are in some sense more sensitive to leakage than other less sensitive codes, that will occur in more or less the same numbers regardless of the amount of leakage. Examples of such more sensitive codes are the “middle codes” ‘100 . . . 00’ and ‘011 . . . 111’. In some embodiments, the relative occurrence of one or more such sensitive codes is compared with the relative occurrence of one or more such less sensitive codes. Such a comparison can provide a measure of the degree of leakage, or “signal decay”, internally in the SAR ADC, and can be used as a basis for selecting the bit weights wk. For example, simulations can be used to estimate the relative occurrences for the different codes for different degrees of leakage, e.g. different values of τclk/τ. For example: “for a given degree of leakage A, the code B is expected to occur in C % more cases than the code D”. Based on this estimated data, the gathered statistics can be used to estimate the actual leakage and consequently to select the appropriate bit weights wk, e.g. based on a table look up. Alternatively, the leakage, or signal decay, can be estimated iteratively, e.g. in terms of a parameter such as τc or Tclk/τc. For example, a start value of the parameter can be selected e.g. as a default value or by means of a table look-up based on gathered statistics as mentioned above. Bit weights wk can then be assigned based on the parameter value. Subsequently, statistics can be gathered on the compensated sequence of numbers y(n), whereby conclusions can be made regarding whether the resulting compensation was insufficient (e.g. τc was selected too large or equivalently τclk/τc was selected too small), correct, or too much (e.g. τc was selected too small or equivalently Tclk/τc was selected too large). The parameter, and corresponding bit weights, can then be updated if needed, iteratively until a satisfactory statistical distribution of the sequence y(n) is obtained.
In some implementations, as described above, the statistics of W(n) might be too coarse in resolution, e.g. due to too few bits in the SAR-ADC 110, to properly reflect the signal decay. For example, if the SAR-ADC 110 is a stage in a pipeline ADC, the effects of the signal decay in the SAR-ADC 110 might be visible first in a subsequent stage of the pipeline ADC.
As described above, in addition to the statistics of the sequence W(n), the residue signal can be considered in the computation of the bit weights wk. Thus, as indicated in
In some embodiments, the auxiliary ADC 155 is a subsequent stage in a pipeline ADC. This is advantageous in that no additional dedicated ADC is needed for converting the residue.
In some embodiments, the post-processing unit 140 is adapted to determine a parameter representative of a time constant for a decay of a signal level in the SAR-ADC 110, and determine the bit weights based on said parameter. The parameter may e.g. be τc or τclk/τc mentioned above, but any other function of τc may be considered for use as well. The postprocessing unit 140 can then determine the bit weights wk based on said parameter. For example, the bit weights wk may be determined based on Eq. (6) or Eq. (7).
Some embodiments concern a method 200 of post processing data from the switched-capacitor SAR-ADC 110. The method 200 may e.g. be performed by the post-processing unit 140 (Fig. The method 200 is generally illustrated with a flowchart in
As for some of the embodiments of the analog-to-digital conversion circuit 100 described above, some of the embodiments of the method 200 concerns a situation where the rate of the clock signal is variable. In such embodiments of the method 200, wherein the bit weights wk depend on the rate of the clock signal.
As illustrated in
yrecombined(n)=y(n)+yres(n) (9)
where yres(n) is a sequence of digital numbers corresponding to the analog residue signal formed as a weighted combination of the bits of Wres(n), e.g.
where dk(n) are the bits of Wres(n), M is the number of bits of Wres(n), uk is the weight of bit dk(n), and C is a normalization constant. If the auxiliary ADC is binary weighted, the weights uk may be selected as
uk=2k (11)
and the normalization constant C may be selected as
C=2−M (12)
thus giving the MSB of Wres(n) an effective weight of C·uM-1=½.
The above example normalization assumes that the input range of the auxiliary ADC 155 exactly fits the expected range of the residue voltage. In some implementations, some degree of redundancy, e.g. in terms of an extra bit, may be introduced in the auxiliary ADC 155 to obtain a design margin so that the input range of the auxiliary ADC 155 is slightly larger than the expected range of the residue voltage. In such cases, the normalization constant should be adjusted accordingly. Making such an adjustment, which corresponds to determining the bit weights of the bits in the auxiliary ADC 155 in relation to the bit weights of the SAR-ADC 110, would be a routine task for a person skilled in the art of pipeline ADC design and is not further discussed herein.
In the presence of non-negligible signal decay, and in the absence of compensation, or with the signal decay being undercompensated (τc>τ), the histogram of the recombined signal yrecombined(n) will have zero-value entries, or at least values lower than surrounding ranges, in a region the center of the number range (as shown in
In other words, if the signal decay has been correctly compensated for, by means of an adequate selection of bit weights wk, the recombined sequence yrecombined(n) should be equal to (a digital representation of) the input signal x(t). Thus, a histogram of yrecombined(n) would then have a smooth distribution. However, as described above with reference to
1) gather statistical data
2) determine m1 and m2
3a) if m1<m2, then increase Pc
3b) if m1>m2, then decrease Pc
4) compute bit weights based on P, then return to 1)
In 3a) and b) above, it is not defined what to do if m1=m2. In some embodiment, the bit weights are left unchanged. In other embodiments, “<” in 3b) is replaced with “≤”, or “>” in 3a) is replaced with “≥”. This has the computational advantage that only one of the comparisons in 3a) and 3b) has to be computed, since the result of one of the comparisons automatically gives the result of the other comparisons as its logical inverse. In case the first and second sub ranges are equally wide, the numbers m1 and m2 may be the actual number of samples in the respective range. If the first and second sub ranges are not equally wide, the numbers m1 and m2 may instead denote an average number of samples per unit width of the respective range, e.g. derived by dividing the actual number of samples in a range with the width of that range.
As has been outlined above, step 210 may thus comprise a step 330 of determining a parameter representative of a time constant for a decay of a signal level in the SAR-ADC 110. This is illustrated in the flow chart in
Other metrics may be derived as indication of compensation needed. For example the number of consecutive zero-value entries in the first histogram (the width of the drop) is one such coarse indication, but this will only work for an undercompensated system. For an overcompensated system one could calculate the number of consecutive entries that is larger by a certain ratio compared to the average of the second histogram. Alternatively, one could use a model that assumes that the system is overcompensated when there are no zero-value entries and adjust the parameter accordingly until the system again becomes undercompensated, which would lead to a system that balances on the boarder of being slightly undercompensated.
It can be further envisioned that a combination of estimation techniques can be used as is common practice in many optimization problems. For example, a first mode of estimation and compensation can be based on coarse estimates (like number of consecutive zero-value entries in first histogram as mentioned above) until no further improvement is obtained. After that a second mode of estimation and compensation can be based on more accurate estimate, like the algorithm described above and with reference to
The receiver circuit 500 may be comprised in a communication apparatus.
In some embodiments, the post-processing unit 140 may be implemented as a dedicated application-specific hardware unit. Alternatively, said post-processing unit 140, or parts thereof, may be implemented with programmable and/or configurable hardware units, such as but not limited to one or more field-programmable gate arrays (FPGAs), processors, or microcontrollers. Thus, the post-processing unit 140 may be a programmable post-processing unit 140. Hence, embodiments of the present invention may be embedded in a computer program product, which enables implementation of the method and functions described herein, e.g. the embodiments of the methods described with reference to
The present invention has been described above with reference to specific embodiments. However, other embodiments than the above described are possible within the scope of the invention. Different method steps than those described above, performing the method by hardware or software, may be provided within the scope of the invention. The different features and steps of the embodiments may be combined in other combinations than those described. The scope of the invention is only limited by the appended patent claims.
Filing Document | Filing Date | Country | Kind |
---|---|---|---|
PCT/EP2016/052852 | 2/10/2016 | WO | 00 |
Publishing Document | Publishing Date | Country | Kind |
---|---|---|---|
WO2017/137078 | 8/17/2017 | WO | A |
Number | Name | Date | Kind |
---|---|---|---|
8344925 | Evans | Jan 2013 | B1 |
8884801 | Ranjbar | Nov 2014 | B1 |
10103742 | Guo | Oct 2018 | B1 |
10965300 | Weng | Mar 2021 | B1 |
20040257257 | Nomasaki | Dec 2004 | A1 |
20050231412 | Confalonieri | Oct 2005 | A1 |
20080186214 | Janakiraman | Aug 2008 | A1 |
20090073018 | Mitikiri | Mar 2009 | A1 |
20100097256 | Hurrell | Apr 2010 | A1 |
20120326901 | Zhao | Dec 2012 | A1 |
20150180496 | Drago | Jun 2015 | A1 |
20160182075 | Devarajan | Jun 2016 | A1 |
Entry |
---|
Cho, Sang-Hyun, et al., “A 550-uW 10-b 40-MS/s SAR ADC With Multistep Addition-Only Digital Error Correction”, IEEE Journal of Solid-State Circuits, vol. 46, No. 8, Aug. 2011, pp. 1881-1892. |
Gan, Jianhua, “Non-Binary Capacitor Array Calibration for a High Performance Successive Approximation Analog-to-Digital Converter”, Dissertation Presented to the Faculty of The Graduate School of The University of Texas at Austin in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy, Dec. 1, 2003, pp. 1-188. |
Hariprasath, V. , et al., “Merged capacitor switching based SAR ADC with highest switching energy-efficiency”, Electronic Letters, vol. 46, No. 9, Apr. 29, 2010, pp. 1-2. |
Hurrell, Christopher Peter, et al., “An 18 b 12.5 MS/s ADC With 93 dB SNR”, IEEE Journal of Solid-State Circuits, vol. 45, No. 12, Dec. 2010, pp. 2647-2654. |
Liu, Wenbo , “Low-Power High-Performance SAR ADC Design with Digital Calibration Techniques”, Dissertation Submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Electrical and Computer Engineering in the Graduate College of the University of Illinois at Urbana-Champaign, Dec. 1, 2010, pp. 1-151. |
Medawar, Samer, et al., “Postcorrection of Pipelined Analog-Digital Converters Based on Input-Dependent Integral Nonlinearity Modeling”, IEEE Transactions on Instrumentation and Measurement, vol. 60, No. 10, Oct. 2011, pp. 3342-3350. |
Verbruggen, Bob, et al., “A 2.1 mW 11b 410 MS/s Dynamic Pipelined SAR ADC with Background Calibration in 28 nm Digital CMOS”, 2013 Symposium on VLSI Circuits Digest of Technical Papers, Jun. 12, 2013, pp. 1-2. |
Zhang, Dai, et al., “Analysis and Calibration of Nonbinary-Weighted Capacitive DAC for High-Resolution SAR ADCs”, IEEE Transactions on Circuitsand Systems—II: Express Beliefs, vol. 61, No. 9, Sep. 2014, pp. 666-670. |
Huang, Xuan-Lun, et al., “An MCT-Based Bit-Weight Extraction Technique for Embedded SAR ADC Testing and Calibration”, Journal of Electronic Testing, vol. 28, No. 5, Oct. 23, 2012, pp. 705-722. |
Office Action issued in corresponding EP Application No. 16703802.5 dated Jan. 28, 2021, 09 Pages. |
Swindlehurst, Eric et al. “Histogram-based calibration of capacitor mismatch in SAR ADCs,” Electronic Letters IEE; vol. 5, No. 25; Dec. 2015; pp. 2096-2098. |
Number | Date | Country | |
---|---|---|---|
20210194490 A1 | Jun 2021 | US |