Non-linearity correction of thermometric DAC coding errors with configurable permutation multiplexers

Abstract

A Digital-to-Analog Converter (DAC - 100), for converting an input thermometric digital signal to an analog output signal, includes at least two configurable permutation multiplexers (CPMUXes - 104), a bank of unit-DACs (106), and a summer circuit (108). Each CPMUX is configured to map a respective partial subset of bits of the input thermometric digital signal into a respective partial subset of bits of a permuted thermometric digital signal, according to a CPMUX configuration. Each unit-DAC is configured to convert a respective bit of the permuted thermometric digital signal into an analog signal. The summer circuit is configured to generate the analog output signal according to a sum of the analog signals produced by the unit-DACs.

Description

[0001] NON-LINEARITY CORRECTION OF THERMOMETRIC DAC CODING ERRORS WITH CONFIGURABLE PERMUTATION MULTIPLEXERS

[0002] CROSS-REFERENCE TO RELATED APPLICATIONS

[0003] This application claims the benefit of U.S. Provisional Patent Application 63 / 713,079, filed October 29, 2024, whose disclosure is incorporated herein by reference.

[0004] FIELD OF THE INVENTION

[0005] The present disclosure relates to digital-to-analog converters (DACs), and more particularly to non-linearity correction techniques for thermometric DACs.

[0006] BACKGROUND OF THE INVENTION

[0007] Digital-to-analog converters (DACs) are fundamental components in electronic systems that convert digital signals into corresponding analog outputs. These devices serve as the interface between digital processing systems and analog circuits, enabling applications ranging from audio equipment to communication systems and instrumentation.

[0008] Thermometric coding represents one approach to DAC implementation that offers advantages in linearity performance compared to traditional binary-weighted architectures. In thermometric coding schemes, each bit in the digital code carries equal weight, and the conversion process typically involves activating a number of identical digital-to-analog conversion elements proportional to the input digital value. This coding method can provide improved monotonicity and reduced differential non-linearity compared to binary-weighted approaches.

[0009] Despite the theoretical advantages of thermometric coding, practical implementations face challenges related to component matching and manufacturing variations. Process variations during fabrication can cause deviations in the actual weights of individual digital-to-analog conversion elements from their intended values. These mismatches can introduce non-linearities in the DAC transfer function, manifesting as differential non-linearity (DNL) and integral nonlinearity (INL) errors that degrade overall conversion accuracy.

[0010] SUMMARY OF THE INVENTION

[0011] An embodiment of the present invention that is described herein provides a Digital-to- Analog Converter (DAC) for converting an input thermometric digital signal to an analog output signal. The DAC includes at least two configurable permutation multiplexers (CPMUXes), a bank of unit-DACs, and a summer circuit. Each CPMUX is configured to map a respective partial subset of bits of the input thermometric digital signal into a respective partial subset of bits of a permuted thermometric digital signal, according to a CPMUX configuration. Each unit- DAC is configured to convert a respective bit of the permuted thermometric digital signal into an analog signal. The summer circuit is configured to generate the analog output signal according to a sum of the analog signals produced by the unit-DACs.

[0012] In some embodiments, the DAC further includes a binary to thermometric-code conversion circuit, configured to convert a digital input signal to the input thermometric digital signal. In example embodiments, at least one of the CPMUXes includes a configurable 2-by-2 multiplexer. In some embodiments, the CPMUX configuration is set to improve a conversion accuracy measure of the DAC. In an example embodiment, the accuracy measure includes a linearity measure of the analog output signal. In a disclosed embodiment, the CPMUX configuration of at least one of the CPMUXes is stored in a Non-Volatile Memory (NVM).

[0013] There is additionally provided, in accordance with an embodiment that is described herein, a method for converting an input thermometric digital signal to an analog output signal. The method includes, using each of at least two configurable permutation multiplexers (CPMUXes), mapping a respective partial subset of bits of the input thermometric digital signal into a respective partial subset of bits of a permuted thermometric digital signal, according to a CPMUX configuration. Using each unit-Digital-to-Analog-Converter (unit-DAC) in a bank of unit-DACs, a respective bit of the permuted thermometric digital signal is converted into an analog signal. The analog output signal is generated according to a sum of the analog signals produced by the unit-DACs.

[0014] There is further provided, in accordance with an embodiment that is described herein, a method for calibrating a Digital-to-Analog Converter (DAC). The method includes estimating a conversion accuracy measure of a thermometric DAC that converts an input thermometric digital signal to an analog output signal, wherein the thermometric DAC includes (i) at least two configurable permutation multiplexers (CPMUXes), each CPMUX configured to map a respective partial subset of bits of the input thermometric digital signal into a respective partial subset of bits of a permuted thermometric digital signal, according to a CPMUX configuration, (ii) a bank of unit-DACs, each unit-DAC configured to convert a respective bit of the permuted thermometric digital signal into an analog signal, and (iii) a summer circuit, configured to generate the analog output signal according to a sum of the analog signals produced by the unit- DACs. The CPMUX configuration is adjusted to improve the conversion accuracy measure.

[0015] In some embodiments, estimating the conversion accuracy measure includes (i) measuring respective strengths of the unit-DACs while the CPMUXes are in a pass-through mode, and (ii) calculating the conversion accuracy measure for a given CPMUX configuration based on the strengths of the unit-DACs.

[0016] In some embodiments, adjusting the CPMUX configuration includes improving a linearity measure of the analog output signal. In an example embodiment, the linearity measure includes an integral non-linearity (INL) of the DAC. In an example embodiment, the linearity measure includes a differential non-linearity (DNL) of the DAC.

[0017] The present invention will be more fully understood from the following detailed description of the embodiments thereof, taken together with the drawings in which:

[0018] BRIEF DESCRIPTION OF THE DRAWINGS

[0019] Fig. 1 is a block diagram that schematically illustrates a digital-to-analog converter (DAC), in accordance with an embodiment of the present invention;

[0020] Fig. 2 is a block diagram that schematically illustrates elements of a 2x2 MUX-based 3- bit DAC, in accordance with an embodiment of the present invention;

[0021] Fig. 3 is a flowchart that schematically illustrates a method for reducing thermometric DAC errors, in accordance with an embodiment of the present invention; and

[0022] Fig. 4 is a graph that schematically illustrates the expected yields of a 2 -bit thermometric DAC as a result of unit-DAC mismatches, in accordance with an embodiment of the present invention.

[0023] DETAILED DESCRIPTION OF EMBODIMENTS

[0024] OVERVIEW

[0025] A thermometric n-bit digital-to-analog converter (DAC) typically converts a therm ometrically encoded 2n-l -bit binary input into an analog signal. The circuit that converts the n-bit binary input into the 2n-l -bit therm ometrically-encoded signal may be external to the DAC, or, as in the examples used hereinbelow, the DAC may comprise an internal binary-to- thermometric conversion circuit.

[0026] In embodiments, the thermometric DAC comprises 2n-l unit-DAC circuits, wherein each unit-DAC is configured to convert a binary input (a single bit) to an analog signal; for example, in an embodiment, each unit-DAC is configured to sink current according to the binary input - e.g., a given amount of current when the binary input is at logic high, and zero current when the binary input is at logic low. The thermometric DAC further comprises a summer circuit (e.g., a summing buffer) that sums the currents that the unit-DACs sink, to produce the analog output signal of the thermometric DAC.

[0027] In embodiments, due to manufacturing variations or other factors, the unit DACs may not be identical, leading to differential non-linearity (DNL) and / or integral non-linearity (INL) errors in the overall conversion process.

[0028] To address this challenge, in some embodiments of the present invention, the DAC comprises one or more Configurable Permuation Multiplexers (CPMUXes), that provide a one- to-one mapping between n input bits to n output bits. In a disclosed embodiment, the CPMUXes comprise 2x2 double-pole double-throw switches, that either transfer the two inputs directly to respective outputs, or implement a crossing connection, wherein the first input is wired to the second output, and the second input is wired to the first output.

[0029] Each setting of the CPMUXes determines which thermometric bit of the input thermometric code will be routed to which of the unit-DACs that are connected to the CPMUX, for conversion. By proper selection of the CPMUX settings, it is possible to reduce the nonlinearities caused by performance variations between the unit-DACs. In a disclosed embodiment, the calibration process of the DAC is described, including a unit-DAC measurement phase and an optimization phase.

[0030] SYSTEM DESCRIPTION

[0031] The following detailed descriptions present techniques for correcting non-linearities in n-bit thermometric digital-to-analog converters (DACs) by modifying the input 2n-l-bit input thermometric digital signal. We will refer hereinbelow to the input thermometric digital signal as a "first 2n- 1 -bit thermometric digital signal" or "input thermometric digital signal". Similarly, we will refer to the modified thermometric digital signal as a "second 2n-l-bit thermometric digital signal" or "permuted thermometric digital signal".

[0032] In embodiments, for a given fabricated thermometric DAC, the performance characteristics of individual unit-DACs may not be identical. The mismatches, arising from manufacturing process variations or other factors, may contribute to DNL and INL errors. In some embodiments, the thermometric code performance of the DAC is measured and then, a translation mapping from the first 2n-l-bit thermometric digital signal to the second 2n-l-bit thermometric digital signal is determined, to reduce the nonlinearity. For best linearity correction, the logic circuitry that translates the first 2n-l-bit thermometric digital signal to the second 2n-l -bit thermometric digital signal may be extremely complex (in terms of gate-count and power consumption) and, hence, impractical.

[0033] The embodiments described below offer simplified suboptimal logic architectures that provide effective non-linearity correction with reduced hardware complexity. The disclosed techniques are based on Configurable Permutation Multiplexers (CPMUXes) that maps (e.g., permutes) a set of m binary inputs to a set of m binary outputs, using a one-to-one mapping scheme. The CPMUXes are configurable in the sense that the permutation between the binary inputs and the binary outputs is configurable. In embodiments, a plurality of CPMUXes may be used, for subsets of the first and the second 2n-l -bit thermometric digital signals. This approach provides good linearity without the extensive hardware overhead associated with more complex correction methods.

[0034] The following simplified example demonstrates how bit permutation can improve the INL level.

[0035] 2

[0036] A 2 -bit DAC, with 3 -bit thermometric code (2 -1), comprises three CPMUXes that may be set (e.g., during a calibration phase) for improved INL / DNL. The CPMUXes are initially configured to transfer the thermometric code unchanged, and the performance of the DAC is measured. It is found that the relative strengths of the three unit-DACs are: unit-DAC 1 : 0.98; unit-DAC 2: 0.99; and, unit-DAC 3: 1.02.

[0037] At this stage, the DAC's output level for input binary values of 0, 1, 2 and 3 are measured and found to be, respectively 0, 0.98, 1.97, 2.99. The DNL absolute errors are, therefore, 0, 0.02, 0.03 and 0.01, and the maximum error is 0.03.

[0038] A mathematical analysis is now run, and a better configuration for the CPMUXes is found, wherein the CPMUXes are configured to change the unit-DAC order:

[0039] Unit-DAC 1 : 0.99 (formerly unit-DAC 2);

[0040] Unit-DAC 2: 1.02 (formerly unit-DAC 3);

[0041] Unit-DAC 3: 0.98 (formerly unit-DAC 1).

[0042] The DAC outputs will now be 0, 0.99, 2.01 and 2.99, and the absolute errors would be 0, 0.01, 0.01 and 0.01 (maximum error is 0.01).

[0043] Fig. 1 is a block diagram that schematically illustrates a digital-to-analog converter (DAC) 100, in accordance with an embodiment of the present invention. DAC 100 comprises a 2-bit binary to thermometric-code conversion circuit 102 that receives a 2-bit digital input signal and converts it to a thermometric code representation (referred to as a first 2 -1-bit thermometric digital signal). In embodiments, the binary to thermometric-code conversion circuit converts an n-bit digital input to 2n-l -bit monotonic code, in which:

[0044] • A binary-0 input is converted to 000. . .0;

[0045] • A binary- 1 input is converted to 000. . . 1;

[0046] • A binary -2 input is converted to 000. . .11; and so on.

[0047] The output of 2-bit binary to thermometric-code conversion circuit 102 is input to a plurality of configurable permutation multiplexers (CPMUXes) 104, which modify the thermometric code to compensate for non-linearities that are caused by manufacturing variations. The modified thermometric code signal, referred to as the second 2n- 1-bit thermometric digital signal, is then supplied to a group of 2n-l unit-DACs, each unit-DAC configured to convert a respective bit of the second 2n- 1-bit thermometric digital signal into an analog signal.

[0048] A summing buffer 108 (or other summer circuit) then sums the outputs of the unit-DACs, to produce the analog output signal of DAC 100.

[0049] 2

[0050] Ideally, the 2 -1 unit-DACs are identical, generating an equal analog signal responsively to a logic-high input, and generating no output signal responsively to a logic-low input. In the example embodiment illustrated in Fig. 1, the analog signal is a current that the unit-DACs sink; each of the unit-DAC sinks a current-unit responsively to a set binary input, or zero current responsively to a cleared binary input. The summing buffer sums up the currents that the unit- DACs produce. In an embodiment, summing buffer 108 may comprise the wiring of the unit- DAC outputs, to manifest a current source that sinks between zero to 2n-l current-units, according to the number of set bits in the second thermometric code.

[0051] In an embodiment, the unit-DACs may not be identical, for example, due to process imperfections. In a calibration process, the CPMUXes may be configured for the best conversion performance.

[0052] According to the example embodiment illustrated in Fig. 1, DAC 100 further comprises a non-volatile memory (NVM) 110 that stores the CPMUXes configuration. To configure the DAC for improved linearity, the content of the NVM may be modified (as will be described below, with reference to Fig. 3). In other embodiments, other media may be used to store the CPMUXes configurations; in an embodiment, external storage may be used.

[0053] BIT PERMUTATION

[0054] Theoretically, conversion linearity errors could be minimized using an unconstrained mapping between the first 2n-l-bit thermometric digital signal and the second 2n-l-bit thermometric digital signal. Such unconstrained mapping may, however, comprise a large logic circuit, occupying a substantial silicon footprint.

[0055] In some embodiments, suboptimal INL / DNL minimalization is used, in which permutation mapping is used, and a one-to-one mapping is defined between the first 2n-l-bit thermometric digital signal and the second 2n-l-bit thermometric digital signal. For example, output bit 1 may be wired to input bit 2, output bit 2 to input bit 6, etc. Thus, the CPMUXes comprise simple multiplexers with configurable code-independent select logic.

[0056] For further simplification, bit permutation is, in some embodiments, done in groups. For example, both the first and the second 2n-l -bit thermometric digital signals may be divided into groups (e.g., 2 -bit groups), and the permutation may be done within the groups.

[0057] Fig. 2 is a block diagram that schematically illustrates elements of a 2x2 MUX-based 3- bit DAC 200, in accordance with an embodiment of the present invention. 2x2 MUX-based 3- bit DAC 200 comprises three CPMUXes 202, that are arranged as double-pole-double-through switches; in other words, each CPMUX 202 can be configured into one of the following two modes:

[0058] • Direct transfer: outl=inl, out2=in2;

[0059] • Cross switch: outl = in2, out2 = ini.

[0060] According to the example embodiment illustrated in Fig. 2, the seventh output is not multiplexed: out7 = in7.

[0061] An example for the operation of 2x2-multiplxer based DAC will now be described.

[0062] The relative strengths of the unit-DACs, from unit-DAC 1 to unit-DAC 7, are: 0.99, 0.99, 0.99, 1.01, 1.01, 1.01, 0.99.

[0063] Without CPMUX reconfiguration, the analog outputs of the DAC for consecutive binary input words (from 0 to 7) are:

[0064] 0, 0.99, 1.98, 2.97, 3.98, 4.99, 6, 6.99; the maximum DNL error is 3%. By configuring the three CPMUXes to the switch their two inputs (cross configuration), the analog outputs will be:

[0065] 0, 0.99, 1.98, 2.99, 3.98, 4.99, 6, 6.99. The maximum error is now 2%.

[0066] In embodiments, 2x2MUX-based DAC 200 further comprises an NVM 204, which is configured to store the configuration of CPMUXes 202. In an embodiment, CPMUXes 202, in response to an all-erased NVM 204, are in the direct-transfer mode. In some embodiments, the CPMUXes configuration may be stored in other types of media; in an embodiment, external storage is used.

[0067] In some embodiments, more complex CPMUXes are used, e.g., 3x3 or 4x4, or a mix of various types of CPMUXes.

[0068] Fig. 3 is a flowchart 300 that schematically illustrates a method for reducing thermometric DAC errors, in accordance with an embodiment of the present invention. The method is typically executed by test equipment, such as an Automated Test Equipment (ATE), for example, as part of fabrication testing of an N-bit thermometric DAC (e.g., DAC 200, (Fig. 2))-

[0069] The flowchart begins at an Initial-CPMUX operation 302, wherein the ATE configures all CPMUXes 104 to a pass-through mapping - that is, the input thermometric code and the output thermometric codes are identical. This operation is needed to facilitate measurement of the unit-DACs characteristics. In some embodiments, pass-through is the default configuration of the CPMUXes (e.g., the configuration that is set when an NVM memory that controls the CPMUX configurations is erased); in this case, operation 302 is not needed.

[0070] Next, at a measure-strengths operation 304, the ATE measures the strength of the 2n-l unit-DACs by successively converting binary values from 0 to n-1, measuring the analog voltages that the thermometric DAC outputs and then calculating:

[0071] Unit-DAC(n) = DAC(n)-DAC(n-l),

[0072] Where Unit-DAC(n) is the relative strength of the nthunit-DAC, and DAC(n) is the measured analog output of the thermometric DAC in response to a binary -n input.

[0073] The ATE now enters modify -thermometric-code operation 306, and changes the set of CPMUX configurations, to select a different CPMUX configurations combination. For example, for the 2x2-multiplxer based DAC described above, with reference to Fig. 2, there are two possible configurations for each CPMUX (cross or pass-through, denoted X and PT below), and eight configuration combinations for the three CPMUXes: {PT,PT,PT},{PT,PT,X},{PT,X,PT},{PT,X,X},{X,PT,PT},{X,PT,X},{X,X,PT} and {X,X,X}. The ATE may select the next combination from this set whenever the ATE enters operation 306.

[0074] Next, at a scan-binary -inputs operation 306, the ATE calculates the conversion value for successive binary inputs (according to the weights of the activated unit-DACs) and calculates an accuracy-measure for the current set of CPMUX configurations. In embodiments, the accuracy -measure may comprise a maximum or an average DNL or INL, or any other suitable accuracy measure.

[0075] In embodiments, the ATE maintains a best-accuracy-measure variable and a bestconfiguration set variable. In an update-best-accuracy-measure operation 310, the ATE compares the accuracy measure calculated in operation 308, and, if the accuracy measure is better than the best accuracy measure variable, updates the best accuracy and best configuration set variables.

[0076] The ATE repeats operations 306, 308 and 310 for all the combinations of CPMUX configurations. After all combinations are processed, the ATE, in a store-best-configuration-set operation 312, stores the best-configuration-set in the NVM, and the flowchart ends.

[0077] The configuration of flowchart 300 illustrated in Fig. 3 and described hereinabove is cited by way of example. Other configurations may be used in alternative embodiments. For example, in an embodiment, the best-accuracy variable is compared against a given target accuracy, and if the target accuracy is met, the scan (comprising operation 306, 308 and 310) ends.

[0078] YIELD CONSIDERATIONS

[0079] The selected CPMUX architecture (e.g., 2x2 muxes, 3x3 muxes, etc.) may affect the DAC manufacturing yield in two ways. On one hand, complex CPMUX structures increase the silicon footprint, decreasing the number of dies in the wafer. On the other hand, complex CPMUX structures may allow DACs with higher unit-DAC variance to meet a given linearity specification and, thus, increase the yield. In some embodiments, the CPMUX architecture is determined according to a maximum DAC manufacturing yield.

[0080] Fig. 4 is a graph 400 that schematically illustrates the expected yields of a 2-bit thermometric DAC as a result of unit-DAC mismatches, in accordance with an embodiment of the present invention. The vertical axis, designated complementary cumulative distribution function (CCDF), represents the expected yield of the thermometric DAC, and the horizontal axis represents the conversion SNR due to the unit-DAC mismatch. A curve 402 depicts SNR vs. CCDF when no correction is done. A curve 404 shows the SNR vs. CCDF when 7-bit CMUXes are used, and a curve 406 represents the CCDF vs SNR when 2x2MUXes are used (as illustrated in Fig. 2).

[0081] Assuming that the specified minimum SNR of the DAC is 32dB, the yields for curves 402, 404 and 406 will be, respectively, 2.7%, 72.3% and 57.8%.

[0082] Obviously, curve 404, which is the most complex to implement, is the optimal solution for best yield. However, circuit complexity may increase the die-size and power consumption, and, in embodiments, the DAC vendor may prefer the sub-optimal solution of curve 406, with compact 2x2 switches.

[0083] HYBRID DACS

[0084] The techniques described above may also be applicable for hybrid-DACs, in which some of the bits are binary-coded and other bits are therm ometrically coded. For example, a 4 bit DAC may comprise two binary coded low-order bits and two thermometrically coded most significant bits:

[0085] 0: 00000 1 : 00001 2: 00010 3: 00011

[0086] 4: 00100 5: 00101 6: 00110 7: 00111

[0087] 8: 01100 9: 01101 10: 01110 11 : 01111

[0088] 12: 11100 13: 11101 14: 11110 15: 11111

[0089] In this case, CPMUXes will be used for the high order bits only.

[0090] The configurations, yield curves and methods described hereinabove, with reference to Figs 1 through 4, including all units and subunits thereof, are example configurations, yield curves and methods that are shown purely for the sake of conceptual clarity. Any other suitable methods, waveforms and configurations may be used in alternative embodiments.

[0091] In various embodiments, CPMUX 104 and CPMUX 202, may be implemented using suitable hardware, such as one or more Application-Specific Integrated Circuits (ASIC) or Field-Programmable Gate Arrays (FPGA), or a combination of ASIC and FPGA.

[0092] Although the embodiments described herein mainly address current-mode thermometric DACs, the methods and systems described herein can also be used in voltage-mode DACs, as well as in thermometric Analog-to-Digital Converters (ADCs).

[0093] It will thus be appreciated that the embodiments described above are cited by way of example, and that the present invention is not limited to what has been particularly shown and described hereinabove. Rather, the scope of the present invention includes both combinations and sub-combinations of the various features described hereinabove, as well as variations and modifications thereof which would occur to persons skilled in the art upon reading the foregoing description and which are not disclosed in the prior art. Documents incorporated by reference in the present patent application are to be considered an integral part of the application except that to the extent any terms are defined in these incorporated documents in a manner that conflicts with the definitions made explicitly or implicitly in the present specification, only the definitions in the present specification should be considered.

Claims

CLAIMS1. A Digital -to- Analog Converter (DAC) to convert an input thermometric digital signal to an analog output signal, the DAC comprising: at least two configurable permutation multiplexers (CPMUXes), each CPMUX configured to map a respective partial subset of bits of the input thermometric digital signal into a respective partial subset of bits of a permuted thermometric digital signal, according to a CPMUX configuration; a bank of unit-DACs, each unit-DAC configured to convert a respective bit of the permuted thermometric digital signal into an analog signal; and a summer circuit, configured to generate the analog output signal according to a sum of the analog signals produced by the unit-DACs.

2. The DAC according to claim 1, further comprising a binary to thermometric-code conversion circuit, configured to convert a digital input signal to the input thermometric digital signal.

3. The DAC according to claim 1, wherein at least one of the CPMUXes comprises a configurable 2-by-2 multiplexer.

4. The DAC according to any of claims 1-3, wherein the CPMUX configuration is set to improve a conversion accuracy measure of the DAC.

5. The DAC according to claim 4, wherein the accuracy measure comprises a linearity measure of the analog output signal.

6. The DAC according to any of claims 1-3, wherein the CPMUX configuration of at least one of the CPMUXes is stored in a Non-Volatile Memory (NVM).

7. A method for converting an input thermometric digital signal to an analog output signal, the method comprising: using each of at least two configurable permutation multiplexers (CPMUXes), mapping a respective partial subset of bits of the input thermometric digital signal into a respective partial subset of bits of a permuted thermometric digital signal, according to a CPMUX configuration; using each unit-Digital-to-Analog-Converter (unit-DAC) in a bank of unit-DACs, converting a respective bit of the permuted thermometric digital signal into an analog signal; and generating the analog output signal according to a sum of the analog signals produced by the unit-DACs.

8. The method according to claim 7, further comprising converting a digital input signal to the input thermometric digital signal.

9. The method according to claim 7, wherein at least one of the CPMUXes comprises a configurable 2-by-2 multiplexer.

10. The method according to any of claims 7-9, and comprising setting the CPMUX configuration to improve a conversion accuracy measure of the DAC.

11. The method according to claim 10, wherein the accuracy measure comprises a linearity measure of the analog output signal.

12. The method according to any of claims 7-9, and comprising storing the CPMUX configuration of at least one of the CPMUXes in a Non-Volatile Memory (NVM).

13. A method for calibrating a Digital -to- Analog Converter (DAC), the method comprising: estimating a conversion accuracy measure of a thermometric DAC that converts an input thermometric digital signal to an analog output signal, wherein the thermometric DAC comprises (i) at least two configurable permutation multiplexers (CPMUXes), each CPMUX configured to map a respective partial subset of bits of the input thermometric digital signal into a respective partial subset of bits of a permuted thermometric digital signal, according to a CPMUX configuration, (ii) a bank of unit-DACs, each unit-DAC configured to convert a respective bit of the permuted thermometric digital signal into an analog signal, and (iii) a summer circuit, configured to generate the analog output signal according to a sum of the analog signals produced by the unit-DACs; and adjusting the CPMUX configuration to improve the conversion accuracy measure.

14. The method according to claim 13, wherein estimating the conversion accuracy measure comprises: measuring respective strengths of the unit-DACs while the CPMUXes are in a pass- through mode; and calculating the conversion accuracy measure for a given CPMUX configuration based on the strengths of the unit-DACs.

15. The method according to claim 13 or 14, wherein adjusting the CPMUX configuration comprises improving a linearity measure of the analog output signal.

16. The method according to claim 15, wherein the linearity measure comprises an integral non-linearity (INL) of the DAC.

17. The method according to claim 15, wherein the linearity measure comprises a differential non-linearity (DNL) of the DAC.

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