FOR EMBEDDED DEVICES

BACKGROUND

[0001] Analog-to-digital converters (ADCs) convert analog input signals into a sequence of digital output codes. The conversion process may involve quantization of the inputs because the analog signal is continuous, while the digital output codes are discrete. ADC measurements may deviate from ideal measurements through various sources of inaccuracy in the conversion process (e.g. quantization errors), as well as variations in manufacturing process (e.g. device-to-device variations). ADC performance may be specified in terms of static performance and dynamic performance. Static performance may include offset error, gain error, differential non-linearity (DNL), and integral non-linearity (INL). Dynamic performance may include total harmonic distortion (TDH) and signal to noise ratio (SNR). Some embedded devices (e.g., digital signal processors (DSPs), systems on chip (SoCs)) may include an on-chip ADC. The performance of the on-chip ADC may be evaluated during production test.

SUMMARY

[0002] In described examples of an on-chip ADC linearity test for embedded devices, a method includes receiving a trigger signal that indicates an ADC input voltage adjustment, and reading an ADC output sample upon receiving the trigger signal. The ADC output sample has value in a range of N integer values that correspond to N discrete ADC output codes. Also, the method includes computing a histogram of code occurrences for M consecutive ADC output codes. The histogram includes M number of bins corresponding to the M consecutive ADC output codes, where M is less than N. Further, the method includes updating a DNL value and an INL value according to the histogram at an interval of K number of ADC output sample readings, and shifting the histogram by one ADC output code after updating the DNL and the INL values.

[0003] In another embodiment, a non-transitory, computer-storage readable device includes computer executable instructions that, when executed by a processor, cause the processor to detect a trigger event that indicates an ADC voltage step increment and read an ADC output sample upon receiving the trigger event. The ADC output sample has a value range of N integer values that correspond to N discrete ADC output codes. The instructions further cause the processor to update a histogram of code occurrences for M consecutive ADC output codes, wherein the histogram includes M number of bins corresponding to the M consecutive ADC output codes, and wherein M is less than N. The instructions further cause the processor to update a maximum DNL value, a minimum DNL value, a maximum INL value, and a minimum INL value according to the histogram at an interval of K number of ADC output sample readings. The instructions further cause the processor to shift the histogram by one ADC output code after updating the maximum DNL value, the minimum DNL value, the maximum INL value, and the minimum INL value.

[0004] In yet another embodiment, an apparatus includes an ADC configured to convert an analog input signal into N discrete ADC output codes and a memory to include a histogram including M number of bins that store the number of occurrences for M consecutive ADC output codes, wherein each bin corresponds to one of the M ADC output codes, and wherein M is less than N. The apparatus further includes a first interface configured to receive a trigger signal that indicates a voltage step increment at the ADC input, wherein an average of K number of received trigger signals corresponds to an ADC output code transition. The apparatus further includes a processor coupled to the ADC, the memory, and the first interface and configured to read an ADC output sample upon receiving the trigger signal and compute the histogram by incrementing a number of occurrences in a bin corresponding to a value of the ADC sample. The processor is further configured to update a maximum code occurrences, a minimum code occurrences, a maximum INL value, and a minimum INL value according to the histogram at an interval of K ADC output sample readings, wherein the maximum code occurrences is proportional to a maximum DNL value, and wherein the minimum code occurrences is proportional to a minimum DNL value. The processor is further configured to shift the histogram by one ADC output code after updating the maximum code occurrences, the minimum code occurrences, the maximum INL value, and the minimum INL value.

[0005] In yet another embodiment, a non-transitory, computer-storage readable device includes computer executable instructions that, when executed by a processor, cause the processor to set a first control code to instruct a voltage step increment, set a second control code to indicate the voltage step increment, and read an ADC measurement report including a maximum code occurrences, a minimum code occurrences, a maximum scaled INL value, and a minimum scaled INL value and the ADC codes corresponding to the maximum code occurrences, the minimum code occurrences, the maximum scaled INL value, and the minimum scaled INL value. The instructions further cause the processor to compute a maximum DNL value, a minimum DNL value, a maximum INL value, and a minimum INL value from the measurement report.

BRIEF DESCRIPTION OF THE DRAWINGS

[0006] FIG. 1 is a graph of an ADC transfer function and corresponding ADC DNL measurements by converting ADC input voltage to discrete level transition points in accordance with various embodiments.

[0007] FIG. 2 is a graph of an ADC transfer function and a corresponding histogram of ADC code occurrences in accordance with various embodiments.

[0008] FIG. 3 is a block diagram of an ADC test set up in accordance with various embodiments.

[0009] FIG. 4 is a block diagram of a Built-in Self-Test (BIST) engine in accordance with various embodiments.

[0010] FIG. 5 is a block diagram of a test engine in accordance with various embodiments.

[0011] FIG. 6 is a graph of an ADC linearity test code range in accordance with various embodiments.

[0012] FIG. 7 is a graphical representation of a moving histogram based method in accordance with various embodiments.

[0013] FIG. 8 is a graphical representation of another moving histogram based method in accordance with various embodiments.

[0014] FIG. 9 is a graph of ADC INL measurements in accordance with various embodiments.

[0015] FIG. 10 is a flowchart of an ADC linearity test calibration method in accordance with various embodiments.

[0016] FIG. 11 is a flowchart of another ADC linearity test calibration method in accordance with various embodiments.

[0017] FIG. 12 is a flowchart of an ADC linearity test method in accordance with various embodiments.

[0018] FIG. 13 is a flowchart of another ADC linearity test method in accordance with various embodiments.

[0019] FIG. 14 is two graphs of ADC INL measurements comparing an all-code histogram based method and a moving histogram based method in accordance with various embodiments. DETAILED DESCRIPTION OF EXAMPLE EMBODIMENTS

[0020] An ADC input may be a continuous voltage with infinite number of values, while an ADC output may be a defined number of discrete codes. Thus, an ADC input-output transfer characteristic is an infinite-to-one mapping. To determine linearity characteristics for an ADC, a one-to-one mapping may be established between the ADC input and the ADC output by representing the ADC input in terms of transition voltages between ADC output codes, where the transition voltages are discrete. When an ADC has no linearity error, the distance between each adjacent transition level (e.g. ADC code widths) is one least significant bit (LSB). DNL is a measure of a measured distance between adjacent transition levels and a reference distance of one LSB. INL is a measure of a distance between each code transition level and a best fit straight line though the code transition levels.

[0021] FIG. 1 shows a graph 100 of an ADC transfer function and corresponding ADC DNL measurements by converting ADC input voltage to discrete level transition points in accordance with various embodiments. Sub-graph 110 illustrates the ADC transfer function, and sub-graph 120 illustrates the ADC DNL measurement. In sub-graph 110, the x-axis may represent input analog voltages in units of Volts, and the y-axis may represent ADC discrete output codes. The curve 111 may represent an output transfer function for a 3-bit ADC in response to input voltages. In sub-graph 120, the x-axis may represent voltage transition levels in units of Volts, and the y-axis may represent ADC output code indices. In sub-graph 120, each of the data points 121 may correspond to an ADC code transition in sub-graph 110. As shown in sub-graphs 110 and 120, the distances between the data points 121 may differ from an ideal value of one LSB, where the differences may represent differential linearity errors (e.g. DNL values). In sub-graph 120, the line 122 drawn between the endpoints of the data points 121 may correspond to a best fit straight line through the data points 121. The distances between each data point 121 and the line 122 may represent integral linearity errors (e.g. INL values).

[0022] In an embodiment, an all-code histogram based method may be employed to measure ADC linearity. In the all-code histogram based method, a histogram of ADC output code occurrences may be generated in response to an input signal level which increases linearly within a full scale range of an ADC. A full scale range may refer to a range between a minimum voltage that corresponds to a minimum ADC output code and a maximum voltage that corresponds to a maximum ADC output code. After collecting a sufficiently large amount of samples from an ADC, a histogram of ADC output code occurrences may be generated to provide an accurate measure of DNL. INL may be computed by numerically integrating the DNL values. The number of bins or the size of a histogram may correspond to the number of ADC output codes in an all- code histogram based method. For example, a histogram with 8 bins may be generated for a 3 -bit ADC that produces eight ADC output codes, while a histogram with 1024 bins may be generated for a 10-bit ADC that produces 1024 ADC output codes.

[0023] FIG. 2 shows a graph 200 of an ADC transfer function and a corresponding histogram of ADC code occurrences in accordance with various embodiments. The ADC transfer function is illustrated in sub-graph 210 and the corresponding histogram of ADC code occurrences is illustrated in sub-graph 220. In sub-graph 210, the x-axis may represent input analog voltage in units of Volts and the y-axis may represent ADC discrete output code values. In sub-graph 210, the curve 211 may represent an output transfer function for a 3 -bit ADC in response to input voltages. In sub-graph 220, the x-axis may represent ADC code index, which may correspond to a histogram bin, and the y-axis may represent the number of ADC code occurrences. As can be observed, the number of code occurrences in each histogram bin is proportional to the distances between each adjacent transition level as shown in curve 211. Thus, a histogram of code occurrences may be employed for measuring ADC DNL and INL.

[0024] In some embodiments, a tester employing an all-code histogram based method may apply a ramp voltage (e.g. in linear constant voltage steps) to an ADC and transfer one or more ADC samples from the ADC output after each voltage step adjustment. After sweeping the ADC input voltage to the ADC full scale range, the tester may generate a histogram for the ADC output code occurrences and determine DNL and INL from the histogram. In such embodiments, the tester may employ a significant amount of memory for storage because the size of the histogram may increase in proportion with the number of ADC output codes. In addition, the test time may be significant as a large amount of ADC samples may be transferred to the tester. For example, when testing a 10 mega samples per second (MSPS) 10-bit ADC with an average of about eight occurrences per ADC output code, a tester may transfer about eight thousand (e.g. 1024 x 8 = 8096) ADC samples from the ADC via a digital communication interface (e.g. an Inter-Integrated Circuit (I2C) with a transfer rate of 1.5 megahertz (MHz)). The test time per ADC may be about five to about six seconds depending on the ADC sample time and other overhead associated with the digital communication interface. Accordingly, ADC production test time may be significant. [0025] Embodiments of the on-chip ADC linearity test for embedded devices disclosed herein include an ADC BIST scheme employing a moving histogram based method. In an embodiment, ADC DNL and INL may be represented in modified forms to reduce computational complexity and a one-time post processing may be applied to the modified DNL and INL to provide DNL and INL measures that are compliant to the Institute of Electrical and Electronics Engineers (IEEE) document 1241-2000, which is incorporated herein by reference as if reproduced in its entirety. The lower computational complexity may enable implementation of the DNL and the INL measures on a low cost and/or low performance microcontroller (MCU) and may reduce computational time, and thus production test time. In another embodiment, an ADC linearity test may employ a moving histogram based method with dynamic DNL and INL computations instead of an all-code histogram with post DNL and INL computations. The dynamic computations may enable a BIST to compute a histogram with a small fixed number of bins that is substantially less (e.g. about eight to about thirty two bins) than a number of ADC output codes and slide the histogram across the ADC output code range accordingly as the DNL and the INL are computed for each ADC output code. The lower computational complexity (e.g. modified form) and smaller memory storage (e.g. a fixed size moving histogram) may enable the BIST to be incorporated in an embedded device with an on-chip ADC for linearity test. The BIST may be executed on a low cost and/or low performance MCU (e.g. 8051 MCU) with a small amount (e.g. about 128 bytes) of Random Access Memory (RAM) for histogram computation. The BIST program code may be stored on a small (e.g. about 800 bytes) Read Only Memory (ROM) in the embedded device. In another embodiment, an initialization procedure may be defined to determine an ADC input voltage range suitable for the modified DNL and INL measurements. The disclosed on-chip ADC linearity test may reduce production test time by an order of about five to about six compared to an all-code histogram based method and may provide DNL and INL measurements comparable to the all-code histogram base method.

[0026] FIG. 3 shows a block diagram of an ADC test set up 300 in accordance with various embodiments. The ADC test setup 300 may be suitable for testing ADC linearity (e.g. DNL and INL). The ADC test set up 300 may include a tester 310 and a device under test (DUT) 320. The tester 310 and the DUT may be connected via an analog connection 330 and a digital connection 340. The analog connection 330 may be any physical link configured to carry analog voltage signals. The digital connection 340 may be any physical link configured to transport digital signals at high speed (e.g. about 1.5 megahertz (MHz) or more). The number of digital signals (e.g. read signal, write signal, command signal, etc.), the format of the digital signals, and the speed of the digital signals may depend on the type of digital communication interface (e.g. Inter-Integrated Circuit (I2C)). In some embodiments, the digital connection 340 may include more than one type of digital wired connections, for example, an I2C interface connection and some general purpose digital pin connections.

[0027] The tester 310 may include an analog voltage source 311 and a test engine 312. The voltage source 311 may be any device configured to generate a high precision (e.g. in millivolt (mV)) linear ramp voltage with a constant step. For example, the voltage source 311 may be a signal generator, a function generation, or any other circuit element suitable for generating a high precision ramp voltage for ADC linearity test. The test engine 312 may be any device configured to control the voltage source 311 via interface 313 (e.g. general purpose interface bus (GPIB), circuits, etc.) and communicate with the DUT 320 via the digital connection 340. For example, the test engine 312 may be a processor, a computer workstation, or any other programmable or nonprogrammable device configured to execute a test program for performing ADC linearity test. The interface 313 may be a digital interface configured to transport voltage control codes.

[0028] The DUT 320 may be any device, such as an embedded device, including an on-chip ADC 321 and a BIST engine 322. For example, the DUT 320 may be a DSP, a SoC, etc. The on- chip ADC 321 may be any device configured to convert a continuous analog input signal to a defined number of discrete output codes. For example, the ADC 321 may be a 3-bit ADC with eight output codes, a 10-bit ADC with 1024 output codes, etc. The BIST engine 322 may be any device, such as a general purpose processor or an MCU, configured to control the ADC 321 (e.g. configuration registers) and collect ADC samples (e.g. via one or more output registers, etc.) from the ADC 321 via interface 323 (e.g. digital signals). In addition, the BIST engine 322 may determine DNL and INL for the on-chip ADC 321 by analyzing the collected ADC samples (e.g. generating histograms and computing DNL and INL deviations).

[0029] In some embodiments, the test engine 312 may determine ADC linearity test configuration parameters, such as a starting voltage, a stopping voltage, and a voltage step, which may be determined according to the ADC 321 (e.g. ADC full scale voltage range and number of ADC output codes). The voltage step may be a constant step and may be determined such that a sufficient amount of ADC samples may be measured for each ADC output code, for example, about eight or more samples per ADC output code. The test engine 312 may cause the voltage source 311 to be set to a specific voltage and may cause the voltage to be adjusted (e.g. increment by a fixed step) via interface 313. The test engine 312 may send a trigger signal (e.g. a pulse) to the DUT 320 via the digital connection 340 at the end of every voltage adjustment to indicate that the ADC 321 may generate a sample for the adjusted voltage and the BIST engine 322 may process the ADC sample and compute DNL and INL parameters. In addition, the test engine 312 may send test configuration parameters to the DUT 320 at the beginning of an ADC linearity test and may read measured parameters from the DUT 320 at the end of the ADC linearity test via the digital connection 340. The ADC test set up 300 may be alternatively configured to employ a higher performance (e.g. high resolution and linear voltage output) digital-to-analog converter (DAC) in place of the voltage source 311, and thus may be positioned on the same DUT 320 as the ADC 321. In addition, the test engine 312's functionalities may be implemented on the BIST engine 322 instead.

[0030] FIG. 4 shows a block diagram of a BIST engine 400 in accordance with various embodiments. The BIST engine 400 may be substantially similar to the BIST engine 322 and may be positioned in any embedded device (e.g. DUT 320) including an on-chip ADC (e.g. ADC 321). The BIST engine 400 may include a processor 410, a memory device 420, a digital interface 430, and an ADC interface 440. The processor 410 may be implemented as a general purpose processor or may be part of one or more processors. The processor 410 may include an ADC linearity measurement module 411 stored in internal non-transitory memory in the processor to permit the processor to implement ADC linearity test methods 1100 and/or 1300, described more fully below. In an alternative embodiment, the ADC linearity measurement module 411 may be implemented as instructions stored in the memory device 420, which may be executed by the processor 410. The memory device 420 may include a cache for temporarily storing content, for example, a RAM. Additionally, the memory device 420 may include a long-term storage for storing content relatively longer, for example, a ROM. For instance, the cache and the long-term storage may include dynamic random access memories (DRAMs), solid-state drives (SSDs), hard disks, or combinations thereof. The digital interface 430 may be any physical link configured to communicate with an ADC tester (e.g. tester 310) and may be substantially similar to digital connection 340. The ADC interface 440 may be any physical link configured to transport ADC samples and/or ADC configurations between an ADC (e.g. ADC 321) and the BIST engine 400. [0031] FIG. 5 shows a block diagram of a test engine 500 in accordance with various embodiments. The test engine 500 may be substantially similar to test engine 312 and may be positioned in any tester (e.g. tester 310). The test engine 500 may include a processor 510, a memory device 520, a digital interface 530, and a voltage control interface 540. The processor 510 may be implemented as a general purpose processor or may be part of one or more processors. The processor 510 may include an ADC linearity measurement module 51 1 stored in internal non- transitory memory in the processor to permit the processor to implement ADC linearity test methods 1000 and/or 1200, described more fully below. In an alternative embodiment, the ADC linearity measurement module 51 1 may be implemented as instructions stored in the memory device 520, which may be executed by the processor 510. The memory device 520 may be substantially similar to the memory device 420. The digital interface 530 may be any physical link configured to communicate with a DUT (e.g. DUT 320) and may be substantially similar to digital connection 340. The voltage control interface 440 may be any physical link (e.g. general purpose interface bus (GPIB), circuits, etc.) configured to send controls to a variable voltage source instrument (e.g. signal generator, functional generator).

[0032] In an embodiment, an N-bit ADC may produce 2 ^N ADC output codes ranging from C _LO (e.g. a value zero) to Chi (e.g. a value of 2 ^N -1). A histogram of ADC output code occurrences may be generated between code C _lo +i and code for DNL and INL measurements. The minimum code Cio and the maximum code CM may be excluded from the histogram, because any ADC underflow may be converted to the minimum code C _LO , and ADC overflow may be converted to the maximum code CM. Thus, the total number of ADC code occurrences excluding the lowest and highest bins may be represented as:

hum = ∑¾o ₊₁ ^¾ (0 Equation (1) where h _sum is the total number of code occurrences and h(i) is the number of occurrences for the 1 ^TH ADC output code (e.g. Q).

[0033] The average number of code occurrences for each bin may be computed as:

Κν ₉ = ^ Equation (2) where h _avg is the average number of code occurrences and dlt is the number of bins in the histogram excluding the lowest and highest bins and may be represented as:

dlt = CM - Ci _o - 1 Equation (3)

[0034] As described herein above, the number of code stored in internal non-transitory memory in the processor to permit the processor to occurrences may be proportional to the distances between adjacent transition levels. Thus, the average number of code occurrences h _avg may correspond to an ideal value of one LSB and the measured number of code occurrences for an 1 ^th ADC code h(i) may correspond to the measured distance between adjacent transition levels. A normalized code width cw(i) for an ADC may be represented as shown below:

cw( = i = C _{l0 +1} , C _{l0 +2} , ... , C _hi - Equation (4)

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[0035] As described herein above, DNL is a measure of a measured distance between adjacent transition levels and an ideal value of one LSB. Thus, a DNL value for an ADC output code may be computed as shown below:

DNL (i = cw(i - 1, i = C _{l0 +1} , C _{l0 +2} , ... , C _hi _ Equation (5) where DNL(i) is a DNL value for the 1 ^th ADC output code . A DNL value as shown in Equation (5) may not have a value less than minus one and a value of minus one may indicate a missing ADC code (e.g. zero occurrences).

[0036] As described herein above, INL is a measure of a distance between each code transition level and a best fit straight line though the code transition levels. Thus, INL may be computed by accumulating DNL values at each ADC code transition as shown below:

INL (i) =∑ _k ^l ₌₁ dnl(k), i = C _{l0 +1} , C _{l0 +2} , ... , C _hi - Equation (6)

[0037] In an embodiment, an ADC performance specification may include DNL parameters and INL parameters. For example, DNL parameters may include a minimum DNL value and a maximum DNL value for an ADC and INL parameters may include a minimum INL value and a maximum INL value for the ADC. Thus, an ADC linearity test may dynamically compute and update the DNL parameters and the INL parameters without storing a histogram for all code occurrences. For example, an ADC linearity test may compute a number of code occurrences for an ADC as ADC samples are read (e.g. at every voltage increment). When the ADC input voltage passes a level sufficiently far from an ADC output code such that the ADC may not produce another output code , the ADC linearity test may compute a DNL value and an INL value for the ADC output code and dynamically update the minimum DNL value, the maximum DNL value, the minimum INL value, and the maximum INL value.

[0038] A DNL value for an ADC output code may be computed in terms of code width (e.g. cw(i) in Equation (5)), where the code width is proportional to the number of code occurrences (e.g. h(i) in Equation (4)). Thus, an ADC linearity test may compute a maximum code occurrences and a minimum code occurrences instead of a maximum DNL value and a minimum DNL value during a voltage sweep. At the end of the voltage sweep, the ADC linearity test may compute the maximum DNL value and the minimum DNL value from the maximum code occurrences and the minimum code occurrences, respectively, by substituting Equations (2), (3), and (4) into Equation (5). Thus, the maximum DNL value and the minimum DNL value may be computed as shown below:

DNL = -^- x dlt - 1 Equation (7) where h(i) may be the maximum code occurrences when computing the maximum DNL value and h(i) may be the minimum code occurrences when computing the minimum DNL value.

[0039] An INL value for an ADC code is a cumulative sum of DNL values. However, the INL value may not be simplified by accumulating the code occurrences in place of DNL values. Because the INL value is a cumulative sum of DNL values, the mean DNL value over a code span dlt may be close to zero for the INL value to be meaningful. A non-zero DNL offset across the code span dlt may be integrated during the INL calculation causing a ramping error in the INL values. As can be observed in Equation (4), each DNL value may be normalized to an average number of code occurrences h _avg (e.g. code width of one LSB) such that the mean DNL value may be close to zero over the span dlt.

[0040] In an embodiment, an INL value may be represented in a modified form to reduce computational complexity. As can be observed in Equation (7), a DNL value is computed with a division operation, which may be expensive in terms of clock cycles and/or memory storage for a low cost MCU (e.g. MCU 8051). However, Equation (7) may be modified to remove the division operation by cross multiplying Equation (7) with the term h _sum as shown below:

DNL _hsum = h _sum x DNL = h(i x dlt - h _sum Equation (8)

[0041] A modified INL value may be computed as shown below:

^INL hsum = ^INL hsum + ^DNL hsum Equation (9)

[0042] Accordingly, an ADC linearity test may compute the modified INL values and dynamically update a maximum modified INL value and a minimum modified INL value. At the end of the ADC linearity test, the maximum INL value and the minimum INL value may be computed by dividing the maximum modified INL value and the minimum modified INL values with h _sum , respectively, where the computed maximum and minimum INL values are compliant to the IEEE document 1241-2000. An all-code histogram based method may compute a total number of code occurrences after generating the all-code histogram, whereas an ADC linearity test that computes INL values dynamically may include a calibration procedure for estimating a total number of code occurrences h _sum prior to taking ADC sample measurements.

[0043] In an embodiment, an ADC linearity test may measure DNL and INL for an ADC by computing a histogram for a small range (e.g. less than about thirty two) of ADC codes and moving the histogram across an ADC code span (e.g. dlt). Accordingly, the histogram may be computed with a small number of bins and the number of bins may not increase in proportion with the number of ADC output codes. An ADC linearity test employing a moving histogram may be referred to as a moving histogram based method. The following tables describe some parameters that may be employed in a moving histogram based method:

Table 1 - ADC linearity Test Parameters

hmax Maximum number of occurrences in any one ADC code bin over ADC code range C _lo+1 to C _hi -i

hmin Minimum number of occurrences in any one ADC code bin over ADC code range C _lo+1 to C -I

C max ADC code corresponding to h _max

C min ADC code corresponding to h _m j _n

INLscaledMax Maximum INL value scaled with h _sum in any one ADC code bin over ADC

code range C _lo +i to Chi-i

INLscaledMin Minimum INL value scaled with h _sum in any one ADC code bin over ADC

code range C _lo +i to Chi-i

ClNLmax ADC code corresponding to INLscaledMax

ClNLmin ADC code corresponding to INL _Sca iedMin

[0044] FIG. 6 shows a graph 600 of an ADC code range for ADC linearity test in accordance with various embodiments. In graph 600, the x-axis may represent ADC output codes, where the ADC output codes may vary from a minimum ADC code Q ₀ to a maximum ADC code CM- A moving histogram based method may exclude the two endpoints C _lo and CM, because any ADC underflow, overflow and/or noise may cause the ADC to produce the minimum code C _lo or the maximum code CM, and thus may distort DNL and INL measurements. Accordingly, a moving histogram based method may begin with setting an ADC input voltage Vi _n at a voltage (e.g. a starting voltage) that corresponds to a code transition 611 at a boundary between C _lo and C _lo+1 and incrementing the ADC input voltage Vi _n in steps of V _ste p until the ADC input voltage Vi _n reaches a voltage (e.g. a stopping voltage) that corresponds to a code transition 612 at a boundary between

[0045] The voltage step V _ste p may be determined such that a sufficient amount of ADC samples (e.g. about eight samples) may be collected for each ADC code over a voltage range for the ADC code, for example, a voltage range for an ADC output code may be divided into eight equal voltage steps and one ADC sample may be read for each voltage step. Accordingly, a total number of ADC code occurrences h _sum may correspond to the total number of voltage steps between the starting voltage and the stopping voltage over a code span dlt 613 (e.g. dlt = Chi - C _lo - 1). However, ADC devices may vary due to process variation, so the starting voltage and the stopping voltage may vary from one device to another device. Accordingly, when applying a moving histogram based method, each ADC device may be calibrated to determine a starting voltage and a stopping voltage prior to linearity measurements such that h _sum may be determined accurately. An inaccurate estimate of h _sum may affect INL calculation significantly (e.g. cumulative along ADC codes), which may be discussed more fully below.

[0046] FIG. 7 shows a graphical representation of a moving histogram based method 700 in accordance with various embodiments. The moving histogram based method 700 may be implemented on a BIST engine (e.g. BIST engine 322 or 400). The steps in a moving histogram based method may be broadly divided into three high level steps, a histogram computation step, a linearity error computation step, and a histogram shifting step. In method 700, a histogram 710 (e.g. h[N _b i _n ]) with eight bins (e.g. N _b i _n =8) may be employed for counting a number of code occurrences. Method 700 may begin when an ADC input voltage (e.g. voltage source 311) Vi _n is at a voltage 721 (e.g. starting voltage) that corresponds to a code transition at a boundary between Ci _o and C _lo+1 . Method 700 may generate a histogram 710 with a lowest bin (e.g. h[0]) corresponding to code C _lo+ i and the highest bin (e.g. h[7]) corresponding to code Ci ₀₊ g. During histogram computation, method 700 may read an ADC sample after each voltage step V _step 723 increment (e.g V _b = Vi _n + V _step ) and compute the histogram accordingly, for example, accumulating a number of occurrences for a bin that corresponds to a value of the ADC sample.

[0047] When the ADC input voltage Vi _n reaches a voltage that corresponds to an ADC code (e.g. Ci _o + ₄ to Ci _o + ₅ ) at about a middle of the histogram710, method 700 may perform linearity error computation. During linearity error computation, method 700 may compute an INL value for an ADC code (e.g. CM) that corresponds to the lowest bin according to Equation (9). In addition, method 700 may compare the number of code occurrences h[0] for the lowest bin to a maximum code occurrences h _max and a minimum code occurrences h _m j _n . For example, h _m j _n may be updated to h[0] when h[0] is less than ^. Similarly, h _max may be updated to h[0] when h[0] is greater than hmax. The maximum code occurrences h _max may be initialized to a value of zero, and the minimum code occurrences h _m i _n may be initialized to a large value (e.g. larger than total number of code occurrences) at the beginning of the test.

[0048] After computing linearity error for the ADC output code corresponding to the lowest bin in the histogram, method 700 may shift the histogram 710 by one ADC code, for example, after shifting the histogram 710, the lowest bin h[0] may corresponds to code Ci ₀₊₂ and the highest bin h[7] may corresponds to code Cb+ ₉ .

[0049] Subsequently, method 700 may continue to perform histogram computation and repeat the linearity error computation and the histogram shifting at each code transition (e.g. after receiving about ha _Vg ADC samples) until the ADC input voltage reaches a voltage corresponding to a code transition from C _h i-i to CM. Because the linearity error computation and the histogram shifting may lag the histogram computation, method 700 may continue to perform linearity error computation and the histogram shifting for the remaining ADC output codes until the lowest bin (e.g. h[0]) of the histogram710 corresponds to the ADC code C _h i-i as shown in FIG. 8.

[0050] FIG. 9 shows a graph 900 of ADC INL measurements in accordance with various embodiments. The x-axis may represent ADC code index. The y-axis may represent INL values in LSBs. The curves 910, 920, and 930 may represent INL values in units of LSBs across ADC codes for a 10-bit ADC on an embedded device. The INL values are measured by employing a moving histogram based method, such as method 700. The INL values are computed according to Equation (9) and then divided by h _sum . The curve 910 may represent INL values when h _sum is the total number of code occurrences computed over a code span dlt in which INL values are computed. The curve 920 may represent INL values when h _sum computation has an error of minus three and the curve 930 may represent INL values when h _sum computation has an error of minus ten. As can be observed from curves 910, 920, and 930, the INL measurement errors due to inaccurate h _sum are significant and may increase as the ADC code increases. Accordingly, INL values measured from a moving histogram based method may depend highly on the accuracies of hsum- Noise may also causes h _sum to be incorrect. For example, h _sum may be computed according to a starting voltage and a stopping voltage for a code span dlt prior to measuring INL. However, some ADC output codes (e.g. outliers) may fall outside of the code range dlt due to noise and may not be counted towards the code occurrences. Thus, if an outlier is detected when the ADC input voltage is close to the starting voltage or the stopping voltage, h _sum may be adjusted accordingly.

[0051] FIG. 10 shows a flowchart of an ADC linearity test calibration method 1000 in accordance with various embodiments. Method 1000 may be implemented on a tester (e.g. tester 310) in a test set up substantially similar to ADC test set up 300. Method 1000 may be employed for determining a starting voltage Vieststart and a stopping voltage Vieststop, where Vxeststart may correspond to a voltage that causes a code transition from C _LO to C _lo +i and Vieststop may correspond to a voltage that causes a code transition from to CM- Method 1000 may begin with sending test configuration parameters to a DUT (e.g. DUT 320) at step 1010. The test configuration parameters may include the two transition codes C _lo+1 and C i.

[0052] At step 1020, method 1000 may set an ADC input voltage Vb of a voltage source (e.g. voltage source 311) to a minimum ADC input voltage VADCmin- At step 1030, method 1000 may send a trigger signal to the DUT. After sending the trigger signal, method 1000 may wait for a period of time at step 1040. During this time period, the DUT may perform an ADC conversion and compute ADC measurements. When the time period is expired, method 1000 may proceed to step 1050. At step 1050, method 1000 may increase the ADC input voltage Vi _n by one voltage step V _s tep (e.g. Vi _n = Vi _n + V _ste p). At step 1060, method 1000 may determine whether the ADC input voltage V is at a maximum ADC input voltage VADCmax- If the ADC input voltage is not at the maximum ADC input voltage VADCmax, method 1000 may proceed to step 1030. Method 1000 may repeat the loop of steps 1030 to 1060 until the ADC input voltage Vb reaches the maximum ADC input voltage V _A DCmax.

[0053] At step 1070, method 1000 may read data from the DUT. The data may include a starting voltage index Vidxio and a stopping voltage index Vidxhi, where the starting voltage index Vidxio may indicate the number of voltage increments at which a code transition from Ci ₀ to C _lo +i is detected and the stopping voltage index Vidxhi may indicate the number of voltage increments at which a code transition from Chi-i to Chi is detected. Method 1000 may compute the starting voltage Vxeststart and the stopping voltage V _Te ststop according to the start voltage index Vid _x i ₀ (e.g.

VxestStart = VADCmin + V _ste p X Vidxio) and the Stopping VOltage index Vidxhi (e.g. V _Te stStop = VADCmin +

V _s tep Vidxhi), respectively. Method 1000 may employ some alternative voltage to index or code mappings, which may depend on the tester and/or the voltage source configurations.

[0054] FIG. 11 shows a flowchart of another ADC linearity test calibration method 1100 in accordance with various embodiments. Method 1100 may be implemented on a BIST engine (e.g. BIST engine 322 and 400) in a test set up substantially similar to ADC test set up 300. Method 1100 may be employed for determining a starting voltage Vxeststart and a stopping voltage Vieststop, where V _Te ststart may correspond to a voltage that causes a code transition from C _lo to Ci ₀₊₁ and Vieststop may correspond to a voltage that causes a code transition from Chi-i to Chi. Method 1100 may begin with receiving initialization parameters from a tester (e.g. tester 310) at step 1110. Initialization parameters may include a first ADC output code (e.g. C _lo + and a second ADC output code (e.g. CM- _I ) for linearity measurements. At step 1120, method 1100 may initialize a counter to zero.

[0055] At step 1130, method 1100 may wait for a trigger signal from the tester. When the trigger signal is received, method 1100 may proceed to step 1131. At step 1131, method 1100 may increment the counter. At step 1132, method 1100 may read an ADC sample. At step 1133, method 1100 may determine whether the value of the ADC sample ADC _va i equals to the first ADC output code Cio+i. If the ADC sample value ADC _va i does not exceed the first ADC output code Cio+i, method 1100 may return to step 1130 and repeat the loop of steps 1130 to 1133. If the ADC sample value ADC _va i exceeds the first ADC output code C _lo +i, method 1100 may proceed to step 1140. At step 1140, method 1100 may store the counter value to a starting voltage index Vid _x i ₀ .

[0056] At step 1150, method 1100 may wait for a trigger signal from the tester. When the trigger signal is received from the tester, method 1100 may proceed to step 1151. At step 1151, method 1100 may increment the counter. At step 1152, method 1100 may read an ADC sample. At step 1153, method 1100 may determine whether the ADC sample value ADC _va i exceeds the second ADC output code Chi-i . If the ADC sample value ADC _va i does not exceed the second ADC output code Chi-i, method 1100 may return to step 1150 and repeat the loop of steps 1150 to 1153. If the ADC output sample value ADC _va i exceeds the second ADC output code C i-i , method 1100 may proceed to step 1160. At step 1160, method 1100 may store the counter value to a stopping voltage index Vidxhi- At step 1170, method 1100 may send the starting voltage index Vid _x i ₀ and the stopping voltage index Vidxhi to the tester. An ADC linearity test may read one ADC sample per voltage increment, so the difference between Vidxio and Vidxhi may correspond to a total number of code occurrences h _sum in the ADC linearity test.

[0057] FIG. 12 shows a flowchart of an ADC linearity test method 1200 in accordance with various embodiments. Method 1200 may be implemented on a tester (e.g. tester 310) in a test set up substantially similar to ADC test set up 300. Method 1200 may be employed for measuring linearity parameters for an ADC (e.g. ADC 321) on a DUT (e.g. DUT 320). Method 1200 may begin after the ADC is calibrated for a starting voltage Vxeststart and a stopping voltage Vieststop, for example, by employing method 1000. The starting voltage V _Te ststart may correspond to a voltage that causes a code transition from Ci ₀ to Ci ₀₊₁ and the stopping voltage Vieststop may correspond to a voltage that causes a code transition from Chi-i to Chi.

[0058] At step 1210, method 1200 may set an ADC input voltage Vb of a voltage source (e.g. voltage source 311) to the starting voltage Vxeststart- At step 1220, method 1200 may send a trigger signal to the DUT. After sending the trigger signal, method 1200 may wait for a period of time at step 1230. During this time period, the DUT may perform an ADC conversion and compute ADC measurements. When the time period is expired, method 1200 may proceed to step 1240. At step 1240, method 1200 may increase the ADC input voltage Vi _n by one voltage step V _ste p. At step 1250, method 1200 may determine whether the ADC input voltage Vb reaches the stopping voltage Vxeststop- If the ADC input voltage is not at the stopping voltage V _Te ststop, method 1200 may proceed to step 1220. Method 1200 may repeat the loop of steps 1220 to 1250 until the ADC input voltage Vi _n reaches the stopping voltage Vxeststop.

[0059] At step 1260, method 1200 may read linearity measurements from the DUT. The measurements may include a maximum code occurrences, a minimum code occurrences, an ADC output code corresponding to the maximum code occurrences, an ADC output code corresponding to the minimum code occurrences, a maximum scaled INL value, a minimum scaled INL value, an ADC output code corresponding to the maximum scaled INL value, and an ADC output code corresponding to the minimum scaled INL value as described in Table 1. In addition, the measurements may further include test data, such as a flag indicating an ADC sample is received with a value outside the test code range dlt.

[0060] At step 1270, method 1200 may compute a minimum DNL value, a maximum DNL value, a minimum INL value, and a maximum INL value for the ADC as shown below: dlt— C _h i— Cio

h-sum

a ^v 3 - dlt

DNL _min = ^h ^

DNL _max = ^, L - 1.0

< ^L avg

I ^NL ScaledMin

h sum

INL _max = ^{/WL iedMa} Equation (10)

" ^■ sum

[0061] FIG. 13 shows a flowchart of another ADC linearity test method 1300 in accordance with various embodiments. Method 1300 may be implemented on a BIST engine (e.g. BIST engine 322 and 400) positioned in an embedded device (e.g. DUT 320) in a test set up substantially similar to ADC test set up 300. Method 1300 may be employed for measuring linearity parameters for an on-chip ADC (e.g. ADC 321) by applying a moving histogram based method, which may be substantially similar to method 700. Method 1300 may begin after the ADC is calibrated for a starting voltage Vxeststart (e.g. at voltage increments count Vidxio) and a stopping voltage Vieststop (e.g. at voltage increment count Vidxhi) and a total code occurrences h _sum is estimated, for example, by employing method 1000.

[0062] At step 1310, method 1300 may wait for a trigger signal from a tester (e.g. tester 310), where the trigger signal may indicate an input voltage (e.g. voltage source 311) at the ADC input is increased by a step V _ste p. Upon receiving the trigger signal, method 1300 may proceed to step 1311. At step 1311, method 1300 may read an ADC sample. At step 1312, method 1300 may compute a histogram of code occurrences h[N _b i _n ] (e.g. histogram 710) for a small range (e.g. Nt, _m = about eight to thirty two) of ADC output codes, where each bin of the histogram may correspond to one ADC code. At step 1313, method 1300 may determine whether the voltage source is at a voltage that may produce an ADC output code corresponding to a bin at about middle of the histogram. If the voltage does not correspond to about the middle bin, method 1300 may return to step 1310 and repeat the loop of steps 1310 to 1313. Otherwise, method 1300 may proceed to step 1320 when the voltage Vi _n correspond to about the middle bin. When the voltage Vi _n corresponds to about the middle bin, method 1300 may already have received all ADC codes Cho corresponding to the lowest bin h[0] (e.g. lowest bin is full).

[0063] At step 1320, method 1300 may compute linearity errors for the lowest bin h[0]. Linearity errors may include a maximum code occurrences, a minimum code occurrences, a maximum modified INL value, and a maximum modified INL value. The following pseudo code may be employed for computing the minimum code occurrences and the maximum code occurrences h _max :

if h[0] < h _mn {

hmin = h[0]; // update minimum code occurrences

Chmin = Cho; // ADC code with minimum code occurrences

}

if h[0] > hmax {

hmax = h[0]; // update maximum code occurrences

Chmax = Cho; // ADC code with maximum code occurrences

} [0064] The modified INL value INL _sca i _e for the code Ch ₀ that corresponds to the lowest bin h[0] may be computed according to equation (9). The following pseudo code may be employed for computing the maximum modified INL value and minimum modified INL value:

if INLscaie < INLscaledMiii {

INLscaiedMin = INL _sca i _e ; // update minimum modified INL value CiNLmin = C oi // ADC code with minimum modified INL value

}

if INLscaie > INLscaledMax {

INLscaiedMin = INL _sca ie; // update maximum modified INL value CiNLmax = C oi // ADC code with maximum modified INL value

}

[0065] After computing the linearity errors, the lowest bin h[0] may be discarded. Thus, at step 1330, method 1300 may shift the histogram by one ADC code at step 1330. The shifting of the histogram may be substantially similar to method 700.

[0066] After shifting the histogram, method 1300 may continue to read ADC sample and update the histogram in steps 1340 to 1342. At step 1340, method 1300 may wait for a trigger signal from the tester. Upon receiving the trigger signal, method 1300 may proceed to step 1341. At step 1341, method 1300 may read an ADC sample. At step 1342, method 1300 may continue to update a number of code occurrences for a bin that corresponds to the ADC sample value. At step 1343, method 1300 may determine whether all ADC samples are received (e.g. according to last voltage increment Vidxhi) from the tester. If not all ADC samples are read, method 1300 may continue to step 1344. At step 1344, method 1300 may determine whether ha _Vg samples are received since the last histogram shift. Method 1300 may proceed to step 1320 when h _avg samples are received since the last histogram shift. Otherwise, method 1300 may proceed to step 1340.

[0067] Returning to step 1343, method 1300 may proceed to step 1350 when all samples are received. At step 1350, method 1300 may compute linearity errors for all bins in h[Nbi _n ], where the linearity errors may be computed in a substantially similar mechanism as in step 1320. At step 1360, method 1300 may send linearity measurements to the tester. For example, the measurements may include a maximum code occurrences, a minimum code occurrences, an ADC output code corresponding to the maximum code occurrences, an ADC output code corresponding to the minimum code occurrences, a maximum scaled INL value, a minimum scaled INL value, an ADC output code corresponding to the maximum scaled INL value, and an ADC output code corresponding to the minimum scaled INL value as described in Table 1.

[0068] When the input voltage is close to the starting voltage Vxeststart, the ADC may produce ADC codes that are lower than the lowest code C _lo in the test code span dlt due to noise or run-to- run variations. Thus, method 1300 may detect codes that lie outside the code range (e.g. outliers) and may adjust the total code occurrences h _sum accordingly for more accurate INL measurements with the moving histogram based method. In addition, method 1300 may set a flag to indicate an error when an ADC code is outside the code range dlt when the voltage is not close to Vxeststart or

VxestStop-

[0069] FIG. 14 shows two graphs of ADC INL measurements comparing an all-code histogram based method versus a moving histogram based method in accordance with various embodiments. The x-axis may represent ADC code index and the y-axis may represent INL values in units of LSBs. Graph 1410 are INL values computed from an all-code histogram based method and graph 1420 are INL values computed from a moving histogram based method (e.g. method 1000, 1100, 1200, 1300). As can be observed, INL values computed from the moving histogram based method are comparable to the INL values computed from the all-code histogram based method.

[0070] Modifications are possible in the described embodiments, and other embodiments are possible, within the scope of the claims.