Imported: 17 Feb '17 | Published: 01 Aug '06

USPTO - Utility Patents

An analog-to-digital converter (ADC) exhibiting an uncorrected non-linear transfer function receives measured analog voltage amplitudes and outputs uncorrected digital values. A calibration circuit receives each uncorrected digital value and outputs a corrected digital value. The measured analog voltage amplitudes received by the ADC and the corresponding corrected digital values output by the calibration circuit define points approximating an ideal linear transfer function of the ADC. The calibration circuit performs piecewise-linear approximation of the uncorrected transfer function and associates each uncorrected digital value with the applicable linear segment that passes through a segment endpoint on the uncorrected transfer function. The calibration circuit calculates each corrected digital value using calibration coefficients associated with the applicable linear segment, such as the slope of the linear segment. The calibration circuit determines the calibration coefficients by calculating the second derivative of the uncorrected transfer function. The calibration coefficients are stored in non-volatile memory.

This application is a continuation of, and claims priority under 35 U.S.C. § 120 from, nonprovisional U.S. patent application Ser. No. 10/844,901 entitled “Adaptive Error Correction in an Oversampled ADC,” now U.S. Pat. No. 6,993,441, filed on May 12, 2004, the subject matter of which is incorporated herein by reference.

The present invention relates to analog-to-digital converters, and more specifically to a memory-saving method of calibrating analog-to-digital converters.

Analog-to-digital converters (ADCs) are widely used to convert analog voltage signals into digital output signals. ADCs are often embedded with other components in integrated circuits, for example, in microcontrollers. The performance of ADCs that are embedded in integrated circuits is often worse than the performance of standalone ADCs with the same specification. The presence of noise on signal lines and power supply lines often results in higher signal interference and output errors in embedded ADCs. Another source of errors in ADCs is the nonlinearity of the transfer functions of the ADCs. Thus, calibrating embedded ADCs to correct for errors can significantly enhance performance.

Ideally, the Vin versus Dout transfer function of an ADC is a straight line. A linearly increasing voltage amplitude is ideally converted by the ADC into a linearly increasing digital value. The extent to which an ADC receives an analog input signal with a linearly increasing voltage amplitude and outputs digital values that do not linearly increase in value is referred to as “integral non-linearity error” (INL error). An ADC exhibits differential non-linearity (DNL) error, the derivative of INL error, where it outputs discontinuous digital values in response to a smoothly changing voltage input. DNL error is the extent to which the digital values output by an ADC do not increase by steps of 1 LSB as the analog input voltage increases gradually. An ADC ideally converts an input of the minimum voltage into a digital value of all zeros. The extent to which the digital output value deviates from digital zero is referred to as “dc offset error.” An ADC ideally converts an input of the maximum voltage into a digital value of all ones. The extent to which the digital output value output deviates from all digital ones is referred to as “gain error.”

There are various known methods for calibrating ADCs to correct for gain error, dc offset error, INL error and DNL error. In one method, the uncorrected digital output of an ADC with a nonlinear transfer function is mapped to the ideal linear transfer function. The calibration method determines a correction factor for each uncorrected digital value output by the ADC and stores the uncorrected value and its associated correction factor in a lookup table. A calibration circuit outputs a corrected digital value on the ideal linear transfer function by adding the appropriate correction factor to each uncorrected digital value output by the ADC. Valuable memory resources must be allocated to the lookup table. A calibration method that consumes less memory resources for a lookup table would be particularly advantageous in an ADC that is embedded in a microcontroller.

Another calibration method involves piecewise linear segmentation. The entire dynamic range of the uncorrected output of an ADC is divided into equally-spaced ranges of digital values. A best-fitting linear segment is then mapped to the distribution of digital values within in each range. Each uncorrected digital output value is associated with a point on a linear segment. Correction factors are then calculated for each point along each linear segment. The output of the ADC is corrected by adding to each uncorrected digital value the correction factor associated with the closest point on the appropriate linear segment.

A calibration method that divides an uncorrected nonlinear transfer function into segments of approximately equal length is less accurate for segments where the uncorrected transfer function is most nonlinear. Moreover, depending on the shape of the uncorrected transfer function, calculating correction factors with additional segments does not necessarily render the calibration more accurate. For an uncorrected, hockey-stick-shaped transfer function, for example, approximating the uncorrected transfer function with successive linear segments along the handle does not provide a better fit than would a single linear segment. Calculating correction factors for the successive linear segments does not significantly improve the resolution of the ADC.

A method is sought for calibrating an analog-to-digital converter that reduces the memory used to store correction factors and that also reduces any calculations that do not significantly improve the resolution of the analog-to-digital converter.

An analog-to-digital converter (ADC) that exhibits an uncorrected non-linear transfer function receives measured analog voltage amplitudes and outputs uncorrected digital values. A calibration circuit receives each uncorrected digital value and outputs a corrected digital value. The calibration circuit performs piecewise-linear approximation of the uncorrected non-linear transfer function and associates each uncorrected digital value with the applicable linear segment that passes through a segment endpoint on the uncorrected transfer function. The corrected digital values output by the calibration circuit and the corresponding measured analog voltage amplitudes received by the ADC define points approximating an ideal linear transfer function of the ADC. In one embodiment, the calibration circuit is the processing unit of a microcontroller.

The calibration circuit calculates each corrected digital value using calibration coefficients associated with the applicable linear segment. One calibration coefficient is the endpoint digital value of a segment endpoint of each linear segment. Another calibration coefficient is the slope of each linear segment. The calibration circuit determines the calibration coefficients by calculating the second derivative of the uncorrected transfer function. The segment endpoint of each linear segment is located on the uncorrected transfer function at a local maximum of a second derivative of the uncorrected transfer function.

The calibration coefficients are stored in non-volatile memory. The corrected digital values are generated using three calibration coefficients plus four additional calibration coefficients for each segment of the piecewise-linear approximation of the uncorrected transfer function. Thus, the calibration circuit can generate the corrected digital values using fewer calibration coefficients than the predetermined number of digital values into which the ADC converts the measured analog voltage amplitudes.

A method calibrates an ADC having a non-linear transfer function by receiving a plurality of uncorrected digital values from the ADC and by outputting a plurality of corrected digital values that approximately track the ideal linear transfer function of the ADC. The method approximates the non-linear transfer function with linear segments. A segment endpoint of each linear segment is located on the non-linear transfer function at a local maximum of the second derivative of the non-linear transfer function. The method calculates a corrected digital value for each uncorrected digital value using calibration coefficients associated with the linear segment applicable to the uncorrected digital value. The calibration coefficients include the endpoint digital values of segment endpoints of each linear segment. The method stores the calibration coefficients in non-volatile memory. In one embodiment, corrected digital values are not generated by adding a separate, stored correction factor to each uncorrected digital value.

Other embodiments and advantages are described in the detailed description below. This summary does not purport to define the invention. The invention is defined by the claims.

Reference will now be made in detail to some embodiments of the invention, examples of which are illustrated in the accompanying drawings.

FIG. 1 shows microcontroller integrated circuit **10** with a calibration circuit **11**, an embedded sigma-delta analog-to-digital converter (ADC) **12**, and a non-volatile memory **13**. Calibration circuit **11** has an input bus **14** and an output bus **15**. ADC **12** has an input lead **16** and an output bus **17**. ADC **12** receives a continuous analog input signal on input lead **16**. The continuous analog input signal comprises a plurality of measured analog voltage amplitudes **18**.

ADC **12** oversamples the continuous analog input signal at a sampling frequency that is at least twice as great as the frequency of the analog input signal. Oversampling spreads quantization noise over a wide frequency range. ADC **12** converts the plurality of measured analog voltage amplitudes **18** into a corresponding plurality of uncorrected digital values **19**. Each of the plurality of measured analog voltage amplitudes **18** is ideally converted into one of a predetermined number of possible digital values. In this embodiment, measured analog voltage amplitudes **18** are ideally converted into 1024 (2^{10}) possible 10-bit digital values. Each uncorrected digital value **19**, however, has twelve bits so that those uncorrected digital values that fall outside the 1024 possible 10-bit digital states can be represented. Each uncorrected digital value **19** has ten regular bits, a sign bit, and an overflow bit. ADC **12** outputs the plurality of 12-bit uncorrected digital values **19** onto 12-bit output bus **17**.

Each measured analog voltage amplitude and the corresponding uncorrected digital value define a point on an uncorrected transfer function of ADC **12**. The uncorrected transfer function of ADC **12** is not linear. The plurality of uncorrected digital values **19** exhibits gain error, dc offset error, INL error and DNL error. ADC **12** would ideally convert linearly increasing analog voltage amplitudes into linearly increasing digital values, resulting in an ideal linear transfer function.

Calibration circuit **11** receives the plurality of uncorrected digital values **19** onto input bus **14** and outputs a plurality of corrected digital values **20** onto output bus **15**. Calibration circuit **11** corrects for total error such that the plurality of measured analog voltage amplitudes **18** received by ADC **12** and the corresponding plurality of corrected digital values **20** output by calibration circuit **11** define points approximating the ideal linear transfer function of ADC **12**. Thus, calibration circuit **11** does not separately correct for gain error, dc offset error, INL error and DNL error. Calibration circuit **11** generates the corrected digital values **20** using calibration coefficients that correspond to linear segments that approximate the plurality of uncorrected digital values **19**. For each measured analog voltage amplitude received by ADC **12**, calibration circuit **11** is capable of calculating a corrected digital value to within +/− one half of the least significant bit (LSB) of the digital value that corresponds to the measured analog voltage amplitude on the ideal linear transfer function.

FIG. 2 is a graph of a hypothetical, uncorrected transfer function **21** of ADC **12**, as well as an ideal linear transfer function **22** for ADC **12**. Uncorrected transfer function **21** correlates physically measured analog voltage amplitudes received by ADC **12** to uncorrected digital values output by ADC **12**. ADC **12** outputs the uncorrected digital values as 12-bit digital values. FIG. 2 shows that DC offset error causes a portion of uncorrected transfer function **21** to extend into negative digital amplitudes. The uncorrected digital values **19** in this negative portion of uncorrected transfer function **21** are output by ADC **12** as negatively signed digital numbers.

FIG. 3 is a flowchart illustrating steps **23**–**39** of a method by which calibration circuit **11** receives the plurality of uncorrected digital values **19** and outputs the plurality of corrected digital values **20**. Calibration circuit **11** thereby calibrates uncorrected, nonlinear transfer function **21** of ADC **12** by outputting the plurality of corrected digital values **20** that approximately track ideal linear transfer function **22**. In a first step **23**, ADC **12** generates uncorrected transfer function **21**. Each point on uncorrected transfer function **21** is defined by a measured analog voltage amplitude and a corresponding uncorrected digital value. In an analysis mode of microcontroller **10**, uncorrected transfer function **21** is analyzed. The analysis mode is, for example, performed during testing after production. Subsequent steps of FIG. 3 are now described in relation to the functions shown in the graphs of FIGS. 4–9.

The analysis mode consists of steps **23** through **34**, in which inflection points on uncorrected transfer function **21** are determined. Uncorrected transfer function **21** is then approximated as multiple piecewise-linear segments, wherein the linear segments join at the inflection points of uncorrected transfer function **21**. The number of linear segments is one more than the number of inflection points, unlike in other calibration methods where the number of linear segments is defined irrespective of characteristics of the uncorrected transfer function.

In a step **24**, uncorrected transfer function **21** is smoothed by filtering in test equipment. FIG. 4 shows the resulting smoothed, uncorrected transfer function **40**. Step **24** is not essential to the method of FIG. 3. The smoothing of uncorrected transfer function **21** reduces the number of closely-spaced inflection points and, therefore, prevents short linear segments to be used in the approximation of uncorrected transfer function **21**. Smoothing reduces the number of calibration coefficients used in the method of FIG. 3, but also reduces the resolution of the calibration achieved by calibration circuit **11**.

In a step **25**, the first derivative of the smoothed, uncorrected transfer function **40** is determined. FIG. 5 is a graph of the first derivative (D**1**) **41** of smoothed, uncorrected transfer function **40**. First derivative (D**1**) **41** depicts the change of uncorrected digital values of smoothed transfer function **40** in relation to the change in the measured input analog voltage amplitude.

In a step **26**, the second derivative of smoothed, uncorrected transfer function **40** is calculated. FIG. 6B shows the second derivative (D**2**) **42** of the smoothed, uncorrected transfer function **40**. Second derivative (D**2**) **42** depicts the change of first derivative (D**1**) **41** in relation to the change in the measured input analog voltage amplitude.

In a step **27**, the absolute value of second derivative **42** of smoothed, uncorrected transfer function **40** is calculated. FIG. 6C shows the absolute value (D**2**_{ABS}) **43** of second derivative (D**2**) **42**.

In a step **28**, absolute value (D**2**_{ABS}) **43** of second derivative (D**2**) **42** is filtered to generate a smoothed function. FIG. 6D shows the smoothed absolute value F(D**2**_{ABS}) **44** of second derivative (D**2**) **42**.

In a step **29**, points on smoothed absolute value F(D**2**_{ABS}) **44** are discarded for amplitude values that fall below a first threshold **45**. First threshold **45** is placed at an amplitude above the noise level of absolute value (D**2**_{ABS}) **43** and smoothed absolute value F(D**2**_{ABS}) **44**. By lowering threshold **45** to an amplitude just above the noise level, the piecewise-linear segments approximate uncorrected transfer function **21** to a resolution of less than +/−½ LSB. Therefore, calibration circuit **11** can correct for DNL error that is greater than +/−½ LSB. DNL error of greater than +/−½ LSB would result in one bit of effective resolution being lost. Further increases in DNL error would cause a missing code phenomenon.

FIG. 6E shows the portions (TH) **46** of smoothed absolute value F(D**2**_{ABS}) **44** that are retained above first threshold **45**. A higher second threshold **47** is then applied to the portions (TH) **46** in order to define valid ranges of input analog voltage in which inflection points on uncorrected transfer function **21** can be located. Two valid ranges **48**–**49** of input analog voltage are shown in FIG. 6E.

In a step **30**, the first derivative of the portions (TH) **46** of smoothed absolute value F(D**2**_{ABS}) **44** are calculated. FIG. 6F shows the first derivative D**1**(TH) **50** of the portions (TH) **46**. First derivative D**1**(TH) **50** depicts the change of portions (TH) **46** in relation to the change in the measured input analog voltage amplitude. A zero crossing signal is generated at the points where first derivative D**1**(TH) **50** crosses zero. A zero valid signal (ZERO_VALID) is generated that indicates the zero-crossing points of the zero crossing signal that fall within the valid ranges **48**–**49** determined with second threshold **47**.

In a step **31**, the measured input analog voltage amplitudes are determined for the valid zero-crossing points. FIG. 6H shows a ZERO_POINTS signal indicating two input analog voltage amplitudes V_{N-1 }and V_{N-2 }corresponding to inflection points on uncorrected transfer function **21**.

In a step **32**, the digital values of the inflection points on uncorrected transfer function **21** that correspond to the valid zero-crossing points are determined. FIG. 7 illustrates that the two input analog voltage amplitudes V_{N-1 }and V_{N-2 }correspond to inflection points **51**–**52** on first derivative (D**1**) **41** and to inflection points **53**–**54** on uncorrected transfer function **21**. Inflection points **53**–**54** represent points at which uncorrected transfer function **21** changes its slope by an amount greater than the slope changes indicated by local maxima of function **43** below first threshold **45** in FIG. 6C. The digital values DATA(V_{N-1}) and DATA(V_{N-2}) of the inflection points **53**–**54** on uncorrected transfer function **21** are then determined empirically in the analysis mode.

End points **55**–**56** on uncorrected transfer function **21** are then empirically chosen that correspond to the ends of the dynamic range of ADC **12**. Inflection points **53**–**54** and end points **55**–**56** are defined to be segment endpoints on uncorrected transfer function **21**. Uncorrected transfer function **21** is then approximated by three linear segments that connect the two inflection points **53**–**54** and the end points **55**–**56**.

FIG. 8 shows that uncorrected transfer function **21** is approximated by three linear segments **57**–**59**. Linear segment **57** joins end point **55** and inflection point **53**; linear segment **58** joins inflection point **53** and inflection point **54**; and linear segment **59** joins inflection point **54** and end point **56**. Uncorrected transfer function **21** is a relatively smooth function and is accurately approximated with just three linear segments. The method of FIG. 3 approximates uncorrected transfer function **21** with fewer linear segments than would have resulted from a conventional piecewise-linear approximation that inserts a linear segment for each predetermined range of digital values. For example, where a conventional piecewise-linear approximation inserts a linear segment for each range of two hundred digital values, uncorrected transfer function **21** would be approximated with about five linear segments. An approximation using five segments over equal digital ranges, as opposed to the three segments generated by the method of FIG. 3, would involve more calculations but would nevertheless result in poorer resolution. The method of FIG. 3 places the endpoints of the linear segments only at inflection points of uncorrected transfer function **21** and thereby concentrates the linear segments in curvy areas of the uncorrected transfer function, which both reduces the number of calibration coefficients and improves resolution.

In a step **33**, the slopes of ideal linear transfer function **22** and of the linear segments **57**–**59** are calculated. FIG. 9 shows a portion of the graph of FIG. 8 and illustrates the calculation of the slope of ideal linear transfer function **22** and the slope of linear segment **57**. Still in the analysis mode, the end points of ideal linear transfer function **22** are empirically determined. Ideal linear transfer function **22** extends from point **64** (V_{MIN}, D_{MIN}) to point **65** (V_{MAX}, D_{MAX}). In this example, V_{MIN }is zero volts and D_{MIN }is digital zero; V_{MAX }is five volts and D_{MAX }is 1023. The slope (mREF) of ideal linear transfer function **22** is (D_{MAX}−D_{MIN})/(V_{MAX}−V_{MIN}) or, in this example, 1023/5 volts. End point **53** of linear segment **57** has the coordinates (V_{N-1}, DATA(V_{N-1})). End point **55** has the coordinates (V_{N}, DATA (V_{N})). Thus, the slope (mK) of linear segment **57** is [DATA (V_{N})−DATA (V_{N-1})]/(V_{N}−V_{N-1}).

In step **33**, the digital values of points **60**–**63** on ideal linear transfer function **22** are also determined empirically. Points **60**–**63** have the same x-coordinates (analog voltage) as do end point **55**, inflection points **53**–**54** and end points **56**, respectively. For example, the digital value of point **62** with an x-coordinate of V_{N-1 }is empirically determined to have a digital value of REF(N−1).

In a last step **34** of the analysis mode, certain calibration coefficients are stored in non-volatile memory **13**. Non-volatile memory **13** can be, for instance, EEPROM or FLASH memory. The slope (mREF) of ideal linear transfer function **22**, the digital value DATA(V_{N}) of the upper endpoint **55** of the highest linear segment **57**, as well as D_{MIN}, are stored in non-volatile memory **13**. Moreover, four additional calibration coefficients are stored for each segment of the piecewise-linear approximation of uncorrected transfer function **21**. For linear segment **57**, for example, V_{N-1}, DATA(V_{N-1}), mK and REF(N−1) are stored, where REF(N−1) is the digital value of the point on ideal linear transfer function **22** that corresponds to endpoint **53** of linear segment **57**. V_{N-1 }is stored as a digital number. Where uncorrected transfer function **21** has been approximated by three linear segments, as shown in FIG. 8, fifteen calibration coefficients are stored in non-volatile memory **13** of microcontroller **10**. Thus, considerably less memory is used in the calibration method of FIG. 3 than is used in conventional calibration methods that store a correction factor in memory for each uncorrected digital value output by an analog-to-digital converter that is to be calibrated.

A correction mode consists of steps **35** through **39**, in which calibration circuit **11** receives the plurality of uncorrected digital values **19** and uses the calibration coefficients determined in the analysis mode to generate the plurality of corrected digital values **20**. The analysis mode is used in the actual operation of microcontroller **10**.

In a step **35**, calibration circuit **11** receives the plurality of uncorrected digital values **19** from ADC **12**, including an uncorrected digital value DATA(V_{K}). The uncorrected digital value DATA(V_{K}) and a corresponding measured analog voltage amplitude V_{K }define a point **66** on uncorrected transfer function **21**.

In a step **36**, calibration circuit **11** associates uncorrected digital value DATA(V_{K}) with linear segment **57** and endpoint **53**. Calibration circuit **11** associates uncorrected digital value DATA(V_{K}) with linear segment **57** by determining that uncorrected digital value DATA(V_{K}) is less than or equal to DATA(V_{N}) and greater than DATA(V_{N-1}).

In a step **37**, a digital difference ΔDATA(K) is determined by subtracting the digital value DATA(V_{N-1}) of endpoint **53** from the uncorrected digital value DATA(V_{K}). Then in a step **38**, the voltage difference ΔV(K) between the measured analog voltage amplitude V_{K }and the analog voltage amplitude V_{N-1 }of endpoint **53** is calculated digitally using the slope mK of linear segment **57**. The voltage difference ΔV(K) is calculated as the digital difference ΔDATA(K) divided by the slope mK. As point **66** on uncorrected transfer function **21** may not lie exactly on linear segment **57**, the voltage difference ΔV(K) is an approximation of the actual voltage difference between the measured analog voltage amplitude V_{K }and the analog voltage amplitude V_{N-1 }of endpoint **53**.

In a final step **39**, a corrected digital value REF(K) is determined. REF(K) is the digital value approximately on ideal linear transfer function **22** that corresponds to measured analog voltage amplitude V_{K}. Corrected digital value REF(K) is calculated by extrapolation from point **62** on ideal linear transfer function **22**. Corrected digital value REF(K) is calculated as the voltage difference ΔV(K) multiplied by the slope mREF, plus the digital value REF(N−1) of point **62**. FIG. 9 shows a point **67** that lies approximately on ideal linear transfer function **22** and has the coordinates (V_{K}, REF(K)).

Calibration circuit **11** calculates and outputs a corrected digital value for each uncorrected digital value received. Thus, calibration circuit **11** outputs the plurality of corrected digital values **20** that approximately track ideal linear transfer function **22**. Each of the corrected digital values **20** fall within the digital range (D_{MIN }to D_{MAX}) of ideal linear transfer function **22** and can be expressed as a 10-bit digital value. Thus, no sign bit or overflow bit is required, and the plurality of corrected digital values **20** can be output onto 10-bit output bus **15**.

In one embodiment, calibration circuit **11** is part of a processing unit of microcontroller **10**. Microcontroller **10** is, for example, a Z8 Encore! microcontroller manufactured by Zilog, Inc. The calculations of steps **24**–**39** are performed by an arithmetic and logical unit (ALU) within the processing unit of microcontroller **10**. In another embodiment, the calculations of steps **24**–**39** are performed in a hardwired calibration circuit separate from the processing unit. The hardwired calibration circuit can be a state machine or engine.

Although the present invention has been described in connection with certain specific embodiments for instructional purposes, the present invention is not limited thereto. Although steps **24** through **34** of the analysis mode are described above as being performed during testing of microcontroller **10**, the calibration coefficients can be recalculated before each use of ADC **12**. Determining updated calibration coefficients prior to each use of ADC **12** can correct for such factors as the current temperature of microcontroller **10**, a lowered maximum voltage V_{MAX }output by the power source of microcontroller **10** and changing characteristics of components of microcontroller **10** caused by aging. Accordingly, various modifications, adaptations, and combinations of various features of the described embodiments can be practiced without departing from the scope of the invention as set forth in the claims.

1. An integrated circuit comprising:

(a) an analog-to-digital converter that converts a measured analog voltage amplitude to an uncorrected digital value, wherein the measured analog voltage amplitude and the uncorrected digital value define a point on an uncorrected transfer function of the analog-to-digital converter, and wherein the uncorrected transfer function has a second derivative; and

(b) a calibration circuit that receives the uncorrected digital value and outputs a corrected digital value, wherein the uncorrected digital value is associated with a linear segment that passes through a segment endpoint on the uncorrected transfer function, wherein the segment endpoint is located on the uncorrected transfer function at a local maximum of the second derivative of the uncorrected transfer function, wherein the segment endpoint has an endpoint digital value, and wherein the calibration circuit calculates the corrected digital value by subtracting the endpoint digital value from the uncorrected digital value.

(a) an analog-to-digital converter that converts a measured analog voltage amplitude to an uncorrected digital value, wherein the measured analog voltage amplitude and the uncorrected digital value define a point on an uncorrected transfer function of the analog-to-digital converter, and wherein the uncorrected transfer function has a second derivative; and

(b) a calibration circuit that receives the uncorrected digital value and outputs a corrected digital value, wherein the uncorrected digital value is associated with a linear segment that passes through a segment endpoint on the uncorrected transfer function, wherein the segment endpoint is located on the uncorrected transfer function at a local maximum of the second derivative of the uncorrected transfer function, wherein the segment endpoint has an endpoint digital value, and wherein the calibration circuit calculates the corrected digital value by subtracting the endpoint digital value from the uncorrected digital value.

2. The integrated circuit of claim 1, wherein the calibration circuit is a processing unit in a microcontroller.

3. The integrated circuit of claim 1, wherein the endpoint digital value is stored in a memory location of a non-volatile memory, wherein the analog-to-digital converter converts a number of measured analog voltage amplitudes to a corresponding number of uncorrected digital values, wherein the calibration circuit receives the number of uncorrected digital values and outputs a corresponding number of corrected digital values, and wherein the non-volatile memory has fewer memory locations than the number of corrected digital values.

4. The integrated circuit of claim 1, wherein the local maximum of the second derivative of the uncorrected transfer function has a magnitude greater than a threshold noise level.

5. The integrated circuit of claim 1, wherein the linear segment has a slope, and wherein the calibration circuit calculates the corrected digital value using the slope.

6. The integrated circuit of claim 1, wherein the analog-to-digital converter converts a plurality of measured analog voltage amplitudes to a corresponding plurality of uncorrected digital values, wherein the calibration circuit receives the plurality of uncorrected digital values and generates a corresponding plurality of corrected digital values, and wherein each of the plurality of corrected digital values is not generated by adding a stored correction factor to each of the plurality of uncorrected digital values.

7. A method comprising:

(a) receiving an uncorrected digital value, wherein the uncorrected digital value and a measured analog voltage amplitude define a point on an uncorrected transfer function of an analog-to-digital converter, and wherein the uncorrected transfer function has a second derivative;

(b) associating the uncorrected digital value with a linear segment that passes through a segment endpoint on the uncorrected transfer function, wherein the segment endpoint is located on the uncorrected transfer function at a local maximum of the second derivative of the uncorrected transfer function, and wherein the segment endpoint has an endpoint digital value; and

(c) outputting a corrected digital value corresponding to the measured analog voltage amplitude, wherein the corrected digital value is determined using the endpoint digital value.

(a) receiving an uncorrected digital value, wherein the uncorrected digital value and a measured analog voltage amplitude define a point on an uncorrected transfer function of an analog-to-digital converter, and wherein the uncorrected transfer function has a second derivative;

(b) associating the uncorrected digital value with a linear segment that passes through a segment endpoint on the uncorrected transfer function, wherein the segment endpoint is located on the uncorrected transfer function at a local maximum of the second derivative of the uncorrected transfer function, and wherein the segment endpoint has an endpoint digital value; and

(c) outputting a corrected digital value corresponding to the measured analog voltage amplitude, wherein the corrected digital value is determined using the endpoint digital value.

8. The method of claim 7, wherein the corrected digital value is determined by subtracting the endpoint digital value from the uncorrected digital value.

9. The method of claim 7, further comprising, before (a):

(d) determining the endpoint digital value of the segment endpoint during production.

(d) determining the endpoint digital value of the segment endpoint during production.

10. The method of claim 7, further comprising:

(d) storing the endpoint digital value in a non-volatile memory, wherein the non-volatile is in a microcontroller.

(d) storing the endpoint digital value in a non-volatile memory, wherein the non-volatile is in a microcontroller.

11. The method of claim 7, further comprising, before (a):

(d) calculating the second derivative of the uncorrected transfer function.

(d) calculating the second derivative of the uncorrected transfer function.

12. The method of claim 7, further comprising:

(d) calculating a slope of the linear segment, wherein the corrected digital value is determined using the slope of the linear segment.

(d) calculating a slope of the linear segment, wherein the corrected digital value is determined using the slope of the linear segment.

13. The method of claim 7, further comprising:

(d) receiving a second uncorrected digital value, wherein the second uncorrected digital value and a second measured analog voltage amplitude define a second point on the uncorrected transfer function;

(e) associating the second uncorrected digital value with the linear segment; and

(f) outputting a second corrected digital value corresponding to the second measured analog voltage amplitude, wherein the second corrected digital value is determined using the endpoint digital value.

(d) receiving a second uncorrected digital value, wherein the second uncorrected digital value and a second measured analog voltage amplitude define a second point on the uncorrected transfer function;

(e) associating the second uncorrected digital value with the linear segment; and

(f) outputting a second corrected digital value corresponding to the second measured analog voltage amplitude, wherein the second corrected digital value is determined using the endpoint digital value.

14. The method of claim 7, wherein the analog-to-digital converter converts multiple measured analog voltage amplitudes to multiple corresponding uncorrected digital values, wherein multiple corrected digital values corresponding to the multiple measured analog voltage amplitudes are output, and wherein each of the multiple corrected digital values is determined using the endpoint digital value.

15. The method of claim 7, wherein a microcontroller comprises the analog-to-digital converter, and wherein the endpoint digital value is stored in the microcontroller.

16. A device comprising:

(a) an analog-to-digital converter that converts a measured analog voltage amplitude to an uncorrected digital value, wherein the measured analog voltage amplitude and the uncorrected digital value define a point on an uncorrected transfer function of the analog-to-digital converter, wherein the uncorrected digital value is associated with a linear segment that passes through a segment endpoint on the uncorrected transfer function, wherein the uncorrected transfer function has a second derivative, wherein the segment endpoint is located at a local maximum of the second derivative of the uncorrected transfer function, and wherein the segment endpoint has an endpoint digital value; and

(b) means for receiving the uncorrected digital value and for outputting a corrected digital value, wherein the means determines the corrected digital value using the endpoint digital value.

(a) an analog-to-digital converter that converts a measured analog voltage amplitude to an uncorrected digital value, wherein the measured analog voltage amplitude and the uncorrected digital value define a point on an uncorrected transfer function of the analog-to-digital converter, wherein the uncorrected digital value is associated with a linear segment that passes through a segment endpoint on the uncorrected transfer function, wherein the uncorrected transfer function has a second derivative, wherein the segment endpoint is located at a local maximum of the second derivative of the uncorrected transfer function, and wherein the segment endpoint has an endpoint digital value; and

(b) means for receiving the uncorrected digital value and for outputting a corrected digital value, wherein the means determines the corrected digital value using the endpoint digital value.

17. The device of claim 16, wherein the means calculates the corrected digital by subtracting the endpoint digital value from the uncorrected digital value.

18. The device of claim 16, wherein the linear segment has a slope, and wherein the means determines the corrected digital value using the slope.

19. A device comprising:

(a) an analog-to-digital converter that converts a measured analog voltage amplitude to an uncorrected digital value, wherein the measured analog voltage amplitude and the uncorrected digital value define a point on an uncorrected transfer function of the analog-to-digital converter, wherein the uncorrected transfer function has a number of inflection points; and

(b) means for receiving the uncorrected digital value and for determining a corrected digital value, wherein the means approximates the uncorrected transfer function as a number of linear segments, wherein the linear segments join at the inflection points of the uncorrected transfer function, and wherein the number of linear segments is one more than the number of inflection points.

(a) an analog-to-digital converter that converts a measured analog voltage amplitude to an uncorrected digital value, wherein the measured analog voltage amplitude and the uncorrected digital value define a point on an uncorrected transfer function of the analog-to-digital converter, wherein the uncorrected transfer function has a number of inflection points; and

(b) means for receiving the uncorrected digital value and for determining a corrected digital value, wherein the means approximates the uncorrected transfer function as a number of linear segments, wherein the linear segments join at the inflection points of the uncorrected transfer function, and wherein the number of linear segments is one more than the number of inflection points.

20. The device of claim 19, wherein the uncorrected digital value is associated with one of the number of linear segment, wherein the one of the number of linear segments passes through a segment endpoint on the uncorrected transfer function, wherein the segment endpoint is located at one of the number of inflection points, wherein the segment endpoint has an endpoint digital value, and wherein the means determines the corrected digital value using the endpoint digital value.

21. The device of claim 20, further comprising:

(c) a non-volatile memory, wherein the endpoint digital value is stored in the non-volatile memory.

(c) a non-volatile memory, wherein the endpoint digital value is stored in the non-volatile memory.