DETAILED DESCRIPTION

[0026] According to a preferred embodiment of the invention, a calibration method is presented to calibrate a DAC, constructed according to a preferred embodiment of the invention. Briefly, the method is to digitally calibrate the DAC based on performance results obtained from a tester using a series of piecewise linear INL approximations, as shown in FIG. 1 . DAC testers to develop integral and differential linearity (INL and DNL) performance information over a range of DAC inputs and outputs are well known in the art, and are not described in detail herein. Using the circuit 15 of FIG. 2 , according to one method of the invention, the steps shown in FIG. 3 at the time of final testing and during subsequent operation of the circuit evaluate INL using the standard tester and the linearity information. INL values at certain specific codes, which are stored, for example, in registers. One way by which this can be achieved is by blowing certain fuses based on the values read from the tester. A controller then selects and uses the values stored by the fuse blowing operation, and the DAC calibrates itself by subtracting an interpolated approximation to its actual INL curve. Interpolation saves memory, thefore die area

[0027] The approach suggested does not actually modify the architecture of the circuit, but digitally calibrates its performance. This is achieved by subtracting a piece-wise linear approximation of the INL error from the output of the main DAC before outputting the signal. This requires an additional calibration DAC along with the main DAC.

[0028] One embodiment of calibration circuit architecture 15 with which the method of the invention can be used is shown in FIG. 2 , to which reference is now made. FIG. 2 shows a block diagram of a calibration circuit architecture 15 for calibrating a DAC with the various circuit components thereof constructed on an integrated circuit chip 16 . The calibration circuit 15 includes a main DAC 17 that is to be calibrated in the final circuit embodiment, a calibration DAC 19 , data registers 23 - 25 , a fuse block 21 containing fuse links to configure the data registers, and digital blocks 2729 for register selection and arithmetic operations.

[0029] The embodiment of the calibration circuit 15 shown in FIG. 2 is a setup circuit to configure and calibrate the overall DAC, as below described, and therefore includes a tester 30 to sample the output from the main DAC 17 to control and configure the fuse links 21 , as below described. In the actual implementation of the circuit 15 after calibration, the tester 30 is not employed in the circuit 15 , but a control circuit 50 , shown in dotted lines in FIG. 2 , is used to select the appropriate piecewise linear correction segment, in a manner below described with reference to FIGS. 3 and 5 . The tester may be implemented by automated test equipment (ATE), the setup and operation of which being within the scope of those skilled in the art.. It should be understood that although the invention is described in the context of a DAC, the principles of the invention may also be applied to an analog-to-digital converter (ADC) as well, since ADCs include internal DACs.

[0030] Thus, as shown, the output of the main DAC 17 is sent to an aanalog summing circuit 8 , from which the output 20 from the overall DAC circuit 15 is derived. The output from the main DAC 17 is also sent to the tester 30 . The output from the tester 30 is used to evaluate the INL from the captured data and to selectively blow fuses in the fuse block 21 based on the evaluated INL values, the fuse selection process being described below in detail. The fuse block 21 contains a number of fuse banks, four banks 33 - 35 . . . 36 being shown for illustration. In practice, one fuse bank may be used for each piecewise linear signal section, as will become apparent below. Each bank of fuses 33 - 35 . . . 36 stores the INL value (in LSBs) at a particular control point, also described in detail below. Other forms of non-volatile memory cana replace fuses

[0031] With reference now back to FIG. 1, a graph is shown of the actual integral nonlinearities (INL) of the main DAC 17 vs. input code word values. The graph of FIG. 1 compares a curve 10 of typical INL values of the signal output of an actual DAC constructed in accordance with a preferred embodiment of the invention with a piecewise linear approximation thereof 12 . The piecewise linear approximation curve 12 is developed from the uncalibrated DAC having the INL profile 10 , which follows the waveform shown, by selecting a set of codes, for example, conveniently based upon the waveshape of the measured, or actual, INL. Each code location X, and the corresponding INL value, Y, at selected codes constitutes a “control point”, C _i (Xi,Yi),C _i+1 (X _i+1 ,Y _i+1 ) . . . C _i+n (X _i+n ,Y _i+n ) 14 , 14 ^l . . . 14 ^Vl The piecewise linear approximation 12 of the INL curve 10 then allows linear interpolation between each adjacent pairs of the control points 14 and 14 ^l , . . . 14 and 14 ^Vl to approximate INL for any input code, for example, at point 14 corresponding to codeword C _k . At this juncture, it should be noted that although the piecewise linear curves are shown as each being a single, continuous linear waveform, the waveforms may follow other piecewise linear curves as well. For example, the piecewise linear curves may be saw-tooth or other convenient waveform. Moreover, although presently piecewise linear INL approximations are preferred, linearity error can also be approximated and removed by implementing higher order polynomials, such as B-Splines, in the digital domain, as shrinking process geometries make this feasible. These approximation curves then can be used to construct and operate a calibrated DAC circuit, such as the calibrated DAC circuit of FIG. 5 , using the steps shown in FIG. 3 . The method and apparatus of this invention makes INL calibration possible through interpolation, without actually storing the INL values for most of the DAC inputs.

[0032] As shown in FIG. 3 , the method of setting up and operating the calibrated DAC of the invention includes first constructing the hardware of the circuit, including the uncalibrated main DAC 17 on an integrated circuit chip 54 . The error values between the actual transfer function of the main DAC 17 and a desired transfer function of the main DAC 17 are then determined 56 . Using the error values determined, a number of control points are established, and the code error values are coded into a memory 58 . The memory may be a number of fuse links of the type shown in FIG. 2 , or other type of memory described below.

[0033] After the error values are coded into the memory, when a code value is applied to the input of the DAC, a determination is made as to between which two adjacent control points the code value lies, and a piecewise linear function is established between the two control points 60 . Finally an error value is interpolated from the piecewise linear function at the applied input code value, and the error value is applied to the input of the calibration DAC to develop an analog output that is subtracted from the output of the main DAC 62 .

[0034] Still more particularly, to determine the control points to use let C _i , C _i+1 , C _i+2 . . . be the X-axis values of the control points and Y _i , Y _i+1 , Y _i+2 . . . be the measured INL values at the corresponding X-axes control point values. Let C _k be any arbitrary input code. The first step in the method is to select the appropriate pair of control points between which the input code lies. The second step is to interpolate and find out the INL valued at the arbitrary input code by using the INL values of the control points between which the input lies.

[0035] Once the approximate value of the INL is obtained at the input code, a calibration DAC is used to convert this digital code to an analog value, which is then subtracted from the output of the main DAC 17 . This results in a value determined in accordance with the following Equation 1: 1 $Y_k=Y_i+\left(\frac{Y_{i+1}-Y_i}{C_{i+1}-C_i}\right)\left(C_k-C_i\right)$

[0036] Thus, to operate the circuit 15 ′ of FIG. 5 for a given arbitrary input code, the “X” axis values of a correct pair of control points between which the arbitrary input lies are determined. The INL value corresponding to the arbitrary input is then obtained by using the slope of the line joining the “Y” axis values (INL values) of the two control points (see FIG. 1 ). The arithmetic logic blocks 27 - 29 hown in FIGS. 1 and 5 perform these operations. The output of the digital block 27 - 29 is then sent to the calibration DAC 19 , whose analog output is then subtracted from the output of main DAC 17 in the adder 18 . As shown, an offset value, Y _i , may be added to the correction value in the adder 31 . The offset value, as can be seen from the control point 14 in FIG. 1 , may be the initial INL value at which the piecewise linear curve begins to enable the particular INL interpolated values to be properly interpreted.

[0037] In the design of the circuit 15 , some tradeoffs may be involved in determining the total number of control points 14 , 14 ^l . . . 14 ^Vl that are employed. Although the number of control points is a matter of design choice, it is apparent that the larger the number of control points, the more accurate is the approximation of the INL that can be obtained. On the other hand, the larger the number of control points, the more fuses that are required to implement the circuit, and increasing the number of fuses jeopardizes the reliability of the circuit. Typically, each control point requires two sets of fuses, one for storing the “X” axis value of the control point, and one for storing the corresponding “Y” value.

[0038] By careful selection of the control points 14 , 14 ^l . . . 14 ^Vl , the required number of fuses can be reduced. More particularly, by selecting control points that have a fixed X axis relationship, the requirement for blowing fuses for the X axis of the control points can be removed, so that one set of fuses to store the Y axis values can be sufficient for each control point. The first and last control points can represent the offset and gain error of the DAC. As an example, in some cases, seven bits (including sign) may be enough for the Y-axis of each control point to represent INL error within ±1 LSB at each control point. (Any more bits may be unnecessary due to the inaccuracy of the piecewise linear approximation to the INL). Therefore, to represent each control point, seven fuses may be used. If an eight-piece segment with nine control points were chosen (including zero scale and full-scale points), a total of 63 fuses would be required. Although this may be a high number of fuses, it is not unreasonable.

[0039] It should be noted that as an option, either the difference in the control point values may be stored in the fuses, or, alternatively, the actual control point value may be stored. Storing the difference in control point values requires eight fuses for each control point (since the difference can range from 128 to 128 LSBs) amounting to a total of 72 fuses. This eliminates the need for a subtraction circuit. However, as can be seen from Equation 1 above, the actual value of each control point is required to evaluate the final expression. Thus, it may be desirable in some cases to store the actual control points rather than the difference.

[0040] In operation, to determine to identify which is the correct pair of control points between which the arbitrary input code lies, the first few MSBs of the input code and the control points may be compared. The arithmetic blocks 28 and 29 then perform division and multiplication functions, as follows. The calculation of slope of the applicable piecewise linear segment in Equation 1 requires division by the difference in the input code values of two adjacent control points. To make this division operation simple, the control points can conveniently be spaced uniformly with a known X axis spacing of “k times a power of 2”. The difference in the x-axis of two adjacent control points is then a power of two, so the division will be a simple arithmetic right shift. The right shift operation can be achieved by just connecting the data buses in an appropriate manner, and thus the requirement of the shift register can be totally eliminated.

[0041] Thus, the function accomplished by the Func 1 block 28 in the circuits of FIGS. 2 and 5 can be C _input -C _i to achieve the delta C value between C _i and the input word. The function accomplished by the Func 2 block 29 then determines the slope of the selected piecewise linear segment and multiplies it times the delta C value. To accomplish the digital multiplication functions based on the INL range of ±64 LSBs, the difference in the Y-axis of two adjacent control points can be maximum +128 or minimum −127. This can be coded in eight bits. Also, 14 bits may represent the difference between the X-axis of the previous control point and the input code. Therefore a 14*8 multiplier may be required for this operation.

[0042] In the example above, the INL can be shown to be ±64 LSBs. This is equivalent to nine-bit accuracy (±0.5 LSB at nine bits). Since the main DAC 17 is accurate to nine bits, the signal that is obtained from the output of the calibration DAC needs to be accurate to at least 11-12 bits to make calibration reasonable. If a more accurate main DAC 17 is desired, design redundancy and tester feedback can be used.

[0043] It should be noted that it may be necessary to establish the full-scale range 40 of the calibration DAC 19 (see FIG. 4 ) to be about twice the INL range 42 of the main DAC 17 . This is because, if ±25% overall scaling error is assumed as discussed above, the calibration DAC 19 should still have enough range to correct for the INL of the main DAC 17 . Thus, as shown in FIG. 4 , with a 25% scaling error 44 on the calibration DAC 19 high voltage and +25% scaling error 46 on the calibration DAC 19 low voltage, the calibration DAC 19 still has enough range to cover the worst case main DAC 17 INL.

[0044] Assuming also that the calibration DAC 19 has sufficient resolution (for example, 8-10 bits, to resolve the range with minor calibration DAC INL and DNL errors), it is reasonable to expect that the zero scale and the full-scale error of the calibration DAC 19 will dominate the overall errors of the calibration DAC 19 . The zero scale error will simply add as an offset to the main DAC 17 . But the full-scale error will be a problem.

[0045] This full-scale error of the calibration DAC 19 can be fixed by evaluating a partial INL once more in the test program, using the following technique.

[0046] First, the tester 30 evaluates the INL with the outputs of the calibration DAC 19 set at a constant zero. Since the INL is evaluated only at the X-axes of the control points, the evaluation is fast. This test shows how much calibration is needed for the main DAC 17 . The corresponding trim words are determined and written into temporary registers.

[0047] Second the tester 30 evaluates the INL again, with the temporary trim words in effect. The INL is evaluated again, but only at the control points. After the first calibration, the INL should be zero at the control points, but it will not be, due to the full-scale error of the calibration DAC 19 . From the new INL readings, the calibration DAC 19 full-scale error can be determined. To take the full-scale error of the calibration DAC 19 into account, the trim coefficients are readjusted.

[0048] Finally, fuses are blown according to the readjusted trim coefficients. At this point, “all codes” INL may be evaluated to assure specification compliance. Thus, the calibration cycle includes two partial INL evaluations, at only control points, and one final evaluation, at all codes. The first partial INL evaluation gives information about the inaccuracies of the main DAC 17 , and the second partial INL evaluation gives information about the calibration DAC 19 . The trim coefficients are then determined based on the results of both partial INL evaluations. Thus, by repeating the test twice, the calibration DAC 19 can also be calibrated. Other methods can also be used to adjust the gain error of the calibration DAC

[0049] To preserve the monotonicity of the circuit, it is important to ensure that the calibration step does not improve INL at the cost of DNL. Therefore, the DNL budget for calibration may be set at not more than ±0.25 LSBs at 16 bits in order to maintain monotonicity. If the range of the calibration DAC 19 is ±1 LSB at 9 bits (assuming scale-down by a factor of 256), and if the calibration DAC 19 has 8 bits of resolution, a related DNL error of ±0.5 LSBs at 16 bits results. This may be too much for some applications. Therefore, the calibration DAC 19 needs to have at least 10 bits of resolution to get a DNL of ±0.125 LSB. This is no extra burden if an R-2R architecture is used for the calibration DAC 19 .

[0050] Furthermore, if the main DAC 17 has a specification of ±64 LSB INL, the worst case INL difference between two consecutive control points can be +128 LSBs or −128 LSBs. This then requires a 10 -bit calibration DAC 19 as explained above. But if a 2× redundancy is included in INL specification of the main DAC 17 , the calibration DAC 19 needs to be set to a range of ±256 LSB at 16 bits. Considering a 7-bit range division, and resolution to 0.125 LSBs at 16 bits, a 12-bit calibration DAC 19 is required. So for good monotonicity, a 128 range divider and a 12-bit calibration DAC 19 are needed. These constitute design choices on a specific main DAC 19 , and are not intended to present global solutions for all main DACs

[0051] Monotonicity should not only be guaranteed by the architecture of the calibration DAC 19 , but also with the quantization of the arithmetic. The DNL transitions related to the outputs of the calibration DAC 19 should be “smooth” between input codes. Assuming a +128 LSB INL error between two control points as a worst case condition, and assuming that there are 8 piecewise linear segments of 8192 codes and 9 control points, it needs to be ensured that no calibration DAC 19 increment larger than 0.125 LSBs is added between two consecutive input-codes. At steps of 0.125 LSBs, 1024 steps are required to correct a 128 LSB INL error. Therefore, only the three last LSBs of the main DAC 17 input word is not needed. In other words, at least 3+10=13 MSBs should be used to guarantee step sizes not larger than 0.125 LSBs at the output. With some margin, 14 MSBs are needed to represent the input code and the control point “X” axes to the digital circuit. These constitute design choices on a specific main DAC 19 , and are not intended to present global solutions for all main DACs

[0052] Re-writing the Equation 1 to reflect the arithmetic quantization, we get Equation 2: 2 $\mathrm{Cal\_dac}{\mathrm{\_out}}_{12\mathrm{MSBs}}=Y_{17\mathrm{MSBs}}+{\left(\frac{{\left(Y_{i+1}-Y_i\right)}_{8\mathrm{MSBs}}}{{\left(C_{i+1}-C_i\right)}_{14\mathrm{MSBs}}}{\left(C_i-C_k\right)}_{14\mathrm{MSBs}}\right)}_{11\mathrm{MSBs}}$

[0053] It should be noted that since each segment is of length 8192, and since the last two LSBs of 16 bits have been ignored, the division is an arithmetic right shift by 13−2=11 bits. The equation is left aligned. The subscript XMSBs means that X most significant digits are used in the arithmetic.

[0054] Thus, the calibration DAC 19 uses seven bits of reference scaling and 12 bits of segmented R-2R. That is, the calibration DAC 19 has 19 bits of resolution and eight bit equivalent full-scale error. The eight bit equivalent full-scale error comes from the inaccuracy of reference scaling. The first seven bits are obtained by scaling the range by a factor of 128. This is twice the range required to correct for worst case INL. The full-scale inaccuracy of the calibration DAC 19 can be measured and corrected within this range. The remaining 12-bits is an R-2R (or a partially segmented R-2R) type of DAC.

[0055] Since the signal at the output of the calibration DAC 19 is of small value, the noise that is generated from the summing circuit may be of significant magnitude. It is necessary to make sure that the circuit noise is not more than the 16-bit level. For low power consumption, the input and the feedback resistors of the summing amplifier should be in the order of 10K ohms. 4 KTRF noise is then 4.031 uV rms (24.18 uV peak) for 100 KHz bandwidth. The exact calculation of the noise and feedback resistor values, of course, should be determined for each particular application.

[0056] Once the control points have been established and the fuses blown, the tester is removed from the circuit, and the control functions are operated by a controller circuit 50 , shown in the circuit 15 ′ in FIG. 5 . The controller circuit 50 determines the pair of control points between which the arbitrary input code word C _k lies and selects the appropriate register 23 . . . 25 to enable the corresponding INL value to be interpolated. Thus, the controller circuit 50 receives as input the arbitrary input word to the main DAC 17 . It also receives as another input the X-axis values of the code words established by the tester, as described above. The two outputs define the register containing the INL values between the control words selected.

[0057] As mentioned, the specific implementation described above has eight piecewise linear segments requiring 9 control points, each control point has eight bits representing the Y-axis INL values. The x-axis locations of these control points may be fixed, as described above (although, of course, they do not necessarily have to be fixed) at DAC input codes, 0, 8192, 2×8192, 3×8192, . . . 7×8192, 8×8192. The flowchart implemented b the control circuit 50 , therefore, is as follows:define 3 most significant bits of the DAC input as Adefine 9 8-bit control points as: control0<7:0>, control1<7:0>, control2<7:0>, control3<7:0>, control4<7:0>, control5<7:0>, control6<7:0>, control7<7:0>, control8<7:0>, inputs are: A, control0<7:0>, control1<7:0>, control2<7:0>, control3<7:0>, control4<7:0>, control5<7:0>, control6<7:0>, control7<7:0>, control8<7:0>outputs are: out1<7:0>, out2<7:0> FLOWCHART:if(A==000), out1<7:0>=control0<7:0>, out2<7:0>=control1<7:0>if(A==001), out1<7:0>=control1<7:0>, out2<7:0>=control2<7:0>if(A==010), out1<7:0>=control2<7:0>, out2<7:0>=control3<7:0>if(A==011), out1<7:0>=control3<7:0>, out2<7:0>=control4<7:0>if(A==100), out1<7:0>=control4<7:0>, out2<7:0>=control5<7:0>if(A==101), out1<7:0>=control5<7:0>, out2<7:0>=control6<7:0>if(A==110), out1<7:0>=control6<7:0>, out2<7:0>=control7<7:0>if(A==111), out1<7:0>=control7<7:0>, out2<7:0>=control8<7:0> Although the circuit embodiment of FIGS. 1 and 5 are constructed using fuse links, other types of memory elements may be equally advantageously employed. For example, as shown in FIG. 6 , the DAC circuit 15 ″ includes memory elements that are provided by more traditional memory devices, such as, for example, EEPROM, flash memory, laser trim links, etc. Additionally, the main DAC 17 may be provided by any suitable DAC structure, such as, for example, a segmented DAC 17 ′, or the like. The segmented DAC 17 ′ may be, for example, a segmented R-2R segmented DAC, a segmented current steering DAC, a segmented voltage out DAC, or the like.

[0058] Finally, it should be noted that the calibration DAC 19 may be incorporated into a portion of the main DAC 17 , as shown in the circuit 15 ′″ in FIG. 7 . In the embodiment shown in FIG. 7 , for example, the LSB portion 74 of the main DAC 72 is used as the calibration DAC 19 , receiving its input from the output of the offset value adder 31 . The MSB portion 74 of the main DAC 72 then receives its input in the same manner as the main DAC 17 in the circuit embodiments of FIGS. 2, 5 , and 6 above. In this scheme, the entire calibration can be done in the digital domain.

[0059] The actual design of the circuit functions herein described can be constructed or realized through the use of software tools for integrated circuit design. Such software tools are often referred to as high-level description language (HDL) or Very High Speed Integrated Circuit Hardware Description Language (VHSIC HDL or VHDL) design tools. Such software tools can transform circuit definitions, specifications, and functions into integrated circuit hardware, without a need to specify any particular hardware implementation, layout, or design. Examples of such software tools are the design compiler available from Synopsys, Inc. of Mountain View, Calif., the Behavior to Structure Translator (BEST) synthesis tool developed by Unisys Corporation, the DesignBook Synthesis tool from Escalade, and the Synergy synthesis tool available from Cadence Design Systems, Inc. A VHDL code by which one embodiment of the DAC circuit of the invention can be constructed is set forth in Appendix A, preceding the claims herein.

[0060] Although the invention has been described and illustrated with a certain degree of particularity, it is understood that the present disclosure has been made only by way of example, and that numerous changes in the combination and arrangement of parts can be resorted to by those skilled in the art without departing from the spirit and scope of the invention, as hereinafter claimed.