Methods and structures that reduce memory effects in analog-to-digital converters

[00002] The present invention is directed to methods and structures that reduce memory effect conversion errors in pipelined ADC systems.

[00003] The novel features of the invention are set forth with particularity in the appended claims. The invention will be best understood from the following description when read in conjunction with the accompanying drawings.

[00014] Pipelined ADC systems of the present invention recognize that memory effect of system components can induce nonlinearities into system converter stages. In particular, conversion errors are induced in one converter cycle because of component memory of the signals in one or more preceding converter cycles. Systems of the invention recognize particular memory sources and provide methods and structures in the following description that reduce their induced conversion errors.

[00015] The pipelined ADC 20 of FIG. 1 includes a sampler 22 and N converter stages 24 that are coupled in a successive pipelined arrangement. The sampler provides samples of an analog input signal received at an input port 25 which converter stage 1 then converts to a corresponding digital word D₁. Converter stage 1 also provides a residue signal S_res to the succeeding converter stage 2. In succession, each of the converter stages 2-N converts its respective residue signal to a respective digital word (e.g., D_i for stage i) and provides a residue signal to the succeeding stage. However, the final stage N differs in that it converts its respective residue signal to a respective digital word D_N but has no need to provide a residue signal.

[00016] All converter stages, therefore, simultaneously convert respective analog input signals to corresponding digital words but at any given moment, each converter stage is processing the residue of a different one of the analog samples provided by the sampler 22. That is, analog sample is successively converted in the converter stages of the system 20. The digital words that correspond to a respective analog sample are then temporally aligned, corrected and combined in an error corrector 26 to thereby provide a corresponding digital code at an output port 27 that corresponds to the analog sample.

[00017] An exemplary converter stage 30 is indicated by extension lines 31 to show that it includes an ADC 32, a digital-to-analog converter (DAC) 33, an adder 34 and an amplifier 35 with a gain G. The ADC 32 converts this stage's residue signal into a corresponding digital word D_i and the DAC 31 converts this digital word to a corresponding analog signal which is provided to the adder 34 where it is subtracted from this stage's residue signal to provide a residue signal S_res for the succeeding stage. The residue signal is preferably gained up in the amplifier 35 before it is provided to the successive stage.

[00018] Although converter stages of the invention are generally directed to the conversion of any number of bits, FIG. 2 illustrates an exemplary 1.5 bit stage 40 which includes a pair of comparators 42, an amplifier 44, first and second capacitors C₁ and C₂ and a DAC 46. The first and second capacitors are preferably matched (i.e., their capacitances are equal) and are coupled between the comparators and the amplifier.

[00019] In each converter cycle of the converter stage 40, the comparators 42 provide the stage's digital word D_i in response to the residue signal S_res of the preceding converter stage and the DAC 46 provides a decision signal DVref in response to the digital word D_i. In response to the preceding residue signal and the decision signal, the first and second capacitors and the associated amplifier then provide a residue signal S_res to the succeeding stage.

[00020] Each converter cycle includes first and second operational phases and, accordingly, FIG. 2A shows the first and second capacitors C₁ and C₂ and the amplifier 44 arranged in a first operational phase 50A and the first and second capacitors C₁ and C₂, the amplifier 44 and the DAC 46 arranged in a second operational phase 50B. The phases 50A and 50B are generally realized with a switch system and a switch system embodiment is indicated in FIG. 2A with the aid of small squares 52 which each represent a closed switch wherein phase 50A is realized with three closed switches 52 and phase 50B is realized with two closed switches 52. In a succeeding phase, each of these switches is open. The switches, first and second capacitors, and amplifier form a unit 48 which is typically referred to as a switched-capacitor multiplying DAC (MDAC).

[00021] The two comparators 42 are respectively biased to compare the input residue signal to −0.25V_ref and +0.25V_ref wherein V_ref is a reference voltage that represents the converter stage's full scale input as shown in the graph 60 of FIG. 2B. Accordingly, the stage's digital word D_i is shown in FIG. 2B (in an upper row 62) to be 00 when the input residue signal is below −0.25V_ref, 01 when it is between −0.25V_ref and +0.25V_ref, and 11 when it is above +0.25V_ref. At the same time, the DAC 46 causes the decision signal DV_ref to be +V_ref when the input residue signal is below −0.25V_ref, zero when it is between −0.25V_ref and +0.25V_ref and +V_ref when it is above +0.25V_ref (i.e., D in the decision signal DVref is correspondingly −1, 0 and +1).

[00022] In the first operational phase 50A, the first and second capacitors C₁ and C₂ receive an electrical charge 54 from the preceding residue signal. In the second operational phase 50B, an electrical charge 56 is transferred from the first capacitor C₁ to the second capacitor C₂. Because the capacitors have equal capacitance, the original electrical charge of the second capacitor is doubled so that the gain of the MDAC 48 is two.

[00023] As shown in the transfer function 64 of FIG. 2B, the output residue signal thus transits between −0.25V_ref and +0.5V_ref for input residue signals between −0.25V_ref and +0.25V_ref. The decision signal DV_ref shifts the transfer function 64 upward by V_ref for input residue signals below −0.25V_ref and downward by V_ref for input residue signals above −0.25V_ref.

[00024] Comparators inevitably include some offset error so that their decision may be in error for input signals close to their reference signal and this error limits the resolution of the comparator's ADC. The 1.5 bit converter stage 40 of FIG. 2A provides redundancy which causes the ADC to be less susceptible to this comparator offset error and which is utilized in the error corrector 26 of FIG. 1 to provide the correct output digital code at the output port 27.

[00025] For example, FIG. 2C illustrates an exemplary error corrector 80 which includes, for each of the converter stages 24 of FIG. 1, a delay 82, an exclusive OR gate 84 and an associated half adder 86. Each set of these elements receives the digital word of a corresponding pair of the comparators 42 of FIG. 2A.

[00026] In operation, the delays 82 are of different length so that they temporally align each stage's output with that of a succeeding stage so that all stages contribute to the conversion of each analog input signal that is provided by the sampler 22 of FIG. 1. That is, the delay 82 assigned to each converter stage exceeds the delay 82 assigned to a succeeding stage by the signal delay through each of the converter stages. The exclusive OR gate 84 then converts its stage's digital word D_i (shown in the upper row 66 of FIG. 2B) to be 00 when the input residue signal is below −0.25V_ref, 01 when it is between −0.25V_ref and +0.25V_ref, and 10 when it is above +0.25V_ref as shown in the lower row 64 of FIG. 2B. Thus, the most significant bit remains the same but the least significant bit is altered.

[00027] Finally, the half adders 86 sum the least significant bit of each stage with the most significant bit of the succeeding stage and a carry-out bit from the stage that succeeds the succeeding stage. The error corrector 80 thus receives digital words from converter stages such as the stage 40 of FIG. 2A and, in response, provides the digital code 88 that corresponds to the signal originally provided by the sampler 22 of FIG. 1.

[00028] Although redundant converter stages such as the 1.5 bit converter stage 40 of FIG. 2A and error correctors such as the error corrector 80 of FIG. 2C reduce conversion errors (due, for example, to ADC offset errors), it has been found that they do not reduce conversion errors caused by memory effect which is a phenomenon in which the output of a converter stage's MDAC (e.g., the MDAC 48 of FIG. 2A) is not solely determined by its current input signal but also by a past output signal even by a past input signal.

[00029] It has been found that a major memory effect contributor is the dielectric relaxation of MDAC capacitors (e.g., the first and second capacitors C₁ and C₂ of FIG. 2A) which generate a relaxation recovery voltage that is a function of the capacitors' material constant κ. For example, silicon nitride capacitors that are often used in radio frequency (RF) circuits have a large material constant κ on the order of 3000 parts per million (ppm) and can cause integral nonlinearity (INL) jumps of 8 least-significant bits (LSBs) in 14-bit pipelined ADCs. Although high-quality Low Pressure Chemical Vapor Deposition (LPCVD) oxide capacitors typically have a much reduced material constant κ on the order of 300 ppm, their relaxation recovery voltage still induces errors in high resolution pipelined ADCs (e.g., resolutions exceeding 14 bits).

[00030] Incomplete resetting of stage amplifiers (e.g., amplifier 44 in FIG. 2A) can also be a memory effect contributor. This contribution increases in pipelined ADCs that operate at high speeds and in pipelined ADCs that do not reset in each conversion cycle because they are also active in the cycle's idle phase (second operational phase 50B of FIG. 2A) to realize other converter activities (e.g., to process a calibration signal).

[00031] Although a variety of techniques have been developed (e.g., capacitor shuffling) to reduce errors caused by imperfect ADC components (e.g., capacitor mismatch and finite amplifier gain), these techniques fail to reduce errors caused by memory effect. FIG. 3A, however, illustrates a pipelined ADC 100 of the present invention that reduces memory effects. The ADC includes the sampler 22 (abbreviated as s'mplr because of limited figure space) and the successive converter stages 24 of the pipelined ADC 20 of FIG. 1 (and its input and output ports 25 and 27). In contrast, however, the ADC 100 replaces the error corrector 26 with first and second error correctors 102 and 104 and a digital filter 106 which is positioned between the two error correctors.

[00032] In operation of this structure, the first error corrector 102 receives the digital words from converter stages 2-N and processes them to provide a corrected digital code in a manner similar to that described above with reference to FIG. 2C. In a significant recognition of the present invention, it is recognized that just as the corresponding digital code provided by the second error corrector 104 is a digital representation of the analog input signal to converter stage 1 (i.e., the analog sample provided by the sampler 22), the corrected digital code provided by the first error corrector 102 is a digital representation of the residue signal S_res of converter stage 1.

[00033] With this recognition, the invention then reduces the memory of converter stage 1 by using the digital filter 106 to filter the corrected digital code to a filtered corrected digital code that is provided to the second error corrector 104 along with the digital word D₁ of converter stage 1. The second error corrector processes these signals in a manner similar to that described above with reference to FIG. 2C to thereby provide a corresponding digital code that corresponds to the original analog sample.

[00034] In the pipelined ADC 100, the digital filter 106 is a Finite Impulse Response (FIR) filter that includes a signal delay 110, a multiplier 112 and an adder 114. The multiplier is positioned between the delay and the adder and receives a delayed signal from the delay and also receives a memory parameter μ₁. The adder 114 sums the corrected digital code and the output of the multiplier 112 to provide the filtered corrected digital code. The delay 110 provides the preceding corrected digital code and the multiplier modifies this digital code in accordance with the memory parameter μ₁. The product of the multiplier then substantially removes the memory effect of the current corrected digital code from the first error corrector 102. The first error corrector 102 and the digital filter 106 thus form a residue calibrator 108 that calibrates the residue signal of converter stage 1.

[00035] If a known signal were applied to converter stage 1 in one converter cycle and a zero signal applied in a succeeding converter cycle, a nonzero output signal in the succeeding cycle forms a measure of the memory parameter μ₁. That is, the applied zero signal should have resulted in a zero output signal and the magnitude of the nonzero output signal is a measure of the memory parameter μ₁ that induced the nonzero signal. For example, if the zero signal is then replaced with a replacement signal that reduces the output signal in the succeeding cycle to zero, the ratio of the replacement signal to the known signal is the desired memory parameter μ₁. To reduce the effect of offset errors in converter stage 1, this procedure can be repeated with a different known signal and the difference in the measurements taken as the memory parameter μ₁.

[00036] In an exemplary method of measuring the memory parameter μ₁, converter stage 1 is provided with a second test set of the first and second capacitors C₁ and C₂ of FIG. 2A. During the second operational phase 50B of FIG. 2A, the test set is arranged to receive an electrical charge from the known signal (in a manner similar to the reception of the electrical charge 54 in the first and second capacitors in the first operational phase 50A).

[00037] During the succeeding first operational phase 50A of FIG. 2A, the test set is arranged about the amplifier 44 to transfer an electrical charge to the second capacitor of the test set (in a manner similar to transfer of the electrical charge 56 during the second operational phase 50B). The memory parameter μ₁ is the ratio of the resultant signal at the converter stage's output to the known signal.

[00038] Alternatively, an unused copy of the converter stage 1 could be provided for measurement of the memory parameter μ₁. In this case, the measurement would not have to be interleaved with the operational phases of converter stage 1.

[00039] In another exemplary method of measuring the memory parameter μ₁, two uncorrelated sequences of input signals are applied to converter stage 1 in an interleaved arrangement and the correlation of the stage's output measured at the output of the digital filter 106 of FIG. 3A. The stage's memory effect will induce correlation in the output signals of the interleaved sequences. The memory parameter μ₁ is a signal applied to the digital filter 106 that reduces the correlation to zero. The memory parameter can be updated to the correct value with an adaptive algorithm (e.g., a least mean squares (LMS) algorithm) that minimizes the correlation. The signal sequences can be applied to a test set of capacitors or to an unused copy of the converter stage 1 as previously described.

[00040] Another pipelined ADC 120 is shown in FIG. 3B. This ADC is similar to the ADC 100 of FIG. 3A with like elements indicated by like reference numbers. In contrast, however, the FIR filter 106 of FIG. 3A is replaced with an Infinite Impulse Response (IIR) filter 126 that includes a signal delay 130, a multiplier 132 and an adder 134. The delay is coupled to the output of the adder and the multiplier is arranged to couple the output of the delay to one input of the adder. The corrected digital code of the first error corrector forms the other input of the adder. The first error corrector 102 and the digital filter 126 thus form a residue calibrator 128 that calibrates the residue signal of converter stage 1.

[00041] In the FIR filter 106 of FIG. 3A, its present output is a function of its past input. The IIR filter 126 has a recursive effect because of delayed signal feedback through the delay 132. Accordingly, its present output is a function of its past output. Although the FIR filter lacks this recursive effect, it is generally more stable.

[00042] The FIR filter 106 of FIG. 3A multiplies the preceding corrected digital code by a memory parameter μ₁ and adds this product to the current corrected digital code to thereby reduce memory effects in the current residue signal of converter stage 1 that were induced by the preceding residue signal. In other embodiments of the invention, it may be desirable to reduce the memory effects in the current corrected digital code that were induced by even earlier residue signals.

[00043] Accordingly, FIG. 4A illustrates an FIR digital filter 140 that can replace the FIR digital filter 106 in FIG. 3A. The filter 140 replaces the adder 114 of the filter 106 with a multiport adder 141 and inserts additional sets of signal delays 110 and multipliers 112 ahead of the set shown in the filter 106. The output of each multiplier is then coupled to a respective port of the multiport adder. Successively older residue signals are provided by the delays and the multipliers multiply these by corresponding memory constants μ₁, μ₂, . . . μ_n. The adder 141 sums the products with the current digital representation of the residue signal to thereby reduces memory effects that were induced by n successively older residue signals.

[00044] Similarly, FIG. 4B illustrates an IIR digital filter 142 that can replace the IIR digital filter 126 in FIG. 3B. The filter 142 uses the multiport adder 141 and inserts additional sets of signal delays 110 and multipliers 112 after the set shown in the filter 126. The output of each multiplier is then coupled to a respective port of the multiport adder. Successively older signals from the adder are provided by the delays and the multipliers multiply these by corresponding memory constants μ₁, μ₂, . . . μ_n. The action of the adder 142 then reduces memory effects in the digital representation of the current residue signal of converter stage 1 that were induced by n successively older residue signals but does it in a recursive fashion.

[00045] As stated above, the FIR filter 106 of FIG. 3A multiplies the preceding corrected digital code by a memory parameter μ₁ and adds this product to the current corrected digital code to thereby reduce memory effects in the current residue signal of converter stage 1 that were induced by the preceding residue signal. In other embodiments of the invention, it may be desirable to reduce memory effects in the current corrected digital code that were induced by the preceding residue signal of converter stage 1 and the preceding input signal of converter stage 1, i.e., the preceding signal provided by the sampler 22.

[00046] As recognized above, the corresponding digital code provided by the second error corrector 104 of FIG. 3A is a digital representation of the analog input signal at the input port 25. Accordingly, FIG. 5A illustrates a pipelined ADC 160 that supplements the pipelined ADC 100 of FIG. 3A with a second FIR filter 162 that has the elements and arrangements of the filter 106 in FIG. 3A. The second FIR filter 162 is positioned to process the output of the second error corrector 104 in accordance with a corresponding memory constant μ₀.

[00047] In operation, the second error corrector 104 provides a digital representation of the current analog input signal to converter stage 1 while the delay 110 of the second FIR filter 162 provides a digital representation of the previous analog input signal to converter stage 1. The multiplier 112 multiplies the digital representation of the previous analog input signal by the memory constant μ₁ and this product is summed with the digital representation of the current analog input signal in the adder 114 to generate the corresponding digital code. The pipelined ADC 160 thus reduces memory effects in the residue signal of converter stage 1 that were induced by both of the preceding output signal and the preceding input signal of converter stage 1.

[00048] Similarly, FIG. 5B illustrates a pipelined ADC 180 that supplements the pipelined ADC 120 of FIG. 3B with a second IIR filter 182 that has the elements and arrangements of the IIR filter 126 in FIG. 3B except that the IIR filter processes with a corresponding memory constant μ₀. Operation of the pipelined ADC 180 is similar to that of the pipelined ADC 160 of FIG. 5A so that memory effects induced by the preceding output signal and the preceding input signal of converter stage 1 are reduced. The IIR filter 182, however has a recursive effect because of delayed signal feedback through its delay 132. Accordingly, its present output is a function of its past output.

[00049] The residue calibrator 108 of FIG. 3A processes the digital representation of the residue signal S_res of converter stage 1 to provide a filtered corrected digital code in which the memory effects of a preceding output signal (a preceding residue signal) have been reduced. Although memory effect errors of converter stage 1 dominate similar errors in downstream converter stages, it may be advantageous to extend the processing of FIG. 3A to one or more of the downstream stages. This is exemplified in the pipelined ADC 200 of FIG. 6 which is similar to the pipelined ADC 100 of FIG. 3 with like elements indicated by like reference numbers.

[00050] The ADC 200, however, replaces the residue calibrator 108 of FIG. 3A with two residue calibrators 202 and 204. The first residue calibrator 202 receives digital words of converter stages 3-N and, in response, provides a filtered corrected digital code 203 which is the filtered digital representation of the residue signal S_res of converter stage 2. As described above, the first residue calibrator 202 reduces memory effects in this residue signal that were induced by the preceding residue signal of converter stage 2.

[00051] The second residue calibrator 204 receives digital words of converter stage 1 and the filtered corrected digital code 203 of the first residue calibrator 202. In response, second residue calibrator 204 provides a filtered corrected digital code 205 which is the filtered digital representation of the residue signal S_res of converter stage 1. Accordingly, the second residue calibrator 204 reduces memory effects in this residue signal that were induced by the preceding residue signal of converter stage 1. The structure exemplified by the ADC 200 can be extended in a similar manner to reduce memory effects in other succeeding converter stages.

[00052] ADC structures have been described above that reduce memory effects of converter stages with digital processing. FIGS. 7A, 7B, 8A and 8B show embodiments of the invention that reduce the memory effects with switched-capacitor structures. In particular, FIG. 7A illustrates a replacement structure 220 for MDACs of the ADC system 20 of FIG. 1. The structure would replace, for example, each of the first and second capacitors C₁ and C₂ in the MDAC 48 of FIG. 2A.

[00053] The switched-capacitor structure 220 has two sub-capacitors 222 and 223 that each have ½ the capacitance of each of the capacitors C₁ and C₂. In FIG. 7A, sub-capacitor 223 is coupled by switches 224 and 225 in a first orientation with sub-capacitor 222. In FIG. 7B, switches 224 and 225 are opened and previously-open switches 226 and 227 are closed to couple sub-capacitor 223 in a second orientation with sub-capacitor 222 that is reversed from the first orientation of FIG. 7A.

[00054] In operation of the MDAC 40 of FIG. 2A, the first and second operational phases 50A and 50B of one converter cycle would be conducted with each of the first and second capacitors C₁ and C₂ configured as in FIG. 7A. The first and second operational phases 50A and 50B of a succeeding converter cycle would be conducted with each of the first and second capacitors C₁ and C₂ configured as in FIG. 7B. The memory effect of sub-capacitor 223 would substantially cancel the memory effect of sub-capacitor 222. In each converter cycle, the switched-capacitor structure 220 would thus substantially cancel any memory effect errors induced in the preceding converter cycle.

[00055] FIG. 8A illustrates a switched-capacitor MDAC 240 which is a differential version of the switched-capacitor MDAC 48 of FIG. 2A. It replaces the amplifier 44 of FIG. 2A with a differential amplifier 242 and provides each differential input of this amplifier with the first and second capacitors C₁ and C₂ of FIG. 2A except that each capacitor is configured as two sub-capacitors with substantially ½ the capacitance. For example, the upper input of the differential amplifier 242 has sub-capacitors C_1a and C_1b which together provide the capacitance of the first capacitor C₁ of FIG. 2A.

[00056] FIG. 8A shows the switched-capacitor MDAC 240 arranged for first and second operational phases 250A and 250B of one converter cycle. These operational phases correspond to the operational phases 50A and 50B of FIG. 2A. FIG. 8B shows the switched-capacitor MDAC 240 arranged for first and second operational phases 250A and 250B of a succeeding converter cycle. A switch system 242 couples the sub-capacitors in one arrangement in FIG. 8A and in a different arrangement in FIG. 8B. A variety of conventional switch systems can be used to realize the arrangements of FIGS. 8A and 8B. Accordingly, the switch system is shown generically which also clarifies the arrangements.

[00057] With attention directed to the sub-capacitors C_1a and C_1b, it is noted in FIG. 8A that sub-capacitor C_1a receives and transfers charges in the first and second operational phases 250A and 250B in a manner similar to the receiving and transferring of charges in first and second operational phases 50A and 50B of FIG. 2A. It is further noted that these operations are in association with a respective differential side (the upper side) of the differential amplifier 242 in both the converter cycle of FIG. 8A and the succeeding converter cycle of FIG. 8B.

[00058] It is noted in FIGS. 8A and 8B that sub-capacitor C_1b also receives and transfers charges in the first and second operational phases 250A and 260B in a manner similar to the receiving and transferring of charges in first and second operational phases 50A and 50B of FIG. 2A. In the converter cycle of FIG. 8A, it is further noted that these operations are in association with the respective differential side of sub-capacitor C_1a (the upper side). In the converter cycle of FIG. 8B, however, it is noted that these operations are in association with the other differential side the differential amplifier 242 (the lower side).

[00059] In general, therefore, each of the capacitors of the switched-capacitor MDAC 240 are formed with first and second sub-capacitors. The first sub-capacitor receives and transfers charges in association with a respective differential side of the differential amplifier 242 in successive converter cycles. In contrast, the second sub-capacitor receives and transfers charges in association with the differential side of the first sub-capacitor in one converter cycle and in association with the other differential side in a succeeding converter cycle. In one converter cycle, the second sub-capacitor thus substantially cancels the memory effect errors induced in the preceding converter cycle.

[00060] Simulations were used to evaluate a 14-bit, 200 megasample/second ADC and a 16-bit, 100 megasample/second ADC that were configured similar to the ACD 100 of FIG. 3A. That is, the residue of converter stage 1 was calibrated with a single memory parameter μ₁. When the 14-bit ADC was simulated with silicon nitride capacitors having a material constant κ of 3000 ppm, it had a signal-to-noise ratio (SNR) of 69 dB and a spurious free dynamic range (SFDR) of 75 dB without calibration and an SNR of 79.5 dB and a SFDR of 103 dB with calibration. The 14-bit ADC was then simulated with silicon nitride capacitors having a material constant κ of 5000 ppm and it exhibited an integral nonlinearity (INL) of 6 LSBs without calibration and an INL of 0.8 LSB with calibration.

[00061] When the 16-bit ADC (4-bit first stage) was simulated with silicon nitride capacitors having a material constant κ of 3000 ppm, it had SNR of 70 dB and a SFDR of 77 dB without calibration and an SNR of 88 dB and a SFDR of 104 dB with calibration. The 16-bit ADC was then simulated with silicon nitride capacitors having a material constant κ of 300 ppm and it exhibited an SNR of 87 dB and a SFDR of 96 dB without calibration and an SNR of 90.5 dB and a SFDR of 110.5 dB with calibration.

[00062] In different realizations of the invention, many of its converter structures may be configured with arrays of logic gates, with appropriately-programmed digital processors and with combinations thereof.

[00063] The embodiments of the invention described herein are exemplary and numerous modifications, variations and rearrangements can be readily envisioned to achieve substantially equivalent results, all of which are intended to be embraced within the spirit and scope of the invention as defined in the appended claims.