Method of digital-to-analog converter mismatch calibration in a successive approximation register analog-to-digital converter and a successive approximation register analog-to-digital converter

Abstract

A method of DAC mismatch calibration in a SAR ADC is disclosed. In one aspect, the method comprises determining a number of bits of an analog input signal (V.sub.IN), detecting if a binary code determined from the analog input signal (V.sub.IN) matches at least one trigger code, using at least one setting code to determine a calibration residue signal (V*.sub.RES) and a calibration bit (B*.sub.LSB), analyzing a least significant bit of the digital signal (C.sub.OUT) and the calibration bit (B*.sub.LSB), determining an indication of a presence of DAC mismatch, and calibrating the DAC mismatch. As the determination of the calibration bit (B*.sub.LSB) requires only one additional comparison, when compared to the normal operation, the normal operation does not need to be interrupted. Therefore, the calibration can be done in the background and, as such, can be performed frequently thereby taking into account time-varying changes due to environmental effects.

Claims

1. A method of digital-to-analog converter (DAC) mismatch calibration in a successive approximation register (SAR) analog-to-digital converter (ADC), the method comprising the steps of: determining, by a first stage ADC, a number of most significant bits (B.sub.MSB) of a digital signal (C.sub.OUT) corresponding to an analog input signal (V.sub.IN); amplifying, by a gain module, a residue signal (V.sub.RES) output from the first stage ADC; determining, by a second stage ADC, a number of least significant bits (BLSB) of the digital signal (C.sub.OUT) corresponding to the analog input signal (V.sub.IN); detecting if a binary code determined from the analog input signal (V.sub.IN) matches at least one trigger code; using at least one setting code corresponding to the at least one trigger code to determine a calibration residue signal (V*.sub.RES) in the first stage ADC and a calibration bit (B*.sub.LSB) in the second stage ADC; analyzing a least significant bit of the digital signal (C.sub.OUT) and the calibration bit (B*.sub.LSB); determining, from the analysis, an indication of a presence of DAC mismatch between a first DAC in the first stage ADC and a second DAC in the second stage ADC; and calibrating DAC mismatch between the first DAC and the second DAC if the presence of DAC mismatch is determined.

2. The method of claim 1, wherein determining the calibration residue signal (V*.sub.RES) further comprises calculating a difference between the analog input signal (V.sub.IN) and an analog signal (V*.sub.MSB) representing a part of the at least one setting code.

3. The method of claim 1, wherein determining the calibration bit (B*.sub.LSB) further comprises comparing an amplified calibration residue signal (V*.sub.AMP) to a further analog signal (V*.sub.LSB) representing a part of the at least one setting code.

4. The method of claim 1, further comprising temporarily storing, by the gain module, the calibration residue signal (V*.sub.RES) until the least significant bit of the digital signal (C.sub.OUT) has been determined.

5. The method of claim 1, wherein determining an indication of DAC mismatch further comprises determining if the least significant bit and the calibration bit (B*.sub.LSB) are different.

6. The method of claim 5, wherein determining an indication of DAC mismatch further comprises determining the value of the least significant bit, and, if it has a value of 0, indicating a downwards calibration, and, if it has a value of 1, indicating an upwards calibration.

7. The method of claim 1, wherein determining an indication of DAC mismatch further comprises determining the value of the least significant bit and of the calibration bit (B*.sub.LSB), and, if the value of both bits is 0, not indicating the presence of DAC mismatch between the first DAC and the second DAC, and, if the value of both bits is 1, not indicating the presence of DAC mismatch between the first DAC and the second DAC, and if the value of the least significant bit is 1 and the value of the calibration bit (B*.sub.LSB) is 0, indicating the presence of DAC mismatch between the first DAC and the second DAC with an upwards calibration, and if the value of the least significant bit is 0 and the value of the calibration bit (B*.sub.LSB) is 1, indicating the presence of DAC mismatch between the first DAC and the second DAC with a downwards calibration.

8. The method of claim 1, wherein calibrating DAC mismatch further comprises calibrating the first stage ADC by adjusting at least one of a plurality of tunable capacitors.

9. A successive approximation register (SAR) analog-to-digital converter (ADC) comprising: a first stage ADC configured to determine a number of most significant bits (B.sub.MSB) of a digital signal (C.sub.OUT) corresponding to an analog input signal (V.sub.IN) and further configured to output a residue signal (V.sub.RES) corresponding to a number of least significant bits (B.sub.LSB) of the digital signal (C.sub.OUT); a gain module configured to receive the residue signal (V.sub.RES) output from the first stage ADC, further configured to amplify the residue signal (V.sub.RES), and further configured to output the amplified residue signal (V.sub.AMP); a second stage ADC configured to receive the amplified residue signal (V.sub.AMP) and further configured to determine a number of least significant bits (B.sub.LSB) of the digital signal (C.sub.OUT) corresponding to the input analog signal (V.sub.IN) from the amplified residue signal (V.sub.AMP); and a control module configured to: control the first stage ADC, the gain module, and the second stage ADC; output the digital output signal (C.sub.OUT) corresponding to the input analog signal (V.sub.IN); store at least one trigger code; detect if a binary code determined from the analog input signal (V.sub.IN) matches the at least one trigger code; provide at least one setting code corresponding to the at least one trigger code to the first stage ADC, wherein the first stage ADC is further configured to determine a calibration residue signal (V*.sub.RES); provide at least one setting code corresponding to the at least one trigger code to the second stage ADC, wherein the second stage ADC is further configured to determine a calibration bit (B*.sub.LSB); analyze a least significant bit of the digital signal (C.sub.OUT) and the calibration bit (B*.sub.LSB); determine, from the analysis, an indication of a presence of DAC mismatch between a first DAC in the first stage ADC and a second DAC in the second stage ADC; and initiate DAC mismatch calibration between the first DAC and the second DAC if the presence of DAC mismatch is determined.

10. The SAR ADC of claim 9, wherein the first stage ADC comprises a residue generation module configured to determine the calibration residue signal (V*.sub.RES) by calculating a difference between the analog input signal (V.sub.IN) and an analog signal (V*.sub.MSB) representing a part of the at least one setting code.

11. The SAR ADC of claim 9, wherein the second stage ADC comprises a comparator configured to determine the calibration bit (B*.sub.LSB) by comparing an amplified calibration residue signal (V*.sub.AMP) to a further analog signal (V*.sub.LSB) representing a part of the at least one setting code.

12. The SAR ADC of claim 9, wherein the gain module comprises: a first amplifier, a second amplifier, a first switch between the first amplifier and the second amplifier, and a second switch after the second amplifier, the control module controlling the first switch and the second switch to store temporarily the calibration residue signal (V*.sub.RES) until the second stage ADC has determined the least significant bit.

13. The SAR ADC of claim 9, wherein the control module further comprises a difference calculation module configured to determine if the least significant bit and the calibration bit (B*.sub.LSB) are different indicating the presence of DAC mismatch between the first DAC and the second DAC.

14. The SAR ADC of claim 13, wherein the control module comprises a DAC mismatch calibration module configured to determine the value of the least significant bit, and, if it has a value of 0, indicating a downwards calibration, and, if it has a value of 1, indicating an upwards calibration.

15. The SAR ADC of claim 9, wherein the control module is further configured to send a signal indicating the presence of DAC mismatch between the first DAC and the second DAC to the first stage ADC that comprises a plurality of tunable capacitors configured to be adjusted in accordance with the signal.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) The disclosed technology will be further explained by means of the following description and the appended figures.

(2) FIG. 1 shows a block diagram of a conventional two-stage pipelined successive approximation register (SAR) analog-to-digital converter (ADC).

(3) FIG. 2A shows a block diagram of a two-stage pipelined SAR ADC according to the disclosed technology.

(4) FIG. 2B shows a block diagram of the control module of the two-stage pipelined SAR ADC of FIG. 2A.

(5) FIG. 2C shows a block diagram of the first SAR ADC of the two-stage pipelined SAR ADC of FIG. 2A.

(6) FIG. 2D shows a block diagram of the gain module of the two-stage pipelined SAR ADC of FIG. 2A.

(7) FIG. 2E shows a block diagram of the second SAR ADC of the two-stage pipelined SAR ADC of FIG. 2A.

(8) FIG. 3 shows a timing diagram of the two-stage pipelined SAR ADC of FIG. 2A during normal operation.

(9) FIG. 4 shows a timing diagram of the two-stage pipelined SAR ADC of FIG. 2A during a DAC mismatch calibration, an amplifier gain calibration, or an offset calibration of the second comparator.

(10) FIG. 5 shows a timing diagram of the two-stage pipelined SAR ADC of FIG. 2A during an offset calibration of the first comparator.

(11) FIG. 6A shows a block diagram of a two-stage pipelined SAR ADC according to the disclosed technology with a DAC mismatch calibration.

(12) FIG. 6B shows a block diagram of the control module of the two-stage pipelined SAR ADC of FIG. 6A.

(13) FIG. 6C shows a block diagram of the first SAR ADC of the two-stage pipelined SAR ADC of FIG. 6A.

(14) FIG. 6D shows a block diagram of the gain module of the two-stage pipelined SAR ADC of FIG. 6A.

(15) FIG. 6E shows a block diagram of the second SAR ADC of the two-stage pipelined SAR ADC of FIG. 6A.

DETAILED DESCRIPTION OF CERTAIN ILLUSTRATIVE EMBODIMENTS

(16) The disclosed technology will be described with respect to particular embodiments and with reference to certain drawings but the disclosed technology is not limited thereto but only by the claims. The drawings described are only schematic and are non-limiting. In the drawings, the size of some of the elements may be exaggerated and not drawn on scale for illustrative purposes. The dimensions and the relative dimensions do not necessarily correspond to actual reductions to practice of the disclosure.

(17) Furthermore, the terms first, second, third and the like in the description and in the claims, are used for distinguishing between similar elements and not necessarily for describing a sequential or chronological order. The terms are interchangeable under appropriate circumstances and the embodiments of the disclosed technology can operate in other sequences than described or illustrated herein.

(18) Moreover, the terms top, bottom, over, under and the like in the description and the claims are used for descriptive purposes and not necessarily for describing relative positions. The terms so used are interchangeable under appropriate circumstances and the embodiments of the disclosed technology described herein can operate in other orientations than described or illustrated herein.

(19) FIG. 1 shows a block diagram of a conventional two-stage pipelined Successive Approximation Register (SAR) analog-to-digital converter (ADC) 100. The two-stage pipelined SAR ADC 100 comprises a first SAR ADC 110, a second SAR ADC 120, a gain module 130 which amplifies an output signal of the first SAR ADC 110, and a control module 140 that controls the two-stage pipelined SAR ADC 100. In FIG. 1, full lines are used to indicate signals being sent until the first SAR ADC 110 has finished its operations, dashed lines are used to indicate signals being sent after the first SAR ADC 110 has finished its operations until the second SAR ADC 120 has finished its operations, and dashed-dotted lines are used to indicate signals being sent after the second SAR ADC 120 has finished its operations.

(20) During operation, an analog input signal V.sub.IN is input into the first SAR ADC 110 which determines a number of Most Significant Bits (MSBs). The MSBs are determined by feeding the analog input signal V.sub.IN into a first Track-and-Hold module 112 which samples the input signal V.sub.IN. The control module 140 inputs a digital code C.sub.MSB into a first digital-to-analog converter (DAC) 114 which converts the digital code C.sub.MSB into a corresponding analog signal V.sub.MSB. A first comparator 116 compares the input signal V.sub.IN with the analog signal V.sub.MSB to determine which of the two signals is the greater. Depending on the comparison result, the first comparator 116 will output a binary value B.sub.MSB.

(21) When the binary value B.sub.MSB is 1, the input signal V.sub.IN is greater than the analog signal V.sub.MSB. Similarly, when the binary value B.sub.MSB is 0, the input signal V.sub.IN is smaller than the analog signal V.sub.MSB. Using a binary-search algorithm, the control module 140 changes the digital code C.sub.MSB until the MSBs of a digital signal corresponding to the input signal V.sub.IN are determined.

(22) It will readily be understood that at least one clock signal (not shown in FIG. 1) is provided to control the timing of the two-stage pipelined SAR ADC 100 to provide iterations for the determination of the MSBs and the LSBs of a digital signal corresponding to the analog input signal V.sub.IN.

(23) For example, in an embodiment, the control module 140 initializes the digital code C.sub.MSB as 1000. Depending on the binary value B.sub.MSB, in the next iteration, the control module 140 sets the digital code C.sub.MSB as either 1100, if the binary value B.sub.MSB is 1, or 0100, if the binary value B.sub.MSB is 0. In this embodiment, four iterations are performed to determine the four MSBs corresponding to the input signal V.sub.IN.

(24) It is clear for a skilled person that any number of MSBs can be determined by the first SAR ADC 110 by using a pre-set number of iterations.

(25) After the MSBs have been determined by the first SAR ADC 110 (i.e. after the pre-set number of iterations have been performed), the first SAR ADC 110 outputs an analog residue signal V.sub.RES that represents the difference between the input signal V.sub.IN and the analog signal V.sub.MSB that corresponds to the digital code C.sub.MSB. This analog signal VREs comprises information on the Least Significant Bits (LSBs) of the input signal V.sub.IN. The signal V.sub.RES is sent through the gain module 130 to amplify the signal.

(26) During operation, the amplified signal V.sub.AMP from the gain module 130 is input into the second SAR ADC 120 which determines a number of LSBs. Specifically, the LSBs are determined by feeding the amplified signal V.sub.AMP into a second Track-and-Hold module 122 which samples the amplified signal V.sub.AMP. The control module 140 inputs a digital code C.sub.LSB into a second DAC 124 which converts the digital code C.sub.LSB into a corresponding analog signal V.sub.LSB. A second comparator 126 compares the amplified signal V.sub.AMP with the analog signal V.sub.LSB to determine which of the two signals is the greater. Depending on the comparison result, the second comparator 126 will output a binary value B.sub.LSB.

(27) When the binary value B.sub.LSB is 1, the amplified signal V.sub.AMP is larger than the analog signal V.sub.LSB. Similarly, when the binary value B.sub.LSB is 0, the input signal V.sub.AMP is smaller than the analog signal V.sub.LSB. Using a binary-search algorithm, the control module 140 changes the digital code C.sub.LSB until the LSBs of the digital signal corresponding to the input signal V.sub.IN are determined.

(28) After the second SAR ADC 120 has finished its pre-set number of iterations, the control module 140 outputs the digital code C.sub.OUT that corresponds to the input signal V.sub.IN. C.sub.OUT is determined by the control module by combining the information on the MSBs determined by the first SAR ADC 110 and the information on the LSBs determined by the second SAR ADC 120.

(29) FIG. 2A shows a block diagram of a two-stage pipelined SAR ADC 200 with a background calibration to correct: a DAC mismatch error between the SAR ADCs 210, 220; an amplifier gain error due to process, voltage and temperature (PVT) variations in the gain module 230; and offset errors of the comparators 216, 226.

(30) In FIG. 2A, full lines are used to indicate signals that occur during normal operation of the two-stage pipelined SAR ADC 200, while dotted lines are used to indicate signals being sent which are related to extra steps that have to be or have been performed for the background calibration.

(31) The normal operation of the two-stage pipelined SAR ADC 200 is the same as a conventional two-stage pipelined SAR ADC 100 as shown in FIG. 1. Specifically, an input signal V.sub.IN is input into the first SAR ADC 210 which iteratively determines a number of MSBs as described above. The first SAR ADC 210 outputs the residue signal V.sub.RES=V.sub.INV.sub.MSB which is then amplified in the gain module 230, and, the amplified signal V.sub.AMP is input to the second SAR ADC 220. The second SAR ADC 220 determines the LSBs of the input signal V.sub.IN based on the amplified signal V.sub.AMP. Both the MSBs and the LSBs are stored in the control module 240 where they are combined and the control module 240 outputs the digital code C.sub.OUT that corresponds to the input signal V.sub.IN.

(32) In an embodiment, the first SAR ADC 210 uses a seven-bit digital code C.sub.MSB, and, thus performs seven comparisons to determine seven bits of the digital signal corresponding to the input signal V.sub.IN, while the second SAR ADC 220 uses an eight-bit digital code C.sub.LSB, and, thus performs eight comparisons. However, due to a redundancy in the two-stage pipelined SAR ADC 200, the second SAR ADC 220 also only determines seven bits of the input signal V.sub.IN. As such, in this embodiment, a total of fifteen comparisons are performed to determine a fourteen-bit digital signal corresponding to the input signal V.sub.IN. This creates an inter-stage redundancy as the LSB of the first SAR ADC 210 is directly linked to the MSB of the second SAR ADC 220 by the gain module 230, namely:
Gain*LSB.sub.1ST=MSB.sub.2nd(1)

(33) A timing diagram of this embodiment is shown in FIG. 3 over two cycles of the conversion process. An external clock signal (generated by a timing module (not shown) in the control module 240) initiates the conversion process.

(34) A first comparator clock signal controls operation of the first comparator (not shown in FIG. 2A) in the first SAR ADC 210. It is clear that the first comparator has seven operation cycles. After the first comparator has finished its operations, the gain module 230 is activated.

(35) As will be described below, the gain module 230 comprises a two-stage amplifier. As such, a first amplifier clock signal indicates when the first amplifier of the two-stage amplifier is active (i.e. the period between the transitions from high to low and then from low to high of the first amplifier clock signal).

(36) Similarly, the second amplifier clock signal indicates when the second amplifier of the two-stage amplifier is active (i.e. the period between the transitions from high to low and then from low to high of the second amplifier control (or clock signal)).

(37) A second comparator clock signal controls the operation of the second comparator (not shown in FIG. 2A) in the second SAR ADC 220. It is clear that the second comparator has eight operation cycles concurrently with the second amplifier being active indicated by the second amplifier clock signal.

(38) It will be appreciated that each SAR ADC 210, 220 may also perform another number of comparisons depending on the architecture in which the two-stage pipelined SAR ADC 200 is used. However, an inter-stage redundancy is maintained which directly links the LSB of the first SAR ADC 210 to the MSB of the second SAR ADC 220.

(39) Returning to FIG. 2A, in the two-stage pipelined SAR ADC 200 of the disclosed technology, the control module 240 performs a detection step after the MSB has been determined by the second SAR ADC 220. Specifically, the control module 240 determines if the binary code containing the MSBs of the first SAR ADC 210 and the MSB of the LSBs of the second SAR ADC 220 matches a pre-set binary code (i.e., a trigger code). If this code, which will be referred to hereinafter as C.sub.DET (not shown), indeed matches a pre-set binary code, a calibration process is triggered (as will be described below). If, on the other hand, this code does not match a pre-set binary code, no calibration process is triggered and the standard operation of the two-stage pipelined SAR ADC 200 continues either until the entire analog input signal V.sub.IN has been converted into a digital signal or until the code C.sub.DET matches a pre-set binary code.

(40) FIG. 2B shows a block diagram of the control module 240 of the two-stage pipelined SAR ADC 200 of FIG. 2A. The control module 240 comprises an interface module 241 that is used for receiving the various input signals and for transmitting various output signals to other modules of the two-stage pipelined SAR ADC 200.

(41) The control module 240 further comprises a memory module 242 that can store the binary codes that are detected by each SAR ADC 210, 220 during the successive approximation of the input signal V.sub.IN. Moreover, the memory module 242 may also store suitable pre-set binary codes that trigger a calibration process as described below.

(42) The control module 240 also comprises a detection module 243 that detects whether the code C.sub.DET matches a pre-set binary code that is stored in the memory module 242. If a pre-set binary code is detected, this detection is communicated to the relevant calibration module (i.e., one of the DAC mismatch calibration module 244, the amplifier gain calibration module 245, and the offset calibration module 246).

(43) Moreover, the control module 240 comprises a difference calculation module 247 which determines a difference between two bit values. The difference calculation module 247 is used in the calibration as described below.

(44) It is clear for a skilled person that the control module 240 further comprises suitable internal connections (not shown) between the different modules in order to transmit signals to and/or receive signals from other modules.

(45) FIG. 2C shows a block diagram of the first SAR ADC 210 of the two-stage pipelined SAR ADC 200 of the disclosed technology. As in the conventional SAR ADC 110 shown in FIG. 1, the first SAR ADC 210 is used to determine m MSBs of the analog input signal V.sub.IN and comprises a Track-and-Hold module 212, a first DAC 214, and a first comparator 216. The Track-and-Hold module 212 samples the input signal V.sub.IN and feeds it, via a first comparator offset correction module 218 (the operation of which is described below) to the first comparator 216.

(46) The first DAC 214 comprises m capacitors 214a, 214b, . . . , 214m, each capacitor being associated with a bit of the m MSBs to be determined. Depending on the digital code C.sub.MSB that is received in the first DAC 214, one or more of the capacitors 214a, 214b, . . . , 214m will be switched on to convert the digital code C.sub.MSB into an analog signal V.sub.MSB.

(47) During normal operation, the first comparator 216 outputs a binary value B.sub.MSB based on the comparison of V.sub.IN and V.sub.MSB. After the MSBs have been determined, a residue generation module 219 in the first SAR ADC 210 generates the residue signal V.sub.RES=V.sub.INV.sub.MSB which is then output from the first SAR ADC 210.

(48) As described above with respect to FIG. 2A, when the detection module 243 detects that the code C.sub.DET matches a pre-set binary code associated with a DAC mismatch calibration, the detection module 243 sends a signal to the DAC mismatch calibration module 244 that a calibration will occur. The DAC mismatch calibration module 244 then sends a specific digital calibration code C*.sub.MSB (i.e., a setting code) to the first DAC 214, thus generating the analog calibration signal V*.sub.MSB.

(49) As the code C.sub.DET is only determined after the first SAR ADC 210 has finished determining the MSBs, the signal V.sub.RES has already been output from the first SAR ADC 210. However, when a DAC mismatch calibration is triggered, the DAC mismatch calibration module 244 will trigger an additional step in the first SAR ADC 210. This additional step calculates a calibration residue signal, namely V*.sub.RES=V.sub.INV*.sub.MSB, which is the difference between the input signal V.sub.IN with the analog calibration signal V*.sub.MSB. The output of this calculation is shown as a dotted line in FIG. 2C to indicate that this is an additional operation which does not occur during normal operation. After the output of the calibration residue signal V*.sub.RES, the first SAR ADC 210 starts sampling the input signal V.sub.IN again, thus starting the next cycle of normal operation.

(50) A timing diagram of the two-stage pipelined SAR ADC during a DAC mismatch calibration is shown in FIG. 4. As shown in FIG. 3, the external clock signal is generated by the control module, the first comparator clock signal controls operation of the first comparator 216 in the first SAR ADC 210, the first amplifier clock signal indicates when the first amplifier of the two-stage amplifier is active, the second amplifier clock signal indicates when the second amplifier of the two-stage amplifier is active, and the second comparator clock signal controls the operation of the second comparator in the second SAR ADC 220.

(51) Referring to FIG. 4, it is clear that during a DAC mismatch calibration, the first and the second amplifier clock signals are changed. Specifically, the first amplifier is reset after the code C.sub.DET has been determined (i.e., after the MSB of the LSBs of the second SAR ADC 220 has been determined).

(52) FIG. 2D shows a block diagram of the gain module 230 of the two-stage pipelined SAR ADC 200 of the disclosed technology. As described above, the gain module 230 is in the form of a two-stage amplifier and comprises a first amplifier 232 and a second amplifier 236. Between the amplifiers 232, 236 is a first switch 234 that can open/close the circuit. A capacitor C.sub.S is located after the first switch 234 so that, when it is closed, an analog signal can be stored thereon.

(53) After the second amplifier 236, the gain module 230 comprises a second switch 238 that can open/close the circuit. When the second switch 238 is closed, the amplified signal V.sub.AMP is output from the gain module 230. The gain module 230 also comprises an offset correction module 231, the operation of which is described below.

(54) Referring to FIG. 3, it is clear that, during normal operation, first and second switches 234 and 238 can be closed in accordance with one of the respective first and second amplifier clock signals such that the signal V.sub.RES can be amplified in the gain module 230 without interruption and V.sub.AMP is output to the second SAR ADC 220 which can determine the LSBs.

(55) However, during a DAC mismatch calibration process, the calibration residue signal V*.sub.RES has already been determined before the second SAR ADC 220 has finished determining the LSBs of the input signal V.sub.IN. Therefore, to ensure that the second SAR ADC 220 can determine the bits of the amplified signal V.sub.AMP corresponding to V.sub.RES (which correspond to the LSBs of the input signal V.sub.IN), the amplified calibration signal V*.sub.AMP corresponding to the calibration residue signal V*.sub.RES cannot be output from the gain module 230 before the second SAR ADC 220 has finished determining the LSBs. To achieve a latency between receiving the calibration residue signal V*.sub.RES and outputting the amplified calibration signal V*.sub.AMP, the two-stage amplifier shown in FIG. 2D is advantageous.

(56) As shown in FIG. 4, after V.sub.RES has been determined by the first SAR ADC 210, the first amplifier 232 becomes active and amplifies the signal V.sub.RES and immediately puts it through to the second amplifier 236 that generates V.sub.AMP. As such, both the first and the second switch 234 and 238 are closed. However, when the first SAR ADC 210 is determining the calibration residue signal V*.sub.RES, the first switch 234 opens to allow the first amplifier 232 to reset. When the first SAR ADC 210 outputs the calibration residue signal V*.sub.RES, the first switch 234 is closed again and the first amplifier 232 amplifies the calibration residue signal V*.sub.RES. This intermediate amplified signal is then stored on the storage capacitor C.sub.S and the first switch 234 is closed again. As such, the first SAR ADC 210 can continue its normal sampling operation of the next cycle without influencing the intermediate amplified signal stored on the storage capacitor C.sub.S. When the second SAR ADC 220 has finished its last comparison (i.e., after having determined all the LSBs of the input signal V.sub.IN) the second amplifier 236 is reset by opening the second switch 238. After being reset, the second amplifier 236 amplifies the intermediate amplified signal stored on the storage capacitor C.sub.S and outputs the amplified calibration signal V*.sub.AMP to the second SAR ADC 220. As will be described below, the second SAR ADC 220 then performs an extra comparison.

(57) FIG. 2E shows a block diagram of the second SAR ADC 220 of the two-stage pipelined SAR ADC 200 of the disclosed technology. As in the conventional SAR ADC 120 shown in FIG. 1, the second SAR ADC 220 is used to determine n LSBs of the analog input signal V.sub.IN and comprises a Track-and-Hold module 222, a second DAC 224, and a second comparator 226.

(58) The Track-and-Hold module 222 samples the input signal V.sub.AMP and feeds it to the second comparator 226. The second DAC 224 comprises n capacitors 224a, 224b, . . . , 224n, each capacitor being associated with a bit of the n LSBs to be determined. Depending on the digital code C.sub.LSB that is received in the second DAC 224, one or more of the capacitors 224a, 224b, . . . , 224n will be switched on to convert the digital code C.sub.LSB into an analog signal V.sub.LSB. During normal operation, the second comparator 226 outputs a binary value B.sub.LSB based on the comparison of V.sub.AMP and V.sub.LSB.

(59) As described above, when the detection module 243 detects that the code C.sub.DET matches a pre-set binary code associated with a DAC mismatch calibration, the detection module 243 sends a signal to the DAC mismatch calibration module 244 that a calibration will occur as indicated by the dotted line in FIG. 2A with the start signal.

(60) As described above, the first SAR ADC 210 outputs calibration residue signal V*.sub.RES which is amplified by the gain module 230 to amplified calibration signal V*.sub.AMP that is input in the second SAR ADC 220 after it has finished determining the LSBs of the digital signal corresponding to the input signal V.sub.IN. The DAC mismatch calibration module 244 then sends a specific digital calibration code C*.sub.LSB to the second DAC 224, thus generating the analog calibration signal V*.sub.LSB. Moreover, an additional compare cycle will be triggered in the second SAR ADC 220. This additional cycle then compares the input signal (i.e. the amplified residue signal V*.sub.AMP) with the analog calibration signal V*.sub.LSB. The output of this comparison is the calibration bit indicated with B*.sub.LSB and is sent to the control module 240.

(61) The difference calculation module 247 then calculates the difference between (e.g., analyzes) the last bit of C.sub.OUT and the calibration bit B*.sub.LSB. Depending on the result of this comparison, the capacitance value(s) of the capacitors 214a, 214b, . . . , 214m in the first DAC 214 is modified to counter the capacitor mismatch between the first DAC in the first SAR ADC 210 and the second DAC in the second SAR ADC 220.

(62) The advantage of this type of calibration is that it can be performed in the background (i.e. the normal operation of the two-stage pipelined SAR ADC 200 is not interrupted). There is only one additional comparison cycle in the second SAR DAC 220, but, as shown on the timing diagrams in FIGS. 3 and 4, the total timing of the two-stage pipelined SAR ADC 200 is not significantly affected.

(63) The DAC mismatch calibration is based on choosing the correct pre-set binary code C.sub.DET. As already described above, the residue signal of the first SAR ADC 210 is given by V.sub.RES=V.sub.INV.sub.MSB and V*.sub.RES=V.sub.INV*.sub.MSB.

(64) Moreover, similar equations apply to the residue signal of the second SAR ADC 220: V.sub.RES2=Gain*V.sub.RESV.sub.LSB and V*.sub.RES2=Gain*V*.sub.RESV*.sub.LSB. Combining these equations shows that:
V*.sub.RES2V.sub.RES=Gain*(V.sub.MSBV*.sub.MSB)(V*.sub.LSBV.sub.LSB)(2)

(65) When assuming that the amplifier gain is ideal (i.e., by assuming that Equation (1) is valid), this leads to:

(66) $\begin{array}{cc}{V}_{\mathrm{RES}2}^{*}-V_{\mathrm{RES}}=\frac{{\mathrm{MSB}}_{2\mathrm{nd}}}{{\mathrm{LSB}}_{1\mathrm{st}}}*\left(V_{\mathrm{MSB}}-V_{\mathrm{MSB}}^{*}\right)-\left(V_{\mathrm{LSB}}^{*}-V_{\mathrm{LSB}}\right)& \left(3\right)\end{array}$

(67) Depending on the value of the pre-set code C.sub.DET and the value to which the binary calibration codes C*.sub.MSB and C*.sub.LSB are set in response, the signs of Equation (3) are known.

(68) In an embodiment, in calibrating the first capacitor 214a in the first DAC to better match with the first capacitor 224a in the second DAC, the pre-set code C.sub.DET=1000000 0XXXXXXX, where X indicates binary values that have not been determined yet by the second SAR ADC 220. In this embodiment, the first SAR ADC 210 uses a seven-bit digital code C.sub.MSB and thus performs seven comparisons to determine seven bits of the digital signal corresponding to the input signal V.sub.IN, while the second SAR ADC 220 uses an eight-bit digital code C.sub.LSB and thus performs eight comparisons. As described above, due to the inter-stage redundancy the LSB of the first SAR ADC 210 is directly linked to the MSB of the second SAR ADC 220. When this specific code C.sub.DET is encountered during the conversion of the input signal V.sub.IN, the detection module 243 will activate the DAC mismatch calibration module 244 which will input C*.sub.MSB=0111111 into the first DAC. Based on this calibration code, the calibration residue signal V*.sub.RES is generated. After the second SAR ADC 220 has determined the last LSB of the digital code corresponding to the input signal V.sub.IN, the DAC mismatch calibration module 244 will input the calibration code C*.sub.LSB=1YYYYYYY into the second DAC, where Y indicates the binary value that was determined by the second SAR ADC 220. Based on these binary codes, ideally, (i.e., assuming that the gain error and the offset error are correctly calibrated), V.sub.MSBV*.sub.MSB=LSB.sub.1st and V*.sub.LSBV.sub.LSB=MSB.sub.2nd which indicates that V*.sub.RES2V.sub.RES=0.

(69) Therefore, the signs of V.sub.RES2 and V*.sub.RES2 should be the same, and, it is exactly these signs that are reflected in the last bit of C.sub.OUT and B*.sub.LSB. Therefore, if the difference of these bits is non-zero, there is a DAC calibration mismatch between the first capacitor 214a of the first DAC and the first capacitor 224a of the second DAC.

(70) After the error has been detected (i.e., if the last two bits (i.e., the last bit of C.sub.OUT and B*.sub.LSB) either form 01 or 10), the error needs to be corrected. This correction is done by tuning the capacitance of the first capacitor 214a of the first DAC. Specifically, if the bits form 01, a correction signal is sent to the first capacitor 214a to decrease the capacitance, while, if the bits form 10, a correction signal is sent to the first capacitor 214a to increase the capacitance. This signal is indicated by the dotted line in FIG. 2A termed correction.

(71) In a similar fashion, other pre-set binary codes are used for other capacitors of the first DAC that result in the same capacitance tuning for those specific capacitors. Specifically, C.sub.DET=0100000 0XXXXXXX and C*.sub.DET=0011111 1YYYYYYY, where C*.sub.DET is a pre-set calibration response code to C.sub.DET, for the second capacitor 214b of the first DAC; C.sub.DET=0110000 0XXXXXXX and C*.sub.DET=0101111 1YYYYYYY for the third capacitor 214c of the first DAC; C.sub.DET=0111000 0XXXXXXX and C*.sub.DET=0110111 1YYYYYYY for the fourth capacitor 214d of the first DAC; and C.sub.DET=0111100 0XXXXXXX and C*.sub.DET=0111011 1YYYYYYY for the fifth capacitor 214e of the first DAC, etc. where X indicates binary values that have not been determined yet by the second SAR ADC 220 and where Y indicates the binary value that was determined by the second SAR ADC 220.

(72) It will be understood that these pre-set codes can be generalized for other number of bits that are determined in the respective SAR ADCs.

(73) The two-stage pipelined SAR ADC 200 of the disclosed technology can also be used to correct changes in the amplifier gain due to PVT variations. The main difference between the amplifier gain calibration and the DAC mismatch calibration described above are the pre-set binary codes C.sub.DET and C*.sub.DET and that the correction is now performed in the second DAC in the second SAR ADC module 220. Specifically, when assuming that there is no capacitor mismatch between the first and the second DAC, Equation (2) becomes:
V*.sub.RES2V.sub.RES=MSB.sub.2ndGain*LSB.sub.1st(4)
which would equal 0 if the gain is calibrated correctly. However, if the gain is not calibrated correctly, the sign of Equation (4) indicates the direction of the gain error. As before, the signs of V.sub.RES2 and V*.sub.RES2 are reflected in the last bit of C.sub.OUT and B*.sub.LSB, and, if the difference of these bits is non-zero, there is a gain calibration error.

(74) For the gain calibration, the pre-set codes are taken as, C.sub.DET=1001000 1XXXXXXX and C*.sub.DET=1001001 0YYYYYYY where X indicate binary values that have not been determined yet by the second SAR ADC 220 and where Y indicates the binary value that was determined by the second SAR ADC 220. For these codes, it would be expected that, if there is no gain error, they would result in the same analog values. However, other pre-set codes are possible, for example, C.sub.DET=ZZZZZ01 1XXXXXXX and C*.sub.DET=ZZZZZ10 0YYYYYYY where X indicate binary values that have not been determined yet by the second SAR ADC 220, where Y indicates the binary value that was determined by the second SAR ADC 220, and where Z indicates an unspecified binary value. The only other limitation in the choice of C.sub.DET and C*.sub.DET is that they should not coincide with pre-set binary codes that would trigger the DAC mismatch calibration.

(75) Therefore, when a pre-set gain calibration code is detected, the detection module 243 will activate the amplifier gain calibration module 245. The amplifier gain calibration module 245 will then determine the calibration code C*.sub.DET that corresponds to the detected code C.sub.DET and will send the calibration code C*.sub.DET to the interface module 241 which sends it to each of the first and the second DACs together with the start signal to the first SAR ADC 210, the second SAR ADC 220, and the gain module 230.

(76) In a similar manner as in the DAC mismatch calibration, the calibration bit B*.sub.LSB will be output from the second SAR ADC 220 and sent to the control module 240. The difference calculation module 247 then calculates the difference and detects if there is an error. After the error has been detected (i.e., if the last two bits (i.e., the last bit of C.sub.OUT and B*.sub.LSB) either form 01 or 10), the error needs to be corrected. This correction is done by tuning the capacitance value(s) of the capacitors 224a, 224b, . . . , 224n of the second DAC 224. Specifically, if the bits form 01, a correction signal is sent to increase the capacitance, while if the bits form 10, a correction signal is sent to decrease the capacitance. This signal is indicated by the dotted line in FIG. 2A termed correction.

(77) The two-stage pipelined SAR ADC 200 of the disclosed technology can also be used to correct errors due to offsets in at least one of the first comparator 216, the gain module 230, and the second comparator 226. If the offsets for the first comparator 216, the gain module 230, and the second comparator 226 are represented by V.sub.1, V.sub.2, and V.sub.3 respectively, the offset on the final residue V.sub.RES2 is

(78) $V_1+V_2-\frac{V_3}{\mathrm{Gain}}$
where Gain indicates the amplifier gain. If this offset value is greater than the redundancy, it is to be expected that the two-stage pipelined SAR ADC 200 could output wrong digital codes. As such, the residue of the second SAR ADC 220 is V.sub.RES2=Gain*(V.sub.IN+V.sub.2)V.sub.LSBV.sub.3.

(79) In an embodiment of the disclosed technology, the cumulated offset error due to the gain module 230 and the second comparator 226 is corrected simultaneously, and, in a similar manner to the DAC mismatch calibration and the gain calibration. For this offset calibration, the pre-set codes can take any binary value. In an exemplary embodiment, a pre-set binary code is selected that does not coincide with any of the pre-set codes used for either the DAC mismatch calibration or the gain error calibration.

(80) If a pre-set offset calibration code C.sub.DET is detected, the detection module 243 will send a signal to the offset calibration module 246, and, the offset calibration module will send a corresponding calibration code C*.sub.DET to the interface 241. The interface 241 will then send this corresponding code together with the start signal to the first SAR ADC 210, the second SAR ADC 220, and the gain module 230.

(81) In offset calibration, besides changing the DAC codes from C.sub.MSB and C.sub.LSB to C*.sub.MSB and C*.sub.LSB respectively, a signal is also sent to the offset correction module 231 in the gain module 230. Specifically, this signal is sent to crossing module 231a in offset correction module 231 (as shown FIG. 2D). When receiving this signal, the crossing module 231a switches the inputs.

(82) In an embodiment, the two-stage pipelined SAR ADC 200 is implemented as a differential circuit. In this embodiment, the crossing module 231a simply crosses the positive signal and the negative signal that enter the offset correction module 231.

(83) In an alternative embodiment, the two-stage pipelined SAR ADC 200 may be implemented as a non-differential circuit. In this embodiment, the crossing module 231a crosses the incoming signal that enters the offset correction module 231 with a reference signal provided to the offset correction module.

(84) In addition to crossing the incoming signal(s), the first and the second DACs are also inverted. In other words, the calibration code C*.sub.DET is the logical inverse of C.sub.DET. As such, the residue of the second SAR DAC 220 is V*.sub.RES2=Gain*(V.sub.IN+V.sub.2)V*.sub.LSBV.sub.3. This leads to

(85) $\begin{array}{cc}{V}_{\mathrm{RES}2}^{*}+V_{\mathrm{RES}}=2*\mathrm{Gain}*\left(V_2-\frac{V_3}{\mathrm{Gain}}\right)& \left(5\right)\end{array}$

(86) In a similar manner as in the DAC mismatch calibration, the calibration bit B*.sub.LSB will be output from the second SAR ADC 220 and sent to the control module 240. The difference calculation module 247 then calculates the difference which corresponds to the sign of Equation (5) and detects if there is an error. After the error has been detected (i.e., if the last two bits (i.e., the last bit of C.sub.OUT and B*.sub.LSB) either form 00 or 11), the error needs to be corrected. This correction is done by tuning a second variable capacitance module 231b in the offset correction module 231 in the gain module 230 as shown in FIG. 2D (the term second referring to the second part of the circuit, namely, the gain module 230 in this case). Specifically, if the bits form 00, a correction signal is sent to increase the capacitance, while if the bits form 11, a correction signal is sent to decrease the capacitance. This signal is indicated by the dotted line in FIG. 2A termed correction.

(87) The reason that the error is now detected due to the two bits (i.e., the last bit of C.sub.OUT and B*.sub.LSB) being the same is because, by crossing the signal, if there would be no offset error in either the gain module 230 or the second comparator 226, both bits would be opposite to one another. Therefore, if this is not the case (i.e., if both bits are equal), there is an offset error in at least one of the gain module 230 and the second comparator 226.

(88) Because the correction signal is sent to the variable capacitance module 231b that is located before the first amplifier 234 and the second amplifier 238 and before the second comparator 226 of the second ADC stage 220, the same signal can be used to correct all of these possible sources of offset signals simultaneously.

(89) As described above, the offset error of the first comparator 216 can also be calibrated. In principle, the same technique is used as for calibrating the offset in the gain module 230 and the second comparator 226, but the timing of the two-stage pipelined SAR ADC 200 in accordance with the disclosed technology is different with respect to the calibration processes described above.

(90) As shown in FIG. 2C, the first SAR ADC 210 comprises a first comparator offset correction module 218 comprising a crossing module 218a and a first variable capacitance module 218b (the term first referring to the first part of the circuit, namely, the first SAR ADC 210 in this case).

(91) As for calibrating the offset in the gain module 230 and the second comparator 226, the crossing module 218 switches the incoming signals when a calibration is triggered. This can again be the positive signal and negative signal if the two-stage pipelined SAR ADC 200 is a differential circuit or the incoming signal and a reference for a non-differential circuit. As before, there is no requirement for the pre-set binary code C.sub.DET, but in an exemplary embodiment, a pre-set binary code may be assigned that does not coincide with any of the pre-set codes for the other calibration methods. Upon crossing the signal, the first DAC 214 is also inverted (i.e., the calibration code C*.sub.DET is the binary inverse of the code C.sub.DET).

(92) In this calibration, no calibration residue signal V*.sub.RES is generated, and there is only one additional comparison cycle in the first SAR ADC 210. As such, there is also no need for the complex timing in the gain module 230 that was described above with respect to other calibration methods.

(93) The timing diagram for the two-stage pipelined SAR ADC 200 in this calibration method is shown in FIG. 5. It is clear that there is only one extra comparison done by the first comparator 216, while the rest of the timing remains similar to normal operation (shown in FIG. 3). The additional comparison results in one calibration bit B*.sub.MSB (shown in a dotted line in FIG. 2A) which is sent to the difference calculation module 247.

(94) The difference calculation module 247 then calculates the difference and detects if there is an error. After the error has been detected (i.e., if the last two bits (i.e. the last bit of the MSBs in C.sub.OUT and B*.sub.MSB) either form 00 or 11), the error needs to be corrected. This correction is done by tuning a first variable capacitance module 218b in the offset correction module 218 in the first SAR ADC 210. Specifically, if the bits form 00, a correction signal is sent to decrease the capacitance, while if the bits form 11, a correction signal is sent to increase the capacitance. This signal is indicated by the dotted line in FIG. 2A termed correction.

(95) Background DAC mismatch calibration, background gain error calibration, and background comparator offset error calibration will now be described separately in more detail. It will readily be understood that each type of background calibration can be used alone or in combination with one or more of the other types of background calibration.

(96) Elements or components previously described with reference to FIGS. 2A to 2E bear the same last two digits but preceded by a 6 (FIGS. 6A to 6E).

(97) FIG. 6A shows a block diagram of a two-stage pipelined SAR ADC 600 according to the disclosed technology. The two-stage pipelined SAR ADC 600 comprises a background DAC mismatch calibration. More specifically, the two-stage pipelined SAR ADC 600 comprises a first SAR ADC 610, a second SAR ADC 620, a gain module 630, and a control module 640.

(98) The normal operation of the two-stage pipelined SAR ADC 600 is the same as the normal operation of the two-stage pipelined SAR ADC 200 described above with reference to FIG. 2 and having the same timing diagram as shown in FIG. 3.

(99) Moreover, the operation of the two-stage pipelined SAR ADC 600 during a DAC mismatch calibration is also the same as described with respect to the two-stage pipelined SAR ADC 200. Therefore, the same timing diagram (as shown in FIG. 4) applies. The main differences between the two-stage pipelined SAR ADC 600 and the two-stage pipelined SAR ADC 200 are that the two-stage pipelined SAR ADC 600 comprises fewer modules and fewer connections between the modules for ease of explanation.

(100) Specifically, during the DAC mismatch calibration, the input signal V.sub.IN is sent to the first SAR ADC 610 which generates the MSBs of a digital signal corresponding to the input signal and outputs the residue signal V.sub.RES. Moreover, the first SAR ADC 610 also receives the calibration code C*.sub.MSB on the basis of which the calibration residue signal V*.sub.RES is calculated.

(101) The gain module 630 amplifies both the residue signal V.sub.RES and the calibration residue signal V*.sub.RES, and outputs both amplified signals V.sub.AMP and V*.sub.AMP to the second SAR ADC 620.

(102) Based on the amplified signal, the second SAR ADC 620 determines the LSBs of the digital signal corresponding to the input signal. After determining the first LSB, the control module 640 determines the calibration code C*.sub.DET comprising the calibration code C*.sub.MSB, and, after all LSBs are determined, C*.sub.LSB, also. Upon receiving the calibration code C*.sub.LSB and the calibration amplified signal V*.sub.AMP, the second SAR ADC 620 calculates the calibration bit B*.sub.LSB that is used in the control module 640 to determine if there is a DAC capacitor mismatch. If there is a DAC capacitor mismatch, the control module 640 also provides a correction signal that is transmitted to the first SAR ADC 610.

(103) As shown in FIG. 6B, the control module 640 comprises an interface module 641, a memory module 642, a detection module 643, a DAC mismatch calibration module 644, and a difference calculation module 647. These modules perform the same functions as described above (FIG. 2B) with respect to the DAC mismatch calibration of the two-stage pipelined SAR ADC 200. However, the memory module 642 now only stores codes C.sub.DET and C*.sub.DET that trigger a DAC mismatch calibration. The codes C.sub.DET and C*.sub.DET can be the same codes that were described above for the DAC mismatch calibration, but they can also be generalized to tune other capacitors as described above.

(104) FIG. 6C shows details of the first SAR ADC 610. The main difference between first SAR ADC 610 and first SAR ADC 210 is that the first comparator offset calibration module 218 is not present as there is no offset calibration in the two-stage pipelined SAR ADC 600. The first SAR ADC 610 comprises a Track-and-Hold module 612, a first DAC 614 with tunable capacitors 614a, 614b, . . . , 614m, a first comparator 616, and a residue generation module 619. These modules perform the same functions as already described above with respect to the DAC mismatch calibration of the two-stage pipelined SAR ADC 200. In particular, the correction signal sent by the control module 640 is sent to the first DAC 614 and results in tuning at least one of the capacitors 614a, 614b, . . . , 614m.

(105) FIG. 6D shows the details of the gain module 630. The main difference between the gain module 630 and the gain module 230 is that the comparator offset calibration module 231 is not present as there is no offset calibration in the two-stage pipelined SAR ADC 600. The gain module 630 comprises first amplifier 632, a second amplifier 636, a first switch 634, a capacitor C.sub.S, and a second switch 638. As described with respect to the gain module 230, these modules perform the same function in that they amplify the residue signal and are able to store a signal temporarily on the capacitor C.sub.s which allows the second SAR ADC 620 to finish determining the LSBs of the input signal before having to perform an additional comparison to determine the calibration bit B*.sub.LSB.

(106) FIG. 6E shows a block diagram of the second SAR ADC 620. This SAR ADC 620 is very similar to the second SAR ADC 220. The second SAR ADC 620 comprises a Track-and-Hold module 622, a second DAC 624, and a second comparator 626. However, the capacitors 624a, 624b, . . . , 624n in the second DAC 624 do not need to be tunable in this embodiment as there is no gain calibration. There is therefore also no incoming correction signal.

(107) It will readily be appreciated that, in another embodiment, it would be possible to implement a similar capacitance correction in the second DAC while keeping the first DAC fixed. In a further embodiment, both DACs can be corrected at the same time.

(108) Although aspects of the disclosed technology have been described with respect to specific embodiments, it will be readily appreciated that these aspects may be implemented in other forms.