Successive-approximation analog-to-digital converter
11070222 · 2021-07-20
Assignee
Inventors
Cpc classification
H03M1/18
ELECTRICITY
H03M1/468
ELECTRICITY
International classification
Abstract
Disclosed is a SAR ADC (Ai) having an input for receiving an input voltage, a comparator, a first switch network configured to be controlled by the SAR state machine and connected to the input of the SAR ADC and to reference voltage nodes, and a first capacitor network. The first capacitor network has a first node connected to an input of the comparator, a second node, and a bridge capacitor (Cb) connected between the first node and the second node. Furthermore, the first capacitor network comprises a first set of capacitors having a first and a second terminal, wherein the first terminal of each capacitor in the first set is connected to the first node and the second terminal of each capacitor in the first set is connected to the switch network. Moreover, the first capacitor network comprises a second set of capacitors having a first and a second terminal, wherein the first terminal of each capacitor in the second set is connected to the second node and the second terminal of each capacitor in the first set is connected to the switch network. The SAR ADC further comprises a second capacitor network configured to control a gain of the SAR ADC.
Claims
1. A successive-approximation, SAR, analog-to-digital converter, ADC, comprising: an input for receiving an input voltage; a comparator; a SAR state machine connected to an output of the comparator; a first switch network configured to be controlled by the SAR state machine and connected to the input of the SAR ADC and to reference voltage nodes; and a first capacitor network, the first capacitor network comprising: a first node connected to an input of the comparator; a second node; a bridge capacitor connected between the first node and the second node; a first set of capacitors having a first and a second terminal, the first terminal of each capacitor in the first set is connected to the first node and the second terminal of each capacitor in the first set is connected to the first switch network; and a second set of capacitors having a first and a second terminal, the first terminal of each capacitor in the second set is connected to the second node and the second terminal of each capacitor in the first set is connected to the first switch network; a first test-signal capacitor having a first and a second terminal, wherein the first terminal is connected to the first node of the first capacitor network; and a second test-signal capacitor having a first and a second terminal, wherein the first terminal is connected to the second node of the first capacitor network; the SAR state machine is configured to control the first switch network such that: the input voltage is sampled on one or more of the capacitors in the union of the first and the second set during a first phase of a sampling clock period; and SAR analog-to-digital, A/D, conversion is performed during a subsequent second phase of the sampling clock period; a second capacitor network connected to the second node of the first capacitor network and configured to control a gain of the SAR ADC; a test sequence interface configured to provide a binary test sequence during a plurality of consecutive sampling clock periods, each of the plurality of sampling clock periods has an associated sample of the binary test sequence; for each of the plurality of consecutive sampling clock periods: the second terminal of the first test-signal capacitor is configured to be supplied with a first voltage representing the associated sample of the binary test sequence; and the second terminal of the second test-signal capacitor is configured to be supplied with a second voltage representing the associated sample of the binary test sequence, such that a contribution of the first voltage at the input of the comparator is counteracted.
2. The SAR ADC of claim 1, wherein the second capacitor network comprises a capacitor ladder.
3. The SAR ADC of claim 2, wherein the capacitor ladder comprises a set of k connection points, in the following numbered from 1 to k, wherein the 1:st connection point is connected to the second node of the first capacitor network; for each j=1, . . . , k−1, the capacitor ladder comprises a bridge capacitor connected between connection point j and connection point j+1; and for each j=1, . . . , k, the capacitor ladder comprises a j:th capacitor having a first terminal connected to connection point j.
4. The SAR ADC of claim 3, wherein the second capacitor network comprises a capacitor connected between connection point k and a ground node.
5. The SAR ADC (Ai) of claim 3, comprising a second switch network, wherein: for each j=1, . . . , k, the second switch network comprises a j:th switch configured to: connect a second terminal of the j:th capacitor of the second capacitor network to a ground node during the second phase of the sampling clock period; and selectively connect the second terminal of the j:th capacitor of the second capacitor network to the ground node or the input of the SAR ADC during the first phase of the sampling clock period to control the gain of the SAR ADC.
6. The SAR ADC of claim 5, wherein the SAR ADC comprises a third switch network configured to connect the k connection points of the second capacitor network to the ground node during the first phase of the sampling clock period and to disconnect the k connection points of second capacitor network from the ground node during the second phase of the sampling clock period.
7. The SAR ADC of claim 1, wherein the second capacitor network comprises a capacitor connected between connection point 1 and a ground node.
8. The SAR ADC of claim 1, wherein the first voltage and the second voltage are selected from a positive reference voltage and a negative reference voltage in response to the binary test sequence.
9. The SAR ADC of claim 1, wherein the second terminal of the first test-signal capacitor is configured to be supplied with the first voltage in one of the first phase and the second phase of the sampling clock period, the second terminal of the second test-signal capacitor is configured to be supplied with the second voltage in the same one of the first phase and the second phase of the sampling clock period, and the first voltage and the second voltage have opposite polarity.
10. The SAR ADC of claim 1, wherein the second terminal of the first test-signal capacitor is configured to be supplied with the first voltage in one of the first phase and the second phase of the sampling clock period the second terminal of the second test-signal capacitor is configured to be supplied with the second voltage in the other one of the first phase and the second phase of the sampling clock period, and the first voltage and the second voltage have the same polarity.
11. The SAR ADC of claim 1, wherein the binary test sequence is a pseudo-random binary sequence.
12. The SAR ADC of claim 1, comprising circuitry configured to estimate a bridge ratio based on output samples the SAR ADC generated during said plurality of sampling clock periods.
13. Verve SAR ADC of claim 1, wherein the SAR ADC is included in a time interleaved ADC as a sub ADC, the time interleaved ADC having a plurality of sub ADCs.
14. A receiver circuit comprising one of: a successive-approximation, SAR, analog-to-digital converter, ADC, comprising: an input for receiving an input voltage; a comparator; a SAR state machine connected to an output of the comparator; a first switch network configured to be controlled by the SAR state machine and connected to the input of the SAR ADC and to reference voltage nodes; and a first capacitor network, the first capacitor network comprising: a first node connected to an input of the comparator; a second node; a bridge capacitor connected between the first node and the second node; a first set of capacitors having a first and a second terminal, the first terminal of each capacitor in the first set is connected to the first node and the second terminal of each capacitor in the first set is connected to the first switch network; a second set of capacitors having a first and a second terminal, the first terminal of each capacitor in the second set is connected to the second node and the second terminal of each capacitor in the first set is connected to the first switch network; a first test-signal capacitor having a first and a second terminal, wherein the first terminal is connected to the first node of the first capacitor network; and a second test-signal capacitor having a first and a second terminal, wherein the first terminal is connected to the second node of the first capacitor network; the SAR state machine is configured to control the first switch network (120) such that: the input voltage is sampled on one or more of the capacitors in the union of the first and the second set during a first phase of a sampling clock period; and SAR analog-to-digital, A/D, conversion is performed during a subsequent second phase of the sampling clock period; a second capacitor network connected to the second node of the first capacitor network and configured to control a gain of the SAR ADC; a test sequence interface configured to provide a binary test sequence during a plurality of consecutive sampling clock periods, each of the plurality of sampling clock periods has an associated sample of the binary test sequence; for each of the plurality of consecutive sampling clock periods: the second terminal of the first test-signal capacitor is configured to be supplied with a first voltage representing the associated sample of the binary test sequence; and the second terminal of the second test-signal capacitor is configured to be supplied with a second voltage representing the associated sample of the binary test sequence, such that a contribution of the first voltage at the input of the comparator is counteracted; and a plurality of SAR ADCs forming a time interleaved ADC.
15. An electronic apparatus comprising one of: a successive-approximation, SAR, analog-to-digital converter, ADC, comprising: an input for receiving an input voltage; a comparator; a SAR state machine connected to an output of the comparator; a first switch network configured to be controlled by the SAR state machine and connected to the input of the SAR ADC and to reference voltage nodes; and a first capacitor network, the first capacitor network comprising: a first node connected to an input of the comparator; a second node; a bridge capacitor connected between the first node and the second node; a first set of capacitors having a first and a second terminal, the first terminal of each capacitor in the first set is connected to the first node and the second terminal of each capacitor in the first set is connected to the first switch network; a second set of capacitors having a first and a second terminal, the first terminal of each capacitor in the second set is connected to the second node and the second terminal of each capacitor in the first set is connected to the first switch network; a first test-signal capacitor having a first and a second terminal, wherein the first terminal is connected to the first node of the first capacitor network; and a second test-signal capacitor having a first and a second terminal, wherein the first terminal is connected to the second node of the first capacitor network; the SAR state machine is configured to control the first switch network (120) such that: the input voltage is sampled on one or more of the capacitors in the union of the first and the second set during a first phase of a sampling clock period; and SAR analog-to-digital, A/D, conversion is performed during a subsequent second phase of the sampling clock period; a second capacitor network connected to the second node of the first capacitor network and configured to control a gain of the SAR ADC; a test sequence interface configured to provide a binary test sequence during a plurality of consecutive sampling clock periods, each of the plurality of sampling clock periods has an associated sample of the binary test sequence; for each of the plurality of consecutive sampling clock periods: the second terminal of the first test-signal capacitor is configured to be supplied with a first voltage representing the associated sample of the binary test sequence; and the second terminal of the second test-signal capacitor is configured to be supplied with a second voltage representing the associated sample of the binary test sequence, such that a contribution of the first voltage at the input of the comparator is counteracted; and a plurality of SAR ADCs forming a time interleaved ADC; and a receiver, the receiver having one of: the SAR ADC; and a plurality of SAR ADCs forming a time interleaved ADC.
16. The electronic apparatus of claim 15, wherein the electronic apparatus is a communication apparatus.
17. The electronic apparatus of claim 16, wherein the communication apparatus is a wireless communication device for a cellular communications system.
18. The electronic apparatus of claim 16, wherein the communication apparatus is a base station for a cellular communications system.
Description
BRIEF DESCRIPTION OF THE DRAWINGS
(1)
(2)
(3)
(4)
(5)
(6)
(7)
(8)
(9)
(10)
(11)
(12)
DETAILED DESCRIPTION
(13) In this description, reference is made to various voltage levels. As is well known to a person skilled in the art of electronic design, what voltage level is considered to be zero volts, or “ground”, can be arbitrarily selected. Often, ground is used to denote the lowest voltage level available in an integrated circuit, but this is not the case in this description. In this description, ground has been selected to be in the middle between two reference voltage levels. These reference voltage levels are referred to as a positive reference voltage +V.sub.ref and a negative reference voltage −V.sub.ref.
(14)
(15) The radio base station 2 and wireless device 1 are examples of what in this disclosure is generically referred to as communication apparatuses. Embodiments are described below in the context of a communication apparatus in the form of the radio base station 2 or wireless device 1. However, other types of communication apparatuses can be considered as well, such as a WiFi access point or WiFi enabled device.
(16)
(17) Furthermore, in the embodiment illustrated in
(18) Moreover, in the embodiment illustrated in
(19)
(20) Before going into more detailed embodiments of the sub ADCs A1-AM, some analyses of bridged capacitor banks are first discussed.
(21)
(22) The bridge ratio is found by applying a step at the input of C.sub.1 and C.sub.2 and evaluating their contributions at the comparator node. The gain H.sub.1 to the comparator node for C.sub.1 is given by
(23)
The gain H.sub.2 to the comparator node for C.sub.2 is given by
(24)
The bridge ratio is given by the ratio
(25)
For a given desired bridge ratio, the capacitance value of the bridge capacitor can be calculated as
(26)
(27) In the following, a normalized measure of capacitance is used where the unit capacitance C=1 for simplicity, but without loss of generality. Suppose an extra capacitor C.sub.e (not shown in
C.sub.1=1
C.sub.2=2.sup.BS-1
C.sub.y=(2.sup.BS-1−1)+C.sub.e (5)
(28) Inserting the above relations into the bridge capacitor equation, the capacitance C.sub.e is given by
C.sub.e=C.sub.b(2.sup.BS-1r−1)+1−2.sup.BS (6)
(29) C.sub.e is the capacitance in the SDAC to (signal) ground in addition to the binary weighted part with BS bits. C.sub.e is plotted for BS=3, 4, 5 with r=2 in
(30) Exemplary capacitor banks are shown in
(31) For r=2, a bridge ratio of two is implemented, which means that all capacitors give a binary weighted contribution at the comparator input.
(32) For r=1, a bridge ratio of unity is achieved. This means that the capacitor with highest capacitance on the SDAC side and the capacitor with the lowest capacitance on the MDAC side have equal weight, while the other capacitors are binary weighted.
(33) An insight that can be drawn as a conclusion of the analyses above is that, for a given desired bridge ratio, it is possible to add one or more additional capacitors (above represented by the additional capacitor C.sub.e) by carefully selecting the capacitance of the bridge capacitor C.sub.b. This insight is exploited in embodiments described below.
(34)
(35)
(36) As described above, the capacitance value of the bridge capacitor C.sub.b can be selected in such a way that an additional capacitive circuit (above referred to as capacitor C.sub.e) can be connected to the second node 150.
(37) In some embodiments, the SAR ADC Ai further comprises a second capacitor network 180 connected to the second node 150 of the first capacitor network and configured to control a gain of the SAR ADC Ai. This is illustrated in
(38) In some embodiments, the second capacitor network 180 comprises a capacitor ladder. An example of this is illustrated in
(39) In order to get the desired total capacitance of the second capacitor network 180, an additional capacitor might need to be added, for example between p1 and ground. This is illustrated in
(40) As is also illustrated in
(41) Above, embodiments are described with reference to
(42) According to some embodiments, the SAR ADC Ai comprises a test sequence interface 200 configured to provide a binary test sequence p[n] during a plurality of consecutive sampling clock periods. In some embodiments, the binary test sequence p[n] is provided at all time when the SAR ADC Ai is in operation, whereby said plurality of consecutive sampling clock periods is, in some sense, all sampling clock periods. In other embodiments, the binary test sequence p[n] is only applied during certain test intervals. In these cases, the plurality of consecutive sampling clock periods refers to the sampling clock periods within one such test interval. Each of the plurality of sampling clock periods, identified by the sequence index n, has an associated sample of the binary test sequence p[n]. In some examples below, where operation during a specific sampling clock period is described, the associated sample (i.e. associated with that sampling clock period) is sometimes referred to as the “current sample”. In some embodiments, the SAR ADC Ai comprises a test signal generator circuit 210 that is configured to generate the binary test sequence p[n] and supply it to the test signal interface 200. In other embodiments, the binary test sequence p[n] is supplied to the test signal interface by a test signal generator external to the SAR ADC Ai. For example, the TI ADC 50 may comprise a test signal generation circuit that is common to all the sub ADCs A1-AM. In other embodiments, the test signal generation circuit may be external to the TI ADC 50. In some embodiments, the binary test sequence p[n] is a pseudo-random binary sequence (PRBS). In such embodiments, the test signal generator circuit 210 may be implemented as a PRBS generator, for instance using a linear-feedback shift register. In some embodiments, the binary test sequence p[n] may be pre-generated and stored in a memory of the test signal generator circuit 210. A PRBS is suitable for estimating the bridge ratio error during “normal operation” of the SAR ADC Ai, where an input signal that can have a significantly higher magnitude than the residue of the binary test sequence p[n] (e.g. measured at the input of the comparator 100) is present. A PRBS is generally uncorrelated to the input signal, and its residue can therefore be recovered from the output signal of the SAR ADC Ai by means of correlation.
(43) According to some embodiments, the first capacitor network 130 comprises a first test-signal capacitor C.sub.T1 and a second test signal capacitor C.sub.T2. The first test-signal capacitor C.sub.T1 has a first and a second terminal, wherein the first terminal is connected to the first node 140 of the first capacitor network 130. Similarly, the second test-signal capacitor C.sub.T2 has a first and a second terminal, wherein the first terminal is connected to the second node 150 of the first capacitor network 130. For each of the plurality of consecutive sampling clock periods, the second terminal of the first test-signal capacitor C.sub.T1 is configured to be supplied with a first voltage V.sub.1[n] in representing the associated sample of the binary test sequence p[n], and the second terminal of the second test-signal capacitor C.sub.T2 is configured to be supplied with a second voltage V.sub.2[n], also representing the associated sample of the binary test sequence p[n], such that a contribution of the first voltage V.sub.1[n] at the input of the comparator 100 is counteracted.
(44) In the following, it is assumed that the sizes of the test signal capacitors are selected such the contribution from the second voltage V.sub.2[n] cancels the contribution from the first voltage V.sub.1[n] at the input of the comparator if the bridge ratio is just right, i.e. that the voltage gain from the second terminal of the second test signal capacitor C.sub.T2 to the input of the comparator 100 is equal to the voltage gain from the second terminal of the first test-signal capacitor C.sub.T1 to the input of the comparator 100. There are some different ways in which the first and second voltages V.sub.1[n] and V.sub.2[n] can be selected and supplied such that the above-mentioned counteraction is obtained. A few of these are mentioned below. For example, the first and second voltages V.sub.1[n] and V.sub.2[n] may have the same amplitude and the capacitors C.sub.T1 and C.sub.T2 may be designed to yield the same voltage gain to the comparator input. This can, for instance, be obtained by using the bridged capacitor bank second from the top of
(45) In some embodiments, the first voltage V.sub.1[n] and the second voltage V.sub.2[n] are selected from a positive reference voltage +V.sub.ref and a negative reference voltage −V.sub.ref in response to the binary test sequence p[n]. A ‘0’ sample in the sequence may correspond to one of +V.sub.ref and −V.sub.ref. A ‘1’ sample in the sequence may correspond to the other one of +V.sub.ref and −V.sub.ref.
(46) In some embodiments, the second terminal of the first test-signal capacitor C.sub.T1 is configured to be supplied with the first voltage V.sub.1[n] in one of the first phase and the second phase of the sampling clock period and the second terminal of the second test-signal capacitor C.sub.T2 is configured to be supplied with the second voltage V.sub.2[n] in the same one of the first phase and the second phase of the sampling clock period. In these embodiments, the first voltage V.sub.1[n] and the second voltage V.sub.2[n] have opposite polarity in order to counteract each other's contributions at the input of the comparator 100. For example, if, for the first voltage V.sub.1[n], a ‘0’ in the test sequence p[n] corresponds to V.sub.1[n]=−V.sub.ref and a ‘1’ in the test sequence p[n] corresponds to V.sub.1[n]=+V.sub.ref, then, for the second voltage V.sub.2[n], a ‘0’ in the test sequence p[n] corresponds to V.sub.2[n]=+V.sub.ref and a ‘1’ in the test sequence p[n] corresponds to V.sub.2[n]=−V.sub.ref.
(47) For instance, the second terminal of C.sub.T1 may be configured to be selectively (in response to the current sample of the test sequence p[n]) supplied with one of +V.sub.ref and −V.sub.ref and the second terminal of C.sub.T2 may be configured to be selectively supplied with the other one of +V.sub.ref and −V.sub.ref in the first phase of the sampling clock period, e.g. under control of the test signal interface 200. The second terminals of C.sub.T1 and C.sub.T2 may be configured to be connected to ground during the second phase of the sampling clock period.
(48) Alternatively, in some embodiments, the second terminal of C.sub.T1 may be configured to be selectively (in response to the current sample of the test sequence p[n]) supplied with one of +V.sub.ref and −V.sub.ref and the second terminal of C.sub.T2 may be configured to be selectively supplied with the other one of +V.sub.ref and −V.sub.ref in the second phase of the sampling clock period, e.g. under control of the test signal interface 200. The second terminals of C.sub.T1 and C.sub.T2 may be configured to be connected to ground or to the receive the input voltage V.sub.II, during the first phase of the sampling clock period. In the latter case, C.sub.T1 and C.sub.T2 contributes to the sampling of the input voltage V.sub.in, and may thus be utilized in the coarse gain control of the SAR ADC Ai.
(49) In some embodiments, the second terminal of the first test-signal capacitor C.sub.T1 is configured to be supplied with the first voltage V.sub.1[n] in one of the first phase and the second phase of the sampling clock period and the second terminal of the second test-signal capacitor C.sub.T2 is configured to be supplied with the second voltage V.sub.2[n] in the other one of the first phase and the second phase of the sampling clock period. In these embodiments, the first voltage V.sub.1[n] and the second voltage have the same polarity in order to counteract each other's contributions at the input of the comparator 100. For example, if, for the first voltage V.sub.1[n], a ‘0’ in the test sequence p[n] corresponds to V.sub.1[n]=−V.sub.ref and a ‘1’ in the test sequence p[n] corresponds to V.sub.1[n]=+V.sub.ref, then, for the second voltage, a ‘0’ in the test sequence p[n] also corresponds to V.sub.2[n]=−V.sub.ref and a ‘1’ in the test sequence p[n] also corresponds to V.sub.2[n]=+V.sub.ref.
(50) For instance, the second terminal of C.sub.T1 may be configured to be selectively (in response to the current sample of the test sequence p[n]) supplied with one of +V.sub.ref and −V.sub.ref in the first phase of the sampling clock period, and the second terminal of C.sub.T2 may be configured to be selectively supplied with the same one of +V.sub.ref and −V.sub.ref in the second phase of the sampling clock period, e.g. under control of the test signal interface 200. The second terminal of C.sub.T1 may be configured to be connected to ground during the second phase of the sampling clock period. The second terminal of C.sub.T2 may be configured to be connected to ground or to receive the input voltage V.sub.in during the first phase of the sampling clock period. In the latter case, C.sub.T2 contributes to the sampling of the input voltage V.sub.in, and may thus be utilized in the coarse gain control of the SAR ADC Ai. During the first phase of the sampling clock period, a contribution from the first voltage V.sub.1[n] is superpositioned onto the current sample of the input signal of the SAR ADC Ai. During the second phase of the sampling clock signal, a corresponding contribution from the second voltage V.sub.2[n] is subtracted therefrom, and a residue of the current sample of the test sequence p[n], which is indicative of the deviation from the intended bridge ratio, remains superpositioned onto the current sample of the input signal.
(51) Alternatively, in some embodiments, the second terminal of C.sub.T1 may be configured to be selectively (in response to the current sample of the test sequence p[n]) supplied with one of +V.sub.ref and −V.sub.ref in the second phase of the sampling clock period, and the second terminal of C.sub.T2 may be configured to be selectively supplied with the same one of +V.sub.ref and −V.sub.ref in the first phase of the sampling clock period, e.g. under control of the test signal interface 200. The second terminal of C.sub.T2 may be configured to be connected to ground during the second phase of the sampling clock period. The second terminal of C.sub.T1 may be configured to be connected to ground or to the receive the input voltage V.sub.II, during the first phase of the sampling clock period. In the latter case, C.sub.T1 contributes to the sampling of the input voltage V.sub.in, and may thus be utilized in the coarse gain control of the SAR ADC Ai. During the first phase of the sampling clock period, a contribution from the second voltage V.sub.2[n] is superpositioned onto the current sample of the input signal of the SAR ADC Ai. During the second phase of the sampling clock signal, a corresponding contribution from the first voltage V.sub.1[n] is subtracted therefrom, and a residue of the current sample of the test sequence p[n], which is indicative of the deviation from the intended bridge ratio, remains superpositioned onto the current sample of the input signal.
(52) As indicated in
(53) An example of how the bridge ratio estimation can be performed is provided in the following. If the two capacitors C.sub.T1 and C.sub.T2 have been designed to yield the same voltage gain to the comparator input the binary test sequence p[n] is cancelled and not visible in the digital output data of the SAR ADC Ai. On the other hand, if a residual of the binary test sequence p[n] is present at the output, the bridge ratio must be corrected. The bridge ratio error can be estimated by means of correlating the SAR ADC Ai output with the binary test sequence p[n]. The correlation output will be proportional to the bridge ratio mismatch. Below, the ADC output signal is s.sub.c [n]=s.sub.in [n]+ws.sub.pn [n] (r.sub.b−1) where s.sub.in is the output of the SAR ADC Ai in the absence of the binary test sequence p[n] and s.sub.pn (∈{−1,1}) is a numerical equivalent of the binary test sequence p[n] (p[n]=‘0’ corresponds to s.sub.pn[n]=−1, p[n]=‘1’ corresponds to s.sub.pn[n]=1). The number r.sub.b is a normalized bridge ratio quantity that ideally should be unity, in which case there will be no residue of s.sub.pn [n] in s.sub.c [n]. The coefficient w is a weight of the binary test sequence p[n], that indicates the nominal transfer of the sequence s.sub.pn [n] from the second terminal of the capacitor C.sub.T1 to the digital output of the SAR ADC Ai as well as from the second terminal of the capacitor C.sub.T2 to the digital output of the SAR ADC Ai. As an explanation of w, consider, for instance, a hypothetical situation where the sequence s.sub.pn [n] is input to the second terminal of C.sub.T1 in the form of the voltage V.sub.1[n]=V.sub.refs.sub.pn [n], the second terminal of C.sub.T2 is kept grounded, and the input voltage v.sub.in is held constantly 0. Furthermore, for this hypothetical situation, let us denote the output signal from the SAR ADC Ai y[n] in order to not confuse it with the above defined output signal s.sub.c [n] when the SAR ADC Ai is in actual use. This digital output signal is y [n]=ws.sub.pn [n], or in other words w=y[n]/s.sub.pn [n].
(54) The bridge ratio deviation Δr.sub.b=r.sub.b−1 may be calculated by correlation as:
(55)
(56) For estimation based on a finite set of N samples this bridge ratio deviation can be estimated as
(57)
(58) The bridge capacitor C.sub.b can be implemented as a variable capacitor configured to be controlled via a digital bridge ratio setting parameter r.sub.s. For example, C.sub.b can be implemented as a capacitor bank with a number of capacitors that can be selectively connected in parallel in response to r.sub.s such that an increase in r.sub.s leads to a decrease in C.sub.b, and thus a larger bridge ratio, and a decrease in r.sub.s leads to an increase C.sub.b, and thus a smaller bridge ratio. Such digitally controllable variable capacitors are, per se, well known and not described in any further detail herein. For each estimation of the bridge ratio deviation Δ{circumflex over (r)}.sub.b, the bridge ratio setting r.sub.s (not to be confused with the actual bridge ratio r.sub.b) can be updated as r.sub.s=r.sub.s/(1+αΔ{circumflex over (r)}.sub.b)≈r.sub.s (1−αΔ{circumflex over (r)}.sub.b) with 0<α<1. In other words, if the bridge ratio is found to be larger than the nominal value, i.e. Δ{circumflex over (r)}.sub.b>0, the bridge ratio setting is reduced by a proportion of |Δ{circumflex over (r)}.sup.b|, and if the bridge ratio is found to be smaller than the nominal value, i.e. Δ{circumflex over (r)}.sub.b<0, the bridge ratio setting is increased by a proportion of |Δ{circumflex over (r)}.sub.b|. More generally, this may be viewed as an optimization problem based on a noisy metric (Δ{circumflex over (r)}.sub.b) and where the relation between the actual bridge ratio and the bridge ratio setting is not necessarily proportional or even linear. As such, there exist many established methods in the field of optimization and this is not further discussed herein.
(59) C.sub.T2 may also be defined to have a value giving a weight different from that of C.sub.T1. In this case, the binary test sequence p[n] will not be fully cancelled, rather the correct bridge ratio will be obtained when there is a specific level of the binary test sequence p[n] left at the digital output data of the SAR ADC Ai. Instead the cancellation of the binary test sequence p[n] can be completed in digital domain. As the cancellation is not complete it will consume a small fraction of the full-scale range. One reason to give different weights to C.sub.T1 and C.sub.T2 is that C.sub.T1 has a smaller capacitance than C.sub.T2 and thus will have a larger capacitance variation in fabrication (mismatch). A larger C.sub.T1 will lead to a smaller relative capacitance variance and thus will improve accuracy.
(60) The bridge ratio error may be calibrated in the analog domain, e.g. by adjusting the bridge capacitor C.sub.b as described above. Alternatively, the bridge ratio error may be compensated for in the digital domain by digital post processing of the output signal from the SAR ADC Ai. For instance, let d.sub.j denote the bits of the output Y=Σ.sub.jw.sub.jd.sub.j from the SAR ADC Ai with nominal weights w.sub.j, for instance w.sub.j=2.sup.j-1 for a binary-weighted architecture with a nominal bridge ratio of 2. A compensated output Ŷ can be calculated as Σ.sub.jŵ.sub.jd.sub.j, where ŵ.sub.j are compensated bit weights computed in response to the estimated bridge ratio. For instance, the compensated bit weights can be computed as ŵ.sub.j=c.sub.SDACw.sub.j for bits d.sub.j of the SDAC and as ŵ.sub.j=c.sub.MDACw.sub.j for bits d.sub.j of the MDAC, where C.sub.SDAC and C.sub.MDAC are compensation factors derived from the estimated bridge ratio {circumflex over (r)}.sub.b=1+Δ{circumflex over (r)}.sub.b such that
(61)
In some embodiments, either C.sub.SDAC or C.sub.MDAC is set to 1.
(62) The SAR ADC Ai may be comprised in a receiver circuit 40, either as a stand-alone ADC or as a sub ADC in another ADC, such as the TI ADC 50. Furthermore, the SAR ADC Ai, may be comprised in an electronic apparatus, either as a separate component or as a part of another circuit, such as the receiver circuit 40 or the TI ADC 50. The electronic apparatus can e.g. be a communication apparatus, such as the wireless communication device 1 or the base station 2 for a cellular communications system.
(63) The disclosure above refers to specific embodiments. However, other embodiments than the above described are possible within the scope of the invention. The different features of the embodiments may be combined in other combinations than those described. For instance, some embodiments described above provides gain-control functionality by means of the second capacitor network 180. Furthermore, some embodiment described above provides test-sequence injection functionality by means of test signal capacitors C.sub.T1 and C.sub.T2. It should be noted that some embodiments can include only one of these functionalities, whereas some embodiments can include both of the functionalities in combination.