ANALOG-TO-DIGITAL CONVERTER

Abstract

An analog-to-digital converter comprises a first quantizer arranged for yielding a first digital signal; an error signal generation block arranged for generating an error signal representative of a difference between an analog input signal and the first digital signal; an analog loop filter arranged for receiving the error signal; a second quantizer arranged for receiving an output signal of the analog loop filter and for outputting a second digital signal; a digital loop filter arranged for receiving the second digital signal and for providing an input signal to the first quantizer; and a recombiner block comprising a first recombination and a second recombination filter, and an adder circuit for adding outputs of the first and second recombination filters. The first and second recombination filters are selected to obtain an analog-to-digital converted output signal being less dependent on quantization noise caused by the first quantizer than a first digital signal.

Claims

1. An analog-to-digital converter comprising: a first quantizer arranged for yielding a first digital signal; an error signal generation block arranged for generating an error signal representative of a difference between an analog input signal and said first digital signal; an analog loop filter arranged for receiving said error signal; a second quantizer arranged for receiving an output signal of said analog loop filter and for outputting a second digital signal; a digital loop filter arranged for receiving said second digital signal and for providing an input signal to said first quantizer; a recombiner block comprising a first recombination filter arranged to receive said first digital signal, a second recombination filter arranged to receive said second digital signal and an adder circuit for adding outputs of said first and said second recombination filter, said first and said second recombination filter being selected to obtain an analog-to-digital converted output signal being less dependent on quantization noise caused by said first quantizer than said first digital signal.

2. The analog-to-digital converter as in claim 1, wherein said analog loop filter has a transfer function substantially equal to the ratio of said first recombination filter's transfer function and said second recombination filter's transfer function.

3. The analog-to-digital converter as in claim 1, wherein said first recombination filter and/or said second recombination filter are Finite Impulse Response filters.

4. The analog-to-digital converter as in claim 1, wherein said first recombination filter and/or said second recombination filter are adaptive.

5. The analog-to-digital converter as in claim 4, wherein said first recombination filter and/or said second recombination filter are adapted to remove a dependency of said analog-to-digital converted output signal from said quantization noise caused by said first quantizer.

6. The analog-to-digital converter as in claim 4, wherein said first recombination filter and/or said second recombination filter has a programmable gain.

7. The analog-to-digital converter as in claim 6, comprising a gain controller unit to determine said programmable gain.

8. The analog-to-digital converter as in claim 1, wherein said first quantizer has a lower resolution than said second quantizer.

9. The analog-to-digital converter as in claim 1, comprising a delay compensation filter to compensate for a delay introduced by said first recombination filter.

10. The analog-to-digital converter as in claim 1, wherein said digital loop filter comprises an accumulator/integrator.

11. The analog-to-digital converter as in claim 10, wherein said digital loop filter comprises a feedforward path for improving the dynamic response of said feedback loop.

12. The analog-to-digital converter as in claim 1, wherein said second quantizer is embedded in an internal feedback loop comprising a further analog loop filter and a feedback digital-to-analog converter.

13. The analog-to-digital converter as in claim 1, wherein said error signal generation block comprises a digital-to-analog conversion circuit.

14. The analog-to-digital converter as in claim 1, wherein said analog input signal is derived from a set of sensor elements.

15. The analog-to-digital converter as in claim 14, comprising a combiner circuit for combining signals from said set of sensor elements and generating said error signal.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0033] The invention will now be described further, by way of example, with reference to the accompanying drawings, wherein like reference numerals refer to like elements in the various figures.

[0034] FIG. 1 illustrates a block scheme of a Sigma-Delta modulator as known in the art.

[0035] FIG. 2 illustrates a block scheme of an A/D converter according to the invention.

[0036] FIG. 3 illustrates an angular sensor operated as a tracking loop, providing an A/D conversion of the input angle according to the invention.

[0037] FIG. 4 illustrates an embodiment of the A/D converter of the invention comprising a filter to compensate delay.

[0038] FIG. 5 illustrates a possible implementation of a delay compensation filter.

[0039] FIG. 6 illustrates an embodiment wherein inner-loop noise shaping is applied.

[0040] FIG. 7 illustrates an embodiment with adaptive gain correction.

DETAILED DESCRIPTION OF ILLUSTRATIVE EMBODIMENTS

[0041] The present invention will be described with respect to particular embodiments and with reference to certain drawings but the invention is not limited thereto but only by the claims.

[0042] Furthermore, the terms first, second and the like in the description and in the claims, are used for distinguishing between similar elements and not necessarily for describing a sequence, either temporally, spatially, in ranking or in any other manner. It is to be understood that the terms so used are interchangeable under appropriate circumstances and that the embodiments of the invention described herein are capable of operation in other sequences than described or illustrated herein.

[0043] It is to be noticed that the term comprising, used in the claims, should not be interpreted as being restricted to the means listed thereafter; it does not exclude other elements or steps. It is thus to be interpreted as specifying the presence of the stated features, integers, steps or components as referred to, but does not preclude the presence or addition of one or more other features, integers, steps or components, or groups thereof. Thus, the scope of the expression a device comprising means A and B should not be limited to devices consisting only of components A and B. It means that with respect to the present invention, the only relevant components of the device are A and B.

[0044] Reference throughout this specification to one embodiment or an embodiment means that a particular feature, structure or characteristic described in connection with the embodiment is included in at least one embodiment of the present invention. Thus, appearances of the phrases in one embodiment or in an embodiment in various places throughout this specification are not necessarily all referring to the same embodiment, but may. Furthermore, the particular features, structures or characteristics may be combined in any suitable manner, as would be apparent to one of ordinary skill in the art from this disclosure, in one or more embodiments.

[0045] Similarly it should be appreciated that in the description of exemplary embodiments of the invention, various features of the invention are sometimes grouped together in a single embodiment, figure, or description thereof for the purpose of streamlining the disclosure and aiding in the understanding of one or more of the various inventive aspects. This method of disclosure, however, is not to be interpreted as reflecting an intention that the claimed invention requires more features than are expressly recited in each claim. Rather, as the following claims reflect, inventive aspects lie in less than all features of a single foregoing disclosed embodiment. Thus, the claims following the detailed description are hereby expressly incorporated into this detailed description, with each claim standing on its own as a separate embodiment of this invention.

[0046] Furthermore, while some embodiments described herein include some but not other features included in other embodiments, combinations of features of different embodiments are meant to be within the scope of the invention, and form different embodiments, as would be understood by those in the art. For example, in the following claims, any of the claimed embodiments can be used in any combination.

[0047] It should be noted that the use of particular terminology when describing certain features or aspects of the invention should not be taken to imply that the terminology is being re-defined herein to be restricted to include any specific characteristics of the features or aspects of the invention with which that terminology is associated.

[0048] In the description provided herein, numerous specific details are set forth. However, it is understood that embodiments of the invention may be practiced without these specific details. In other instances, well-known methods, structures and techniques have not been shown in detail in order not to obscure an understanding of this description.

[0049] The present invention aims to propose an analog-to-digital converter (also referred to as A/D converter or ADC) comprising a feedback loop with so called dual in-loop quantization, i.e. having a structure wherein two quantizers are applied in the feedback loop.

[0050] The A/D converter according to the invention is advantageously a tracking loop. A tracking loop keeps track of an external phase, angle or position in an incremental way, based on comparing a predicted output to the actual phase/angle/position. Such tracking loops can cope better with non-stationary situations, e.g. in which the phase/angle/position changes continuously with time. This occurs for instance in motor applications, where the rotation angle of the rotor typically changes with a relatively constant but possibly high speed, and thus the actual angle increases linearly with time. In such applications, tracking loops may, for instance, be beneficially used for providing a near-zero latency output. This means that an accurate output phase/position/angle is provided even when the input phase/position/angle changes with constant but possibly very high (angular) speed. The tracking loop may also be optimized for good dynamic responses, e.g. a fast response to steps or sudden speed changes.

[0051] The tracking loop according to the present invention may relate to a position sensor. Position may refer to a linear displacement, a rotation angle, etc. With the position to be measured, an input phase .sub.i is associated. The position sensor may be an angular sensor, in which case the input phase .sub.i may be the same as the mechanical rotation angle .sub.mech, i.e. .sub.i=.sub.mech a (linear) function of the mechanical rotation angle, e.g. .sub.i=k. .sub.mech+.sub.0 with k some proportionality factor, and .sub.0 the phase at a zero position. The position sensor may be a linear displacement sensors, in which case the input phase .sub.i may be a linear function of the mechanical displacement x.sub.mech, e.g. .sub.i=k. x.sub.mech+.sub.0 with k some proportionality factor, and .sub.0 the phase at a zero position.

[0052] The position sensor may be a magnetic position sensor which, for instance, measures the displacement of a magnetic field with respect to the position sensor, or which measures the angle of a magnetic field relative to the sensor orientation. In these magnetic position sensors the magnetic field may be generated by a magnet or it may be generated by an excitation coil. In magnetic position sensors, the sensing elements may be based on horizontal or vertical Hall elements, GMR or TMR sensing elements, etc. This may be in combination with a magnetic layer (e.g. an integrated layer or IMC) that locally alters the magnetic field, e.g. change its direction, e.g. from an in-plane magnetic field to a vertical magnetic field. Magnetic position sensor may also rely on an angle-dependent mutual inductance between a driving coil and one or more sense coils, for instance an electrical resolver.

[0053] A scheme of an analog-to-digital converter with dual in-loop quantization according to the present invention is shown in FIG. 2. A first quantizer (13) provides a digital output value (D.sub.1) of the loop (hence appearing at the end of the forward path). This first quantizer may typically have a limited number of bits, e.g. for reducing the complexity associated with error evaluation. Contrary to many prior art systems, this first quantizer is in the digital domain and its input is provided by a digital loop filter having a transfer function H.sub.d. The loop further comprises an analog loop filter having a transfer function H.sub.a followed by a second quantizer. The second quantizer provides the input of the digital loop filter H.sub.d. The operation of the quantizers can be modelled as adding a quantization error to the respective quantizer input signal, the quantization error being defined as the difference between the output and the input of the quantizer. Therefore two extra sources can be identified in the system, being Q.sub.1 and Q.sub.2 representing the quantization error of the first and second quantizer, respectively. Note that Q.sub.1 may be considered a knowable quantity in present system, since both the input and the output of the first quantizer are in the digital domain, and hence these signals can be digitally subtracted to obtain Q.sub.1. In contrast, Q.sub.2 cannot be determined (without extra measurements) because the input of the second quantizer is an unknown analog signal. A classical approach is therefore to consider Q.sub.2 as a source of random noise. With respect to Q.sub.1, the situation may be different. Since perfect knowledge of Q.sub.1 can be obtained, it may be possible to compensate the effects caused by it. A key question is of course how to do this and to what extent this is possible when there are uncertainties in the system, such as when one has only imprecise knowledge of the analog filter transfer function H.sub.a. If no such compensation is implemented, Q.sub.1 again needs to be treated as a source of random noise that has an impact on the resolution of the overall system. The purpose of the A/D converter circuit of the present invention is to largely eliminate the effects of Q.sub.1. Some disclosed embodiments are capable of coping with imprecise knowledge of the analog filter transfer function H.sub.a, and even allow adapting to time-varying changes in this filter.

[0054] Using linear system analysis, the two digital outputs D.sub.1 and D.sub.2 in the above system can be determined as a function of the input signal V.sub.i and the two quantization error sources Q.sub.1 and Q.sub.2:

[00001]$\begin{array}{cc}\{\begin{array}{c}{D}_1=\mathrm{STF}.Math.V_i+\mathrm{NTF}.Math.Q_1+H_d.Math.\mathrm{NTF}.Math.Q_2\\ D_2=\frac{\mathrm{STF}}{H_d}.Math.V_i-H_a.Math.\mathrm{NTF}.Math.Q_1+\mathrm{NTF}.Math.Q_2\end{array}& \left(1\right)\end{array}$

In this expression the following transfer functions appear:

[00002]$\begin{array}{cc}\{\begin{array}{c}\mathrm{STF}=\frac{H_a.Math.H_d}{1+H_a.Math.H_d}\\ \mathrm{NTF}=\frac{1}{1+H_a.Math.H_d}\end{array}& \left(2\right)\end{array}$

These transfer functions are known in the context of Sigma-Delta modulators as the signal transfer function (STF) and the noise transfer function (NTF).

[0055] In accordance with the present invention, the two digital quantizer outputs D.sub.1 and D.sub.2 are filtered by digital filters A(z) and B(z), respectively, and then added. The thus obtained recombined output D.sub.out can be expressed as:

D.sub.out(z)A(z)D.sub.1(z)+B(z)D.sub.2(z)(3)

Substituting expression (1) in (3) it can be easily shown that if

[00003]$\begin{array}{cc}\frac{A\left(z\right)}{B\left(z\right)}=H_a& \left(4\right)\end{array}$

then

[00004]$\begin{array}{cc}{D}_{\mathrm{out}}\left(z\right)=A\left(z\right).Math.\left(V_i+\frac{1}{H_a\left(z\right)}.Math.Q_2\right)& \left(5\right)\end{array}$

Since Q.sub.1 does not appear in the compensated output D.sub.out(z), the proposed recombination has completely eliminated the contribution of Q.sub.1. It is, however, shown later in this description that it is not strictly needed that the ratio of the transfer functions of the digital filters A(z) and B(z) exactly equals H.sub.a.

[0056] The advantage of the dual-quantization scheme is that the first quantizer may have a low resolution (i.e. a low number of bits), because the corresponding quantization error Q.sub.1 can be eliminated in the above explained manner. This way, the number of feedback levels may be restricted, which can significantly simplify the design of the error evaluation block. For instance, for the case of an SDM, a feedback DAC with at most a few bits makes it easier to optimize the system for good linearity. In an extreme embodiment a one-bit quantizer can be used. The corresponding one-bit feedback DAC is considered inherently linear, because it only has two input-output pairs, which necessarily lie on a straight line.

[0057] Another advantage offered by the invention can be understood by observing the transfer of the input signal V.sub.i to the digital output. In the compensated output (5) of the A/D converter according to the present invention, this transfer is A(z). In case of the prior art method US2011/050475 and also when using D.sub.1 as (uncompensated) output, the signal transfer function is STF(z) as defined in (2). This STF(z) is fixed by the choices for the analog and digital loop filters H.sub.a and H.sub.d, respectively. In contrast, it can be seen that (4) allows much freedom in selecting the recombination filters A(z) and B(z). It is therefore possible to exploit this freedom to arrive at a more beneficial signal transfer function A(z).

[0058] As an example an angular sensor is considered which is operated as a tracking loop. FIG. 3 illustrates such a system. The tracking loop in this example contains: [0059] N Hall plates arranged to receive different projections of a magnetic field having an angle .sub.i relative to the angle sensor [0060] a combiner circuit which simultaneously combines all Hall element signals with an array of weights that depends on a quantized feedback angle (D.sub.1) and outputs an error signal representative of the difference between the input angle .sub.i and the feedback angle, [0061] an analog integrator that integrates the error signal [0062] an ADC that quantizes the integrator output and produces samples thereof at a rate 1/T [0063] a digital filter comprising an accumulator/integrator of the ADC output and a feedforward path to improve the feedback loop dynamic response [0064] an angle quantization unit that maps the digital filter output to a limited number (e.g. 16) of allowed feedback angles

[0065] Further there is a recombiner block. As detailed below, a delay compensation filter can optionally be provided as well. In FIG. 3 a possible sizing of the loop filter is detailed, wherein f.sub.n represents a normalized frequency that controls the bandwidth of the loop (relative to the sample frequency 1/T).

[0066] In general, the interconnection complexity of the combiner circuit reduces when the number of bits of the angle quantizer is lowered. A small number of bits implies a larger angle quantization error, and the strategy to deal with angle quantization error as disclosed in present invention is therefore highly relevant.

[0067] An important quantity is the delay nexpressed as a number of sample intervals (T)between the digital feedback signal (D.sub.1) and the digital output of the ADC (D.sub.2). Contributions to this delay may come from a delay in the feedback path, a delay associated with the integrator circuit, the conversion time of the ADC, etc.

[0068] The more compact system-level diagram of FIG. 4 can then be derived for the system as described. In the present example, the error evaluation block produces an output signal proportional to the sine of the difference between input angle and the feedback angle corresponding with D.sub.1. Because sin xx for x sufficiently small, the non-linear characteristic can often be neglected when in tracking mode. In the system level diagram the (total) delay n has been included in the analog filter transfer function H.sub.a, while the feedback path and the first quantizer are idealized as having no delay. In the considered exemplary case, the analog filter has a transfer function given by

[00005]$H_a=K.Math.\frac{z^{-n}}{1-z^{-1}},$

with K a proportionality factor accounting for a multitude of scale factors (such as the magnetic field strength, the Hall element sensitivity, the time constant of the integrator, etc.).

[0069] In this exemplary embodiment the recombiner block uses the following recombination filters:

[00006]$\begin{array}{cc}\{\begin{array}{c}A\left(z\right)=z^{-n}.Math.\\ B\left(z\right)=\frac{z^{-n}}{H_a\left(z\right)}\end{array}& \left(6\right)\end{array}$

For this choice the condition (4) is obviously met. The reason why the extra delay z.sup.n is introduced, is to make the filter B(z) physically realizable. For this example one obtains

[00007]$B\left(z\right)=\frac{1-z^{-1}}{K},$

which represents a realizable FIR filter.

[0070] The choice A(z)=z.sup.n implies that the input signal is also delayed by n samples, which can be seen from (5). In case of angular sensors operating at high rotation speeds, this extra delay may cause noticeable angle errors, especially if n>1. In such cases, an optional delay compensation filter may be added to the system whose purpose is to compensate the delay n of the filter A(z). One example of a compensation filter for compensating a delay n is:

[00008]$\begin{array}{cc}C\left(z\right)=1+\frac{a\left(1-z^{-1}\right)}{1-\left(1-\frac{a}{n}\right).Math.z^{-1}}& \left(7\right)\end{array}$

One way to realize this filter is shown in FIG. 5. In (7) a denotes an extra parameter, typically between zero and one, to control the trade-off between overshoot and high-frequency gain (which becomes smaller when a is lowered) on the one hand and on the other hand the settling time (which becomes smaller when a is increased). When choosing a=n, the filter reduces to 1+n(1z.sup.1), which is an intuitive way for compensating delay based on a speed estimate by differencing the signal, but this choice has a very high overshoot and strongly amplifies high frequencies.

[0071] As explained before, the input signal transfer function has been changed to the transfer A(z) of the first recombination filter, possibly with the delay thereof being compensated by a delay compensation filter. This is particularly interesting for angular sensors which provide an A/D conversion of a possibly fast-changing angle, because it allows improving the dynamic response, e.g. by providing a faster step response.

[0072] Additional digital filtering may be added to any of the exemplary embodiments of present invention, e.g. for increasing the signal-to-noise ratio by reducing the (noise) bandwidth. If such filtering incurs extra delay that cannot be tolerated in the envisioned application, this delay can be compensated, e.g. using the above type of delay compensation filter. Also, filters can be designed that provide filtering with near-zero latency, for instance by means of a tracking loop that is completely in the digital domain. Such digital PLL-like structures are known in the art. Also digital counterparts of the tracking loops in the present invention may be used. Note that in all these digital-domain tracking loops the issue of variability is absent, i.e. there are no uncertainties on loop filters, nor mismatch-related nonlinearity problems in the error evaluation block.

[0073] FIG. 6 shows an embodiment of the A/D converter according to the invention wherein inner-loop noise shaping is applied. The second quantizer Q.sub.2 is embedded in an internal feedback loop, having an analog loop filter with transfer function H.sub.b, and a local feedback DAC. The dynamics of the local loop is dictated by its signal transfer function H.sub.b/(1+H.sub.b). For a first-order filter H.sub.b=z.sup.1/(1z.sup.1) this signal transfer function is a simple delay z.sup.1. This simple delay can be directly incorporated in the total delay n of the global feedback loop. The delay may also be avoided by adding the optional path shown on the figure. This optional path has the known effect that it makes the signal transfer function of the local loop equal to one. In such cases the local loop does not alter the dynamic behaviour of the global feedback loop. The main effect of the local loop is therefore that it applies noise-shaping to the quantization noise Q.sub.2 of the second quantizer. The equivalent quantization noise of the inner loop (which can be considered a quantizer on its own) is Q.sub.2/(1+H.sub.b).

[0074] An additional advantage of the system with inner-loop noise-shaping is that the non-linearity of the local feedback DAC is suppressed by the global loop. This means that multi-bit DACs can be applied with less stringent conditions on the linearity.

[0075] It is not required that both quantizers Q.sub.1 and Q.sub.2 operate at the same rate. For instance, the inner feedback loop around Q.sub.2 and possibly also the digital filter with transfer function H.sub.d may be operated at a higher rate compared to the global feedback loop. The first quantizer Q.sub.1 then subsamples the digital filter output H.sub.d.

[0076] In electronic systems process, supply voltage and temperature (PVT) are important sources of variability. The analog filter transfer H.sub.a is typically affected by these PVT effects. For instance, a continuous-time integratora particular choice for the analog filtercan easily have a time constant which deviates 30% from its nominal design value. Even larger deviations may exist, for instance in certain tracking loops where the overall proportionality factor or gain of the error generation block depends on an amplitude of some input signals, as is for instance the case in a multiplier-based phase detector. Another example is a tracking loop position/rotation sensor based on sensing the direction of a magnetic field. The strength of the magnetic field may then represent another variable factor affecting the gain of the analog filter transfer H.sub.a.

[0077] Some embodiments with adaptive schemes are now presented that can provide effective cancellation of Q.sub.1 even in view of variability of the analog transfer function H.sub.a. First, the impact of mismatch is discussed.

[0078] The condition (4) links two digital filters to an analog transfer function H.sub.a. Because the analog transfer function is subject to various sources of variability, the equation is in general not met exactly. In order to investigate the impact of mismatch between the real H.sub.a on the one hand, and the nominal transfer used for the choice of the digital recombination filters H.sub.a,nom=A(z)/B(z) on the other hand, the relative mismatch may be defined as

[00009]$\begin{array}{cc}\left(z\right)=\frac{H_a\left(z\right)}{A\left(z\right)/B\left(z\right)}-1& \left(8\right)\end{array}$

Note that (z) is identical zero if and only if the condition (4) is met.

[0079] Consider, as an example, an uncertainty in the gain K of the analog transfer H.sub.a, which deviates from the nominal value K.sub.nom that is used for sizing the recombination filters A and B. Then, in this case (8) reduces to

[00010]$=\frac{K-K_{\mathrm{nom}}}{K_{\mathrm{nom}}},$

i.e. then represents a measure for the relative deviation of K from K.sub.nom.

[0080] Taking into account a relative mismatch (8), an analysis as set out above can be made. The compensated output D.sub.out is then:

[00011]$\begin{array}{cc}{D}_{\mathrm{out}}\left(z\right)=A\left(z\right).Math.\left\{\left[1+\left(z\right).Math.\mathrm{NTF}\left(z\right)\right].Math.\left(V_i+\frac{1}{H_a\left(z\right)}.Math.Q_2\right)-\left(z\right).Math.\mathrm{NTF}\left(z\right).Math.Q_1\right\}& \left(9\right)\end{array}$

As expected, this equation reduces to expression (5) when =0. From (9), it can be deduced that the analog-to-digital converted output signal D.sub.out as provided by the present invention has a signal transfer function A(z) [1+(z)NTF(z)]. A minor effect of a non-zero is that it somewhat alters the transfer A(z) of the input signal V.sub.i with an extra factor 1+(z)NTF(z). This can in most cases be neglected. In any case the signal transfer function A(z) can be chosen more freely compared to the classical output D.sub.1 which has a signal transfer function determined by the loop filters.
More important for present application are terms in (9) related to Q.sub.1. From the last term of the above expression, it can be seen that a non-zero leads to leakage of Q.sub.1 noise into the compensated output D.sub.out. Luckily, this leaked noise is shaped by NTF(z), which is the noise shaping created by both the analog filter H.sub.a and the digital filter H.sub.d. When referred to the input, the leaked quantization noise is given by (z)NTF(z)/(1+(z)NTF(z))Q.sub.1. For the classical output D.sub.1 of the feedback loop as given by the first expression of (1), one has the input-referred contribution NTF(z)/STF(z)Q.sub.1. The former is preferably smaller in some sense than the latter, which can only be the case when the relative mismatch is restricted in some way. The following theorem can be proven:
If for a definite frequency f one has that

|(z)|<1/(|STF(z)|+|NTF(z)|) with z=exp(j2f)(10)

then the magnitude of the input-referred Q.sub.1 noise at frequency f is smaller for the analog-to-digital converted output signal D.sub.out compared to the magnitude of the input-referred Q.sub.1 noise when using the classical output D.sub.1. Note that (10) is not a necessary condition, but merely provides a convenient sufficient condition. Fortunately, equation (10) is in most cases not very restrictive and relative mismatches in the order of a few percent, even 10% and more are likely to agree with (10). Furthermore, if (10) is met for all frequencies f, it is guaranteed less input-referred Q.sub.1 noise is present in D.sub.out compared to D.sub.1. However, even if expression (10) would be violated for some frequencies, it is still possible that the integrated power of the leaked quantization noise is smaller than the integrated power of the quantization noise Q.sub.1 present in the classical output D.sub.1. In other words, if there is more Q.sub.1-related noise at some frequencies this can be offset by less noise being present at other frequencies. Therefore, it can be concluded that a very broad range of recombination filters A(z) and B(z) exist which result in the analog-to-digital converted output signal D.sub.out being less dependent on the quantization noise Q.sub.1 compared to the classical output D.sub.1 of the feedback loop. The latter may be quantified by comparing the signal-to-noise ratio (SNR) of D.sub.out to the SNR of the classical output D.sub.1. While the recombination filters A(z) and B(z) may be chosen starting from (4) and taking into account the design freedom indicated by (8) and (9), other design procedures are also possible. For instance, one may A(z) and/or B(z) to be parameterized filters, e.g. an FIR filter with variable coefficients, and then determine the optimum filter parameters which maximize the SNR of D.sub.out. When the optimum SNR of D.sub.out turns out to be lower than the SNR of D.sub.1, a choice is obtained for A(z) and B(z) that by construction provides a compensated output D.sub.out being less dependent on the quantization noise Q.sub.1 compared to the classical output D.sub.1 of the feedback loop. Such an optimization approach also provides extra flexibility for introducing a signal transfer function (corresponding to the recombination filter A(z), as explained above) of a preferred form.

[0081] In another embodiment the gain-variability of the analog filter H.sub.a is counteracted by introducing a compensating scale factor, for instance in the second recombination filter. This approach is illustrated in FIG. 7. In this embodiment the second recombination filter (22) comprises a programmable gain G, which allows scaling a signal in accordance with a gain control signal. The gain control signal is generated by a gain controller unit (4) which receives the output of the recombiner block (2) and the quantization noise Q.sub.1. The quantization noise Q.sub.1 can for instance be calculated by subtracting the input of the first quantizer from its output, both input and output being signals in the digital domain. The gain controller unit (4) comprises filtering means D(z) (41) and E(z) (42) for filtering its input signals, a multiplier (43) for making the product of these filtered signals and an adaptation controller (44) which adapts its output until its input signal becomes on the average zero.

[0082] Equation (9) provides the basis for understanding how the above and other more general adaptive schemes operate. For this, expression (9) is rewritten in the following more compact form:

D.sub.out=A(z)V.sub.i+A(z)/H.sub.a(z)Q.sub.2(z)A(z)NTF(z)Q.sub.1(11)

For reasons of clarity, the effect has on the signal transfer function is disregarded. Note that this approximation is not strictly needed, because the adaptive scheme makes small, so the approximation becomes more accurate over time. The three terms in (11), corresponding to V.sub.i, Q.sub.1 and Q.sub.2 respectively, may be considered statistically uncorrelated. Optionally a filter D(z) may now be applied to the analog-to-digital converted output signal D.sub.out e.g. for reducing the signal-related component V.sub.i. For instance, when V.sub.i occupies relatively low frequencies (as may be the case in an angular sensor), D(z) could be a first order difference 1z.sup.1 or a second order difference (1z.sup.1).sup.2 which would largely eliminate the input signal component. The filtered output signal (i.e. D(z)D.sub.out) is then given by eqn. (11) multiplied with D(z). The last term of the filtered output signal is then of the form (z)E(z)Q.sub.1 with E(z)=D(z)A(z)NTF(z). Because A(z), D(z) and also NTF(z) are known digital filter (see equation (2) for the NTF), E(z) is also a known filter. Now Q.sub.1 is a calculable digital signal, and this can be filtered with the filter E(z). The filtered signals D(z)D.sub.out and E(z)Q.sub.1 may then be multiplied, as is done in FIG. 7. The output of this multiplier provides a measure of the relative mismatch (in a statistical sense). This multiplier output may be considered an error signal of the adaptation loop (which is to be minimized). It can indeed be shown that the expected value of the multiplier output is proportional to , because the cross-terms in the product which relate to V.sub.i and Q.sub.2 average to zero (since V.sub.i and Q.sub.2 are uncorrelated to Q.sub.1). Therefore, in accordance with present invention, the recombination filter A(z) and/or B(z) may be taken as adaptive filter. The parameters of the adaptive filter(s) may then be adapted in accordance to methods known in the art for minimizing the error signal, e.g. minimizing this error signal in a mean squared sense.

[0083] While the invention has been illustrated and described in detail in the drawings and foregoing description, such illustration and description are to be considered illustrative or exemplary and not restrictive. The foregoing description details certain embodiments of the invention. It will be appreciated, however, that no matter how detailed the foregoing appears in text, the invention may be practiced in many ways. The invention is not limited to the disclosed embodiments.

[0084] Other variations to the disclosed embodiments can be understood and effected by those skilled in the art in practicing the claimed invention, from a study of the drawings, the disclosure and the appended claims. In the claims, the word comprising does not exclude other elements or steps, and the indefinite article a or an does not exclude a plurality. A single processor or other unit may fulfil the functions of several items recited in the claims. The mere fact that certain measures are recited in mutually different dependent claims does not indicate that a combination of these measures cannot be used to advantage. A computer program may be stored/distributed on a suitable medium, such as an optical storage medium or a solid-state medium supplied together with or as part of other hardware, but may also be distributed in other forms, such as via the Internet or other wired or wireless telecommunication systems. Any reference signs in the claims should not be construed as limiting the scope.