WO2006087667A1 - Ad converter arrangement - Google Patents

Ad converter arrangement Download PDF

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Publication number
WO2006087667A1
WO2006087667A1 PCT/IB2006/050463 IB2006050463W WO2006087667A1 WO 2006087667 A1 WO2006087667 A1 WO 2006087667A1 IB 2006050463 W IB2006050463 W IB 2006050463W WO 2006087667 A1 WO2006087667 A1 WO 2006087667A1
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Prior art keywords
modulator
primary
quantization noise
transfer function
filter
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PCT/IB2006/050463
Other languages
French (fr)
Inventor
Marcel Pelgrom
Kathleen Philips
Petrus A. C. M. Nuijten
Raf L. J. Roovers
Lucien J. Breems
Original Assignee
Koninklijke Philips Electronics N.V.
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Application filed by Koninklijke Philips Electronics N.V. filed Critical Koninklijke Philips Electronics N.V.
Priority to JP2007554725A priority Critical patent/JP2008530890A/en
Priority to EP06710890A priority patent/EP1854217A1/en
Priority to US11/815,980 priority patent/US20080094268A1/en
Publication of WO2006087667A1 publication Critical patent/WO2006087667A1/en

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Classifications

    • H—ELECTRICITY
    • H03—ELECTRONIC CIRCUITRY
    • H03M—CODING; DECODING; CODE CONVERSION IN GENERAL
    • H03M3/00—Conversion of analogue values to or from differential modulation
    • H03M3/30—Delta-sigma modulation
    • H03M3/39—Structural details of delta-sigma modulators, e.g. incremental delta-sigma modulators
    • H03M3/412—Structural details of delta-sigma modulators, e.g. incremental delta-sigma modulators characterised by the number of quantisers and their type and resolution
    • H03M3/414—Structural details of delta-sigma modulators, e.g. incremental delta-sigma modulators characterised by the number of quantisers and their type and resolution having multiple quantisers arranged in cascaded loops, each of the second and further loops processing the quantisation error of the loop preceding it, i.e. multiple stage noise shaping [MASH] type
    • H03M3/418—Structural details of delta-sigma modulators, e.g. incremental delta-sigma modulators characterised by the number of quantisers and their type and resolution having multiple quantisers arranged in cascaded loops, each of the second and further loops processing the quantisation error of the loop preceding it, i.e. multiple stage noise shaping [MASH] type all these quantisers being single bit quantisers

Definitions

  • the invention relates to an AD converter arrangement comprising a primary and a secondary ⁇ -modulator each with an input terminal for receiving an analog input signal, filtering means in a forward path between said input terminal and a quantizer, an output terminal connected to the output of the quantizer and a feedback path connected from the output of the quantizer to the filtering means, the AD converter arrangement further comprising means to apply an analog input signal to the input terminal of the primary ⁇ - modulator, means to isolate the quantization noise generated in the primary ⁇ -modulator, means to apply said isolated quantization noise to the input terminal of the secondary ⁇ - modulator and means to derive a combination of the digital output signals of the two ⁇ - modulators so as to substantially reduce the quantization noise of the primary ⁇ -modulator in said combination.
  • AD-converter arrangement is known from the article "A Cascaded Continuous-time ⁇ -modulator with 67 dB Dynamic Range in 10 MHz Bandwidth" in 2004 IEEE International Solid-State Circuits Conference/ Session 4/Oversampled ADC's/4.1.
  • the ⁇ -modulator has become a leading principle in analog-to- digital (AD) conversion.
  • AD analog-to- digital
  • the order of the filter in the converter determines to a large extend its quality (expressed as signal-to-noise ratio).
  • signal-to-noise ratio the quality of the quantization noise to higher frequencies and therewith the suppression of the noise in the base-band becomes better and consequently the signal to noise ratio and the dynamic range improve.
  • the higher order of the filter causes the loop of the ⁇ -modulator to become potentially unstable. Instability becomes significant at high input voltage excursions.
  • a solution to this problem is found in the so-called cascaded ⁇ -modulator.
  • the primary ⁇ -modulator has a relatively low order so that the stability is not in danger at the cost of higher quantization noise in the frequency band of the input signal.
  • this quantization noise is fed in analog form to the secondary ⁇ -modulator, whose output delivers the quantization noise of the primary ⁇ -modulator in digitized format.
  • the output signals of the two ⁇ -modulators are subtracted from each other so that the quantization noise of the primary ⁇ -modulator is cancelled by the isolated quantization noise digitized by the secondary ⁇ -modulator.
  • the quantization noise originated in the secondary ⁇ -modulator itself is not cancelled, but is of lower level.
  • the quantization noise in the output of the primary ⁇ -modulator is filtered (shaped) with the inverse of the transfer function of the filtering means of this modulator. Therefore in the abovementioned article, the output signal of the secondary ⁇ - modulator is filtered, in the digital domain, with a filter characteristic that is inverted to that of the (analog) filtering means of the primary ⁇ -modulator. If the analog filter of the primary ⁇ -modulator is realized in time discrete switched capacitor technology, then a reasonable match can be obtained between the filtering means of the primary ⁇ -modulator and the inverse digital filter in the output of the secondary ⁇ -modulator. However, if he analog filter is realized in time-continuous technology (e.g. gm-C technology) the component spread forces to apply additional tracking measures such as tuning of one of the filters to the other (as was done in the above mentioned paper on ISSCC2004).
  • time-continuous technology e.g. gm-C technology
  • the present invention has for its object to overcome this inconvenience and the AD-converter arrangement according to the invention is therefore characterized by filtering means in the feedback path of the secondary ⁇ -modulator that have a transfer function which is, for the frequency band of the analog input signal, substantially equal to the transfer function of the open loop of the primary ⁇ -modulator.
  • filtering means in the feedback path of the secondary ⁇ -modulator that have a transfer function which is, for the frequency band of the analog input signal, substantially equal to the transfer function of the open loop of the primary ⁇ -modulator.
  • the transfer function of the feedback path of the secondary modulator has to be a substantial replica of the transfer function of the open loop of the primary modulator.
  • the two transfer functions are realized in the same technology and with the same structure, e.g. both in time discrete switched capacitor technology or both in time-continuous gm-C technology. Further improvements of the matching between the two transfer functions may be obtained when the elements constituting these transfer functions have equal values.
  • the impedances of the secondary modulator could be higher than those of the primary modulator, resulting in lower currents and smaller capacitances than those of the primary modulator and consequently in lesser chip area and lower power consumption.
  • Fig. 1 a first embodiment of an AD converter arrangement according to the invention
  • Fig. 2 a second embodiment of an AD converter arrangement according to the invention.
  • the AD converter arrangement of Figure 1 comprises a standard primary ⁇ - modulator M 1 .
  • This ⁇ -modulator has an input terminal 1 for receiving an analog input signal X(z).
  • This input signal may be a continuous time or a discrete time (sampled) analog signal. In this description the time discrete notation is followed.
  • the input signal is fed through a subtraction point 2 to a filter 3 with transfer function G 1 (Z).
  • the filter 3 is usually a low pass filter and serves the shaping of the quantization noise to higher frequencies, however the invention equally applies to other filter iunctions such as band-pass filtering means.
  • the analog output signal of the filter 3 is applied to a quantizer that delivers a digital signal Y(z) to an output terminal 4 of the ⁇ -modulator.
  • the quantizer is represented by an amplifier 5 with amplification factor C 1 and an addition point 6 through which quantization noise N 1 (Z) is added to the signal.
  • the base band frequency content of the digital signal Y(z) is equal to the input signal of the quantizer multiplied by the factor C 1 and anything else in the digital output signal Y(z) is the quantization noise N 1 (Z).
  • the digital output signal Y(z) of the quantizer is applied through a DA converter 7 to the minus input of the subtraction point 2 so that a closed loop configuration is obtained.
  • the following equation may be derived:
  • the input signal X(z) is preserved substantially without filtering in the digital output signal Y(z).
  • the quantization noise is decreased at the base band frequencies where the product C 1 -G 1 (Z) is large and increases at higher frequencies where this product is small. With other words: the quantization noise is shaped to the higher frequencies above the base band.
  • the shaping of the quantization noise is more effective when the sample rate of the input signal X(z) is higher.
  • the sample rate of the signal is often limited.
  • a different approach is to increase the order of the filter because a higher order filter gives a better noise shaping and therefore a better signal to noise ratio in the base band.
  • a drawback of a higher order filter however is that the loop of the ⁇ - modulator becomes potentially unstable for large signal excursions.
  • the transfer function G 1 (Z) of the filter 3 is chosen of a low filter order (typical first or second order) so that there is still a too high amount of quantization noise in the base band of the output signal Y(z). This is reduced in the following way: the quantization noise N 1 (Z) is isolated, the isolated quantization noise is digitized in a secondary ⁇ -modulator M 2 and the so digitized quantization noise Z(z) is subtracted from the output signal Y(z) in a subtraction point S to obtain a signal Y(z)-Z(z) with reduced quantization noise.
  • the quantization noise N 1 (Z) is isolated in the analog domain by means of an amplifier 8 with amplification iactor C 1 and a subtraction point 9.
  • the amplifier 8 is needed because the interconnection between the amplifier 5 and the addition point 6 is not accessible in practice.
  • the subtraction point 9 delivers the quantization noise N 1 (z) without signal component, provided that the amplification of the amplifier 8 is equal to the base band amplification (C 1 ) of the quantizer (5,6) and provided that the amplification d of the DA converter 7 is unity.
  • the DA converter provides some amplification or attenuation (d ⁇ 1) the amplification of the amplifier 8 has to be C 1 . d.
  • the isolated noise N 1 (Z) is fed as input signal to a secondary ⁇ -modulator M 2 in which the signal is applied through a subtraction point 10 and a low pass filter 11 with transfer function G 2 (z) to a quantizer (12, 13).
  • This quantizer is again represented by an amplifier 12 with amplification iactor C 2 and an addition point 13 where quantization noise N 2 (z) is added.
  • the digital output signal Z(z) of the quantizer is fed back to the minus input of the subtraction point 10 through a feed-back path comprising in cascade an AD-converter 14, a filter 15 with transfer function G'i(z) and an amplifier 16 with amplification C 1 .
  • the following equation applies:
  • the stability in the secondary ⁇ -modulator is better controlled as this ⁇ - modulator sees less strong excursions then the primary ⁇ -modulator. Moreover any malfunction of the secondary ⁇ -modulator can be suppressed with limiters thereby only slightly reducing the overall performance, as the primary ⁇ -modulator will continue to work correctly.
  • the amplification factors d of the two DA converters need not to be unity, but for optimum noise suppression they have to be equal. It is also noted that usually a digital delay of some sample-periods (not shown in the figure) is included in the output lead (4) of the primary ⁇ -modulator to cope with the intrinsic delay of the secondary ⁇ -modulator. It is apparent from equation (IV) that the output signal Y(z) -Z(z) of the arrangement still has in band quantization noise N 2 (z) originating from the secondary ⁇ - modulator M 2 . However this noise is shaped by both filters G 1 (Z) and G 2 (z). Therefore, when each of these filters is a 2 nd order filter, the noise N 2 (z) is effectively shaped by a 4 th order filter, without the stability of the primary ⁇ -modulator being endangered. As stated above the transfer function of the feedback path of the secondary
  • ⁇ -modulator M 2 has to correspond with the open loop transfer function of the primary ⁇ - modulator M 1 .
  • This also holds for a ⁇ -modulator with more complicated filter structures then the single filter G 1 (Z).
  • This is illustrated in Figure 2 in which elements that correspond with those of Figure 1 have been given the same reference numerals.
  • the primary ⁇ -modulator of Figure 2 contains a filter 21 with transfer function G la (z), a subtraction point 22 and a second filter 23 with transfer function G ll3 (z) in cascade.
  • the output signal Y(z) is, after DA conversion in the DA converter 7, applied directly to the minus input of subtraction point 2 and, through a sealer 24 with scaling factor ⁇ , to the minus input of subtraction point 22.
  • ⁇ -modulators with such more complicated filter structures are well known in the art, see for instance applicants' prior patent application (PHNL 030766).
  • the open loop transfer function of this ⁇ -modulator i.e. the transfer function from for instance the output of addition point 6 through the elements 7, 2, 21, 22, 23, 24 and 5 to the input of addition point 6, is equal to ⁇ /. ⁇ G l ⁇ (z) + ⁇ .G li .Ci .
  • the feedback path of the secondary ⁇ -modulator M 2 should have the same transfer function.
  • This is implemented in Figure 2 by the cascade of the DA converter 14, a filter 25 with transfer function G la (z), an addition point 26, a filter 27 with transfer function G ll3 (z) and the amplifier 16.
  • the output of the DA converter 14 is applied through a sealer 28 with scaling factor ⁇ to the addition point 26.
  • These six elements together constitute a path with transfer function d. ⁇ G la (z) + ⁇ ⁇ .G lb .C 1 i.e. the same as the open loop transfer of the modulator M 1 .
  • the elements may be identical in implementation to the corresponding elements of the primary ⁇ -modulator so that optimum filter matching is obtained.

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  • Engineering & Computer Science (AREA)
  • Theoretical Computer Science (AREA)
  • Compression, Expansion, Code Conversion, And Decoders (AREA)

Abstract

In an AD converter a primary ΣΔ-modulator digitizes the analog input signal. The quantization noise generated thereby is isolated in the analog domain and digitized in a secondary ΣΔ-modulator. The quantization noise so digitized by the secondary ΣΔ-modulator is subtracted from the quantization noise in the output of the primary ΣΔ-modulator. Because the quantization noise generated by the primary ΣΔ-modulator is subject to filtering (shaping) the quantization noise digitized in the secondary ΣΔ-modulator should also be filtered. This is performed by similar filtering in the feedback path of the secondary ΣΔ-modulator.

Description

AD converter arrangement
The invention relates to an AD converter arrangement comprising a primary and a secondary ΣΔ-modulator each with an input terminal for receiving an analog input signal, filtering means in a forward path between said input terminal and a quantizer, an output terminal connected to the output of the quantizer and a feedback path connected from the output of the quantizer to the filtering means, the AD converter arrangement further comprising means to apply an analog input signal to the input terminal of the primary ΣΔ- modulator, means to isolate the quantization noise generated in the primary ΣΔ-modulator, means to apply said isolated quantization noise to the input terminal of the secondary ΣΔ- modulator and means to derive a combination of the digital output signals of the two ΣΔ- modulators so as to substantially reduce the quantization noise of the primary ΣΔ-modulator in said combination. Such AD-converter arrangement is known from the article "A Cascaded Continuous-time ΣΔ-modulator with 67 dB Dynamic Range in 10 MHz Bandwidth" in 2004 IEEE International Solid-State Circuits Conference/ Session 4/Oversampled ADC's/4.1.
Presently the ΣΔ-modulator has become a leading principle in analog-to- digital (AD) conversion. In ΣΔ-modulators the order of the filter in the converter determines to a large extend its quality (expressed as signal-to-noise ratio). At higher orders the shaping of the quantization noise to higher frequencies and therewith the suppression of the noise in the base-band becomes better and consequently the signal to noise ratio and the dynamic range improve. However the higher order of the filter causes the loop of the ΣΔ-modulator to become potentially unstable. Instability becomes significant at high input voltage excursions. A solution to this problem is found in the so-called cascaded ΣΔ-modulator. Two ΣΔ- modulators are now employed: the primary ΣΔ-modulator has a relatively low order so that the stability is not in danger at the cost of higher quantization noise in the frequency band of the input signal. By means of a subtraction point this quantization noise is fed in analog form to the secondary ΣΔ-modulator, whose output delivers the quantization noise of the primary ΣΔ-modulator in digitized format. Subsequently the output signals of the two ΣΔ-modulators are subtracted from each other so that the quantization noise of the primary ΣΔ-modulator is cancelled by the isolated quantization noise digitized by the secondary ΣΔ-modulator. The quantization noise originated in the secondary ΣΔ-modulator itself is not cancelled, but is of lower level. However, the quantization noise in the output of the primary ΣΔ-modulator is filtered (shaped) with the inverse of the transfer function of the filtering means of this modulator. Therefore in the abovementioned article, the output signal of the secondary ΣΔ- modulator is filtered, in the digital domain, with a filter characteristic that is inverted to that of the (analog) filtering means of the primary ΣΔ-modulator. If the analog filter of the primary ΣΔ-modulator is realized in time discrete switched capacitor technology, then a reasonable match can be obtained between the filtering means of the primary ΣΔ-modulator and the inverse digital filter in the output of the secondary ΣΔ-modulator. However, if he analog filter is realized in time-continuous technology (e.g. gm-C technology) the component spread forces to apply additional tracking measures such as tuning of one of the filters to the other (as was done in the above mentioned paper on ISSCC2004).
The present invention has for its object to overcome this inconvenience and the AD-converter arrangement according to the invention is therefore characterized by filtering means in the feedback path of the secondary ΣΔ-modulator that have a transfer function which is, for the frequency band of the analog input signal, substantially equal to the transfer function of the open loop of the primary ΣΔ-modulator. When the feedback path of the primary ΣΔ-modulator does not have any filtering, then the open loop transfer function of this ΣΔ-modulator corresponds with the transfer function of its forward path and consequently the filtering in the feedback path of the secondary ΣΔ-modulator corresponds to the filtering in the forward path of the primary ΣΔ-modulator. On the other hand, when for any reason, e.g. for some filtering of the desired base band signals or for stability reasons, some filtering is included in the feedback path of the primary modulator or multiple feedback paths are provided to various points of the forward path of the primary modulator, then the transfer function of the feedback path of the secondary modulator has to be a substantial replica of the transfer function of the open loop of the primary modulator.
Preferably, to improve the tracking between the transfer functions of the open loop of the primary ΣΔ-modulator and the feedback path of the secondary ΣΔ-modulator the two transfer functions are realized in the same technology and with the same structure, e.g. both in time discrete switched capacitor technology or both in time-continuous gm-C technology. Further improvements of the matching between the two transfer functions may be obtained when the elements constituting these transfer functions have equal values. However because lower requirements with regard to dynamic range and S/N ratio have to be met by the secondary ΣΔ-modulator the impedances of the secondary modulator could be higher than those of the primary modulator, resulting in lower currents and smaller capacitances than those of the primary modulator and consequently in lesser chip area and lower power consumption.
The invention will be described with reference to the accompanying figures. Herein shows:
Fig. 1 a first embodiment of an AD converter arrangement according to the invention and
Fig. 2 a second embodiment of an AD converter arrangement according to the invention.
The AD converter arrangement of Figure 1 comprises a standard primary ΣΔ- modulator M1. This ΣΔ-modulator has an input terminal 1 for receiving an analog input signal X(z). This input signal may be a continuous time or a discrete time (sampled) analog signal. In this description the time discrete notation is followed. The input signal is fed through a subtraction point 2 to a filter 3 with transfer function G1(Z). The filter 3 is usually a low pass filter and serves the shaping of the quantization noise to higher frequencies, however the invention equally applies to other filter iunctions such as band-pass filtering means. The analog output signal of the filter 3 is applied to a quantizer that delivers a digital signal Y(z) to an output terminal 4 of the ΣΔ-modulator. In Figure 1 the quantizer is represented by an amplifier 5 with amplification factor C1 and an addition point 6 through which quantization noise N1(Z) is added to the signal. The base band frequency content of the digital signal Y(z) is equal to the input signal of the quantizer multiplied by the factor C1 and anything else in the digital output signal Y(z) is the quantization noise N1(Z). Finally the digital output signal Y(z) of the quantizer is applied through a DA converter 7 to the minus input of the subtraction point 2 so that a closed loop configuration is obtained. For this ΣΔ-modulator the following equation may be derived:
Figure imgf000006_0001
When for the base band frequencies of X(z) the amplification C1G1(Z) of the forward path of the ΣΔ-modulator is substantially larger then 1, this equation simplifies to
Figure imgf000006_0002
Therefore, the input signal X(z) is preserved substantially without filtering in the digital output signal Y(z). In contradistinction therewith the quantization noise is decreased at the base band frequencies where the product C1-G1(Z) is large and increases at higher frequencies where this product is small. With other words: the quantization noise is shaped to the higher frequencies above the base band.
The shaping of the quantization noise is more effective when the sample rate of the input signal X(z) is higher. However in practical transmission systems the sample rate of the signal is often limited. A different approach is to increase the order of the filter because a higher order filter gives a better noise shaping and therefore a better signal to noise ratio in the base band. A drawback of a higher order filter however is that the loop of the ΣΔ- modulator becomes potentially unstable for large signal excursions.
In the arrangement of Figure 1 the transfer function G1(Z) of the filter 3 is chosen of a low filter order (typical first or second order) so that there is still a too high amount of quantization noise in the base band of the output signal Y(z). This is reduced in the following way: the quantization noise N1(Z) is isolated, the isolated quantization noise is digitized in a secondary ΣΔ-modulator M2 and the so digitized quantization noise Z(z) is subtracted from the output signal Y(z) in a subtraction point S to obtain a signal Y(z)-Z(z) with reduced quantization noise.
The quantization noise N1(Z) is isolated in the analog domain by means of an amplifier 8 with amplification iactor C1 and a subtraction point 9. The amplifier 8 is needed because the interconnection between the amplifier 5 and the addition point 6 is not accessible in practice. It can easily be shown that the subtraction point 9 delivers the quantization noise N1 (z) without signal component, provided that the amplification of the amplifier 8 is equal to the base band amplification (C1) of the quantizer (5,6) and provided that the amplification d of the DA converter 7 is unity. In case the DA converter provides some amplification or attenuation (d ≠ 1) the amplification of the amplifier 8 has to be C1. d. The isolated noise N1(Z) is fed as input signal to a secondary ΣΔ-modulator M2 in which the signal is applied through a subtraction point 10 and a low pass filter 11 with transfer function G2(z) to a quantizer (12, 13). This quantizer is again represented by an amplifier 12 with amplification iactor C2 and an addition point 13 where quantization noise N2(z) is added. The digital output signal Z(z) of the quantizer is fed back to the minus input of the subtraction point 10 through a feed-back path comprising in cascade an AD-converter 14, a filter 15 with transfer function G'i(z) and an amplifier 16 with amplification C1. For this secondary ΣΔ-modulator the following equation applies:
Figure imgf000007_0001
In case the loop gain of the secondary ΣΔ-modulator C1C1(Z)C2C2(Z) is substantially larger then 1 this equation simplifies to
Figure imgf000007_0002
It is noted that, when the transfer function C1(Z) of the filter 15 is (substantially) equal to the transfer function G1(Z) of the filter 3 and the two amplification factors C1(Z) and C1 '(z) are also equal, the term for N1(Z) in this equation (IV) is the same as the term for N1(Z) in equation (II) for the output signal Y(z) of the primary ΣΔ-modulator. Then the output signal Y(z) - Z(z) of the subtraction point S is equal to:
Figure imgf000007_0003
This result is obtained with a filter 15 in the feedback path of the secondary ΣΔ-modulator that has the same transfer function as the filter 3 in the forward path of the primary ΣΔ-modulator. Moreover the two filters are both in the analog domain and therefore may be implemented in the same technology. The two filters 3 and 15 can therefore be made with perfect matching with the result that optimal suppression of the N1(Z) noise in the output of the arrangement can be obtained. This in contrast to the prior art arrangement of the above mentioned article in which the filtering of the quantization noise N1(Z) is realized by a filter in the output lead of the secondary ΣΔ-modulator. The transfer function of this filter should be inverse to the filter G1(Z) of the primary ΣΔ-modulator and has to be implemented in the digital domain. The stability in the secondary ΣΔ-modulator is better controlled as this ΣΔ- modulator sees less strong excursions then the primary ΣΔ-modulator. Moreover any malfunction of the secondary ΣΔ-modulator can be suppressed with limiters thereby only slightly reducing the overall performance, as the primary ΣΔ-modulator will continue to work correctly.
In the above explanation of the operation of the arrangement of Figure 1 it has been assumed that the two DA-converters 7 and 14 have no amplification or attenuation (d = 1). A further analysis of the arrangement of the invention shows that for optimum suppression of the N1(Z) noise the transfer function of the feedback path of the secondary ΣΔ- modulator M2 should be equal to the open loop transfer function of the primary ΣΔ- modulator M1. In the arrangement of Figure 1 the open loop transfer function of the modulator M1 is d.G1(z).C1 whereas he transfer function of the feedback path of the modulator M2 is also d.G1(z).C1. Therefore the amplification factors d of the two DA converters need not to be unity, but for optimum noise suppression they have to be equal. It is also noted that usually a digital delay of some sample-periods (not shown in the figure) is included in the output lead (4) of the primary ΣΔ-modulator to cope with the intrinsic delay of the secondary ΣΔ-modulator. It is apparent from equation (IV) that the output signal Y(z) -Z(z) of the arrangement still has in band quantization noise N2(z) originating from the secondary ΣΔ- modulator M2. However this noise is shaped by both filters G1(Z) and G2(z). Therefore, when each of these filters is a 2nd order filter, the noise N2(z) is effectively shaped by a 4th order filter, without the stability of the primary ΣΔ-modulator being endangered. As stated above the transfer function of the feedback path of the secondary
ΣΔ-modulator M2 has to correspond with the open loop transfer function of the primary ΣΔ- modulator M1. This also holds for a ΣΔ-modulator with more complicated filter structures then the single filter G1(Z). This is illustrated in Figure 2 in which elements that correspond with those of Figure 1 have been given the same reference numerals. Instead of the single filter 3 in the primary ΣΔ-modulator of Figure 1 the primary ΣΔ-modulator of Figure 2 contains a filter 21 with transfer function Gla(z), a subtraction point 22 and a second filter 23 with transfer function Gll3(z) in cascade. The output signal Y(z) is, after DA conversion in the DA converter 7, applied directly to the minus input of subtraction point 2 and, through a sealer 24 with scaling factor α, to the minus input of subtraction point 22. ΣΔ-modulators with such more complicated filter structures are well known in the art, see for instance applicants' prior patent application (PHNL 030766). The open loop transfer function of this ΣΔ-modulator, i.e. the transfer function from for instance the output of addition point 6 through the elements 7, 2, 21, 22, 23, 24 and 5 to the input of addition point 6, is equal to </.{GlΛ (z) + α}.Gli.Ci .
To obtain optimal suppression of the quantization noise N1(Z) in the output signal of the arrangement, the feedback path of the secondary ΣΔ-modulator M2 should have the same transfer function. This is implemented in Figure 2 by the cascade of the DA converter 14, a filter 25 with transfer function Gla(z), an addition point 26, a filter 27 with transfer function Gll3(z) and the amplifier 16. Moreover the output of the DA converter 14 is applied through a sealer 28 with scaling factor α to the addition point 26. These six elements together constitute a path with transfer function d.{Gla (z) + α }.Glb .C1 i.e. the same as the open loop transfer of the modulator M1. The elements may be identical in implementation to the corresponding elements of the primary ΣΔ-modulator so that optimum filter matching is obtained.

Claims

CLAIMS:
1. AD converter arrangement comprising a primary (M1) and a secondary (M2) ΣΔ-modulator each with an input terminal for receiving an analog input signal, filtering means in a forward path between said input terminal and a quantizer, an output terminal connected to the output of the quantizer and a feedback path connected from the output of the quantizer to the filtering means, the AD converter arrangement further comprising means (1) to apply an analog input signal to the input terminal of the primary ΣΔ-modulator, means (7,8) to isolate the quantization noise N1(Z) generated in the primary ΣΔ-modulator, means to apply said isolated quantization noise to the input terminal of the secondary ΣΔ-modulator and means (S) to derive a combination of the digital output signals of the two ΣΔ-modulators so as to substantially reduce the quantization noise of the primary ΣΔ-modulator in said combination characterized by filtering means (14, 15, 16) in the feedback path of the secondary ΣΔ-modulator that have a transfer function which is, for the frequency band of the analog input signal, substantially equal to the transfer function of the open loop of the primary ΣΔ-modulator.
2. Arrangement as claimed in claim 1 characterized in that the transfer function of the open loop of the primary ΣΔ-modulator and of the feedback path of the secondary ΣΔ- modulator are implemented in the same technology and with the same structure.
3. Arrangement as claimed in claim 2 characterized in that the impedance level of elements of the feedback path of the secondary modulator is higher than that of the corresponding elements of the feedback path and the forward path of the primary modulator.
PCT/IB2006/050463 2005-02-15 2006-02-13 Ad converter arrangement WO2006087667A1 (en)

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JP2007554725A JP2008530890A (en) 2005-02-15 2006-02-13 AD converter
EP06710890A EP1854217A1 (en) 2005-02-15 2006-02-13 Ad converter arrangement
US11/815,980 US20080094268A1 (en) 2005-02-15 2006-02-13 Ad Converter Arrangement

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CN102270990B (en) * 2010-06-01 2013-09-25 北京大学深圳研究生院 Modulator and designing method thereof
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US20080094268A1 (en) 2008-04-24

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