WO2006008188A1 - A method and apparatus for analog-to-digital conversion with symmetry correction - Google Patents

A method and apparatus for analog-to-digital conversion with symmetry correction Download PDF

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Publication number
WO2006008188A1
WO2006008188A1 PCT/EP2005/008740 EP2005008740W WO2006008188A1 WO 2006008188 A1 WO2006008188 A1 WO 2006008188A1 EP 2005008740 W EP2005008740 W EP 2005008740W WO 2006008188 A1 WO2006008188 A1 WO 2006008188A1
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Prior art keywords
signal
converter
output
analog
complex
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PCT/EP2005/008740
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French (fr)
Inventor
Michel Robbe
Roland Stoffel
Stephan Doucet
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Eads Secure Networks
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Publication of WO2006008188A1 publication Critical patent/WO2006008188A1/en

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    • HELECTRICITY
    • H03ELECTRONIC CIRCUITRY
    • H03MCODING; DECODING; CODE CONVERSION IN GENERAL
    • H03M3/00Conversion of analogue values to or from differential modulation
    • H03M3/30Delta-sigma modulation
    • H03M3/322Continuously compensating for, or preventing, undesired influence of physical parameters
    • H03M3/324Continuously compensating for, or preventing, undesired influence of physical parameters characterised by means or methods for compensating or preventing more than one type of error at a time, e.g. by synchronisation or using a ratiometric arrangement
    • HELECTRICITY
    • H03ELECTRONIC CIRCUITRY
    • H03MCODING; DECODING; CODE CONVERSION IN GENERAL
    • H03M3/00Conversion of analogue values to or from differential modulation
    • H03M3/30Delta-sigma modulation
    • H03M3/39Structural details of delta-sigma modulators, e.g. incremental delta-sigma modulators
    • H03M3/40Arrangements for handling quadrature signals, e.g. complex modulators

Definitions

  • the present invention relates to analog-to-digital converters of complex signals having two channels in quadrature. More particularly, the invention addresses the problem of symmetry in signal processing between the two channels in a complex bandpass converter.
  • analog-to-digital converters there exist so-called sigma-delta analog-to-digital converters. These converters present an oversampling frequency that is well above the Nyquist frequency of the input signal, and as a result they make it possible to obtain a large amount of resolution for relatively low cost.
  • Converters of that type also enable quantization noise to be rejected to outside the working frequency band of the output signal, which band possesses a center frequency f 0 .
  • quantization noise is controlled by the combined action of feedback loop- signals and a complex filter.
  • Bandpass sigma-delta converters can convert complex analog signals into complex digital signals. They then present two channels in quadrature, conventionally referenced I for in-phase and Q for quadrature.
  • Such converters present advantages over real signal converters in terms of stability and width of the passband.
  • Figure 1 shows a complex bandpass sigma-delta converter for converting a complex analog signal into a complex digital signal.
  • a converter comprises two channels in quadrature referenced I and Q. Each channel has an input 101, 102.
  • the incoming signal on the input 101, 102 is added by means of a respective adder 103, 104 to the feedback loop signal 114, 115.
  • the signal then passes through a complex filter 105. It is then processed by respective quantizers 106, 107 before being delivered on respective outputs 108, 109.
  • Each feedback loop includes at least one digital-to-analog converter 112, 113 for providing the feedback signal.
  • FIG. 2 is a graph plotting a curve 202 showing the shape of noise from a complex signal converter.
  • noise is rejected to outside the working frequency band 201 of center frequency f 0 , thereby enabling the signal/noise ratio to be improved, and as a result improving the performance of the converter.
  • the invention is based on the observation that the rejection of quantization noise to outside the working frequency band of the signal is very sensitive to the processing on the I and Q channels being symmetrical. Any asymmetry in signal processing between these tlwo channels leads to quantization noise being folded 'into the working frequency band of the signal output by the converter, and as a result considerably degrades the signal/noise ratio of the converter. Such asymmetry may relate to the phase of the signal or to gain.
  • symmetry and asymmetry are used below with reference to the symmetry or asymmetry on the I and Q channels that relates to gain.
  • a quantization noise signal is obtained at the output from the converter at the center frequency of the working signal, and of amplitude that is substantially proportional to the symmetry error between the I and Q channels.
  • US patent No. 6 329 939 proposes averaging symmetry errors by using a common integrator for integrating the incoming real and imaginary signals.
  • the common integrator is used in alternation on one channel and then on the other channel of the converter.
  • Such a converter consumes a large amount of time and energy for putting the common integrator back into the initial state on each change of channel.
  • the present invention seeks to mitigate those drawbacks.
  • the present invention provides a method of adjusting an analog-to-digital converter having two channels in quadrature, each having an associated input and output, for converting a complex analog input signal into a complex digital output signal in a working frequency band having a determined center frequency f 0 , each output being looped back to the associated input in such a manner as to form first and second feedback loops.
  • the method comprises the steps consisting in: • injecting a first reference signal into said first feedback loop and simultaneously a second reference signal into said second feedback loop, said first and second signals being synchronized to each other so as to form a complex signal centered on an image frequency of said determined center frequency;
  • the analog-to-digital bandpass ⁇ igma- delta converter of complex signals is preferably a multibit converter.
  • the feedback signals in the feedback loops are encoded on a plurality of bits and control can be performed with relatively high precision.
  • the amplitude of the signal output in the working frequency band is substantially proportional to the symmetry error between the I and Q channels, as is described in the section below.
  • one or more electronic components are adjusted in order to reduce the amplitude of the signal in the working frequency band. This enables the asymmetry between the I and Q channels to be corrected.
  • the amplitude of the signal at the center frequency f 0 is reduced, that means that the quantization noise has been rejected to outside the working frequency band of the output signal, arid as a result the asymmetry between the I and Q channels has ' been corrected.
  • an embodiment of the present invention enables the channel symmetry of a bandpass analog-to-digital converter for complex signals to be adjusted before it is used in order to increase its signal-to-noise ratio, and thus improve its conversion performance on complex signals during normal operation.
  • a frequency band is determined about the center frequency prior to performing the steps consisting in:
  • each of the two feedback loops can also be advantageous for each of the two feedback loops to include an electronic component suitable for being adjusted.
  • the invention covers any method of evaluating the amplitude of an output signal at the center frequency or in a frequency band about the center of frequency.
  • the adjustment value for the electronic component can be determined efficiently.
  • the invention also covers any other method enabling an adjustment value to be determined for the electronic component in order to reduce the amplitude of the output signal.
  • said value is preferably stored for use of the analog-to- digital converter during normal operation outside
  • the invention provides a ⁇ analog-to-digital converter having two channels in' quadrature each comprising an associated input and output, for converting a complex analog input signkl into a complex digital output signal in a working frequency band having a determined center frequency f 0 , each output being looped back to the associated input so as to form first and second feedback loops.
  • the converter comprises:
  • At least one adjustable electronic component for reducing the amplitude of the output signal at the center frequency f 0 , said electronic component being included in the first and/or the second feedback loop.
  • Such a converter may include a signal generator for injecting the first and second reference signals.
  • such a converter includes a first signal generator for injecting the first reference signal and a second signal generator for injecting the second reference signal, with the first and second generators being synchronized.
  • the first generator respectively the second generator, comprises a multiplexer stage adapted to shift the first feedback loop signal digitally, respectively the second feedback loop signal, and thus inject the first reference signal, respectively the second reference signal.
  • the first generator respectively the second generator, comprises an adder and/or subtracter stage adapted to perform addition or substraction on the first feedback loop signal, respectively the second feedback loop signal, and thus inject the first reference signal, respectively the second reference signal.
  • the converter further includes a link with a detector unit adapted to detect an output signal and to send signal detection information to said converter via said connection. Under such circumstances, in the converter, an output signal at the frequency f 0 is detected by receiving said information from said detector unit.
  • a converter further includes a detector unit adapted to detect an output signal. Under such circumstances, in the converter, an output signal is detected at the frequency f 0 via the detector unit, with said detection being performed locally.
  • a converter may also include means for determining an adjustment value of the electronic component as a function of the power value of the output signal at the center frequency. The power value can then be calculated by the signal detector unit, regardless of whether the signal detector unit is included within the converter or is external to the converter. If it is external, the power value is sent over the connection.
  • a frequency band is determined around the center frequency.
  • the converter then further includes, means for determining an adjustment value for the electronic component as a function of a power value of the output signal inl said determined frequency band, said power value preferably being calculated by the signal detector unit, regardless of whether the signal detector unit is included within the converter or is external to the converter. Whbn it is external, the power value is transmitted over the connection.
  • the converter preferably further includes a memory for storing the adjustment value for use of the analog- to-digital converter in normal operation outside an adjustment stage.
  • the present invention provides an analog-to-digital conversion method for converting a complex analog input signal into a complex digital output signal in a working frequency band having a determined center frequency f 0 by a converter having two channels in quadrature each having an associated input and output, each output being looped back to said associated input in such a manner as to form first and second feedback loops, in which at least one electronic component included in the first and/or second feedback loop applies a stored and predetermined value for adjusting the symmetry of the two channels.
  • Such a conversion method thus enables complex analog signals to be converted into complex digital signals presenting very good performance.
  • the present invention provides an analog-to-digital converter for converting a complex analog input signal into a complex digital output signal in a working frequency band having a determined center • frequency f 0 , said converter having two channels in quadrature each comprising an associated input and output, each output being looped back to said associated input in such a manner as to form first and second feedback loops, in which at least one electronic component included in the first and/or second feedback loop is adapted to apply a stored and predetermined value for adjusting the symmetry of the two channels.
  • Such a converter when adjusted using the method of the first aspect of the present invention presents symmetry of processing in the I and Q channels enabling very good performance to be obtained.
  • Figure 1 is a block diagram of a complex bandpass sigma-delta analog-to-digital converter of the prior art, as described above;
  • Figure 2 is a graph plotting the shape of noise from a bandpass sigma-delta analog-to-digital converter of complex signals, as described above;
  • Figure 3 is a block diagram of a complex bandpass sigma-delta analog-to-digital converter constituting an embodiment of the present invention
  • Figure 4 is a graph plotting the shape of quantization noise while adjusting a bandpass sigma-delta analog-to-digital converter constituting an embodiment of the present invention
  • Figure 5 is a block diagram of a complex bandpass sigma-delta analog-to-digital converter constituting an embodiment of the present invention
  • Figure 6 shows a feedback loop of a complex bandpass sigma-delta converter in a preferred embodiment of the present invention
  • Figure 7 shows the various states of counters on the I and Q channels in an embodiment of the inveption
  • Figure 8 shows a digital reference signal generator with shifting in an embodiment of the present invention
  • Figure 9 is a block diagram of a complex bandpass sigma-delta analog-to-digital converter constituting an embodiment of the present invention.
  • FIG. 3 shows a complex sigma-delta analog-to- digital converter 300 constituting an embodiment of the present invention.
  • the analog-to-digital converter comprises a complex filter 105, a respective quantizer 106 or 107 on each of its outputs 108 and 109, and a feedback loop from each of its outputs 108 and 109 towards the corresponding input 101 or 102.
  • Each feedback loop comprises at least a digital-to-analog converter 111 or 113, for generating the corresponding feedback signal 114, 115. These feedback signals are added to the input signals via the respective adders 103 and 104.
  • the inputs 101 and 102 are short-circuited. Then a reference signal is injected into each of the feedback loops of the I and Q channels.
  • the feedback loops.110 and 111 include respective adders 301, 302.
  • a first generator 306 injects a first reference signal via the adder 301.
  • a second generator 307 injects a second reference signal via the adder 302.
  • the first and second reference signals are synchronous, with the first and second generators being synchronized.
  • the first and second reference signals form a complex signal of frequency equal to the image frequency of the center frequency f 0 of the working frequency band of the output signal from the converter 300. ' • • .
  • the present invention covers any configuration enabling a complex signal to be injected at the image frequency of a determined frequency f 0 .
  • the first and second reference signals may be generated in particular by a single generator.
  • the generator (s) is/are included in the complex bandpass sigma-delta converter.
  • FIG. 6 shows a first feedback loop for a complex bandpass converter 300 in which a reference signal is injected in a preferred embodiment of the present invention, with the architecture of the second feedback loop being similar.
  • the generator 306 of the first feedback loop is included in the feedback loop in this example.
  • the generator 306 is a digital generator, injecting a cyclical reference signal by digitally shifting the signal input into the generator 306, the cyclical reference signal presenting a fundamental component at an image frequency of the fundamental frequency of the output signal in the feedback loop.
  • a generator is suitable for being activated by a control signal.
  • the structure for making such a generator is based on a multiplexer stage performing digital shifting on the signal input into the generator 306. This shifting corresponds either to one bit up or to one bit down depending on the control signal.
  • the signal is conventionally represented in the form of a bar graph or "thermometer" .
  • the control signal can be supplied by an 8-state counter 601 of programmable initial state.
  • the two generators in the two feedbacks are synchronized. Thus, it is easy to adjust the phase difference on the channels I and Q by acting on the synchronization between the two generators.
  • Figure 7 shows the various states of the counters on the channels I and Q in an embodiment of the invention.
  • the states 71 of the counter 601 supplying the control signal to the generator 306 that is included in the first feedback loop.
  • the states 72 of the counter supplying the control signal to the generator that is included in the sebond feedback loop.
  • the signal 73 is injected into the first feedback loop of the channel I
  • the signal 74 is injected into the second feedback loop of the channel Q.
  • the fundamental component of the channel I may be written Scos (2 ⁇ f 0 t) and the fundamental component of the channel Q can be written -Ssin (2 ⁇ f 0 t) , where f 0 is the fundamental frequency of the output signal and S is the amplitude of the output signal.
  • Figure 8 shows such a digital generator 306 with shifting. The value of the input signal 82 to the generator 306 is shifted as a function of the control signal 81 that has three states, 1, 0, or -1, thereby giving an output signal 83 corresponding to the feedback loop signal received at the input of the generator 306 plus the signal injected by the generator.
  • a method of injecting reference signals as described above is particularly well adapted to a multibit complex bandpass sigma-delta analog-to-digital converter. Preferably, such a converter operates at an . oversampling frequency that is eight times greater than the Nyquist frequency of the input signal. Under such circumstances, a digital generator with shifting as described above is easier to implement than at other oversampling
  • such a digital generator with shifting does not introduce errors into the method of adjustment in an embodiment of the invention.
  • the first reference signal can be written in the following form:
  • the amplitude A of such a signal is preferably determined in such a manner that the complex filter is not saturated so that its linearity property is conserved.
  • a signal is detected at the output from the converter with a component at the center frequency f 0 having amplitude that is substantially proportional to the symmetry error between the channels I and Q.
  • This component corresponds to the quantization noise multiplied by the symmetry error between the two channels and taken to the center frequency of the working signal.
  • a line 402 can be seen at the frequency f 0 . In such a context of asymmetry between the channels I and Q, it can be seen that a sigma-delta converter no longer rejects quantization noise to outside the working frequency band.
  • a working frequency band 401 is determined around the center frequency f 0 .
  • the signal output by the converter in the determined working frequency band is detected.
  • Such detection is performed by a detector unit 310.
  • the signal detected in this way in the frequency band 401 is of an amplitude that is substantially proportional to the quantization noise signal.
  • output signal detection is performed by calculating the power of the output signal.
  • the detector unit is marked as being a power measuring unit 310. Nevertheless, the present invention also covers other methods of detecting the output signal.
  • the detected signal corresponds solely to the quantization noise signal associated with the asyrtimetry of the channels I and Q. Otherwise, particularly ' when matching differences between the current sources used by the digital-to-analog converters in the feedback lbops give rise to errors that can generate a noise signal in the working frequency band 401, then the noise signal detected at the output can comprise both quantization noise due to asymmetry between the channels I and Q and also the noise coming from other types of error. The noise coming from types of error other than symmetry error between the channels I and Q is negligible, particularly when the injected reference signals are of relatively high amplitude A.
  • the present invention thus makes it possible to reduce very significantly the quantization noise of the complex analog-to-digital converter, regardless of whether or not the converter presents noise of some other type in the determined working frequency band.
  • the noise signal at the output from the analog-to- digital converter is preferably detected by the power measuring unit 310.
  • the power value of the output signal is calculated by the unit for measuring signal power.
  • the power measuring unit 310 may be included in the converter 300 as shown in Figure 3, or else it may be external to the converter 300 as -shown in Figure 9.
  • the calculated power value is sent to the analog-to-digital converter via a determined connection 901.
  • a table is used that takes the calculated power as its input and makes it correspond to a symmetry adjustment value.
  • the present invention covers any other method enabling such an adjustment value to be determined.
  • a converter in an embodiment of the invention has at least one electronic component for adjusting symmetry in at least one of its feedback loops.
  • Figure 3 shows such a converter.
  • the electronic components 304 and 305 for adjusting symmetry apply their respective adjustment values (1- ⁇ ) and (1+ ⁇ ) simultaneously. Under such circumstances, the overall gain of the converter remains unchanged.
  • this configuration requires a component in each of the feedback loops. It is also more complex to implement.
  • the power measuring unit 310 is advantageously synchronized with the generators 306 and 307 so as to make it possible to deduce the sign of the error ⁇ by observing the position of the (I, Q) vector in a baseband representation of the output signal, where I is the imaginary component of the output signal on channel I, and Q is the real component of the output signal on channel Q.
  • such an electronic component is adapted to apply a negative adjustment value - ⁇ for adjusting symmetry on one of the channels I and Q as a function of a switch that serves to select the channel to which the symmetry adjustment value is to be applied.
  • Figure 5 shows such a converter.
  • the symmetry adjustment component 501 applies an adjustment value of - ⁇ to one channel or the other depending on the symmetry error.
  • the present invention covers any other configuration enabling a symmetry adjustment value ⁇ to be applied to one or both channels.
  • a converter in an embodiment of the invention may include an electronic adjustment component adapted to apply a positive symmetry adjustment value ⁇ to one or other of the channels I and Q as a function of a switch position.
  • the switch applies the adjustment value to one or other channel.
  • an adjustment value ⁇ is applied to only one of the channels I and Q, the overall gain of the converter is changed. Nevertheless, such a configuration is simple to implement.
  • the quantization noise signal is rejected to outside the . working frequency band 401.
  • Symmetry between the channels I and Q is corrected for such an analog-to-digital converter of complex signals.
  • the electronic component (s) is/are preferably adapted to store such an adjustment.
  • the present invention can thus be used to adjust the symmetry of the channels I and Q of a complex sigma-delta converter. In this way, the performance of such an analog-to-digital converter is improved.
  • the power of the signal in a determined working frequency band is calculated in the manner described above.
  • the output signal in the determined frequency band it is preferable for the output signal in the determined frequency band to be constituted solely by the signal associated with the injected signal.
  • the current sources used in the digital-to-analog converters of the analog-to-digital converter can constitute the sources of noise which can be taken into the determined frequency band at the output. It is therefore preferable to reduce such noise in order to optimize determining the symmetry adjustment value for the two channels.
  • a multibit complex sigma-delta analog-to-digital converter in an embodiment of the invention preferably includes a block for cross- connecting the current sources used by the digital-to- analog converters in the feedback loops of the complex sigma-delta converter.
  • a cross-connect block serves to minimize the errors due to matching differences between the various current sources in the digital-to- analog converters of the sigma-delta analog-to-digital converter.
  • the current cross-connect block interchanges bits of the bus in random manner so as to avoid always selecting the same current source for a given bit. Current source error is. thus spread and all of the sources present an identical error on average.
  • an embodiment of the present invention thus provides effective and inexpensive adjustment of the processing symmetry on the channels I and Q, and consequently improves the analog-to-digital conversion performance of complex signals and more particularly improves the conversion performance op multibit analog-to-digital complex bandpass sigma-delta converters operating at an oversampling frequency that is eight times greater than the Nyquist frequency of the signal.

Abstract

A method of adjusting an analog-to-digital converter (300) having two channels in quadrature (I, Q), each having an associated input (101, 102) and output (108, 109), for converting a complex analog input signal into a complex digital output signal in a working frequency band having a determined center frequency (f0), each output being looped back to said associated input in such a manner as to form first and second feedback loops. For a zero input signal, a first reference signal is injected into the first feedback loop and simultaneously a second reference signal is injected into the second feedback loop, said signals being synchronized with each other to form a complex signal centered on an image frequency of the determined center frequency. An output signal at the center frequency (f0) is then detected. Finally, amplitude of the detected signal is reduced by adjusting an electronic component (501) in the first and/or second feedback loop.

Description

A METHOD AND APPARATUS FOR ANALOG-TO-DIGITAL CONVERSION WITH SYMMETRY CORRECTION
The present invention relates to analog-to-digital converters of complex signals having two channels in quadrature. More particularly, the invention addresses the problem of symmetry in signal processing between the two channels in a complex bandpass converter.
Amongst analog-to-digital converters, there exist so-called sigma-delta analog-to-digital converters. These converters present an oversampling frequency that is well above the Nyquist frequency of the input signal, and as a result they make it possible to obtain a large amount of resolution for relatively low cost.
Converters of that type also enable quantization noise to be rejected to outside the working frequency band of the output signal, which band possesses a center frequency f0. In such a converter, quantization noise is controlled by the combined action of feedback loop- signals and a complex filter. Bandpass sigma-delta converters can convert complex analog signals into complex digital signals. They then present two channels in quadrature, conventionally referenced I for in-phase and Q for quadrature.
Such converters present advantages over real signal converters in terms of stability and width of the passband.
Figure 1 shows a complex bandpass sigma-delta converter for converting a complex analog signal into a complex digital signal. Such a converter comprises two channels in quadrature referenced I and Q. Each channel has an input 101, 102. The incoming signal on the input 101, 102 is added by means of a respective adder 103, 104 to the feedback loop signal 114, 115. The signal then passes through a complex filter 105. It is then processed by respective quantizers 106, 107 before being delivered on respective outputs 108, 109. Each feedback loop includes at least one digital-to-analog converter 112, 113 for providing the feedback signal.
In theory, in a complex bandpass sigma-delta converter, signal processing on the I and Q channels is symmetrical, and as a result signal quantization noise is rejected outside the working frequency band of the signal at the output from the converter. Figure 2 is a graph plotting a curve 202 showing the shape of noise from a complex signal converter. Thus, noise is rejected to outside the working frequency band 201 of center frequency f0, thereby enabling the signal/noise ratio to be improved, and as a result improving the performance of the converter.
The imperfections of analog circuits can lead to asymmetry between the two channels. In practice, it is difficult and expensive to make a complex bandpass sigma- delta converter for complex signals in which the two channels I and Q are perfectly symmetrical.
The invention is based on the observation that the rejection of quantization noise to outside the working frequency band of the signal is very sensitive to the processing on the I and Q channels being symmetrical. Any asymmetry in signal processing between these tlwo channels leads to quantization noise being folded 'into the working frequency band of the signal output by the converter, and as a result considerably degrades the signal/noise ratio of the converter. Such asymmetry may relate to the phase of the signal or to gain.
It is found that asymmetry relating to phase induces effects that are negligible compared with asymmetry relating to gain. Consequently, the terms "symmetry" and "asymmetry" are used below with reference to the symmetry or asymmetry on the I and Q channels that relates to gain. When the signal processing on the I and Q channels is not symmetrical in a bandpass analog-to-digital converter of complex signals, a quantization noise signal is obtained at the output from the converter at the center frequency of the working signal, and of amplitude that is substantially proportional to the symmetry error between the I and Q channels. Various proposals have already been made to mitigate this drawback of analog-to-digital converters of complex signals.
Thus, in an article entitled "Mismatch cancellation in quadrature bandpass ΔΣ modulators using an error- shaping technique" by J. Riches and N. Erdol, published in IEEE on February 2, 2002, a method is proposed of adjusting the symmetries of the two channels of a sigma- delta converter by managing random time-sharing between the various electronic components of the channels. To be effective, such a method requires a relatively difficult implementation of time-sharing management. In addition, the converter as obtained in that way is very sensitive to thermal noise since such a method does not correlate the thermal noise of the various components. In addition, such a converter consumes a large amount of time and energy for putting each electronic component back into its initial state on each change of channel.
US patent No. 6 329 939 proposes averaging symmetry errors by using a common integrator for integrating the incoming real and imaginary signals. Thus, the common integrator is used in alternation on one channel and then on the other channel of the converter. Such a converter consumes a large amount of time and energy for putting the common integrator back into the initial state on each change of channel.
The article "Mismatch cancellation for complex bandpass sigma-delta modulators" by L. Yu and M. Snelgrove, proposes processing the signal output from the converter and filtering the noise due to asymmetry between the I and Q channels. Such a method of noise reduction associated with channel asymmetry is expensive in terms of calculation and as a result consumes a large amount of energy. Furthermore, the response time of such signal processing is long.
The present invention seeks to mitigate those drawbacks. In a first aspect, the present invention provides a method of adjusting an analog-to-digital converter having two channels in quadrature, each having an associated input and output, for converting a complex analog input signal into a complex digital output signal in a working frequency band having a determined center frequency f0, each output being looped back to the associated input in such a manner as to form first and second feedback loops.
For a zero input signal, the method comprises the steps consisting in: • injecting a first reference signal into said first feedback loop and simultaneously a second reference signal into said second feedback loop, said first and second signals being synchronized to each other so as to form a complex signal centered on an image frequency of said determined center frequency;
detecting an output signal at the center frequency f0 at the output of the analog-to-digital converter; and
• reducing the amplitude of the detected signal by adjusting at least one electronic component in the first and/or second feedback loop.
Consequently, the analog-to-digital bandpass ^igma- delta converter of complex signals is preferably a multibit converter. Thus, the feedback signals in the feedback loops are encoded on a plurality of bits and control can be performed with relatively high precision.
By means of these dispositions, it is possible to adjust a complex bandpass sigma-delta analog-to-digital converter so as to correct the asymmetry of the I and Q channels and thus improve the performance of such a converter. For this purpose, in order to have a zero input signal, it is possible to short-circuit the inputs of the converter. A reference signal is then injected into both feedback loops in order to detect any asymmetry in the I and Q channels. If, after injecting the reference signal, a signal is detected in the working frequency band at the output from the converter, then it can be deduced that the I and Q channels are not symmetrical. Furthermore, the amplitude of the signal output in the working frequency band is substantially proportional to the symmetry error between the I and Q channels, as is described in the section below. Thereafter, one or more electronic components are adjusted in order to reduce the amplitude of the signal in the working frequency band. This enables the asymmetry between the I and Q channels to be corrected. When, under such conditions, by adjusting at least one electronic component, the amplitude of the signal at the center frequency f0 is reduced, that means that the quantization noise has been rejected to outside the working frequency band of the output signal, arid as a result the asymmetry between the I and Q channels has ' been corrected. Advantageously, an embodiment of the present invention enables the channel symmetry of a bandpass analog-to-digital converter for complex signals to be adjusted before it is used in order to increase its signal-to-noise ratio, and thus improve its conversion performance on complex signals during normal operation.
In an embodiment of the present invention, depending on the adjustment method used on the analog-to-digital converter, a frequency band is determined about the center frequency prior to performing the steps consisting in:
• calculating a power value for the output signal in said determined frequency band; and
• determining an adjustment value for the electronic1 component as a function of said calculated power value. In some circumstances, it can be advantageous to determine an adjustment value for the electronic component as a function of a calculated power value for the output signal in order to reduce the amplitude of the output signal.
It can also be advantageous for each of the two feedback loops to include an electronic component suitable for being adjusted.
The invention covers any method of evaluating the amplitude of an output signal at the center frequency or in a frequency band about the center of frequency.
Whatever the method used for calculating a power value for the output signal, it is possible to determine the adjustment value for the electronic component by using a table of predetermined adjustment values that are accessed as a function of the calculated power value. Thus, the adjustment value can be determined efficiently. The invention also covers any other method enabling an adjustment value to be determined for the electronic component in order to reduce the amplitude of the output signal.
Then, once the adjustment value has been determined, said value is preferably stored for use of the analog-to- digital converter during normal operation outside| an adjustment stage.
In a second aspect, the invention provides aτ\ analog-to-digital converter having two channels in' quadrature each comprising an associated input and output, for converting a complex analog input signkl into a complex digital output signal in a working frequency band having a determined center frequency f0, each output being looped back to the associated input so as to form first and second feedback loops. The converter comprises:
a first channel for receiving a first reference signal in said first channel loop, and a second channel for simultaneously receiving a second reference signal in said second feedback loop, said first and second signals being synchronized with each other to form a complex signal centered on an image frequency of said determined center frequency;
means arranged to detect an output signal at the center frequency f0 at the output from the analog-to- digital converter; and
• at least one adjustable electronic component for reducing the amplitude of the output signal at the center frequency f0, said electronic component being included in the first and/or the second feedback loop. Such an analog-to-digital converter of complex signals enables the symmetry of processing on the I and Q channels to be adjusted using the adjustment method of the first aspect of the present invention.
Such a converter may include a signal generator for injecting the first and second reference signals.
Or else, such a converter includes a first signal generator for injecting the first reference signal and a second signal generator for injecting the second reference signal, with the first and second generators being synchronized.
In an embodiment, the first generator, respectively the second generator, comprises a multiplexer stage adapted to shift the first feedback loop signal digitally, respectively the second feedback loop signal, and thus inject the first reference signal, respectively the second reference signal.
In another embodiment, the first generator, respectively the second generator, comprises an adder and/or subtracter stage adapted to perform addition or substraction on the first feedback loop signal, respectively the second feedback loop signal, and thus inject the first reference signal, respectively the second reference signal.
In an embodiment of the invention, the converter further includes a link with a detector unit adapted to detect an output signal and to send signal detection information to said converter via said connection. Under such circumstances, in the converter, an output signal at the frequency f0 is detected by receiving said information from said detector unit.
In another embodiment of the invention, a converter further includes a detector unit adapted to detect an output signal. Under such circumstances, in the converter, an output signal is detected at the frequency f0 via the detector unit, with said detection being performed locally. Such a converter may also include means for determining an adjustment value of the electronic component as a function of the power value of the output signal at the center frequency. The power value can then be calculated by the signal detector unit, regardless of whether the signal detector unit is included within the converter or is external to the converter. If it is external, the power value is sent over the connection. In another embodiment of the present invention, a frequency band is determined around the center frequency. The converter then further includes, means for determining an adjustment value for the electronic component as a function of a power value of the output signal inl said determined frequency band, said power value preferably being calculated by the signal detector unit, regardless of whether the signal detector unit is included within the converter or is external to the converter. Whbn it is external, the power value is transmitted over the connection.
It may be advantageous to determine the adjustment value on the basis of a table comprising predetermined adjustment values that are accessible as a function of the calculated power value.
The converter preferably further includes a memory for storing the adjustment value for use of the analog- to-digital converter in normal operation outside an adjustment stage. In a third aspect, the present invention provides an analog-to-digital conversion method for converting a complex analog input signal into a complex digital output signal in a working frequency band having a determined center frequency f0 by a converter having two channels in quadrature each having an associated input and output, each output being looped back to said associated input in such a manner as to form first and second feedback loops, in which at least one electronic component included in the first and/or second feedback loop applies a stored and predetermined value for adjusting the symmetry of the two channels.
Such a conversion method thus enables complex analog signals to be converted into complex digital signals presenting very good performance.
In a fourth aspect, the present invention provides an analog-to-digital converter for converting a complex analog input signal into a complex digital output signal in a working frequency band having a determined center • frequency f0, said converter having two channels in quadrature each comprising an associated input and output, each output being looped back to said associated input in such a manner as to form first and second feedback loops, in which at least one electronic component included in the first and/or second feedback loop is adapted to apply a stored and predetermined value for adjusting the symmetry of the two channels.
Thus, such a converter when adjusted using the method of the first aspect of the present invention presents symmetry of processing in the I and Q channels enabling very good performance to be obtained.
Other aspects, objects, and advantages of the invention appear on reading the following description of an embodiment. The invention will also be better understood with the help of the drawings, in which: Figure 1 is a block diagram of a complex bandpass sigma-delta analog-to-digital converter of the prior art, as described above;
• Figure 2 is a graph plotting the shape of noise from a bandpass sigma-delta analog-to-digital converter of complex signals, as described above;
• Figure 3 is a block diagram of a complex bandpass sigma-delta analog-to-digital converter constituting an embodiment of the present invention; ' Figure 4 is a graph plotting the shape of quantization noise while adjusting a bandpass sigma-delta analog-to-digital converter constituting an embodiment of the present invention;
• Figure 5 is a block diagram of a complex bandpass sigma-delta analog-to-digital converter constituting an embodiment of the present invention;
• Figure 6 shows a feedback loop of a complex bandpass sigma-delta converter in a preferred embodiment of the present invention; • Figure 7 shows the various states of counters on the I and Q channels in an embodiment of the inveption;
• Figure 8 shows a digital reference signal generator with shifting in an embodiment of the present invention; and • Figure 9 is a block diagram of a complex bandpass sigma-delta analog-to-digital converter constituting an embodiment of the present invention.
Figure 3 shows a complex sigma-delta analog-to- digital converter 300 constituting an embodiment of the present invention. The analog-to-digital converter comprises a complex filter 105, a respective quantizer 106 or 107 on each of its outputs 108 and 109, and a feedback loop from each of its outputs 108 and 109 towards the corresponding input 101 or 102. Each feedback loop comprises at least a digital-to-analog converter 111 or 113, for generating the corresponding feedback signal 114, 115. These feedback signals are added to the input signals via the respective adders 103 and 104.
In an embodiment of the present invention, in order to adjust symmetry between the I and Q channels of an analog-to-digital converter of complex signals, the inputs 101 and 102 are short-circuited. Then a reference signal is injected into each of the feedback loops of the I and Q channels. For this purpose, in an embodiment, the feedback loops.110 and 111 include respective adders 301, 302.
A first generator 306 injects a first reference signal via the adder 301. A second generator 307 injects a second reference signal via the adder 302. The first and second reference signals are synchronous, with the first and second generators being synchronized. The first and second reference signals form a complex signal of frequency equal to the image frequency of the center frequency f0 of the working frequency band of the output signal from the converter 300. ' • • . The present invention covers any configuration enabling a complex signal to be injected at the image frequency of a determined frequency f0. The first and second reference signals may be generated in particular by a single generator. In an embodiment of the present invention, the generator (s) is/are included in the complex bandpass sigma-delta converter. The invention covers any configuration for injecting these signals, in particular when the generator (s) is/are external to the converter. Figure 6 shows a first feedback loop for a complex bandpass converter 300 in which a reference signal is injected in a preferred embodiment of the present invention, with the architecture of the second feedback loop being similar. The generator 306 of the first feedback loop is included in the feedback loop in this example. The generator 306 is a digital generator, injecting a cyclical reference signal by digitally shifting the signal input into the generator 306, the cyclical reference signal presenting a fundamental component at an image frequency of the fundamental frequency of the output signal in the feedback loop. Preferably, such a generator is suitable for being activated by a control signal.
The structure for making such a generator is based on a multiplexer stage performing digital shifting on the signal input into the generator 306. This shifting corresponds either to one bit up or to one bit down depending on the control signal. The signal is conventionally represented in the form of a bar graph or "thermometer" .
The control signal can be supplied by an 8-state counter 601 of programmable initial state. The two generators in the two feedbacks are synchronized. Thus, it is easy to adjust the phase difference on the channels I and Q by acting on the synchronization between the two generators. Figure 7 shows the various states of the counters on the channels I and Q in an embodiment of the invention. Thus, there can be seen the states 71 of the counter 601 supplying the control signal to the generator 306 that is included in the first feedback loop. There can allso be seen the states 72 of the counter supplying the control signal to the generator that is included in the sebond feedback loop. In this example, the signal 73 is injected into the first feedback loop of the channel I, and the signal 74 is injected into the second feedback loop of the channel Q. The fundamental component of the channel I may be written Scos (2πf0t) and the fundamental component of the channel Q can be written -Ssin (2πf0t) , where f0 is the fundamental frequency of the output signal and S is the amplitude of the output signal. Figure 8 shows such a digital generator 306 with shifting. The value of the input signal 82 to the generator 306 is shifted as a function of the control signal 81 that has three states, 1, 0, or -1, thereby giving an output signal 83 corresponding to the feedback loop signal received at the input of the generator 306 plus the signal injected by the generator. A method of injecting reference signals as described above is particularly well adapted to a multibit complex bandpass sigma-delta analog-to-digital converter. Preferably, such a converter operates at an . oversampling frequency that is eight times greater than the Nyquist frequency of the input signal. Under such circumstances, a digital generator with shifting as described above is easier to implement than at other oversampling frequencies.
Advantageously, such a digital generator with shifting does not introduce errors into the method of adjustment in an embodiment of the invention.
The first reference signal can be written in the following form:
51 = Acos (2πf0t) and the second reference signal can be written in the following form:
52 = -Asin(2πf0t) where A is the amplitude of the injected signal.
The amplitude A of such a signal is preferably determined in such a manner that the complex filter is not saturated so that its linearity property is conserved.
By injecting a signal as defined in this way into a converter that presents a symmetry error, a signal is detected at the output from the converter with a component at the center frequency f0 having amplitude that is substantially proportional to the symmetry error between the channels I and Q. This component corresponds to the quantization noise multiplied by the symmetry error between the two channels and taken to the center frequency of the working signal. Such a signal is illustrated in Figure 4. A line 402 can be seen at the frequency f0. In such a context of asymmetry between the channels I and Q, it can be seen that a sigma-delta converter no longer rejects quantization noise to outside the working frequency band. In an embodiment of the present invention, a working frequency band 401 is determined around the center frequency f0. Thus, after injecting the reference signals into the feedback loops of the complex bandpass sigma- delta converter, the signal output by the converter in the determined working frequency band is detected. Such detection is performed by a detector unit 310. The signal detected in this way in the frequency band 401 is of an amplitude that is substantially proportional to the quantization noise signal. Preferably, such output signal detection is performed by calculating the power of the output signal. Thus, the detector unit is marked as being a power measuring unit 310. Nevertheless, the present invention also covers other methods of detecting the output signal. When no other error signal is generating a noise signal at the output in the working frequency band, then the detected signal corresponds solely to the quantization noise signal associated with the asyrtimetry of the channels I and Q. Otherwise, particularly 'when matching differences between the current sources used by the digital-to-analog converters in the feedback lbops give rise to errors that can generate a noise signal in the working frequency band 401, then the noise signal detected at the output can comprise both quantization noise due to asymmetry between the channels I and Q and also the noise coming from other types of error. The noise coming from types of error other than symmetry error between the channels I and Q is negligible, particularly when the injected reference signals are of relatively high amplitude A.
The present invention thus makes it possible to reduce very significantly the quantization noise of the complex analog-to-digital converter, regardless of whether or not the converter presents noise of some other type in the determined working frequency band.
The noise signal at the output from the analog-to- digital converter is preferably detected by the power measuring unit 310. This power measuring unit is preferably adapted to calculate a power value for the signal in the determined working frequency band 401. Power calculation can be written in the following form: Poutput = I2 + Q2 where Poutput ^s the power of the signal output by the converter in the determined frequency band, and I and Q are the amplitudes of the signals on each of the channels I and Q respectively in the determined frequency band. In an embodiment of the present invention, the power value of the output signal is calculated by the unit for measuring signal power.
The power measuring unit 310 may be included in the converter 300 as shown in Figure 3, or else it may be external to the converter 300 as -shown in Figure 9. When the power measuring unit is external to the converter, as shown in Figure 9, the calculated power value is sent to the analog-to-digital converter via a determined connection 901. Depending on the calculated power value, it is possible to determine an adjustment value for adjusting symmetry between the channels. Preferably, a table is used that takes the calculated power as its input and makes it correspond to a symmetry adjustment value. The present invention covers any other method enabling such an adjustment value to be determined.
A converter in an embodiment of the invention has at least one electronic component for adjusting symmetry in at least one of its feedback loops. In an embodiment of the invention, it is possible to apply different adjustment values, respectively (1-ε) and (1+ε) simultaneously on the channels I and Q. Figure 3 shows such a converter. The electronic components 304 and 305 for adjusting symmetry apply their respective adjustment values (1-ε) and (1+ε) simultaneously. Under such circumstances, the overall gain of the converter remains unchanged. However this configuration requires a component in each of the feedback loops. It is also more complex to implement.
In an embodiment of the invention, the power measuring unit 310 is advantageously synchronized with the generators 306 and 307 so as to make it possible to deduce the sign of the error ε by observing the position of the (I, Q) vector in a baseband representation of the output signal, where I is the imaginary component of the output signal on channel I, and Q is the real component of the output signal on channel Q.
In addition, depending on the synchronization between the power measuring unit 310 and the generators 306 and 307, it is possible advantageously to simplify power calculation. Thus, by measuring power at instants when the (I, Q) vector is at an angle substantially equal to π/4 or 3π/4 or 5π/4 or indeed In/A1 power calculations can be simplified. When measurements are performed on a vector at an angle substantially equal to π/4, the1 power P can be calculated approximately by one of the following equations:
VP = max (I,Q) + - min(I,Q)
Figure imgf000017_0001
where max(a,b) is equal to the maximum of a and b, and min(a,b) is equal to the minimum of a and b. In another embodiment of the present invention, such an electronic component is adapted to apply a negative adjustment value -ε for adjusting symmetry on one of the channels I and Q as a function of a switch that serves to select the channel to which the symmetry adjustment value is to be applied. Figure 5 shows such a converter. The symmetry adjustment component 501 applies an adjustment value of -ε to one channel or the other depending on the symmetry error. The present invention covers any other configuration enabling a symmetry adjustment value ε to be applied to one or both channels. Thus, a converter in an embodiment of the invention may include an electronic adjustment component adapted to apply a positive symmetry adjustment value ε to one or other of the channels I and Q as a function of a switch position. The switch applies the adjustment value to one or other channel. When an adjustment value ε is applied to only one of the channels I and Q, the overall gain of the converter is changed. Nevertheless, such a configuration is simple to implement.
Thus, after correcting symmetry in this way, the quantization noise signal is rejected to outside the . working frequency band 401. Symmetry between the channels I and Q is corrected for such an analog-to-digital converter of complex signals. The electronic component (s) is/are preferably adapted to store such an adjustment.
Advantageously, the present invention can thus be used to adjust the symmetry of the channels I and Q of a complex sigma-delta converter. In this way, the performance of such an analog-to-digital converter is improved.
In an embodiment of the present invention, in order to determine the symmetry correction to be applied, the power of the signal in a determined working frequency band is calculated in the manner described above. In order to be able to determine a precise symmetry adjustment value, it is preferable for the output signal in the determined frequency band to be constituted solely by the signal associated with the injected signal. Unfortunately, other errors can also produce a noise signal in the determined frequency band. The current sources used in the digital-to-analog converters of the analog-to-digital converter can constitute the sources of noise which can be taken into the determined frequency band at the output. It is therefore preferable to reduce such noise in order to optimize determining the symmetry adjustment value for the two channels.
For this purpose, a multibit complex sigma-delta analog-to-digital converter in an embodiment of the invention preferably includes a block for cross- connecting the current sources used by the digital-to- analog converters in the feedback loops of the complex sigma-delta converter. Such a cross-connect block serves to minimize the errors due to matching differences between the various current sources in the digital-to- analog converters of the sigma-delta analog-to-digital converter. More precisely, the current cross-connect block interchanges bits of the bus in random manner so as to avoid always selecting the same current source for a given bit. Current source error is. thus spread and all of the sources present an identical error on average.
Advantageously, an embodiment of the present invention thus provides effective and inexpensive adjustment of the processing symmetry on the channels I and Q, and consequently improves the analog-to-digital conversion performance of complex signals and more particularly improves the conversion performance op multibit analog-to-digital complex bandpass sigma-delta converters operating at an oversampling frequency that is eight times greater than the Nyquist frequency of the signal.

Claims

1. A method of adjusting an analog-to-digital converter (300) having two channels in quadrature (I, Q) each having an associated input (101, 102) and output (108, 109), for converting a complex analog input signal into a complex digital output signal in a working frequency band having a determined center frequency (f0), each output being looped back to the associated input in such a manner as to form first and second feedback loops, said method comprising, for a zero input signal, the steps consisting in:
• injecting a first reference signal into said first feedback loop and simultaneously a second reference signal into said second feedback loop, said first and second signals being synchronized to each other so as to form a complex signal centered on an image frequency of said determined center frequency;
• detecting an output signal at the center frequency (f0) at the output of the analog-to-digital converter; and. • reducing the amplitude of -the detected signal by adjusting at least one electronic component (304, 305) in the first and/or second feedback loop.
2. A method according to claim 1, wherein the digital signals of the feedback loops are encoded on a plurality of bits.
3. A method according to claim 1 or claim 2, wherein a frequency band is determined about the center frequency, said method including the steps consisting in:
• calculating a power value for the output signal in said determined frequency band; and
• determining an adjustment value for the electronic component as a function of said calculated power value.
4. A method according to claim 3, wherein the adjustment value is determined by using a table comprising predetermined adjustment values accessible as a function of the calculated power value.
5. A method according to claim 3 or claim 4, further comprising a step of storing the adjustment value for use of the analog-to-digital converter during normal operation, outside an adjustment stage.
β. An analog-to-digital converter (300) having two channels in quadrature each comprising an associated input and output, for converting a complex analog input signal into a complex digital output signal in a working frequency band having a determined center frequency (f0) , each output (108, 109) being looped back to the associated input so as to form first and second feedback loops, said converter comprising:
• a first channel for receiving a first reference signal in said first channel loop, and a second channel for simultaneously receiving a second reference signal in said second feedback loop, said first and second signals being synchronized with each other to form a complex signal centered on an image frequency of said determined center frequency;
means (310) arranged to detect an output signal at the center frequency (f0) at the output from the analog- to-digital converter; and
• at least one adjustable electronic component (304, 305) for reducing the amplitude of the output signal at the center frequency (f0) , said electronic component being included in the first and/or the second feedback loop.
7. A converter according to claim 6, wherein the feedback loop signals are encoded on a plurality of bits.
8. A converter according to claim 6 or claim 7, further including a signal generator for injecting the first and second reference signal. 9. A converter according to claim 6 or claim 7, further including a first signal generator (306) for injecting the first reference signal and a second signal generator
5 (307) for injecting the second reference signal, said first and second generators being synchronized.
10. A converter according to claim 9, wherein the^ first generator, respectively the second generator, comprises a
10 multiplexer stage adapted to shift the first feedback loop signal digitally, respectively the second feedback loop signal, and thus inject the first reference signal, respectively the second reference signal.
15 11. A converter according to claim 9, wherein the first generator, respectively the second generator, comprises an adder and/or subtracter stage adapted to perform addition or substraction on the first feedback ' loop signal, respectively the second feedback loop signal, and1 VM". 20 thus inject the first reference signal, respectively the second reference signal.
12. A converter according to any one of claims 6 to 11, further including a connection (910) with a detector unit
25 (310) adapted to detect an output signal and to send signal detection information to said converter via said connection (910), wherein an output signal at the center frequency is detected by receiving said information from said detector unit (310) .
30
13. A converter according to claim 12, wherein a frequency band (401) is determined about the center frequency, said converter further including means for determining an adjustment value for the electronic
35 component as a function of a power value for the output signal in said determined frequency band, said power value being calculated by the signal detector unit (310) . 14. A converter according to claim 13, wherein the means for determining the adjustment value include a table of predetermined adjustment values accessible as a function of the calculated power value.
15. A converter according to any one of claims 6 to 14, wherein the electronic component (304, 305) further includes a memory for storing the adjustment value for use of the analog-to-digital converter during normal operation, outside an adjustment stage.
16. An analog-to-digital conversion method for converting a complex analog input signal into a complex digital output signal in a working frequency band having a determined center frequency (f0) by a converter having two channels in quadrature each having an associated input and output, each output (108, 109) being looped back to said associated input in such a manner as to form first and second feedback loops, wherein at least one electronic component (304, 305) included in the first and/or second feedback loop applies a stored and predetermined value for adjusting the symmetry of lthe two channels.
17. An analog-to-digital converter for converting ^ complex analog input signal into a complex digital output signal in a working frequency band having a determined center frequency (f0) , said converter having two channels in quadrature each comprising an associated input and output, each output (108, 109) being looped back to said associated input in such a manner as to form first and second feedback loops, wherein at least one electronic component (304, 305) included in the first and/or second feedback loop is adapted to apply a stored and predetermined value for adjusting the symmetry of the two channels.
PCT/EP2005/008740 2004-07-20 2005-07-12 A method and apparatus for analog-to-digital conversion with symmetry correction WO2006008188A1 (en)

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Citations (4)

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US4583239A (en) * 1983-10-29 1986-04-15 Stc Plc Digital demodulator arrangement for quadrature signals
GB2232022A (en) * 1989-05-26 1990-11-28 Marconi Gec Ltd Analogue-to-digital converter
JP2000068839A (en) * 1998-08-20 2000-03-03 Fujitsu Ltd Sigma delta type a/d converter, demodulator, receiver and disk device
US20010038350A1 (en) * 2000-03-01 2001-11-08 Eric Andre System of DAC correction for a delta sigma modulator

Patent Citations (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US4583239A (en) * 1983-10-29 1986-04-15 Stc Plc Digital demodulator arrangement for quadrature signals
GB2232022A (en) * 1989-05-26 1990-11-28 Marconi Gec Ltd Analogue-to-digital converter
JP2000068839A (en) * 1998-08-20 2000-03-03 Fujitsu Ltd Sigma delta type a/d converter, demodulator, receiver and disk device
US20010038350A1 (en) * 2000-03-01 2001-11-08 Eric Andre System of DAC correction for a delta sigma modulator

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* Cited by examiner, † Cited by third party
Title
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