Abstract:
A digital to digital Sigma-Delta modulator comprises an input which receives a digital input value encoded over N bits, an output which delivers a digital output value encoded over n bits, where n is less than N, and at least a first Sigma-Delta cell which includes a quantizer having a quantization interval which is a prime number. The choice of a prime number decreases the power of the limit cycles (lines with a power value higher than the local mean value) which may appear depending on the input code of the modulator and on the initial conditions. Application is proposed to a digital frequency synthesizer.

Description:
BACKGROUND OF THE INVENTION  
         [0001]    1. Technical Field  
           [0002]    The present invention relates to digital to digital Sigma-Delta modulators (Σ-Δ modulator). In particular, it is applicable to digital frequency synthesizers or DMS (Digitally Modulated Synthesizer) circuits. Such circuits are especially used in the radio frequency transmitters of mobile terminals or of stationary stations of a radio communications system.  
           [0003]    A digital to digital Σ-Δ modulator is a device for encoding a digital signal using a small number of steps, and a sampling frequency which is high compared to the passband of the signal to be encoded. This device shapes the spectrum of the quantization noise by pushing its power back into a frequency band not occupied by the spectrum of the useful signal. This spectral separation makes it possible, by filtering the encoded signal, to retain a signal-to-noise ratio complying with given specifications.  
           [0004]    2. Related Art  
           [0005]    A known digital to digital Sigma-Delta modulator comprises:  
           [0006]    an input in order to receive a digital input value encoded over a given number N of bits, where N is a specified integer;  
           [0007]    an output in order to deliver a digital output value encoded over a given number n of bits, where n is a specified integer less than N; and  
           [0008]    one or more Sigma-Delta cells placed between the input and the output of the modulator.  
           [0009]    Each cell may be of the first order or of a higher order. When the modulator comprises several cells, the latter may be arranged according to a structure known to the one skilled in the art by the name of “MASH structure”. In this case, the cells are often identical to each other, but this is not mandatory. In particular, some may be of the first order, and others of a higher order.  
           [0010]    In all cases, each Sigma-Delta cell comprises, at a minimum, the following elements:  
           [0011]    a subtractor comprising a first input, a second input, and an output, the first input being coupled to the input of the modulator in order to receive the digital input value or a value derived therefrom;  
           [0012]    an integrator comprising an input coupled to the output of the subtractor, and an output; and  
           [0013]    a quantizer having an input coupled to the output of the integrator and an output coupled to the second input of the subtractor. Furthermore, the output of the quantizer is coupled to the output of the modulator in order to deliver the digital output value or a contribution thereto. The quantizer has a specified quantization interval.  
           [0014]    In practice, the input of the modulator receives successive values of a digital input signal, occupying a passband much lower than the sampling frequency. The corresponding output values form an output signal, which is a digital signal.  
           [0015]    A particularly awkward problem for implementing such a modulator resides in the unpredictable (except for exhaustive simulations which in practice are sometimes unachievable) appearance of limit cycles. These limit cycles depend on the value of the input signal, on the architecture of the Σ-Δ modulator and on the initial conditions. They are apparent from the concentration of a considerable part of the output signal power in a small number of lines (lines with a power value which is higher than the local mean value). These situations impair the desired encoding performance by increasing the power of the encoding noise in the passband of the useful signal.  
           [0016]    Analysis of the behaviour of a digital to digital Σ-Δ modulator comes within the study of systems called “sequential Mealy machines” and of non-linear servo-control systems. The “harmonic” analysis of a digital to digital Σ-Δ modulator makes it possible to predict its transfer function and its encoding performance by assuming that the quantizer introduces an encoding error, the spectrum of which is that of decorrelated white noise for the input signal. With this assumption, the behaviour of the Σ-Δ modulator according to the simulation is predicted, except during the appearance of limit cycles.  
           [0017]    It has not been possible to describe any device having the encoding of properties a digital to digital Σ-Δ modulator without the drawbacks of the existence of unpredictable limit cycles.  
         SUMMARY OF THE INVENTION  
         [0018]    A first aspect of the invention relates to a modulator of the aforementioned type, in which the quantization interval of the quantizer is a prime number.  
           [0019]    Thus, as will appear more clearly on reading the following description, this feature makes it possible to extend the duration of the output signal cycles as much as possible. It then follows that, since the energy of this signal is distributed over a larger number of lines, the latter are of lower power. The mechanisms leading to the appearance of limit cycles produce the latter with a decreased power (this phenomenon has been observed during simulation).  
           [0020]    A second aspect of the invention relates to a digital frequency synthesizer comprising a phase-locked loop having a variable frequency divider in the feedback path, and further comprising a digital to digital Σ-Δ modulator according to the first aspect, in order to encode a signal for controlling the division ratio of the variable frequency divider. 
       
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS  
       [0021]    [0021]FIG. 1 is a diagram of a digital to digital Σ-Δ modulator having a first-order cell;  
         [0022]    [0022]FIG. 2 is a graph showing the properties of a quantizer having two output levels;  
         [0023]    [0023]FIGS. 3 a  to  3   d  are graphs showing the change, as a function of time, of the signal I at the input of the quantizer and of the output signal Y of a modulator according to FIG. 1, respectively for four specified pairs of values of the input signal X of the modulator and of the quantization interval q of the quantizer;  
         [0024]    [0024]FIGS. 4 a  to  4   d  are graphs showing the spectrum of the output signal Y of a modulator according to FIG. 1, respectively for each of the pairs of values of the input signal X of the modulator and of the quantization interval q of the quantizer of FIGS. 3 a  to  3   d;    
         [0025]    [0025]FIG. 5 is a graph showing the response of a quantizer with a given number (2×K)+1 of output levels, where K is an integer;  
         [0026]    [0026]FIG. 6 is a diagram illustrating a digital to digital Σ-Δ modulator having three first-order cells arranged according to a MASH structure;  
         [0027]    [0027]FIGS. 7 a  to  7   d  are graphs showing the spectrum of the output signal Y of a modulator according to FIG. 6, each one for a specified pair of values of the input signal X of the modulator and of the quantization interval q of the quantizer; and  
         [0028]    [0028]FIG. 8 is a diagram illustrating a digital frequency synthesizer incorporating a digital to digital Σ-Δ modulator according to the invention.  
     
    
     DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS  
       [0029]    To illustrate the effect produced by the invention, the case of a digital to digital Σ-Δ modulator, such as the modulator shown schematically in FIG. 1, may be considered. Such a modulator is as simple as possible, since it comprises only a single Σ-Δ cell, and since this cell is of the first order.  
         [0030]    The modulator comprises an input  10  in order to receive the successive digital values, each one encoded over N bits, where N is a specified integer, of a digital input signal X. Hereinafter, the letter X denotes both the input signal of the modulator and a particular value of this signal.  
         [0031]    The modulator also comprises an output  20  in order to deliver the successive digital values, each one encoded over a given number n of bits, where n is a specified integer less than N, of a digital output signal Y. Hereinafter, the letter Y denotes both the output signal of the modulator and a particular value of this signal.  
         [0032]    The signal Y is equivalent to the signal X encoded using the modulator. Since the signal Y is encoded over a number of bits which is smaller than the number of bits used to encode the signal X, an encoding error is introduced. The structure of the digital to digital Σ-Δ modulator makes it possible to shape this encoding noise (or quantization noise).  
         [0033]    The exemplary embodiment of the modulator illustrated by FIG. 1 comprises a single Σ-Δ cell, denoted  100 . In this embodiment, the cell  100  is of the first order. It comprises the following elements:  
         [0034]    a subtractor S 1  comprising a first input  11 , a second input  12  and an output  13 . The input  11  is coupled to the input  10  of the modulator in order to receive the digital input value X;  
         [0035]    an integrator I 1  comprising an input  14  and an output  15 . The input  14  is coupled to the output  13  of the subtractor S 1 . The output  15  delivers a signal I encoded over n bits. The integrator is a digital integrator. In a known manner, such an integrator may be made in the form of an accumulator register set to a particular sampling frequency F s ; and,  
         [0036]    a quantizer Q 1  having an input  16  and an output  17 . The input  16  is coupled to the output  15  of the integrator I 1  in order to receive the signal I delivered thereby. The output  17  is coupled to the second input  12  of the subtractor S 1 . Furthermore, the output  17  is coupled to the output  20  of the modulator in order to deliver the digital values of the output signal Y at the sampling frequency F s . The quantizer Q 1  has a specified quantization interval, denoted q hereinbelow and in the figures.  
         [0037]    The output I(t) of the integrator I 1  of the first-order modulator is expressed, at the time t=n×T s , where T s  denotes the sampling period (T s =1/F s ), by the following equation:  
           I ( n×T   s )= I (( n− 1)× T   s )+( X (( n− 1)× T   s )− Y (( n− 1)× T   s ))  (1)  
         [0038]    The output value Y(t) of the modulator is, for a quantizer having two output levels, for example, equal to q1 if I(t)  
           I        (   t   )       ≥     q   2       ,                         
 
         [0039]    otherwise it is equal to 0. The response of such a quantizer with two output levels is illustrated by the graph of FIG. 2. The signal Y output from the modulator is then encoded over a single bit (n=1).  
         [0040]    The graphs of FIGS. 3 a  to  3   d  show the change, as a function of time, of the signal I at the input of the quantizer Q 1  (bottom graph) and of the output signal Y (top graph) of a modulator according to FIG. 1 for four specified pairs of the quantization interval q of the quantizer Q 1  and of the value of the input signal X, respectively:  
         [0041]    in FIG. 3 a , q is equal to 6 and X is equal to 4 (q1=6; X=4);  
         [0042]    in FIG. 3 b , q is equal to 7 and X is equal to 4 (q1=7; X=4);  
         [0043]    in FIG. 3 c , q is equal to 6 and X is equal to 5 (q1=6; X=5); and  
         [0044]    in FIG. 3 d , q is equal to 7 and X is equal to 5 (q1=7; X=5).  
         [0045]    The value I(t) changes with each period T s . Thus, as can be seen, the value of Y also changes with time, thereby being periodic. The period of the signal Y(t) will be denoted T. This period corresponds to the maximum duration of one cycle of the accumulator. The time T is shown on the top graph by a horizontal arrow. In some ways, this is the mean value of the signal Y(t) over a period T which determines the encoded input value X.  
         [0046]    For the same value of X, the time T may vary depending on the value of q. Similarly, for the same value of q, the time T may vary depending on the value of X. It can be demonstrated that the period T is defined by the following equation:  
             T   =       q   D     ×     T   s               (   2   )                               
 
         [0047]    where D is the highest common denominator (HCD) between X and q, that is D=HCD (X, q).  
         [0048]    Thus, the time T of a cycle is a maximum when the values X and q1 are relatively prime.  
         [0049]    [0049]FIGS. 4 a  to  4   d  show the spectrum of the quantization noise for the four examples corresponding to FIGS. 3 a  to  3   d , respectively, with F s =13 MHz (megahertz) This is a line spectrum in the frequency band close to the sampling frequency F s .  
         [0050]    Thus, as can be seen, in each case, the noise spectrum comprises a line  41  at about −12 dB (decibels), at a particular frequency F, such that  
       F   =       1   T     =       D   q     ×       F   s     .                               
 
         [0051]    In the case of FIG. 4 a , this line  41  is located at the frequency F=F s /3, since D is equal to 2. In the case of FIGS. 4 b ,  4   c  and  4   d , this line  41  is located at  
         F   s     q                         
 
         [0052]    since D is equal to one. However, in the case of FIGS. 4 b ,  4   c  and  4   d , the spectrum comprises other lines  42  and  43 . It follows that the energy of the quantization noise is distributed between several lines, and is therefore easier to remove by filtering.  
         [0053]    It shall therefore be noted that if q and X are relatively prime values, the quantization energy is distributed over a larger number of lines (FIGS. 4 b ,  4   c  and  4   d ) than otherwise (FIG. 4 a ).  
         [0054]    Since no a priori assumption can be made on the values of the input signal X to be encoded, the invention proposes to give the quantization interval q the value of a prime number. The values q and X will therefore always be relatively prime. Their HCD will therefore always be equal to one, such that the time T will always be a maximum. For a Σ-Δ modulator of the first order, this results in a spectrum of the output signal which is independent of the input code, with a minimum line level. In the case of a Σ-Δ modulator of higher order, the limit cycles (appearing for certain input codes) are not removed but they are attenuated.  
         [0055]    Of course, the invention is not limited to the case of a quantizer having only two output levels.  
         [0056]    The graph of FIG. 5 illustrates an example of the response of the quantizer when the latter has a given number (2×K)+1 of different output levels. In this example, the quantization is called uniform since the quantization interval q 1  has a constant value whatever the value of the signal I(t). This response is stepped, and corresponds to an examplary quantization called “rounded”. This is because any value of the signal I(t) between  
         (     j   -     1   2       )     ×   q                 and                   (     j   +     1   2       )     ×   q                         
 
         [0057]    is rounded to j×q, when j is between −K and K, where K is a specified integer.  
         [0058]    It can be noted that, in the case of a quantizer thus having (2×K)+1 output levels, the aforementioned number D is equal to the highest common denominator of the value X and of the value 2×K×q, that is HCD (X,  2 ×K×q).  
         [0059]    Of course, nor is the invention limited to the case of a first-order digital to digital Σ-Δ modulator. The cell  100  of the modulator may be of the second order or more. Furthermore, the modulator may comprise a given number P−1 of other (additional) Sigma-Delta cells, where P is an integer greater than or equal to 2. In this case, the P Sigma-Delta cells are preferably arranged according to a MASH structure. Thus a modulator of order P is obtained, when each cell is of the first order. More generally, the order of the modulator is then the sum of the respective orders of the Sigma-Delta cells of the modulator.  
         [0060]    An example of a modulator of this type, comprising three cells  100 ,  200  and  300 , that is for the case where P is equal to three (P=3), is shown schematically in FIG. 6. In this figure, the same elements as in FIG. 1 bear the same references. In this case, in addition to the cell  100 , the modulator comprises two additional cells  200  and  300 .  
         [0061]    Preferably, the three cells have identical structures. This simplifies the production on silicon. In this example, they are first order cells, that is they have the same structure as the cell  100  of the modulator shown in FIG. 1 and described above. The terms “structure of a cell” in this case refer to the overall structure of the cell, that is the type, the number and the arrangement of the elements of which it is formed. These elements have been described above with regard to the cell  100  shown in FIG. 1.  
         [0062]    For convenience, the respective subtractors of the cells  100 ,  200  and  300  will be denoted S 1 , S 2  and S 3 , respectively. Similarly, the respective integrators of the cells  100 ,  200  and  300  will be denoted I 1 , I 2  and I 3 , respectively. Finally, the respective quantizers of the cells  100 ,  200  and  300  will be denoted Q 1 , Q 2  and Q 3 , respectively.  
         [0063]    The first input of the subtractor S 1  of the cell  100  is coupled to the input  10  of the modulator. The output of the quantizer Q 1  is coupled to a first input  61  of an adder S 12  through a delayer D 1 . The output of the adder S 12  is coupled to the output  20  of the modulator in order to deliver the signal Y.  
         [0064]    The first input of the subtractor S 2  of the cell  200  is coupled to the output of the integrator I 1  of the cell  100 . The output of the quantizer Q 2  is coupled to a first input  63  of another adder S 23  through another delayer D 2 . The output of the adder S 23  is coupled to a second input  62  of the adder S 12  through another delayer D 12 .  
         [0065]    The first input of the subtractor S 3  of the cell  300  is coupled to the output of the integrator I 2  of the cell  200 . The output of the quantizer Q 3  is coupled to a second input  64  of the adder S 23  through another delayer D 23 .  
         [0066]    Stated otherwise, the first input of the subtractor S 2  of the second cell  200  receives a signal derived from the input signal X. More specifically, it is coupled to the input  10  in order to receive the signal X through the subtractor S 1  and the integrator I 1  of the first cell  100 . Similarly, the first input of the subtractor S 3  of the third cell  300  receives a signal derived from the input signal X. More specifically, it is coupled to the input  10  in order to receive the signal X through the subtractor S 1  and the integrator I 1  of the first cell  100 , and in addition through the subtractor S 2  and the integrator I 2  of the second cell  200 .  
         [0067]    The delayer D 1  introduces a delay corresponding to three periods T s . Similarly, the delayer D 2  introduces a delay corresponding to two periods T s .  
         [0068]    The output signal Y results from the additive contribution of the signals delivered by the quantizers Q 1 , Q 2  and Q 3  of the cells  100 ,  200  and  300 , respectively.  
         [0069]    A MASH structure as described above is known to a person skilled in the art, and its operation does not call for any particular comment.  
         [0070]    The respective quantization intervals of the quantizers Q 1 , Q 2  and Q 3  of each of the cells  100 ,  200  and  300 , respectively, are all equal to the same prime number denoted q.  
         [0071]    In FIGS. 7 a  to  7   d , graphs showing the spectrum of the output signal Y of a modulator according to FIG. 6 are shown, each one for a specified pair of values of the input signal X of the modulator and of the quantization interval q of the quantizer of each of the Σ-Δ cells, with a quantizer having three output levels (−q, 0 and q) and with Fs=13 MHz:  
         [0072]    in FIG. 7 a , q is equal to 65536 and X is equal to 23168;  
         [0073]    in FIG. 7 b , q is equal to 65537 and X is equal to 23168;  
         [0074]    in FIG. 7 c , q is equal to 65536 and X is equal to 23167; and  
         [0075]    in FIG. 7 d , q is equal to 65537 and X is equal to 23167.  
         [0076]    The numbers 65537 and 23167 are prime numbers. As can be seen, the energy of the quantization noise (high-frequency noise) is distributed over many more lines in the graphs of FIGS. 7 b ,  7   c  and  7   d  than in that of FIG. 7 a . Moreover, the level of these lines is clearly much lower than in the case of FIG. 7 a , and this whatever the frequencies that are considered between 10 kHz (kilohertz) and 1.5 MHz.  
         [0077]    [0077]FIG. 8 illustrates diagramatically an exemplary embodiment of a digital frequency synthesizer incorporating a digital to digital Σ-Δ modulator according to the first aspect of the invention.  
         [0078]    The synthesizer comprises a phase-locked loop (PLL) with a charge pump. The PLL comprises the following elements in a loop:  
         [0079]    a phase frequency detector (PFD)  81 ;  
         [0080]    a charge pump (CP)  82 ;  
         [0081]    a loop filter  83 , which is a low-pass filter (integrator);  
         [0082]    a voltage controlled oscillator (VCO)  84 ;  
         [0083]    a variable frequency divider  85 , the variable ratio of which is denoted M in the figure and hereinafter.  
         [0084]    The phase detector  81  detects the phase difference between a reference frequency F ref  and the frequency F vco  of the output signal of the VCO divided by the ratio M of the frequency divider  85 . It applies charge-up and charge-down pulses U and D, respectively, to the charge pump  82 . These pulses are used to switch voltage or current sources, which charge or discharge a capacitor of the loop filter  83 . The loop filters these pulses and delivers a resulting control voltage to the VCO. The oscillation frequency F vco  of the VCO is altered as a function of this control voltage. Thus, the PLL forms a looped system in which the frequency F vco  of the signal at the output of the VCO is locked onto the frequency F ref ×M. The output from the system is the output from the VCO. The frequency divider is included in the feedback path. It comprises a control signal for the division ratio M, which receives a control signal (also denoted M for convenience) making it possible to change the value of the frequency F vco  of the output signal of the PLL.  
         [0085]    Thus, as is known per se, the control signal for the division ratio M of the frequency divider  85  is generated by a digital to digital Σ-Δ modulator.  
         [0086]    In the example shown, the ratio M comprises an integer part Int(M) and a fractional part Frac(M) which are added in an adder  86 . The output of the adder  86  delivers the control signal M. The synthesizer comprises a digital to digital Σ-Δ modulator  87  according to the first aspect of the invention, for example of the type described in FIG. 1 or in FIG. 6, in order to encode the fractional part Frac(M) of the signal M before it is added to the integer path Int(M) of this signal.  
         [0087]    Stated otherwise, the modulator  87  receives as an input the signal Frac(M) encoded over N bits, and delivers at the output a corresponding signal encoded over n bits, where n is less than N, which is added to the signal Int(M) in the adder  86  in order to form the control signal for the division ratio M of the frequency divider  85  of the PLL. The interference lines of the signal over n bits at the output of the Σ-Δ modulator are eliminated by the low-pass filtering of the PLL.  
         [0088]    In certain applications, the signal Int(M) may determine the frequency of a channel and the signal Frac(M) may be a phase or frequency modulation signal. This is only one example of an application. It is understood that the invention can be used in this type of application, since it makes it possible to preserve the spectral purity of the output signal of the VCO. This is advantageous, in particular, in the applications of the synthesizer to a radio frequency transmitter.