Abstract:
A bandpass continuous-time delta-sigma modulator. The filters of the modulator are LC resonators directly connected in series. Direct connection of the resonators eliminates the need for active components in the modulator, increases linearity and decreases noise.

Description:
BACKGROUND 
   1. Field 
   The present disclosure relates to the field of delta-sigma modulators. In particular, it relates to a continuous time bandpass delta-sigma modulator using LC resonators. 
   2. Related Art 
     FIG. 1  shows a schematic representation of a prior art continuous-time bandpass delta-sigma modulator, showing an input  10 , a first transconductor G 0 , a first second-order resonator  11 , a second transconductor G 2 , a second second-order resonator  12 , and a quantizer  13 . The delta-sigma modulator of  FIG. 1  is a fourth-order delta-sigma modulator, due to the presence of the two second-order resonators, which provide a fourth-order transfer function. Usually, also a feedback loop is present, comprising circuitry  14 , which will not be discussed here in detail, because not relevant to the present disclosure. Additionally, although  FIG. 1  shows a single feedback loop, multiple feedback and/or feed-forward loops can also be provided. 
   In a delta-sigma modulator, the poles of the feed-forward open loop are also the zeros of the noise transfer function NTF, i.e. the transfer function between the quantizer noise n and the output. Thus, four zeros in the noise transfer function NTF can, for example, be obtained by inserting four poles in the corresponding feed-forward loop. For example, in the diagram of  FIG. 1 , four poles are present in the feed-forward loop, due to the presence of the two second-order resonators  11  and  12 . 
   The delta-sigma modulator shown in  FIG. 1  can use either active resonators or passive resonators. Active resonators are disclosed, for example, in G. Raghavan, J. F. Jensen et al, “Architecture, design, and test of continuous-time tunable intermediate-frequency bandpass delta-sigma modulators,” IEEE J. Solid-State Circuits, vol. 36, pp. 5–13, January 2001. 
   Passive resonators, such as LC resonators, are shown in  FIG. 2 .  FIG. 2  is similar to the schematic diagram of  FIG. 1  and shows a prior art arrangement taken from J. A. Cherry “On the Design of a Fourth-Order Continuous-Time LC Delta-Sigma Modulator for UHF A/D Conversion”, IEEE Transactions on Circuits and Systems—II: Analog and Digital Signal Processing, Vol. 47, No. 6, June 2000. 
   The arrangement of  FIG. 2  shows second-order LC resonators  15  and  16  acting as analog filtering circuits. The first LC resonator  15  has a resonant frequency f 1  and the second LC resonator  16  has a resonant frequency f 2 . 
   The transfer function for this chain of resonators is found by multiplying each of the elements G 0 , G 1 ,  15 , and  16  in  FIG. 2  together, and is shown in Equation (1). 
   
     
       
         
           
             
               
                 
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                     0 
                   
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                           s 
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                 Equation 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 
                   ( 
                   1 
                   ) 
                 
               
             
           
         
       
     
   
   The input  10  is usually a voltage analog input. The output of the transconductor G 0  is a current signal which is input into the LC resonator  15  and output as a voltage signal  17 . Also the second LC resonator  16  has a current input and a voltage output. Therefore, a further transconductor G 1  is needed, which converts the voltage signal  17  to a current signal  18 . The voltage output  19  of the LC resonator  16  is then input into the analog-to-digital converter or quantizer  11 . 
   The presence of the transconductor G 1  introduces noise and distortion in the feed-forward loop. In  FIG. 2 , n 1  and d 1  represent noise and distortion terms in G 1 . These refer back to the input by dividing by the gain to obtain 
   
     
       
         
           
             
               
                 
                   n 
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                     input 
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                       n 
                       1 
                     
                     
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                       0 
                     
                   
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                       1 
                     
                   
                 
               
             
             
               
                 Equation 
                 ⁢ 
                 
                     
                 
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                   ( 
                   2 
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   At the resonant frequency 
             f   1     =     1         L   1     ⁢     C   1                 
of the resonator  15 , n(input)=0. However, away from this resonance frequency, n(input) is not zero and can affect the performance of the modulator. In particular, if resonator  15  has a resonant frequency f 1  and resonator  16  has a resonant frequency
 
               f   2     =     1         L   2     ⁢     C   2             ,         
the noise at f 2  is higher than the noise at f 1 , as shown in  FIG. 3 , which shows the spectrum of the output signal power. The portion A of the waveform of  FIG. 3  shows the noise floor, while portion B shows the desired output signal. In order to obtain the highest signal-to-noise ratio possible, the noise floor should be kept as low as possible.
 
   In particular, for narrowband applications, n(input) is reduced by the gain of the first LC resonator  15  at the desired frequency. However, as the bandwidth increases, to achieve optimal signal-to-noise ratio SNR over a bandwidth, the resonator poles are split apart. As a consequence, the noise of the second, third, etc. resonators is no longer reduces by the same degree because the following resonator poles are located at a different location than the first resonator pole. 
   SUMMARY 
   According to a first aspect, a bandpass continuous-time delta-sigma modulator is disclosed, comprising: a transconductor, having a voltage analog input and a current analog output; a filtering arrangement, having a current input comprising, at least in part, the current analog output of the transconductor and a voltage analog output; and a quantizer having an input formed by the voltage analog output of the filtering arrangement, wherein the filtering arrangement comprises a first second-order resonator and a second second-order resonator directly connected in series with the first second-order resonator. 
   According to a second aspect, a bandpass continuous-time delta-sigma modulator is disclosed, comprising: an input circuit transforming a first analog voltage signal into a first analog current signal; a filtering circuit comprising a first LC resonator and a second LC resonator directly connected with the first LC resonator; and an analog-to-digital converter connected with the filtering circuit, wherein: a second analog current signal is input into the filtering circuit, the second analog current signal being formed, at least in part, by the first analog current signal; and a second analog voltage signal is input into the analog-to-digital converter, the second analog voltage being read out from the filtering circuit. 
   According to a third aspect, a bandpass continuous-time delta-sigma modulator is disclosed, comprising: a filtering arrangement having a current analog input and a voltage analog output: and a quantizer having an input formed by the voltage analog output of the filtering arrangement, wherein the filtering arrangement comprises three or more second-order resonators, at least two of the three or more second-order resonators being directly connected to each other. 
   According to a fourth aspect, a method to convert an analog voltage signal to a digital voltage signal is disclosed, comprising: providing a first analog voltage signal; converting the first analog voltage signal to a first analog current signal; adding the first analog current signal to a second analog current signal to form a third analog current signal; providing the third analog current signal to an analog filtering circuit comprising a first LC resonator and a second LC resonator in series with the first LC resonator to generate a second analog voltage signal, wherein an output of the first LC resonator forms an input of the second LC resonator; and quantizing the second analog voltage signal to generate the digital voltage signal. 
   According to a fifth aspect, a lowpass continuous-time delta-sigma modulator is disclosed, comprising: a transconductor, having a voltage analog input and a current analog output; a filtering arrangement, having a current input comprising, at least in part, the current analog output of the transconductor and a voltage analog output; and a quantizer having an input formed by the voltage analog output of the filtering arrangement, wherein the filtering arrangement comprises at least one second-order resonator directly connected with at least one capacitor. 

   
     BRIEF DESCRIPTION OF THE DRAWINGS 
     The present disclosure will be understood and appreciated more fully from the following detailed description taken in conjunction with the drawings in which: 
       FIGS. 1 and 2 , already discussed above, show schematic representations of a prior art delta-sigma modulator; 
       FIG. 3 , already discussed above, shows a frequency spectrum related to the delta-sigma modulator of  FIGS. 1 and 2 ; 
       FIG. 4  shows a schematic representation of a first embodiment of the present disclosure; 
       FIG. 5  shows a frequency spectrum related to the delta-sigma modulator of  FIG. 4 ; 
       FIG. 6  shows a schematic representation of a second embodiment of the present disclosure; and 
       FIG. 7  shows a further embodiment for a lowpass delta-sigma modulator. 
   

   DETAILED DESCRIPTION 
   The present disclosure improves the circuital arrangement discussed above because it provides for a fourth or higher order delta-sigma modulator by directly connecting the LC resonators in series so that the output of the first resonator is directly connected to the input of the second resonator, as shown in  FIG. 4 . According to  FIG. 4 , the second resonator  16  is placed upstream of the transconductor G 0  and in series with the resonator  15 . 
   The transfer function for the embodiment shown in  FIG. 4  is as follows. 
   
     
       
         
           
             
               
                 
                   
                     
                       
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                 Equation 
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                   3 
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   It should be noted that the poles in Equation (3) are the same as in Equation (1). Therefore, it is possible to design a delta-sigma modulator with the same noise transfer function in either the configuration of  FIG. 2  or  FIG. 4 . However, differently from the configuration of the prior art, the configuration according to the present disclosure does not need a transconductor G 1 . 
   With reference to  FIG. 4 , the input to the resonators  15  and  16  is the sum of the current signals  17  (output of the transconductor G 0 ) and  18  (feedback loop). The quantizer  11  reads a voltage input V, which equals to the sum I of the current signals  17  and  18  times the impedance Z of the resonators  15  and  16 . 
     FIG. 5  shows the spectrum of the output signal power in accordance with the present disclosure, where the noise floor at the resonant frequency f 1  is the same as the noise floor at the resonant frequency f 2 . The resonant frequencies can be anywhere from 0 to Fs/2, wherein Fs is the sampling frequency of the delta-sigma modulator. 
   The elimination of active components such as the transconductor G 1 , and further transconductors in case of a sixth-order, eighth-order, etc. delta-sigma modulator, increases linearity and decreases noise, particularly in applications with lower oversampling ratios, for example applications where the oversampling ratio is less than 400. 
     FIG. 6  shows a further embodiment of the present disclosure, where both the first resonator  15  and the second resonator  16  are parallel LC resonators. Also in this embodiment, the first resonator is directly connected to the second resonator. 
   The present disclosure shows an embodiment dealing with a fourth-order modulator. The person skilled in the art will note that also sixth-order, eighth-order, and so on delta-sigma modulators can be provided, by just adding additional LC resonators in series to the two resonators shown in  FIGS. 4 and 6 . In those higher-order embodiments, at least two resonators, and preferably all resonators, will be directly connected to each other, similarly to what shown in  FIGS. 4 and 6 . 
   Additionally, a further embodiment for a lowpass delta-sigma modulator is possible where one or more LC resonators are directly connected in series with one or more capacitors, as shown in  FIG. 7  which shows, by way of example, a series C 3 -L 2 C 2 -C 4 -L 1 C 1 -C 5 -C 6 . By doing this, the transfer function has at least one pole at DC and also one or more poles at higher frequencies. This embodiment can give a desirable noise transfer function for lowpass delta-sigma modulators. 
   It will be appreciated that the present disclosure is not limited to what has been particularly shown and described herein above. Rather the scope of the present disclosure is defined by the claims which follow.