Abstract:
An apparatus for performing digital-to-analog conversion with an increased SFDR is provided. An incoming M-bit sample is split into first and second N-bit samples. Preferably, M=16, and N=12. The first N-bit sample contains information relating to the M-bit sample when outside a first predetermined range, and the second N-bit sample contains information relating to the M-bit sample when inside said first predetermined range. A first DAC processes the first N-bit sample to produce a first analog signal, and a second DAC for processing the second N-bit sample to produce a second analog signal. An attenuator attenuates the second analog signal to produce a third analog signal. Finally, a summer is provided adding the first analog signal to the third analog signal representative of the M-bit sample. Preferably, the second predetermined range is a range having a size equal to the range of the second N-bit DAC which is centered at the midpoint of the range the M-bit sample. Advantageously, most transitions in the signal occur in the second analog signal, and as such there is more noise in the second analog signal. However, the second analog signal is the signal which is attenuated, and this attenuation also attenuates the noise. Thus, when the two analog signals are combined, a lower overall noise level results. The result is a digital-to-analog converter apparatus which is suitable for wideband applications which require large SFDR.

Description:
FIELD OF THE INVENTION 
     The invention relates to digital-to-analog converters, and to methods of performing digital-to-analog conversion. 
     BACKGROUND OF THE INVENTION 
     Some digital-to-analog converters (DAC) take baseband digital samples and convert them to an IF (intermediate frequency) analog signal. The particular IF is determined by the frequency of a clock applied to the DAC. The spectrum of the analog signal is centred at the intermediate frequency, and typically drops off on either side of the intermediate frequency. All DACs introduce an interference effect known as spurs. These are spikes in the frequency domain representation of the converted signal which are caused by the design of the DAC, and may be a function of the clock, and certain input signal characteristics for example. While the maximum meaningful output of a DAC is determined by the number of bits in the DAC, the minimum is determined by the magnitude of the spurs. The SFDR (spurious free dynamic range) of the DAC is the maximum meaningful output minus the maximum spur magnitude, this representing the range of signal magnitudes to which the spurs contribute negligibly. It is a characteristic of existing DACs that the SFDR decreases with increasing frequency, and this limits the maximum frequency for which a given DAC will be useful. One result of this is that state of the art DACs do not have a sufficient SFDR for wideband/multi-carrier next generation wireless systems. 
     SUMMARY OF THE INVENTION 
     It is an object of the invention to obviate or mitigate one or more of the above identified disadvantages. 
     An apparatus for performing digital-to-analog conversion with an increased SFDR is provided. An incoming M-bit sample is split into first and second N-bit samples. Preferably, M=16, and N=12. The first N-bit sample contains information relating to the M-bit sample when outside a first predetermined range, and the second N-bit sample contains information relating to the M-bit sample when inside the first predetermined range. A first DAC processes the first N-bit sample to produce a first analog signal, and a second DAC for processing the second N-bit sample to produce a second analog signal. An attenuator attenuates the second analog signal to produce a third analog signal. Finally, a summer is provided for adding the first analog signal to the third analog signal representative of the M-bit sample. Preferably, the second predetermined range is a range having a size equal to the range of the second N-bit DAC which is centred at the midpoint of the range the M-bit sample. 
     Advantageously, most transitions in the signal occur in the second analog signal, and as such there is more noise in the second analog signal. However, the second analog signal is the signal which is attenuated, and this attenuation also attenuates the noise in the second analog signal. Thus, when the two analog signals are combined, a lower overall noise level results. The result is a digital-to-analog converter apparatus which is suitable for wideband applications which require large SFDR. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     Preferred embodiments of the invention will now be described with reference to the attached drawings in which: 
     FIG. 1 is a block diagram of a stacked digital-to-analog converter apparatus according to an embodiment of the invention; 
     FIGS. 2,  3 A,  3 B,  4 A,  4 B,  5 A,  5 B,  6 A,  6 B and  7  are plots of various functions at different points in the processing of a sequence of digital samples by the apparatus of FIG. 1; and 
     FIG. 8 is a flowchart for a method of performing digital-to-analog conversion according to an embodiment of the invention. 
    
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
     Referring now to FIG. 1, a stacked DAC according to an embodiment of the invention comprises a digital sample splitter  10  having outputs connected to a first DAC  12  a second DAC  14 . The first DAC  12  has an output connected to a summer  16 . The second DAC  14  has an output which is connected to an attenuator  18  which in turn has an output which is connected to the summer  16 . The summer  16  produces the DAC&#39;s overall result. 
     The digital sample splitter  10  receives an input signal S 0  which consists of M-bit digital samples, either parallel or serial. The digital sample splitter  10  performs some manipulation of the M-bit digital samples, the details of this manipulation being provided below, and produces two output signals S 1 ′ and S 2  each of which are N-bit digital words, where N&lt;M. The first DAC  12  is a conventional N-bit DAC which converts the N-bit samples of S 1 ′ into a first analog signal A 1 . Similarly, the second DAC  14  is a conventional N-bit DAC which converts the N-bit samples of S 2  into a second analog signal A 2 . The attenuator  18  performs an analog attenuation on the output A 2  of the second DAC  14  to produce an attenuated signal A 2 ′, and the summer  16  adds together the first analog signal A 1  and the attenuated second analog signal A 2 ′ to produce the overall result A 0 . 
     The circuit can be implemented using separate components for each of the digital sample splitter  10 , the first and second DACs  12 ,  14 , and the attenuator  18 . The digital sample splitter  10  may be a circuit, for example an FPGA, ASIC or other suitable device suitably designed and/or programmed. The DACs  12 ,  14  and the attenuator  18  may be off-the-shelf components. Alternatively a custom device incorporating combinations of two or more or even all of the functions of the digital sample splitter  10 , the first and second DACs  12 ,  14  and the attenuator  18 . 
     The stacked digital-to-analog converter will now be described further with an example in which M, the width of the input digital samples, is selected to be  16 , and in which N, the sample size for the two DACs  12 ,  14  is selected to be 12. For the purpose of explanation, an example plot of a series of digital samples is included in FIG.  2 . It is assumed that for this example offset binary (or positive binary) is the format of the digital samples, and as such the 16-bit samples can range from 0 (which is the all zeros sample (0000000000000000) to 2 16 −1 (which is the all ones sample (1111111111111111). Also indicated in FIG. 2 are three demarcation lines labelled T 0 , T 1  and T 2 . The first demarcation line T 0  is at 2 15 . This is the midpoint in the range of values a 16-bit sample can represent. The second and third demarcation lines are selected such that they contain a range of values centred at T 0  which are representable by 12-bit samples. Thus T 1 =2 15 −2 11 , and T 2 =2 15 +2 11 −1 respectively. The range of values which may be within the two demarcation lines is given by T 2 −T 1 =(2 15 +2 11 −1)−(2 15 −2 11 ) =2 12 −1, and this is the range of a 12-bit DAC. 
     The purpose of the digital sample splitter  10  of FIG. 1 is to represent information falling outside the two thresholds T 1  and T 2  by the first 12-bit sample S 1 ′, and to represent information falling inside the thresholds T 1  and T 2  by the second 12-bit sample S 2 . The processing performed to determine S 2  and subsequently to determine the attenuated analog representation A 2 ′ of S 2  will now be described. S 2  is determined according to the following equations: 
     
       
           S   0 &gt;( T 2=2 15 +2 11 −1)−&gt; S   2 =2 12 −1  
       
     
     
       
           S   0 &lt;( T 1=2 15 −2 11 )−&gt;S 2 =0  
       
     
     
       
           T 1&lt;= S     0  &lt;=T   2 −&gt;S   2   =S   0 −2 15 −2 11 .  
       
     
     S 2  for the example of FIG. 2 is illustrated in FIG.  3 A. It can be seen that S 2  is basically equivalent to S 0  clipped to be in between the T 1  and T 2 , and then shifted to be in the range 0 to 2 12 −1. This value is then processed by the second DAC  14  which has a full scale of −V max  to +V max  volts to produce an analog signal A 2  such as illustrated in FIG.  5 A. (Nothing happens in FIG.  4 A). It is assumed that the fullscale of the overall output A 0  is also to be −V max  to +V max  volts. The output of the second DAC  14  corresponds to an input in the range 0 to 2 12 −1, while the overall output is to correspond to an input in the range 0 to 2 16 −1, thus, to put the output of the second DAC  14  in the proper scale for consideration as the output of a 16-bit DAC, the output of the second DAC  14  needs to be attenuated by a factor of {fraction (1/2+L )} 16−12 ={fraction (1/2+L )} n   ={fraction (1/16+L )}, where n is the difference between M and N. This may be also be expressed as an attenuation of  10 −6.0206n/20  which can be approximated by 10 −6n/20  which is an attenuation of 6n dB. Attenuating the signal results in a signal within a range −V max ′ to V max ′, where V max ′=V max ×10 −6.0206n/20 . The attenuated signal A 2 ′ is illustrated in FIG.  6 A. 
     Turning now to the processing for S 1 ′, S 1 is determined according to the following equations: 
     
       
           S   0 &gt;( T 2=2 15 +2 11 −1)−&gt; S   1   =S   0 −(2 11 −1)  
       
     
     
       
           S   0 &lt;( T 1=2 15 −2 11 )−&gt; S   1   =S   0 +2 11    
       
     
     
       
           T 1&lt;× S   0   &lt;=T 2 −&gt; S   1 =2 15 .  
       
     
     S 1  for the above example is illustrated in FIG.  3 B. It can be seen that S 1  is equivalent to the amount clipped from S 0  in creating S 2  and shifted so as to be centred at 2 15 . This value is then shifted to the left by M−N=n=4 bits resulting in a 12-bit sample S 1  ′ suitable for processing by a 12-bit DAC. The shifted version of the signal S 1 ′ is illustrated in FIG.  4 B. This sample is then processed by the first DAC  12  which has a full scale of −V max  to +V max  volts to produce an analog signal A 1  such as illustrated in FIG.  5 B. 
     Referring to FIG. 5B, where S 1  had a contiguous range of (2 11  to 2 16 −2 11 ), after the shift, S 1 ′ has a range of (2 7  to 2 12 −2 7 ). Given that  2   11  yields a converted voltage of 0 in a 12-bit DAC, the largest output which will ever result from the first DAC  12  is the converted voltage for 2 12 −2 7  which is a fraction {fraction (15/16+L )} of DAC&#39;s full scale range V max . Thus despite the first DAC  12  having a fullscale output of −V max  to +V max , the actual output of the first DAC for this design will always be in the range −{fraction (15/16+L )} V max  to {fraction (15/16+L )} V max . Recalling that V max ′={fraction (1/16+L )} V max , the range of A 1  can be rewritten as −(V max −V max ′) to V max −V max ′ and this range is indicated in FIG.  6 B. 
     The summer  16  combines the two analog signals A 1  and A 2 ′ producing the signal A 0  illustrated in FIG.  7 . This signal has a range of −V max  to +V max , this being the sum of the ranges of its two constituent signals. A 0  is a true analog representation of the input signal S 0 . 
     Performing the digital-to-analog conversion in this manner has significant advantages in terms of noise reduction. To begin, an assumption being made is that most of the transitions in the incoming digital signal S 0  will occur within the range T 1  to T 2 , and thus will end up existing in S 2 . Correspondingly, there are very few transitions in S 1 . This has the effect of reducing substantially the noise floor in S 1 , while the noise floor for S 2  will be similar to that of the original signal S 0 . However, S 2 , after conversion to A 2 , is passed through an attenuator which attenuates both A 2  and its noise, resulting in a noise floor which is attenuated by 6n dB, 24 dB in the specific example given above. Then, when adding A 1  to A 2 ′, a signal with a very low noise floor results, which may be as much as 6n dB lower than that of a conventional design. This translates directly into a 6n dB improvement in the SFDR. 
     A very specific implementation/embodiment of the invention has been described for the case where 16-bit samples are split into two 12-bit samples which are then processed separately until their resulting analog values are summed. It is to be understood that the invention has a much more general application than this. This more general application will be described below with reference to a flowchart in FIG. 8, and how the above specific example fits in with the general application will be described. 
     More generally, the desired analog fullscale of the stacked M-bit (M≧2, preferably ≧4, and more preferably ≧8) digital-to-analog converter can be defined to have a plurality K of subranges which need not necessarily be contiguous, K being at least two. In preferred embodiments k=2,3 and 4 respectively. In the example given above, there were two (K=2) subranges consisting firstly of (−V max  to −V max +V max ′, V max −V max ′ to V max ) and secondly of (−V max ′ to V max ′). Next, a corresponding digital subrange of 0 to 2 M −1 is defined for each analog subrange. In the example given above, the corresponding digital subrange for (−V max  to −V max +V max ′, V max −V max ′ to V max ) was (0 to 2 15 −2 11 −1, 2 15 +2 11  to 2 16 −1) and the corresponding digital subrange for (−V max ′ to V max ′) was (2 15 −2 11  to 2 15 +2 11 −1). Having defined the various analog and digital subranges, in step  8 -A each M-bit digital sample is converted into K digital samples each having a respective sample size N k , k=1, . . . ,K one for each subrange, (N k &lt;M, N k ≧1, preferably ≧2 and more preferably ≧4). In the example given above, M=16, and N 1 =12 and N 2 =12. Preferably, N k ,k=1, . . . ,K are equal in size, but this need not necessarily be the case. Preferably, the ranges are selected so that they are centred at the midrange of the overall device, i.e., the analog ranges are selected to be centred at 0, and the digital ranges are centred at 2 M−1 . This is the case for the example given above. The steps involved in this conversion may involve one or more of subtraction, addition, clipping, bit shifting. 
     Next, in step  8 -B a respective digital-to-analog converter performs a digital-to-analog conversion on each of the K digital samples to produce a respective analog signal. In the example given above, this resulted in the two analog signals A 1  and A 2 . 
     Next, in step  8 -C a respective attenuation is applied to each of the analog signals so as to result in an analog signal having a dynamic range equal to the analog subrange corresponding with the analog signal&#39;s digital sample&#39;s digital subrange. In the example above, the dynamic range of the first analog signal A 1  was correct, and so no attenuation was applied (or an attenuation of 0 dB was applied). The dynamic range of the second analog signal A 2  was too large, and an attenuation of 24 dB was applied. 
     As indicated at step  8 -D, in the event that a given range was not centred at the midrange of the overall device as preferred, the analog signal needs to be DC offset such that it is in the correct location. This ensures that it makes sense to add all of the attenuated values directly together. For example, if a range of (2 15  to 2 15 +2 12 −1) was selected for a particular sample, this needs to produce an analog signal in the range of 0 to 2V max ′. However, the DAC will produce a signal in the range of −V max  to +V max . Thus, it needs to be offset by V max  so as to be in the range of 0 to 2V max . When attenuated, 0 to 2V max  will become 0 to 2V max ′ as required. More generally, each analog signal must be offset and/or attenuated such that will have a range equal in size and position to its desired corresponding analog range. 
     Finally, in step  8 -E the overall result is determined by adding together all of the attenuated analog signals. 
     The required DC offset can be achieved by adding a constant value to the output of the DAC before attenuation. Equivalently, after attenuation an appropriate (different) DC offset may be applied to the same effect. In this particular example, offsetting by V max ′ after attenuation will produce the same result. Overall, the attenuation and offsetting must collectively be done in any manner such that the required analog range results. Circuitry which can perform the required combination of attenuation and offsetting will be referred to as level conversion circuitry. In FIG. 8, the step  8 -F of applying level conversion to one or more samples can be performed in place of steps of  8 -C and  8 -D. 
     Furthermore, where the examples have all assumed an attenuation is required, more generally some sort of gain adjustment may be required. For example, the overall output may have a desired dynamic range which is larger than that of the DACs in which case gains might be required on the DAC outputs. 
     Numerous modifications and variations of the present invention are possible in light of the above teachings. It is therefore to be understood that within the scope of the appended claims, the invention may be practised otherwise than as specifically described herein. 
     Where the above described examples have assumed binary offset formatted samples, other sample formats could be alternatively used assuming the appropriate adjustments in the splitter function are made.