Abstract:
A method is provided. A noise shaped signal having a plurality of instants is generated with each instant being associated with at least one of a plurality of output levels. A next phase is selected for each instant, where each next phase is a circularly shifted phase based at least in part on a previous phase for the associated output level for its instant. A plurality of PWM signals is then generated using the phase for each instant, and an amplified signal is generated from the plurality of PWM signals.

Description:
TECHNICAL FIELD 
       [0001]    The invention relates generally to reducing distortion and, more particularly, to reducing distortion using a phase averaged pulse width modulator (PWM). 
       BACKGROUND 
       [0002]    Turning to  FIGS. 1-3 , an example of a PWM amplifier  100  can be seen. In operation, the PWM amplifier  100  receives input signal IN at the noise shaping circuit  102  (which is typically a sigma-delta modulator). Assuming that the noise shaping circuit  102  is a sigma-delta modulator or SDM that uses oversampling, this noise shaping circuit  102  can spread the total noise power over the oversampling frequency band (which is generally larger than the band-of-interest) so as to reduce in-band noise. The noise shaped signal is then applied to the digital PWM  104  so as to generate a PWM signal for use by the amplification stage  106  (which can, for example, be comprised of a digital-to-analog converter (DAC)  108  and amplifier  110  (i.e., class AB) as shown in  FIG. 2  or a switching amplifier  112  (i.e., class D) as shown in  FIG. 3 ). 
         [0003]    One problem with this amplifier  100  is the nonlinear nature of the digital PWM  104 . Some of the in-band nonlinearity associated with the digital PWM  104  can be corrected using predistortion or feedback control, but signal images and nonlinear components can be created at high frequencies (as shown in  FIGS. 4A and 4B ). As a result of having this high frequency content, the amplification stage  106  should have high linearity; otherwise the high frequency content will fold in-band, limiting in-band linearity. Additionally, this high frequency content can unnecessarily use power. These high frequency content also should be attenuated by high-order analog filters in order to meet spectral requirements. Thus, there is a need for an improved PWM amplifier. 
         [0004]    Some examples of conventional systems are: U.S. Pat. No. 7,209,064; U.S. Pat. No. 7,327,296; U.S. Pat. No. 7,425,853; U.S. Pat. No. 7,782,238; and U.S. Pat. No. 7,830,289. 
       SUMMARY 
       [0005]    An embodiment of the present invention, accordingly, provides an apparatus. The apparatus comprises a noise shaping circuit having a plurality of output levels; a pulse width modulator (PWM) that is configured to generate a plurality of PWM phases; a phase rotator that is coupled between the noise shaping circuit and the PWM, wherein the phase rotator circularly rotates each output level through the plurality of PWM levels; and an amplification stage that is coupled to the PWM. 
         [0006]    In accordance with an embodiment of the present invention, the PWM further comprises a digital PWM having: a plurality of phases rotated PWM circuits that are each coupled to the noise shaping circuit; and a multiplexer that is coupled to each of the plurality of phases rotated PWM circuits and to the phase rotator. 
         [0007]    In accordance with an embodiment of the present invention, the multiplexer further comprises a first multiplexer, and wherein the phase rotator further comprises: a plurality of tracking branches that are each coupled to the noise shaping circuit and that are each associated with at least one of the output levels; and a second multiplexer that is coupled to each tracking branch, the noise shaping circuit, and the first multiplexer, wherein the second multiplexer controls the first multiplexer, and wherein noise shaping circuit controls the second multiplexer. 
         [0008]    In accordance with an embodiment of the present invention, each of the plurality of tracking branches further comprises: a comparator that is coupled to the noise shaping circuit and that receives a reference signal; and a tracking circuit that is coupled between the comparator and the second multiplexer. 
         [0009]    In accordance with an embodiment of the present invention, the noise shaping circuit further comprises a sigma-delta modulator. 
         [0010]    In accordance with an embodiment of the present invention, the amplification stage further comprises: a digital-to-analog converter (DAC) that is coupled to the first multiplexer; and an amplifier that is coupled to the DAC. 
         [0011]    In accordance with an embodiment of the present invention, the amplification stage further comprises a switching amplifier that is coupled to the first multiplexer. 
         [0012]    In accordance with an embodiment of the present invention, a method is provided. The method comprises generating a noise shaped signal having a plurality of instants, wherein each instant is associated with at least one of a plurality of output levels; selecting a next phase for each instant, wherein each next phase is a circularly shifted phase based at least in part on a previous phase for the associated output level for its instant; generating a plurality of PWM signals using the phase for each instant; and generating an amplified signal from the plurality of PWM signals. 
         [0013]    In accordance with an embodiment of the present invention, the step of selecting further comprises: comparing each instant to a plurality of references so as to identify its associated output level; for each instant, determining the previous phase for its associated output level; for each instant, generating a next phase based at least in part on the previous phase; and for each instant, storing the next phase. 
         [0014]    In accordance with an embodiment of the present invention, the step of generating the plurality of PWM signals further comprises: for each instant, selecting a phase rotated PWM circuit associated with the next phase; and for each instant, producing at least one of the PWM signals. 
         [0015]    In accordance with an embodiment of the present invention, the step of generating the noise shaped signal further comprises generating a modulated signal with a sigma-delta modulator. 
         [0016]    In accordance with an embodiment of the present invention, the step of generating the amplified signal further comprise: converting the plurality of PWM signals to an analog signal; and amplifying the analog signal. 
         [0017]    In accordance with an embodiment of the present invention, the step of generating the amplified signal further comprises applying the plurality of PWM signals to a switching amplifier. 
         [0018]    In accordance with an embodiment of the present invention, an apparatus is provided. The apparatus comprises a noise shaping circuit that is configured to generate a noise shaped signal having a plurality of instants; a digital PWM that is configured to generate a plurality of PWM phases; a phase rotator including: an identification circuit that is coupled to the noise shaping circuit and that is configured to associated each instant with at least one of a plurality of output levels; and a selection circuit that is coupled to the identification circuit and the digital PWM, wherein the selection circuit is configured to select at least one of the PWM phases for each instant, and wherein each selection is circularly rotated based at least in part on a previously selected PWM phase for its associated output level; and an amplification stage that is coupled to the digital PWM. 
         [0019]    In accordance with an embodiment of the present invention, the digital PWM further comprises: a plurality of phases rotated PWM circuits that are each coupled to the noise shaping circuit; and a multiplexer that is coupled to each of the plurality of phases rotated PWM circuits and to the selection circuit. 
         [0020]    In accordance with an embodiment of the present invention, the identification circuit further comprises a plurality of comparators that are each coupled to the noise shaping circuit. 
         [0021]    In accordance with an embodiment of the present invention, the multiplexer further comprises a first multiplexer, and wherein the selection circuit further comprises: a plurality of tracking circuits, where each tracking circuit that is coupled to at least one of the comparator; and a second multiplexer that is coupled to each tracking circuit, the noise shaping circuit, and the first multiplexer, wherein the second multiplexer controls the first multiplexer, and wherein noise shaping circuit controls the second multiplexer. 
         [0022]    In accordance with an embodiment of the present invention, the amplification stage further comprises a switching amplifier that is coupled to the first multiplexer. 
         [0023]    The foregoing has outlined rather broadly the features and technical advantages of the present invention in order that the detailed description of the invention that follows may be better understood. Additional features and advantages of the invention will be described hereinafter which form the subject of the claims of the invention. It should be appreciated by those skilled in the art that the conception and the specific embodiment disclosed may be readily utilized as a basis for modifying or designing other structures for carrying out the same purposes of the present invention. It should also be realized by those skilled in the art that such equivalent constructions do not depart from the spirit and scope of the invention as set forth in the appended claims. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0024]    For a more complete understanding of the present invention, and the advantages thereof, reference is now made to the following descriptions taken in conjunction with the accompanying drawings, in which: 
           [0025]      FIG. 1  is a diagram of an example of a conventional PWM amplifier; 
           [0026]      FIGS. 2 and 3  are diagrams of examples of the amplification stage of  FIG. 1 ; 
           [0027]      FIGS. 4A and 4B  are, respectively, linear-scale and log-scale plots depicting signal images and nonlinear components created as a result of the nonlinear behavior of the digital PWM of  FIG. 1 ; 
           [0028]      FIG. 5  is a diagram of an example of a PWM amplifier in accordance with an embodiment of the present invention; 
           [0029]      FIG. 6  is a diagram of an example of circular phase averaging; 
           [0030]      FIG. 7  is a diagram of an example of the phase rotator and digital PWM of  FIG. 5 ; and 
           [0031]      FIGS. 8-10B  are diagrams depicting example operations of the PWM amplifier of  FIG. 5 . 
       
    
    
     DETAILED DESCRIPTION 
       [0032]    Refer now to the drawings wherein depicted elements are, for the sake of clarity, not necessarily shown to scale and wherein like or similar elements are designated by the same reference numeral through the several views. 
         [0033]    Turning to  FIG. 5 , an example of a system  200  in accordance with the present invention can be seen. As shown in this example, system  200  is similar to system  100 , except that digital PWM  104  has been replaced with digital PWM  204  and that phase rotator  202  has been included. The digital PWM  204  and phase rotator  202  allow for dynamic PWM coding waveform selection using a circular phase shift. Essentially, the PWM waveform sequence can be selected such that nulls are created at spectral locations where harmonics (i.e., nonlinear components) and signal images are otherwise created. This causes a significant attenuation of these nonlinear components and signal images, essentially helping to linearize the digital PWM  204 . This can be referred to as circular phase averaging. 
         [0034]    To elaborate, an example of circular phase averaging can be seen in  FIG. 6 . In this example, there are four phases PH 1  to PH 4 , and the signal X R (k) for each of phases PH 1  to PH 4  (denoted by subscript R) can be represented at discrete frequency points (represented by k) as follows: 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       X 
                       R 
                     
                      
                     
                       ( 
                       k 
                       ) 
                     
                   
                   = 
                   
                     
                       ∑ 
                       
                         n 
                         = 
                         0 
                       
                       3 
                     
                      
                     
                         
                     
                      
                     
                       
                         x 
                          
                         
                           ( 
                           n 
                           ) 
                         
                       
                        
                       
                          
                         
                            
                            
                           
                             
                               π 
                                
                               
                                   
                               
                                
                               nk 
                             
                             2 
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   1 
                   ) 
                 
               
             
           
         
       
     
         [0000]    For this example, the values of 0, 1, 2, and 3 of k represent direct current (DC), FCLK/4, FCLK/2, and 3*FCLK/4, respectively (where FCLK is a clock frequency that is used to generate the PWM period). When applied to phases PH 1  to PH 4 , equation (1) yields: 
         [0000]    
       
         
           
             
               
                 
                   PH 
                    
                   
                       
                   
                    
                   1 
                    
                   
                     { 
                     
                       
                         
                           
                             
                               
                                 X 
                                 1 
                               
                                
                               
                                 ( 
                                 0 
                                 ) 
                               
                             
                             = 
                             
                               
                                 
                                   ∑ 
                                   
                                     n 
                                     = 
                                     0 
                                   
                                   3 
                                 
                                  
                                 
                                     
                                 
                                  
                                 
                                   x 
                                    
                                   
                                     ( 
                                     n 
                                     ) 
                                   
                                 
                               
                               = 
                               
                                 
                                   1 
                                   + 
                                   1 
                                 
                                 = 
                                 2 
                               
                             
                           
                         
                       
                       
                         
                           
                             
                               
                                 X 
                                 1 
                               
                                
                               
                                 ( 
                                 1 
                                 ) 
                               
                             
                             = 
                             
                               
                                 
                                   ∑ 
                                   
                                     n 
                                     = 
                                     0 
                                   
                                   3 
                                 
                                  
                                 
                                     
                                 
                                  
                                 
                                   
                                     x 
                                      
                                     
                                       ( 
                                       n 
                                       ) 
                                     
                                   
                                    
                                   
                                      
                                     
                                        
                                        
                                       
                                         
                                           π 
                                            
                                           
                                               
                                           
                                            
                                           n 
                                         
                                         2 
                                       
                                     
                                   
                                 
                               
                               = 
                               
                                 1 
                                 + 
                                 
                                    
                                   
                                      
                                      
                                     
                                       π 
                                       2 
                                     
                                   
                                 
                               
                             
                           
                         
                       
                       
                         
                           
                             
                               
                                 X 
                                 1 
                               
                                
                               
                                 ( 
                                 2 
                                 ) 
                               
                             
                             = 
                             
                               
                                 
                                   ∑ 
                                   
                                     n 
                                     = 
                                     0 
                                   
                                   3 
                                 
                                  
                                 
                                     
                                 
                                  
                                 
                                   
                                     x 
                                      
                                     
                                       ( 
                                       n 
                                       ) 
                                     
                                   
                                    
                                   
                                      
                                     
                                       π 
                                        
                                       
                                           
                                       
                                        
                                       n 
                                     
                                   
                                 
                               
                               = 
                               
                                 1 
                                 + 
                                 
                                    
                                   π 
                                 
                               
                             
                           
                         
                       
                       
                         
                           
                             
                               
                                 X 
                                 1 
                               
                                
                               
                                 ( 
                                 3 
                                 ) 
                               
                             
                             = 
                             
                               
                                 
                                   ∑ 
                                   
                                     n 
                                     = 
                                     0 
                                   
                                   3 
                                 
                                  
                                 
                                     
                                 
                                  
                                 
                                   
                                     x 
                                      
                                     
                                       ( 
                                       n 
                                       ) 
                                     
                                   
                                    
                                   
                                      
                                     
                                        
                                        
                                       
                                         
                                           3 
                                            
                                           π 
                                            
                                           
                                               
                                           
                                            
                                           n 
                                         
                                         2 
                                       
                                     
                                   
                                 
                               
                               = 
                               
                                 1 
                                 + 
                                 
                                    
                                   
                                      
                                      
                                     
                                       
                                         3 
                                          
                                         π 
                                       
                                       2 
                                     
                                   
                                 
                               
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   2 
                   ) 
                 
               
             
             
               
                 
                   PH 
                    
                   
                       
                   
                    
                   2 
                    
                   
                     { 
                     
                       
                         
                           
                             
                               
                                 X 
                                 2 
                               
                                
                               
                                 ( 
                                 0 
                                 ) 
                               
                             
                             = 
                             
                               
                                 
                                   ∑ 
                                   
                                     n 
                                     = 
                                     0 
                                   
                                   3 
                                 
                                  
                                 
                                     
                                 
                                  
                                 
                                   x 
                                    
                                   
                                     ( 
                                     n 
                                     ) 
                                   
                                 
                               
                               = 
                               
                                 
                                   1 
                                   + 
                                   1 
                                 
                                 = 
                                 2 
                               
                             
                           
                         
                       
                       
                         
                           
                             
                               
                                 X 
                                 2 
                               
                                
                               
                                 ( 
                                 1 
                                 ) 
                               
                             
                             = 
                             
                               
                                 
                                   ∑ 
                                   
                                     n 
                                     = 
                                     0 
                                   
                                   3 
                                 
                                  
                                 
                                     
                                 
                                  
                                 
                                   
                                     x 
                                      
                                     
                                       ( 
                                       n 
                                       ) 
                                     
                                   
                                    
                                   
                                      
                                     
                                        
                                        
                                       
                                         
                                           π 
                                            
                                           
                                               
                                           
                                            
                                           n 
                                         
                                         2 
                                       
                                     
                                   
                                 
                               
                               = 
                               
                                 
                                   
                                      
                                     
                                        
                                        
                                       
                                         π 
                                         2 
                                       
                                     
                                   
                                   + 
                                   
                                      
                                     π 
                                   
                                 
                                 = 
                                 
                                   
                                      
                                     
                                        
                                        
                                       
                                         π 
                                         2 
                                       
                                     
                                   
                                    
                                   
                                     ( 
                                     
                                       1 
                                       + 
                                       
                                          
                                         
                                            
                                            
                                           
                                             π 
                                             2 
                                           
                                         
                                       
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                         
                       
                       
                         
                           
                             
                               
                                 X 
                                 2 
                               
                                
                               
                                 ( 
                                 2 
                                 ) 
                               
                             
                             = 
                             
                               
                                 
                                   ∑ 
                                   
                                     n 
                                     = 
                                     0 
                                   
                                   3 
                                 
                                  
                                 
                                     
                                 
                                  
                                 
                                   
                                     x 
                                      
                                     
                                       ( 
                                       n 
                                       ) 
                                     
                                   
                                    
                                   
                                      
                                     
                                       π 
                                        
                                       
                                           
                                       
                                        
                                       n 
                                     
                                   
                                 
                               
                               = 
                               
                                 
                                   
                                      
                                     π 
                                   
                                   + 
                                   
                                      
                                     
                                       2 
                                        
                                       π 
                                     
                                   
                                 
                                 = 
                                 
                                   
                                      
                                     π 
                                   
                                    
                                   
                                     ( 
                                     
                                       1 
                                       + 
                                       
                                          
                                         π 
                                       
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                         
                       
                       
                         
                           
                             
                               
                                 X 
                                 2 
                               
                                
                               
                                 ( 
                                 3 
                                 ) 
                               
                             
                             = 
                             
                               
                                 
                                   ∑ 
                                   
                                     n 
                                     = 
                                     0 
                                   
                                   3 
                                 
                                  
                                 
                                     
                                 
                                  
                                 
                                   
                                     x 
                                      
                                     
                                       ( 
                                       n 
                                       ) 
                                     
                                   
                                    
                                   
                                      
                                     
                                        
                                        
                                       
                                         
                                           3 
                                            
                                           π 
                                            
                                           
                                               
                                           
                                            
                                           n 
                                         
                                         2 
                                       
                                     
                                   
                                 
                               
                               = 
                               
                                 
                                   
                                      
                                     
                                        
                                        
                                       
                                         
                                           3 
                                            
                                           π 
                                         
                                         2 
                                       
                                     
                                   
                                   + 
                                   
                                      
                                     
                                       3 
                                        
                                       π 
                                     
                                   
                                 
                                 = 
                                 
                                   
                                      
                                     
                                        
                                        
                                       
                                         
                                           3 
                                            
                                           π 
                                         
                                         2 
                                       
                                     
                                   
                                    
                                   
                                     ( 
                                     
                                       1 
                                       + 
                                       
                                          
                                         
                                            
                                            
                                           
                                             
                                               3 
                                                
                                               π 
                                             
                                             2 
                                           
                                         
                                       
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   3 
                   ) 
                 
               
             
           
         
       
     
         [0000]    By combining the signal X R (k) for the corresponding frequency points, equations (2) through (5) yield: 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       
                         
                           
                             X 
                             TOTAL 
                           
                            
                           
                             ( 
                             0 
                             ) 
                           
                         
                         = 
                           
                          
                         
                           
                             ∑ 
                             
                               j 
                               = 
                               1 
                             
                             4 
                           
                            
                           
                               
                           
                            
                           
                             
                               X 
                               j 
                             
                              
                             
                               ( 
                               0 
                               ) 
                             
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         8 
                       
                     
                   
                 
               
               
                 
                   ( 
                   6 
                   ) 
                 
               
             
             
               
                 
                   
                     
                       
                         
                           
                             X 
                             TOTAL 
                           
                            
                           
                             ( 
                             1 
                             ) 
                           
                         
                         = 
                           
                          
                         
                           
                             ∑ 
                             
                               j 
                               = 
                               1 
                             
                             4 
                           
                            
                           
                               
                           
                            
                           
                             
                               X 
                               j 
                             
                              
                             
                               ( 
                               1 
                               ) 
                             
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           
                             
                               ( 
                               
                                 1 
                                 + 
                                 
                                    
                                   
                                      
                                      
                                     
                                       π 
                                       2 
                                     
                                   
                                 
                               
                               ) 
                             
                              
                               
                              
                             
                               ( 
                               
                                 1 
                                 + 
                                 
                                    
                                   
                                      
                                      
                                     
                                       π 
                                       2 
                                     
                                   
                                 
                                 + 
                                 
                                    
                                   π 
                                 
                               
                               ) 
                             
                           
                           + 
                           1 
                           + 
                           
                              
                             
                                
                                
                               
                                 
                                   3 
                                    
                                   π 
                                 
                                 2 
                               
                             
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           
                             
                               ( 
                               
                                 1 
                                 + 
                                 i 
                               
                               ) 
                             
                              
                             
                               ( 
                               
                                 1 
                                 + 
                                 i 
                                 - 
                                 1 
                               
                               ) 
                             
                           
                           + 
                           1 
                           - 
                           i 
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           
                             ( 
                             
                               i 
                               - 
                               1 
                             
                             ) 
                           
                           + 
                           1 
                           - 
                           i 
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         0 
                       
                     
                   
                 
               
               
                 
                   ( 
                   7 
                   ) 
                 
               
             
             
               
                 
                   
                     
                       
                         
                           
                             X 
                             TOTAL 
                           
                            
                           
                             ( 
                             2 
                             ) 
                           
                         
                         = 
                           
                          
                         
                           
                             ∑ 
                             
                               j 
                               = 
                               1 
                             
                             4 
                           
                            
                           
                               
                           
                            
                           
                             
                               X 
                               j 
                             
                              
                             
                               ( 
                               2 
                               ) 
                             
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           
                             
                               ( 
                               
                                 1 
                                 + 
                                 
                                    
                                   π 
                                 
                               
                               ) 
                             
                              
                             
                               ( 
                               
                                 1 
                                 + 
                                 
                                    
                                   π 
                                 
                                 + 
                                 
                                    
                                   
                                     2 
                                      
                                     π 
                                   
                                 
                               
                               ) 
                             
                           
                           + 
                           1 
                           + 
                           
                              
                             
                               3 
                                
                               π 
                             
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           
                             
                               ( 
                               
                                 1 
                                 - 
                                 1 
                               
                               ) 
                             
                              
                             
                               ( 
                               
                                 1 
                                 - 
                                 1 
                                 + 
                                 1 
                               
                               ) 
                             
                           
                           + 
                           1 
                           - 
                           1 
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         0 
                       
                     
                   
                 
               
               
                 
                   ( 
                   8 
                   ) 
                 
               
             
             
               
                 
                   
                     
                       
                         
                           
                             X 
                             TOTAL 
                           
                            
                           
                             ( 
                             4 
                             ) 
                           
                         
                         = 
                           
                          
                         
                           
                             ∑ 
                             
                               j 
                               = 
                               1 
                             
                             4 
                           
                            
                           
                               
                           
                            
                           
                             
                               X 
                               j 
                             
                              
                             
                               ( 
                               4 
                               ) 
                             
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           
                             
                               ( 
                               
                                 1 
                                 + 
                                 
                                    
                                   
                                      
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         [0000]    As shown in equations (6) through (9), the higher frequency components are substantially eliminated by performing the circular phase averaging shown in  FIG. 6 . 
         [0035]    To accomplish circular phase averaging, the phase rotator  202  monitors the noise shaped signal from the noise shaping circuit  102  and selects the appropriate phase shifted PWM pattern for the digital PWM  104  to output. In the example shown in  FIG. 7 , the noise shaping circuit  102  has 2N output levels (spanning from −N to N), and the phase rotator, in this example, has 2N tracking branches (which generally comprise comparators  302 - 1  to  302 - 2 N that receive reference signals REFN to REFMN, respectively, and tracking circuits  304 - 1  to  304 - 2 N) that correspond to these 2N output levels and that are coupled to multiplexer or mux  306 . Collectively, the comparators  302 - 1  to  302 - 2 N can also be referred to as an identification circuit, and the tracking circuits  304 - 1  to  304 - 2 N and multiplexer  306  can be referred to as a selection circuit. This allows the tracking branches (i.e., comparators  302 - 1  to  302 - 2 N and tracking circuits  304 - 1  to  304 - 2 N) to track or monitor output levels of noise shaping circuit  102  and select the appropriate phase for each. With the phase rotated PWM circuits  308 - 1  to  308 -M of digital PWM  204 , each can generate a phase shifted PWM pattern or signal using the clock signal CLK, and multiplexer  310 , which is controlled by the output of multiplexer  306 . 
         [0036]    Turning to  FIG. 8 , an example of the operation of the phase rotator  202  and digital PWM  204  can be seen. In this example, the noise shaping circuit  102  is a sigma-delta modulator with output levels from −3 to 3; instants I 1  to I 9  of the noise shaped signal are also shown. Since, in this example, the output levels range from −3 to 3, the phase rotator  202  has comparators  302 - 1  to  302 - 6  and tracking circuits  304 - 1  to  304 - 6 , and digital PWM  204 , in this example, has phase rotated PWM circuits  308 - 1  to  308 - 4 , which correspond to phase-0, phase-8, phase-16, and phase-24. Focusing on output level  1  (which is labeled SDM=1), instants I 1 , I 4 , I 6 , I 7 , and I 9  of noise shaped signal are associated with this output level, meaning that the noise shaped signal (either alone or with intervening logic) controls multiplexer  306  to select the tracking branch with comparator  302 - 1  and tracking circuit  304 - 1  and meaning that comparator  302 - 1  detects that the noise shaped signal corresponds to this level. The tracking circuit  304 - 1  (through multiplexer  306 ) controls multiplexer  310  so as to select the appropriate next phase based on the previous phase. For example and as shown, for instant I 4 , tracking circuit  304 - 1  would select phase-8 (which is associated with phase rotated PWM circuit  308 - 2 ) as the next phase because the previous phase at instant I 1  was phase-0 (which is associated with phase rotated PWM circuit  308 - 2 ). This next phase is then stored in tracking circuit  304 - 1  for use with the next instant associated with output level  1  (i.e., instant I 6 ). These phase rotations for each output level then continues in a circular fashion (i.e., phase-0→phase-8→phase-16→phase-24→phase-0). As a result, the PWM amplifier  200  can be dramatically improved. As shown in  FIGS. 9 and 9B  (which are, respectively, linear-scale and log-scale plots averaging half of all possible phases) and in  FIGS. 10A and 10B  (which are, respectively, linear-scale and log-scale plots averaging all possible phases), the majority of images and high frequency components have been removed (as compared to the  FIG. 4 . 
         [0037]    Having thus described the present invention by reference to certain of its preferred embodiments, it is noted that the embodiments disclosed are illustrative rather than limiting in nature and that a wide range of variations, modifications, changes, and substitutions are contemplated in the foregoing disclosure and, in some instances, some features of the present invention may be employed without a corresponding use of the other features. Accordingly, it is appropriate that the appended claims be construed broadly and in a manner consistent with the scope of the invention.