Patent Publication Number: US-2018041176-A1

Title: System and Methods of RF Power Transmission, Modulation, and Amplification, Including Control Functions to Transition an Output of a MISO Device

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     The present application is a continuation of U.S. application Ser. No. 13/565,007, filed Aug. 2, 2012, now allowed, which is a continuation of U.S. application Ser. No. 13/069,155, filed Mar. 22, 2011, now U.S. Pat. No. 8,410,849, which is a continuation of U.S. patent application Ser. No. 12/236,079, filed Sep. 23, 2008, now U.S. Pat. No. 7,911,272, which is a continuation-in-part of U.S. patent application Ser. No. 12/142,521, filed Jun. 19, 2008, now U.S. Pat. No. 8,013,675, which claims the benefit of U.S. Provisional Patent Application No. 60/929,239, filed Jun. 19, 2007, and U.S. Provisional Patent Application No. 60/929,584, filed Jul. 3, 2007, all of which are incorporated herein by reference in their entireties. 
     The present application is related to U.S. patent application Ser. No. 11/256,172, filed Oct. 24, 2005, now U.S. Pat. No. 7,184,723 and U.S. patent application Ser. No. 11/508,989, filed Aug. 24, 2006, now U.S. Pat. No. 7,355,470, both of which are incorporated herein by reference in their entireties. 
    
    
     BACKGROUND 
     Field 
     Embodiments of the present invention relate generally to RF (radio frequency) power transmission, modulation, and amplification. 
     Background 
     Today&#39;s RF power amplifiers are required to generate complex RF signals with stringent output power and linearity requirements. For example, in order to comply with the requirements of a WCDMA waveform, a power amplifier needs to support approximately 30-40 dB of instantaneous output power dynamic range at a given power output level. This is mainly due to the ACPR (Adjacent Channel Power Ratio) and the ACLR (Adjacent Channel Leakage Ratio) requirements of the WCDMA waveform, which require very deep nulls as the output power waveform crosses zero. 
     Generally, the ACLR and ACPR that a power amplifier can achieve are related to the linearity of the power amplifier over the output power range of the desired waveform. Modern RF waveforms (e.g., OFDM, CDMA, WCDMA, etc.) are characterized by their associated PAP (Peak-to-Average Power) ratios. As such, in order to generate such waveforms, the power amplifier needs to be able to operate in a largely linear manner over a wide output power range that encompasses the output power range of the desired waveforms. 
     Outphasing amplification or LINC (Linear Amplification with Nonlinear Components) provides an amplification technique with the desirable linearity to amplify RF waveforms with large PAP ratios. Outphasing works by separating a signal into equal and constant envelope constituents, linearly amplifying the constituents, and combining the amplified constituents to generate the desired output signal. To preserve linearity when combining the amplified constituents, existing outphasing techniques use an isolating and/or a combining element, which provides the needed isolation between the branches of the outphasing amplifier to reduce non-linear distortion. 
     In several respects, however, existing outphasing techniques are not suitable for implementation in modern portable devices. For example, the isolating and/or combining element that they use causes a degradation in output signal power (due to insertion loss and limited bandwidth) and, correspondingly, low power amplifier efficiency. Further, the typically large size of isolating/combining elements precludes having them in monolithic amplifier designs. 
     There is a need therefore for outphasing amplification systems and methods that eliminate the isolating/combining element used in existing outphasing techniques, while providing substantially linear amplification over a wide output power dynamic range to support modern RF waveforms. 
     BRIEF SUMMARY 
     Embodiments of the present invention relate generally to RF power transmission, modulation, and amplification. 
     An embodiment of the present invention includes a method for control of a multiple-input-single-output (MISO) device. The method can include partitioning a waveform constellation space into a plurality of regions, where each region of the plurality of regions is associated with one or more control functions of a multiple-input-single-output (MISO) device. The method can also include transitioning the MISO device between a plurality of classes of operation based on the one or more control functions. 
     Another embodiment of the present invention includes a system. The system includes a multiple-input-single-output (MISO) device and a transfer function module. The transfer function module is configured to transition the MISO device between a plurality of classes of operation based on one or more control functions, wherein the one or more control functions are each associated with a region from a plurality of regions partitioned from a waveform constellation space. 
     Further embodiments, features, and advantages of the present invention, as well as the structure and operation of the various embodiments of the present invention, are described in detail below with reference to the accompanying drawings. 
    
    
     
       BRIEF DESCRIPTION OF THE FIGURES 
       The accompanying drawings, which are incorporated herein and form a part of the specification, illustrate the present invention and, together with the description, further serve to explain the principles of the invention and to enable a person skilled in the pertinent art to make and use the invention. 
         FIG. 1  illustrates the theoretical error-free normalized amplitude of a phasor as a function of the differential phase between the constituents of the phasor. 
         FIG. 2  illustrates the theoretical error in the amplitude of a phasor as a function of the differential phase between the constituents of the phasor, when the constituents are combined with infinite isolation. 
         FIG. 3  illustrates the theoretical error in the amplitude of a phasor as a function of the differential phase between the constituents of the phasor, when the constituents are combined with 20 of dB isolation. 
         FIG. 4  compares the theoretical error-free normalized amplitude of a phasor and the theoretical amplitude of the phasor when the constituents are combined with 20 of dB isolation, as a function of the differential phase between the constituents of the phasor. 
         FIG. 5  compares the theoretical error-free normalized amplitude of a phasor and the theoretical normalized amplitude of the phasor when the constituents are combined with 20 dB of isolation, as a function of the differential phase between the constituents of the phasor. 
         FIG. 6  compares the theoretical error-free normalized amplitude of a phasor and the theoretical normalized amplitude of the phasor when the constituents are combined with 25 dB of isolation, as a function of the differential phase between the constituents of the phasor. 
         FIG. 7  illustrates the derivative of the theoretical error in the amplitude of a phasor as a function of the differential phase between the constituents of the phasor, when the constituents are combined with 25 dB of isolation. 
         FIG. 8  illustrates the derivative of the theoretical phasor error in the amplitude of a phasor as a function of the differential phase between the constituents of the phasor, when the constituents are combined with 30 dB of isolation. 
         FIG. 9  compares blended control amplification according to an embodiment of the present invention and outphasing amplification, with respect to the level of control over the constituents of a desired phasor. 
         FIG. 10  illustrates an example blended control amplification system according to an embodiment of the present invention. 
         FIG. 11  illustrates the relationship between the error (in amplitude and phase) in a phasor and the imbalance (in amplitude and phase) between the constituents of the phasor. 
         FIG. 12  illustrates the power output associated with a phasor as a function of the differential phase between the constituents of the phasor, when no imbalance in amplitude and phase exists between the constituents of the phasor. 
         FIG. 13  compares the power output associated with a phasor as a function of the differential phase between the constituents of the phasor, for different scenarios of amplitude and phase imbalance between the constituents of the phasor. 
         FIG. 14  compares the amplitude error in the power output associated with a phasor as a function of the differential phase between the constituents of the phasor, for different scenarios of amplitude and phase imbalance between the constituents of the phasor. 
         FIG. 15  compares the phase error in the power output associated with a phasor as a function of the differential phase between the constituents of the phasor, for different scenarios of amplitude and phase imbalance between the constituents of the phasor. 
         FIG. 16  illustrates an example blended control amplification function according to an embodiment of the present invention. 
         FIG. 17  illustrates real-time blended control amplification for an example output power waveform according to an embodiment of the present invention. 
         FIG. 18  is an example that illustrates the output stage theoretical efficiency of a blended control amplification system according to an embodiment of the present invention, as function of the output stage current. 
         FIG. 19  compares the output power transfer characteristic of a blended control amplification system according to an embodiment of the present invention and the output power transfer characteristic of an ideal outphasing amplification system. 
         FIGS. 20-23  illustrate using a blended control amplification function according to an embodiment of the present invention to generate an example modulated ramp output. 
         FIGS. 24-26  illustrate example blended control methods according to embodiments of the present invention. 
     
    
    
     The present invention will be described with reference to the accompanying drawings. Generally, the drawing in which an element first appears is typically indicated by the leftmost digit(s) in the corresponding reference number. 
     DETAILED DESCRIPTION 
     In commonly owned U.S. patent(s) and application(s), cross-referenced above, VPA (Vector Power Amplification) and MISO (Multiple-Input-Single-Output) amplification embodiments were introduced. VPA and MISO provide combiner-less RF power amplification, which results in high power amplifier efficiency. At the same time, despite minimal or zero branch isolation, VPA and MISO amplification include innovative amplifier bias functions that effectively result in highly linear amplification over the entire output power range of desired waveforms. 
     In the following sections, embodiments of a blended control function for operating a MISO amplifier embodiment are provided. The blended control function allows for the mixing of various output power control functions enabled by VPA and MISO, to generate a desired waveform with high accuracy. In Section 2, the relationship between branch isolation (i.e., isolation between the branches of an outphasing amplifier) and output power error is described. This serves as an introduction to the practical limitations of a pure outphasing system, which are described in Section 3. In Section 4, blended control amplification is introduced. In Section 5, design considerations related to blended control amplification are described. Section 6 describes an example blended control function and associated performance results. Finally, Section 7 presents example blended control methods according to embodiments of the present invention. 
     1. Relationship Between Branch Isolation and Output Power Error 
     Equation (1) below describes the sum of two sine waves (or phasors) of equal amplitude, A, and frequency, ω c , but having a differential phase θ: 
         R  sin(ω c   t +δ)= A  sin ω c   t+A  sin(ω c   t +θ).  (1)
 
     The resulting phasor has amplitude R and phase δ. Equation (1) further indicates that any desired phasor of given amplitude and phase can be obtained from the sum of two equal amplitude phasors with appropriate differential phase between the two. The equal amplitude phasors are commonly referred to as the constituents of the desired phasor. 
     From equation (1), it can be further noted that the amplitude of the resulting phasor is a function of the differential phase, θ, between its constituents, as follows: 
     
       
         
           
             
               
                 
                   
                     R 
                      
                     
                       ( 
                       θ 
                       ) 
                     
                   
                   = 
                   
                     A 
                      
                     
                       
                         
                           
                             sin 
                              
                             
                               ( 
                               
                                 
                                   ω 
                                   c 
                                 
                                  
                                 t 
                               
                               ) 
                             
                           
                           + 
                           
                             sin 
                              
                             
                               ( 
                               
                                 
                                   
                                     ω 
                                     c 
                                   
                                    
                                   t 
                                 
                                 + 
                                 θ 
                               
                               ) 
                             
                           
                         
                         
                           sin 
                            
                           
                             ( 
                             
                               
                                 
                                   ω 
                                   c 
                                 
                                  
                                 t 
                               
                               + 
                               
                                 δ 
                                  
                                 
                                   ( 
                                   θ 
                                   ) 
                                 
                               
                             
                             ) 
                           
                         
                       
                       . 
                     
                   
                 
               
               
                 
                   ( 
                   2 
                   ) 
                 
               
             
           
         
       
     
     Similarly, the phase, δ(θ), of the resulting phasor is a function of the differential phase, θ, between its constituents. 
       FIG. 1  illustrates the theoretical error-free normalized amplitude of a phasor as a function of the differential phase between its constituents. As shown, the differential phase is swept from 0 degrees to approximately 150 degrees. At zero degrees, the constituents are phase-aligned with each other and result in a maximum normalized phasor amplitude of 2. At approximately 150 degrees, the constituents are separated in phase by approximately 150 degrees and result in a normalized phasor amplitude of approximately 0.5. 
     In the context of power amplification, phasor amplitude curve  102  shown in  FIG. 1  may represent the output power amplitude of an outphasing power amplifier as a function of the differential phase between the constituents of the output waveform. Thus, the output power dynamic range spanned by the amplitude curve  102  would be approximately 12 dB (20 log (0.5/2)). More particularly, phasor amplitude curve  102  would represent the output power amplitude generated by an ideal outphasing power amplifier. In other words, phasor amplitude curve  102  would result when infinite isolation and infinite vector accuracy exists between the branches of the outphasing amplifier. As described above, however, this is impractical to design due to the power, cost, and size inefficiencies introduced by isolating/combining elements, which are typically used in conventional outphasing systems. Alternatively, if no isolating/combining element is used, the branches of the outphasing amplifier would have to be located on distinct substrates, which necessarily precludes a monolithic, compact design suitable for today&#39;s portable devices. 
     Therefore, for practical outphasing amplifier designs, a finite isolation between the branches of an outphasing amplifier is to be assumed. This finite isolation results in crosstalk between the branches of the amplifier (i.e., the signal in one branch causes an undesired effect on the signal in the other branch), effectively causing an error signal to appear at the output of the power amplifier. 
     In the worst case scenario, the crosstalk between the branches of the amplifier is entirely non-linear. The resulting error signal at the output of the power amplifier can therefore be written as: 
         R   nonlinear  sin(ω c   t +δ)= A   a  sin(ω c   t )·( A   b  sin(ω c   t +θ))+ A   a  sin(ω c   t +θ)· A   b  sin(ω c   t )  (3)
 
     where A a  represents the desired phase amplitude and A b  represents the amplitude of the crosstalk between the branches of the amplifier. 
     A a  and A b  are related to each other according to A b =1−A a  (where the sum of A a  and A b  is normalized to 1). The relative isolation in dB between the branches of the amplifier can be calculated as −20 log (A b ). For example, for A a =0.5, A b =0.5 and the relative isolation is −20 log (0.5)=6 dB. 
     From equation (3) above, the amplitude of the error signal at the output of the amplifier is a function of the differential phase, θ, and can be described as: 
     
       
         
           
             
               
                 
                   
                     
                       R 
                       nonlinear 
                     
                      
                     
                       ( 
                       θ 
                       ) 
                     
                   
                   = 
                   
                     2 
                      
                     
                       A 
                       a 
                     
                      
                     
                       
                         sin 
                          
                         
                           ( 
                           
                             
                               ω 
                               c 
                             
                              
                             t 
                           
                           ) 
                         
                       
                       · 
                       
                         A 
                         b 
                       
                     
                      
                     
                       
                         
                           sin 
                            
                           
                             ( 
                             
                               
                                 
                                   ω 
                                   c 
                                 
                                  
                                 t 
                               
                               + 
                               θ 
                             
                             ) 
                           
                         
                         
                           sin 
                            
                           
                             ( 
                             
                               
                                 
                                   ω 
                                   c 
                                 
                                  
                                 t 
                               
                               + 
                               
                                 δ 
                                  
                                 
                                   ( 
                                   θ 
                                   ) 
                                 
                               
                             
                             ) 
                           
                         
                       
                       . 
                     
                   
                 
               
               
                 
                   ( 
                   4 
                   ) 
                 
               
             
           
         
       
     
     In equation (4), A a =1 or equivalently A b =0 corresponds to infinite isolation between the branches of the amplifier. The error amplitude would thus be zero as illustrated in  FIG. 2 , which shows the error amplitude as a function of the differential phase, θ, between the constituents of the desired phasor. 
     For A a =0.9 or equivalently A b =0.1, the branch isolation is 20 dB (−20 log (0.1)) and the error amplitude as a function of θ is as described by error amplitude curve  302  in  FIG. 3 . As shown in  FIG. 3 , the error amplitude is near zero for small values of θ but begins to deviate from zero as θ moves away from zero. This is because as θ increases, the amplitude of the desired phasor decreases and the effect of crosstalk between the branches becomes greater. 
     2. Practical Limitations of Pure Outphasing 
     From the resulting error amplitude curve  302  of  FIG. 3 , the amplitude of the phasor when the constituents are combined with 20 dB of isolation can be determined. This is illustrated in  FIG. 4 , which compares the theoretical error-free normalized amplitude of a phasor (curve  102 ) and the theoretical amplitude of the phasor when the constituents are combined with 20 of dB isolation (curve  402 ), as a function of the differential phase between the constituents of the phasor. Amplitude curve  402  is obtained by summing error amplitude curve  302  and error-free normalized amplitude curve  102 . 
     As shown in  FIG. 4 , curve  402  deviates from curve  102  over most of the differential phase range, illustrating the effect of the non linear crosstalk error on the amplitude of the desired phasor. Note, however, that curve  402  is not normalized as curve  102 . 
     In  FIG. 5 , curve  402  is normalized such that the maximum amplitude corresponds to the value of 2, resulting in normalized amplitude curve  502 . As shown in  FIG. 5 , curve  502  and curve  102  align with one another over a portion of the differential phase range (approximately 50 degrees in each direction moving away from 0 degrees). This indicates that in the worst case scenario (i.e., error entirely nonlinear), even with only 20 dB of branch isolation, a pure outphasing system (i.e., system that relies exclusively on modulating the phases of the constituent phasors with no additional calibration) matches the performance of an ideal outphasing system with infinite isolation (i.e., provide comparable linear amplification) over a portion of the differential phase range. From an output power range perspective, the pure outphasing system matches the waveform performance of an ideal outphasing system over a portion of the output power dynamic range of the desired waveform. In  FIG. 5 , this is approximately 2.5 dB of output power control range (−20 log (1.5/2)). 
     Increasing the branch isolation to 25 dB would further increase the output power control range that can be achieved using only a pure outphasing system. This is shown in  FIG. 6 , which compares the desired phasor normalized amplitude with 25 dB of branch isolation (curve  602 ) and the theoretical error-free normalized amplitude (curve  102 ). Curve  604  is the error amplitude as function of the differential phase with 25 dB of branch isolation. As shown in  FIG. 6 , curves  102  and  602  are aligned with each other over an even larger portion of the differential phase range. From an output power range perspective, this is approximately 6 dB of output power control range, over which the pure outphasing system (with 25 dB of branch isolation) and an ideal outphasing system (infinite isolation) would achieve identical amplification performance. 
     The differential phase range over which a pure outphasing system can be used exclusively (while matching the performance of an ideal outphasing system) can be further determined by examining the derivative of the error amplitude as a function of the differential phase. This is illustrated for 25 dB and 30 dB of branch isolation respectively in  FIGS. 7 and 8 . As shown in  FIG. 7 , the error amplitude derivative curve is relatively flat between −120 degrees and +120 degrees, which indicates an insignificant variation in error amplitude over that phase range. Similarly, with 30 dB of branch isolation, the error amplitude derivative curve is flat over an even larger range of the differential phase, as shown in  FIG. 8 . 
     It should be noted that the analysis above represents a worst case scenario because it assumes that the crosstalk error is entirely nonlinear. In practice, a portion of the crosstalk error will be linear, which further increases the differential phase range over which pure outphasing can be used with no additional calibration or, alternatively, allows for lower branch isolation to be used. What can be further noted is that a pure outphasing system can be used to generate a portion of the output power range of a desired waveform with comparable performance to an ideal outphasing system. For waveforms with small output power dynamic range, pure outphasing may be used exclusively to generate such waveforms. However, for waveforms with larger output power dynamic range, practical limitations (i.e., finite branch isolation, crosstalk, etc.) may preclude the use of a pure outphasing solution when highly accurate, distortion-free amplification is desired. 
     3. Blended Control Amplification 
     In this section, a blended control amplification approach according to an embodiment of the present invention will be presented. The blended approach combines pure outphasing with bias and/or amplitude control to yield an accurate, practical, and producible system with substantially comparable performance to that of an ideal outphasing system, but without the extreme isolation and accuracy requirements of outphasing alone. The blended approach provides a high degree of control over the constituent phasors (whether in terms of amplitude and/or phase) in order to generate the desired phasor. This allows for a reduction in both the branch isolation requirements and the phase/amplitude accuracy requirements (as related to the constituent phasors) as compared to a pure outphasing or ideal outphasing system. 
     A comparison between the blended approach of the present invention and pure outphasing with respect to the level of control over constituent phasors is provided in  FIG. 9 . 
     As shown in  FIG. 9 , using pure outphasing, the constituent phasors are restricted in amplitude in that they must fall on the unit circle. In other words, the only controllable parameter in generating a desired phasor is the differential phase between the constituent phasors. As a result, in order to accurately generate a desired waveform, high accuracy in terms of the differential phase is needed. However, as described above, when the objective is to reduce branch isolation and generate complex waveforms with large PAP ratios, accuracy requirements become very stringent as to become almost impractical. This is especially the case when generating a waveform with a deep null (e.g., 30-40 dB null), which requires the constituents to be exactly phase differenced by 180 degrees (i.e., differential phase is 180 degrees) and at which point the error amplitude is greatest, as can be noted from  FIGS. 5-8 , for example. 
     On the other hand, using the blended approach of the present invention, the constituent phasors can be varied both in terms of phase and amplitude to generate the desired waveform. As a result, not only can any desired phasor be generated without having the differential phase exceed a given amount (e.g., limiting the differential phase to the range over which the error is negligible), but also the amplitude of the constituent phasors can be reduced at given output levels, which increases the operational output power range and repeatability of the overall system. 
     In  FIG. 9 , an example control range of the constituent phasors according to an embodiment of the present invention is provided by the shaded circle area contained within the unit semi-circle. As shown, when the desired phasor amplitude is large (i.e., high output power), the amplitude of the constituent phasors approaches the radius size of the unit circle. In other words, for large output power levels, the amplitude of the constituent phasors under the blended control approach is comparable to its corresponding amplitude under a pure outphasing approach. However, as the desired phasor amplitude decreases, the amplitude of the constituent phasors recedes from the unit circle and begins to deviate from its corresponding amplitude under a pure outphasing approach. 
     As a result of the blended approach of the present invention, the accuracy requirements in terms of phase/amplitude of the constituent phasors can be significantly reduced, which accommodates the branch isolations, vector accuracy, and phase accuracy that can be practically expected. For example, in an embodiment of the blended approach of the present invention, when the desired output power tends to zero, the constituent phasors are also driven to zero amplitude, which essentially eliminates any accuracy requirements regarding the differential amplitude and phase between the constituent phasors or, in other words, entirely reduces the system&#39;s sensitivity to branch phase imbalance, for that particular output power range. 
     Another advantage of the blended approach of the present invention can also be gleaned from  FIG. 9 . This relates to the ability of the blended approach of the present invention to generate any desired phasor amplitude (except for the maximum amplitude) using any one of an infinite number of constituent phasor configurations. This is very significant when compared to an ideal outphasing system, in which there exists a single configuration of the constituent phasors for any desired phasor amplitude (i.e., the constituent phasors must fall on the unit circle and are symmetrically opposed to each other relative to the cosine axis). 
     According to an embodiment of the present invention, the shaping of the constituent phasors in phase and/or amplitude, as described above, is performed substantially instantaneously or in real time in accordance with the desired waveform output power trajectory. In an embodiment, this is performed using a combination of phase, bias, and amplitude controls, with the control combination (or blend) dynamically changing according to the desired waveform output power trajectory. An example amplification system according to an embodiment of the present invention, which may be used to implement a blended control approach as described above, is now presented with reference to  FIG. 10 . 
     Referring to  FIG. 10 , example amplification system  1000  uses a MISO amplifier. Amplification system  1000  includes a transfer function  1006 , vector modulators  1008  and  1010 , driver amplifiers  1014  and  1016 , and a MISO amplifier  1018 . Further detail regarding embodiments of these components as well as the operation of system  1000  (according to various embodiments) can be found in commonly owned related patents and applications, indicated above in the cross-reference section of this patent application, and incorporated herein by reference in their entireties. In addition, the MISO amplifier could be replaced with a traditional Outphasing or LINC output amplifier arrangement which includes two power amplifiers and a power combiner. 
     According to an embodiment, which shall now be described, system  1000  includes a blended control implementation, which is implemented as a combination of phase, bias, and amplitude controls. For example, phase control (i.e., control of the phases of the constituent phasors) in system  1000  can be performed using one or more of transfer function module  1006  and vector modulators  1008  and  1010 . Bias control, which includes biasing power amplifiers  1620  and  1622  within MISO amplifier  1018  to affect the amplitude of the desired phasor, is done via bias control signal  1024  generated by transfer function module  1006 . Note also that bias control can be affected at drivers  1014  and  1016  via driver bias control signal  1026 . Amplitude control, which includes controlling the input signals into MISO amplifier  1018  in order to affect the amplitude of the constituent phasors, can be performed using one or more of transfer function module  1006  and drivers  1014  and  1016 , for example. 
     According to embodiments of the present invention, system  1000  may use one or more of phase, bias, and amplitude control with varying degrees of weight given to each type of control according to the desired waveform. Example blended control functions according to the present invention are described below in Section 6. 
       FIG. 19  compares the output power transfer characteristic of system  1000  and that of an ideal outphasing amplification system. As shown, the output power performance of system  1000  is almost identical to that of an ideal outphasing system. Yet, as described above, system  1000  requires only 20-25 dB of branch isolation, and other embodiments may require less. 
     4. Practical Design Considerations 
     As would be understood by a person skilled in the art based on the teachings herein, the optimum combination of controls as well as the degrees of weight given to each type of control within an amplification system according to the present invention will depend on both the characteristics of the system itself (e.g., branch isolation, phase/amplitude branch imbalance, etc) and design consideration such as the desired waveform output power. Therefore, it is important in order to design a system with such optimum combination and use of controls to understand the practical effects of system characteristics on the output performance (i.e., accuracy of the output waveform) of the system. 
     In the following, the effects of phase and amplitude branch imbalance on the output performance of an example amplification system according to the present invention are examined. For ease of analysis and illustration, it is assumed that the constituent phasors (A 1  and A 2 ) are constrained to the first and fourth quadrants of the unit circle, and that they are designed to be of equal amplitude and symmetrical to each other with respect to the cosine axis, as illustrated in  FIG. 11 . Note that in practice the constituent phasors may occur within any quadrant of the unit circle and are not required to be equal and/or symmetrical to each other with respect to the cosine axis. It is further assumed that the output power is normalized to a maximum of 30 dB. 
     Note from the assumptions above that if phasors A 1  and A 2  are indeed equal in amplitude and symmetrical to each other with respect to the cosine axis (i.e., no amplitude/phase imbalance between the branches of the amplifier), the resulting phasor will be perfectly aligned with the cosine axis (i.e., zero phase error in the output waveform). The power output associated with such resulting phasor will be as illustrated in  FIG. 12 , which shows the power output as a function of the differential phase between the constituent phasors in an ideal outphasing system. 
     In practice, however, phase/amplitude branch imbalance cannot be entirely reduced to zero for a variety of reasons, including finite branch isolation for example, and will affect the choice of combination of controls. In the analysis below, phase/amplitude branch imbalance is introduced into an example amplification system according to the present invention, and the output performance of the system is examined. The example amplification system uses phase control only. 
     In  FIG. 13 , the power output associated with a phasor as a function of the differential phase between the constituents of the phasor is examined for various scenarios of phase/amplitude branch imbalance. Power output curve  1302  illustrates the power output with 0 dB of amplitude imbalance and 0 degrees of phase imbalance between the branches of the amplification system. In other words, curve  1302  illustrates the power output of an ideal outphasing system. Power output curve  1304  illustrates the power output for 0.5 dB of amplitude branch imbalance and 5 degrees of phase branch imbalance. Power output curve  1306  illustrates the power output for 1 dB of amplitude branch imbalance and 10 degrees of phase branch imbalance. 
     As can be seen from  FIG. 13 , power output curves  1304  and  1306  begin to diverge from power output curve  1302  at differential phase values of approximately 80 to 100 degrees. 
       FIGS. 14 and 15  illustrate the power output amplitude error and the power output phase error, respectively, as a function of the differential phase between the constituents of the phasor, for the same phase/amplitude branch imbalance scenarios as in  FIG. 13 . 
     The results from  FIGS. 13-15  can be used, based on system design criteria, to determine an operating range (in terms of differential phase) over which phase control only can be used. For example, system design criteria may require a maximum allowable power output error of 0.5 dB and a maximum allowable power output phase error of 5 degrees. Accordingly, for a system with 0.5 dB of amplitude branch imbalance and 5 degrees of phase branch imbalance, the phase control only range would be approximately 0 to 110 degrees (lower of 110 and 140 degrees). Phase control only would thus be able to vary the output power by 4.8 dB with a high degree of accuracy. Similarly, for a system with 1 dB of amplitude branch imbalance and 10 degrees of phase branch imbalance, the phase control only range would be approximately 0 to 70 degrees (lower of 70 and 100 degrees). Phase control only would thus be able to vary the output power by 1.7 dB with a high degree of accuracy. 
     Nonetheless, phase control only would not be able on its own to achieve output power control ranges of 30-40 dB, as desired for complex waveforms, without degrading the accuracy of the desired waveform at low output powers. Therefore, one or more additional types of control (e.g., bias control, amplitude control) may be needed as used in embodiments of the present invention to enable a practical, accurate amplifier design for complex waveforms. 
     5. Example Blended Control Function and Performance Results 
     An example blended control function according to an embodiment of the present invention will now be presented. The example blended control function is designed to optimize the output performance (i.e., power output accuracy) of an amplification system according to an embodiment of the present invention for a QPSK waveform output. The example blended control function is illustrated in  FIG. 16 , wherein it is imposed on top of a QPSK constellation in the complex space defined by cos(wt) and sin(wt). The blended control function partitions the QPSK constellation space into three control regions  1602 ,  1604 , and  1606 , as shown in  FIG. 16 . 
     In an embodiment, the blended control function determines the type of control or controls used depending on the instantaneous power of the desired output waveform. For example, as would be understood by a person skilled in the art, a QPSK signal moves from one constellation point to another to encode information. However, although all four constellation points correspond to equal power, the signal does not move instantaneously from one constellation point to another and thus will have to traverse the trajectory connecting the constellation points, as shown in  FIG. 16 . Accordingly, the signal will traverse at least two control regions of the blended control function as it moves from any constellation point to any other. As it does, the types of controls applied within the amplification system to generate the output power will also vary. 
     In an embodiment, the example blended control function of  FIG. 16  is such that control region  1602  is a phase control-biased region (i.e., higher weight is given to phase control compared to bias control and amplitude control). In another embodiment, control region  1602  is a phase control only region. Control region  1604  is a phase control, bias control, and amplitude control region. All three types of controls may be combined with equal or different weights in control region  1604 . In an embodiment, higher weight is given to bias control than phase control and amplitude control in control region  1604 . Control region  1606  is a bias control and amplitude control region. Bias control and amplitude control may be combined with equal or different weights in control region  1606 . In an embodiment, control region  1606  is amplitude control-biased, i.e., amplitude control is given higher weight than bias control in control region  1606 . 
     In an embodiment, the example blended control function of  FIG. 16  enables a variable weighted combination of controls, whereby weights given to each type of control vary according to the desired waveform output power. In an embodiment, the variable weighted combination of controls varies from a phase control-biased combination to a bias/amplitude control-biased combination as the desired waveform output power varies from high to low power levels. 
     As would be understood by persons skilled in the art, control regions  1602 ,  1604 , and  1606  in  FIG. 16  are provided for purposes of illustration only and are not limiting. Other control regions can be defined according to embodiments of the present invention. Typically, but not exclusively, the boundaries of the control regions are based on the Complementary Cumulative Density Function (CCDF) of the desired output waveform and the sideband performance criteria. Accordingly, the control regions&#39; boundaries as well as the type of controls used within each control region can vary according to the desired output waveform, according to embodiments of the present invention. 
       FIG. 17  illustrates an example output power waveform and a corresponding output stage current generated by a MISO amplifier operating according to the example blended control function described above. The blended control function is also shown in  FIG. 17  to illustrate, by direct mapping, the control region used to generate any given value of the output power waveform or the output stage current. For example, when the output power waveform goes through a zero crossing, the blended control function is operating in control region  1606 . 
     As shown in  FIG. 17 , the output stage current closely follows the output power waveform. In particular, it is noted that the output stage current goes completely to zero when the output power waveform undergoes a zero crossing. In an embodiment, this corresponds to the MISO amplifier being operated in amplitude control-biased control region  1606 . In other words, the MISO amplifier current is driven to zero by mainly controlling the amplitudes of the input signals of the MISO amplifier. 
       FIG. 17  further illustrates the MISO amplifier classes of operation as a function of the output power waveform and the blended control function. As shown, the MISO amplifier transitions between various classes of operation (e.g., class S through class A) as the combination of controls used within the MISO amplifier is varied. For example, the MISO amplifier operates as a class A or B amplifier when the blended control function operates in control region  1606 . On the other hand, the MISO amplifier operates in switching mode (class S) when the blended control function operates in control region  1602 . This allows for optimizing the efficiency of the MISO amplifier as a function of the instantaneous output power of the desired waveform. 
       FIG. 18  is an example that illustrates the output stage theoretical power efficiency as a function of the output stage current for a MISO amplifier operating according to the example blended control function described above. As shown, the MISO amplifier operates at 100% theoretical efficiency at all times that it operates as a class S-class C amplifier. The MISO amplifier operates at 50% theoretical efficiency when it operates as a class A or B amplifier. However, as shown in  FIG. 18 , the MISO amplifier spends very short time operating as class A or class B amplifier. Accordingly, in an embodiment, the MISO amplifier operates at 100% theoretical efficiency for 98% (or greater) of the time while generating typical cell phone waveforms. 
       FIGS. 20-23  illustrate using a blended control function to generate an example modulated ramp output according to an embodiment of the present invention. For example, the blended control function may be used within amplification system  1000  described above. 
       FIG. 20  illustrates an exemplary desired output amplitude response As shown, the desired output amplitude transitions linearly from a maximum value of 2 to a minimum of zero, before returning linearly to the maximum of 2. 
       FIG. 21  compares the blended control function and pure outphasing with respect to the differential phase between the constituent phasors, to generate the desired output amplitude of  FIG. 20 . Pure outphasing is represented by curve  2102 , and the blended control function is represented by curve  2104 . As shown, for pure outphasing, the differential phase spans the entire 180 degrees range, varying from 0 degrees to generate the maximum amplitude of 2 to 180 degrees to generate the minimum amplitude of zero. On the other hand, for the blended control function, the differential phase is restricted to a much smaller range (0 to approximately 70 degrees), while other type of controls are also used to generate the desired output. In an embodiment, bias control is used to complement phase control to generate the desired output. Accordingly, the MISO amplifier and/or driver amplifiers that precede the MISO amplifier are bias controlled.  FIG. 22  illustrates example bias control signals (represented as voltages  2202  and  2204 ) provided to bias the MISO amplifier and the driver amplifiers to implement bias control. For example, voltages  2202  and  2204  may be provided through bias control signals  1024  and  1026  in amplification system  1000  described above. 
     Note from  FIGS. 21 and 22  that bias control is used at the same time as phase control within the phase control range (0 to 70 degrees), though phase control may be used with much higher weight than bias control within that range. This can be noted from voltages  2202  and  2204 , which are modified within the phase control range. Voltages  2202  and  2204  continue to vary outside the phase control range and tend to zero as the desired output amplitude tends to the minimum value of zero. It is noted that the weights shown in the figures and discussed herein are provided solely for illustrative purpose and are not limiting. Other weight values can be used depending on the situation and the desired outcome. 
     In an embodiment, when bias control is applied, variations occur in the S (reverse isolation) parameters of the amplifiers of the system, resulting in an associated phase error at the output. Fortunately, this can be easily compensated for by applying a rotational transform at the vector modulators of the system.  FIG. 22  illustrates the phase modification applied to compensate for the phase error resulting from bias control. As shown, minimal correction is needed for the first 30 or 40 degrees of the differential phase range. This is because bias control is used with much lower weight than phase control. However, as the desired output amplitude approaches zero, bias control is used more heavily and the associated phase error correction becomes greater. Note that the phase error correction inverts 180 degrees at the zero amplitude crossing, since the desired output is a single sideband suppressed carrier waveform. 
     6. Example Blended Control Methods 
       FIGS. 24-26  illustrate example blended control methods according to embodiments of the present invention. 
       FIG. 24  illustrates a process flowchart  2400  of a method for control in a power amplifier. Process  2400  begins in step  2402 , which includes determining an instantaneous power level of a desired output waveform of the power amplifier. In an embodiment, referring to  FIG. 10 , step  2402  can be performed by transfer function module  1006  based on received I and Q data reflecting the desired output waveform. 
     Subsequently, in step  2404 , process  2400  includes determining a control point of operation of the power amplifier based on the determined instantaneous power level. In an embodiment, the control point of operation enhances one or more of linearity and accuracy of the power amplifier for the determined instantaneous power level. In an embodiment, referring to  FIG. 10 , step  2404  can be performed by transfer function module  1006  based on the determined instantaneous power level. 
     Subsequently, in step  2406 , process  2400  includes controlling the power amplifier to operate according to the determined control point of operation. In an embodiment, step  2406  includes performing one or more of (a) controlling the phase of input signals of the power amplifier; (b) controlling the bias of the power amplifier; and (c) controlling the amplitude of the input signals of the power amplifier. In an embodiment, referring to  FIG. 10 , step  2406  is performed by transfer function module  1006 , which accomplishes step  2406  by controlling signals for performing (a), (b), and (c). For example, to control the phase of the input signals of the power amplifier, transfer function  1006  may control the signals it inputs into vector modulators  1008  and  1010 . Similarly, to control the bias of the power amplifier, transfer function  1006  may vary bias signals  1024  and  1026  that it provides to driver amplifiers  1014  and  1016  and MISO amplifier  1018 . 
     According to an embodiment, the control point of operation can be within a first, second, or third control regions, depending on the determined instantaneous power level. For example, in an embodiment, the control point of operation is within a first control region when the instantaneous power level is greater than a first threshold; within a second control region when the instantaneous power level is greater than a second threshold but lower than the first threshold; and within a third control region when the instantaneous power level is lower than the second threshold. According to an embodiment, boundaries of the first, second, and third control regions are based on the Complementary Cumulative Density Function (CCDF) of the desired output waveform. 
     According to an embodiment of the present invention, when the control point of operation is within the first control region, the controlling step  2406  of process  2400  includes performing (a) only, or performing (a), (b), and (c). In the latter case, in an embodiment, step  2406  includes performing (a) more often than (b) or (c). When the control point of operation is within the second control region, the controlling step  2406  includes performing (a), (b), and (c). Further, controlling step  2406  may include performing (b) more often than (a) or (c). When the control point of operation is within the third control region, the controlling step  2406  includes performing (b) and (c) only. In an embodiment, controlling step  2406  further includes performing (c) more often than (b). 
     According to an embodiment, controlling step  2406  includes performing one or more of (a), (b), and (c) according to respective weights given to (a), (b), and (c). In an embodiment, the respective weights are determined according to one or more of error/system characteristics within the power amplifier (e.g., branch phase imbalance, branch amplitude imbalance, branch isolation) and the instantaneous power level. 
       FIG. 25  illustrates another process flowchart  2500  of a method for control in a power amplifier. Process  2500  begins in step  2502 , which includes determining a required change in power output from a first output power level to a second output power level in the power amplifier. In an embodiment, referring to  FIG. 10 , step  2502  is performed by transfer function module  1006  based on received I and Q data reflecting a desired output waveform. 
     Subsequently, in step  2504 , process  2500  includes varying one or more weights associated with respective power controls of the power amplifier to cause the required change in power output, wherein the power controls include one or more of (a) control of phase of input signals of the power amplifier, (b) control of bias of the power amplifier, and (c) control of amplitude of the input signals of the power amplifier. In an embodiment, referring to  FIG. 10 , step  2504  is performed by transfer function module  1006 , which accomplishes step  2504  by varying control signals for performing (a), (b), and (c). For example, to control the phase of the input signals of the power amplifier, transfer function  1006  may control the signals it inputs into vector modulators  1008  and  1010 . Similarly, to control the bias of the power amplifier, transfer function  1006  may vary bias signals  1024  and  1026  that it provides to driver amplifiers  1014  and  1016  and MISO amplifier  1018 . 
     According to an embodiment, the weights associated with the respective power controls of the power amplifier are determined according to one or more of branch phase imbalance, branch amplitude imbalance, and branch isolation within the power amplifier. 
     According to an embodiment, varying the weights causes the power amplifier to transition between various classes of operation. For example, in an embodiment, varying the weights causes the power amplifier to transition between class S and class A. In another embodiment, varying the weights causes the power amplifier to transition from linear operation to non-linear operation, and vice versa. 
       FIG. 26  illustrates another process flowchart  2600  of a method for control in a power amplifier. Process  2600  begins in step  2602 , which includes determining a desired power output trajectory of a desired output waveform of the power amplifier. In an embodiment, referring to  FIG. 10 , step  2602  can be performed by transfer function module  1006  based on received I and Q data reflecting the desired output waveform. 
     Subsequently, step  2604  includes determining one or more of (a) branch phase imbalance; (b) branch amplitude imbalance; and (c) branch isolation, between branches of the power amplifier. In an embodiment, step  2604  is performed by various error/system measurement modules of the power amplifier, which report measurements to transfer function module  1006 . 
     In step  2606 , process  2600  includes calculating one or more weights based on one or more of the determined branch phase imbalance, branch amplitude imbalance, and branch isolation. In an embodiment, referring to  FIG. 10 , step  2606  is performed by transfer function module  1006 . 
     Finally, in step  2608 , process  2600  includes applying one or more power controls according to the one or more weights to control the power amplifier to generate the desired power output trajectory. In an embodiment, the power controls include one or more of (a) control of phase of input signals of the power amplifier, (b) control of bias of the power amplifier, and (c) control of amplitude of the input signals of the power amplifier. As noted above, in an embodiment, step  2608  is performed by transfer function module  1006 , which controls different power control mechanisms of the power amplifier to apply (a), (b), and (c). For example, to control the phase of the input signals of the power amplifier, transfer function  1006  may control the signals it inputs into vector modulators  1008  and  1010 . Similarly, to control the bias of the power amplifier, transfer function  1006  may vary bias signals  1024  and  1026  that it provides to driver amplifiers  1014  and  1016  and MISO amplifier  1018 . 
     7. Conclusion 
     It is to be appreciated that the Detailed Description section, and not the Summary and Abstract sections, is intended to be used to interpret the claims. The Summary and Abstract sections may set forth one or more but not all exemplary embodiments of the present invention as contemplated by the inventor(s), and thus, are not intended to limit the present invention and the appended claims in any way. 
     The present invention has been described above with the aid of functional building blocks illustrating the implementation of specified functions and relationships thereof. The boundaries of these functional building blocks have been arbitrarily defined herein for the convenience of the description. Alternate boundaries can be defined so long as the specified functions and relationships thereof are appropriately performed. 
     The foregoing description of the specific embodiments will so fully reveal the general nature of the invention that others can, by applying knowledge within the skill of the art, readily modify and/or adapt for various applications such specific embodiments, without undue experimentation, without departing from the general concept of the present invention. Therefore, such adaptations and modifications are intended to be within the meaning and range of equivalents of the disclosed embodiments, based on the teaching and guidance presented herein. It is to be understood that the phraseology or terminology herein is for the purpose of description and not of limitation, such that the terminology or phraseology of the present specification is to be interpreted by the skilled artisan in light of the teachings and guidance. 
     The breadth and scope of the present invention should not be limited by any of the above-described exemplary embodiments, but should be defined only in accordance with the following claims and their equivalents.