Patent Publication Number: US-11398852-B2

Title: Envelope tracking power amplifier apparatus

Description:
RELATED APPLICATIONS 
     This application claims the benefit of provisional patent application Ser. No. 62/865,669, filed Jun. 24, 2019, the disclosure of which is hereby incorporated herein by reference in its entirety. 
    
    
     FIELD OF THE DISCLOSURE 
     The technology of the disclosure relates generally to radio frequency (RF) power amplifier circuits. 
     BACKGROUND 
     Mobile communication devices have become increasingly common in current society for providing wireless communication services. The prevalence of these mobile communication devices is driven in part by the many functions that are now enabled on such devices. Increased processing capabilities in such devices means that mobile communication devices have evolved from being pure communication tools into sophisticated mobile multimedia centers that enable enhanced user experiences. 
     Fifth-generation new radio (5G-NR) wireless communication technology has been widely regarded as the next wireless communication standard beyond the current third-generation (3G) communication standard, such as wideband code division multiple access (WCDMA), and the fourth-generation (4G) communication standard, such as Long-Term Evolution (LTE). As such, a 5G-NR capable mobile communication device is expected to achieve significantly higher data rates, improved coverage range, enhanced signaling efficiency, and reduced latency compared with a conventional mobile communication device supporting only the 3G and 4G communication standards. 
     The 5G-NR capable mobile communication device can be configured to transmit a radio frequency (RF) signal(s) in a millimeter wave (mmWave) RF spectrum that is typically above 6 GHz. Notably, RF signals transmitted in the mmWave RF spectrum are more susceptible to propagation attenuation and interference. In this regard, the 5G-NR capable mobile communication device typically employs a power amplifier circuit(s) to help improve signal-to-noise ratio (SNR) and/or signal-to-interference-plus-noise ratio (SINR) of the RF signal(s). To mitigate the propagation attenuation, the 5G-NR capable mobile communication device may be configured to explore multipath diversity by simultaneously transmitting the RF signal(s) via multiple antennas. Furthermore, by simultaneously transmitting the RF signal(s) via multiple antennas, the 5G-NR capable mobile communication device may be able to increase data rates through spatial multiplexing. 
     Envelope tracking (ET) is a power management technique designed to improve operating efficiency of the power amplifier(s) to help reduce power consumption and thermal dissipation. More specifically, the power amplifier(s) is configured to amplify the RF signal(s) based on an ET voltage that rises and falls in accordance to an amplitude of the RF signal(s). Understandably, the better the ET voltage tracks the amplitude of the RF signal(s), the higher efficiency can be achieved in the power amplifier(s). In this regard, it may be desirable to provide the ET voltage in accordance to the amplitude of the RF signal(s), particularly when the 5G-NR capable mobile communication device is configured to support multiple-input multiple-output (MIMO) diversity and/or spatial multiplexing. 
     SUMMARY 
     Embodiments of the disclosure relate to an envelope tracking (ET) power amplifier apparatus. The ET power amplifier apparatus includes a pair of power amplifiers configured to amplify a pair of radio frequency (RF) signals based on a pair of ET voltages. In one aspect, each of the RF signals is split before amplification and recombined after amplification. As such, the power amplifiers can be configured to operate based on half peak power of the RF signals to help improve operating efficiency of the power amplifiers. In another aspect, the RF signals are pre-processed prior to amplification to form a pair of composite RF signals with similar average power such that the power amplifiers can operate based on substantially similar ET voltages. As a result, it may be possible to employ a single ET integrated circuit (ETIC) to provide the ET voltages to the power amplifiers, thus helping to reduce cost and footprint of the ET power amplifier apparatus. 
     In one aspect, an ET power amplifier apparatus is provided. The ET power amplifier apparatus includes a first signal output coupled to a first antenna. The ET power amplifier apparatus also includes a second signal output coupled to a second antenna. The ET power amplifier apparatus also includes a first power amplifier configured to amplify a first composite RF signal comprising a first RF signal and a second RF signal based on a first ET voltage. The ET power amplifier apparatus also includes a second power amplifier configured to amplify a second composite RF signal comprising the first RF signal and the second RF signal based on a second ET voltage. The ET power amplifier apparatus also includes an output circuit. The output circuit is configured to receive the first composite RF signal and the second composite RF signal from the first power amplifier and the second power amplifier, respectively. The output circuit is also configured to regenerate the first RF signal and the second RF signal from the first composite RF signal and the second composite RF signal. The output circuit is also configured to provide the first RF signal and the second RF signal to the first signal output and the second signal output, respectively. 
     Those skilled in the art will appreciate the scope of the present disclosure and realize additional aspects thereof after reading the following detailed description of the preferred embodiments in association with the accompanying drawing figures. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWING FIGURES 
       The accompanying drawing figures incorporated in and forming a part of this specification illustrate several aspects of the disclosure, and together with the description serve to explain the principles of the disclosure. 
         FIG. 1  is a schematic diagram of an exemplary conventional envelope tracking (ET) power amplifier apparatus configured to amplify a pair of radio frequency (RF) signals for concurrent transmission using a pair of ET integrated circuits (ETICs) and two pairs of power amplifiers; 
         FIG. 2  is a schematic diagram of an exemplary ET power amplifier apparatus configured according to an embodiment of the present disclosure to amplify a pair of RF signals for concurrent transmission with a fewer number of power amplifiers and ETICs than the conventional ET power amplifier apparatus of  FIG. 1 ; 
         FIG. 3  is a schematic diagram providing a further illustration of the ET power amplifier apparatus of  FIG. 2 ; 
         FIGS. 4A-4B  are schematic diagrams of exemplary inductor circuits configured according to embodiments of the present disclosure and can be provided in the ET power amplifiers of  FIG. 3 ; 
         FIG. 5  is a schematic diagram of an ET power amplifier apparatus configured according to another embodiment of the present disclosure; and 
         FIG. 6  is a schematic diagram of an exemplary ET power amplifier apparatus configured according to another embodiment of the present disclosure. 
     
    
    
     DETAILED DESCRIPTION 
     The embodiments set forth below represent the necessary information to enable those skilled in the art to practice the embodiments and illustrate the best mode of practicing the embodiments. Upon reading the following description in light of the accompanying drawing figures, those skilled in the art will understand the concepts of the disclosure and will recognize applications of these concepts not particularly addressed herein. It should be understood that these concepts and applications fall within the scope of the disclosure and the accompanying claims. 
     It will be understood that, although the terms first, second, etc. may be used herein to describe various elements, these elements should not be limited by these terms. These terms are only used to distinguish one element from another. For example, a first element could be termed a second element, and, similarly, a second element could be termed a first element, without departing from the scope of the present disclosure. As used herein, the term “and/or” includes any and all combinations of one or more of the associated listed items. 
     It will be understood that when an element such as a layer, region, or substrate is referred to as being “on” or extending “onto” another element, it can be directly on or extend directly onto the other element or intervening elements may also be present. In contrast, when an element is referred to as being “directly on” or extending “directly onto” another element, there are no intervening elements present. Likewise, it will be understood that when an element such as a layer, region, or substrate is referred to as being “over” or extending “over” another element, it can be directly over or extend directly over the other element or intervening elements may also be present. In contrast, when an element is referred to as being “directly over” or extending “directly over” another element, there are no intervening elements present. It will also be understood that when an element is referred to as being “connected” or “coupled” to another element, it can be directly connected or coupled to the other element or intervening elements may be present. In contrast, when an element is referred to as being “directly connected” or “directly coupled” to another element, there are no intervening elements present. 
     Relative terms such as “below” or “above” or “upper” or “lower” or “horizontal” or “vertical” may be used herein to describe a relationship of one element, layer, or region to another element, layer, or region as illustrated in the Figures. It will be understood that these terms and those discussed above are intended to encompass different orientations of the device in addition to the orientation depicted in the Figures. 
     The terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting of the disclosure. As used herein, the singular forms “a,” “an,” and “the” are intended to include the plural forms as well, unless the context clearly indicates otherwise. It will be further understood that the terms “comprises,” “comprising,” “includes,” and/or “including” when used herein specify the presence of stated features, integers, steps, operations, elements, and/or components, but do not preclude the presence or addition of one or more other features, integers, steps, operations, elements, components, and/or groups thereof. 
     Unless otherwise defined, all terms (including technical and scientific terms) used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this disclosure belongs. It will be further understood that terms used herein should be interpreted as having a meaning that is consistent with their meaning in the context of this specification and the relevant art and will not be interpreted in an idealized or overly formal sense unless expressly so defined herein. 
     Embodiments of the disclosure relate to an envelope tracking (ET) power amplifier apparatus. The ET power amplifier apparatus includes a pair of power amplifiers configured to amplify a pair of radio frequency (RF) signals based on a pair of ET voltages. In one aspect, each of the RF signals is split before amplification and recombined after amplification. As such, the power amplifiers can be configured to operate based on half peak power of the RF signals to help improve operating efficiency of the power amplifiers. In another aspect, the RF signals are pre-processed prior to amplification to form a pair of composite RF signals with similar average power such that the power amplifiers can operate based on substantially similar ET voltages. As a result, it may be possible to employ a single ET integrated circuit (ETIC) to provide the ET voltages to the power amplifiers, thus helping to reduce cost and footprint of the ET power amplifier apparatus. 
     Before discussing an ET power amplifier apparatus of the present disclosure, a brief overview of a conventional ET power amplifier apparatus is first provided with reference to  FIG. 1  to help understand the challenges associated with amplifying multiple RF signals for concurrent transmission. The discussion of specific exemplary aspects of an ET power amplifier apparatus of the present disclosure starts below with reference to  FIG. 2 . 
     In this regard,  FIG. 1  is a schematic diagram of an exemplary conventional ET power amplifier apparatus  10  configured to amplify a first RF signal  12  and a second RF signal  14  for concurrent transmission at a first time-variant power P 1  and a second time-variant power P 2 , respectively. Notably, the first time-variant power P 1  and the second time-variant power P 2  can be associated with a first peak power P PEAK1  and a second peak power P PEAK2 , respectively. 
     The conventional ET power amplifier apparatus  10  includes a first signal splitter  16  and a first signal combiner  18 . The first signal splitter  16  is configured to split the first RF signal  12  into a first in-phase RF signal  12 I and a first quadrature RF signal  12 Q. The conventional ET power amplifier apparatus  10  includes a pair of first power amplifiers  20 I and  20 Q configured to amplify the first in-phase RF signal  12 I and the first quadrature RF signal  12 Q, respectively, based on a first ET voltage V CCA . The first ET voltage V CCA  may be generated by a first ET integrated circuit (ETIC)  22 . The first signal combiner  18  is configured to combine the first in-phase RF signal  12 I and the first quadrature RF signal  12 Q after amplification to regenerate the first RF signal  12  for transmission via a first antenna  24 . 
     The conventional ET power amplifier apparatus  10  also includes a second signal splitter  26  and a second signal combiner  28 . The second signal splitter  26  is configured to split the second RF signal  14  into a second in-phase RF signal  14 I and a second quadrature RF signal  14 Q. The conventional ET power amplifier apparatus  10  includes a pair of second power amplifiers  30 I and  30 Q configured to amplify the second in-phase RF signal  14 I and the second quadrature RF signal  14 Q, respectively, based on a second ET voltage V CCB . The second ET voltage V CCB  may be generated by a second ETIC  32 . The second signal combiner  28  is configured to combine the second in-phase RF signal  14 I and second quadrature RF signal  14 Q after amplification to regenerate the second RF signal  14  for transmission via a second antenna  34 . 
     The conventional ET power amplifier apparatus  10  may be configured to transmit the first RF signal  12  and the second RF signal  14  concurrently based on a multiple-input multiple-output (MIMO) spatial multiplexing scheme or a MIMO diversity scheme. In this regard, the first time-variant power P 1  of the first RF signal  12  may be different from the second time-variant power P 2  of the second RF signal  14 . Accordingly, the first peak power P PEAK1  of the first RF signal  12  may be different from the second peak power P PEAK2  of the second RF signal  14 . As such, the conventional ET power amplifier apparatus  10  needs to employ the two pairs of power amplifiers  20 I/ 20 Q and  30 I/ 30 Q as well as the pair of ETICs  22  and  32  to amplify the first RF signal  12  and the second RF signal  14  for concurrent transmission. As a result, the conventional ET power amplifier apparatus  10  may have to be built with a higher cost and larger footprint. In this regard, it may be desirable to improve the conventional ET power amplifier apparatus  10  to reduce cost and footprint. 
     In this regard,  FIG. 2  is a schematic diagram of an exemplary ET power amplifier apparatus  36  configured according to an embodiment of the present disclosure to amplify a first RF signal  38  and a second RF signal  40  for concurrent transmission with a fewer number of power amplifier and ETIC than the conventional ET power amplifier apparatus  10  of  FIG. 1 . In examples discussed herein, the ET power amplifier apparatus  36  is configured to pre-process the first RF signal  38  and the second RF signal  40  before amplification to form a first composite RF signal  42  and a second composite RF signal  44 . The ET power amplifier apparatus  36  includes an output circuit  46  configured to re-process the first composite RF signal  42  and the second composite RF signal  44  after amplification to regenerate the first RF signal  38  and the second RF signal  30 . The output circuit  46  then provides the first RF signal  38  and the second RF signal  40  to a first signal output  48  and a second signal output  50  for concurrent transmission via a first antenna(s)  52  and a second antenna(s)  54 , respectively. 
     More specifically, the ET power amplifier apparatus  36  is configured to cause the first composite RF signal  42  and the second composite RF signal  44  to be so generated to have substantially similar average power. Accordingly, the ET power amplifier apparatus  36  can amplify the first composite RF signal  42  and the second composite RF signal  44  based on a single pair of power amplifiers, namely a first power amplifier  56  and a second power amplifier  58 , and a single ETIC, namely an ETIC  60 . As a result, the ET power amplifier apparatus  36  can eliminate one pair of power amplifiers as well as one ETIC from the conventional ET power amplifier apparatus  10 , thus making it possible to reduce cost and footprint of the ET power amplifier apparatus  36 . 
     Notably, a key aspect for reducing the number of power amplifiers and ETICs in the ET power amplifier apparatus  36  is to generate the first composite RF signal  42  and the second composite RF signal  44  with substantially similar average power. In this regard, a mathematical analysis is provided below to help explain what the ET power amplifier apparatus  36  needs to do to cause the first composite RF signal  42  and the second composite RF signal  44  to have the substantially similar average power. 
     To facilitate reference and discussion, the first RF signal  38  and the second RF signal  40  are herein represented by respective baseband vector forms as shown in equations (Eq. 1.1-1.2), respectively.
 
 {right arrow over (a)}=|a|*e   θ     a     (Eq. 1.1)
 
 {right arrow over (b)}=|b|*e   θ     b     (Eq. 1.2)
 
     In the equations (Eq. 1.1-1.2), θ a  represents a first phase term of the first RF signal  38  and θ b  represents a second phase term of the second RF signal  40 . In a non-limiting example, the ET power amplifier apparatus  36  includes an input circuit  62  configured to generate the first composite RF signal  42  and the second composite RF signal  44  from the first RF signal  38  and the second RF signal  40 . Although the input circuit  62  is shown as being part of the ET power amplifier apparatus  36 , it should be appreciated that it is also possible to provide the input circuit  62  outside the ET power amplifier apparatus  36 , such as in a signal processing circuit  64  (e.g., a transceiver circuit) coupled externally to the ET power amplifier apparatus  36 . 
     The input circuit  62  can be configured to split the first RF signal {right arrow over (a)} into an in-phase component {right arrow over (a I )} and a quadrature component {right arrow over (a Q )}, each having one-half (½) the power of the first RF signal {right arrow over (a)}. Likewise, the input circuit  62  can be configured to split the second RF signal {right arrow over (b)} into an in-phase component {right arrow over (b I )} and a quadrature component {right arrow over (b Q )}, each having ½ the power of the second RF signal {right arrow over (b)}. 
     The input circuit  62  is further configured to generate the first composite RF signal  42 , which is represented by vector {right arrow over (ab 1 )}, to include the quadrature component {right arrow over (a Q  )} of the first RF signal d and the in-phase component {right arrow over (b I )} of the second RF signal {right arrow over (b)} ({right arrow over (ab 1 )}={right arrow over (a Q )}+{right arrow over (b I )}). Likewise, the input circuit  62  generates the second composite RF signal  44 , which is represented by vector {right arrow over (ab 2 )}, to include the in-phase component {right arrow over (a I )} of the first RF signal {right arrow over (a)} and the quadrature component {right arrow over (b Q )} of the second RF signal {right arrow over (b)} ({right arrow over (ab 2 )}={right arrow over (a I )}+{right arrow over (b Q )}). 
     Since each of the quadrature component {right arrow over (a Q )} and the in-phase component {right arrow over (b I )} is half-powered, the first composite RF signal  42  is likewise half-powered. Similarly, given that each of the in-phase component {right arrow over (a I )} and the quadrature component {right arrow over (b Q )} is half-powered, the second composite RF signal  44  is also half-powered. As such, it may be possible to configure the first power amplifier  56  and the second power amplifier  58  to operate at half the peak power of the first RF signal  38  and the second RF signal  40 , thus helping to improve operating efficiency of the first power amplifier  56  and the second power amplifier  58 . Notably, the first RF signal  38  and the second RF signal  40  may correspond to different peak powers. In this regard, each of the first power amplifier  56  and the second power amplifier  58  may be configured to operate at half of a higher peak power between the first RF signal  38  and the second RF signal  40 . 
     The first composite RF signal {right arrow over (ab 1 )} and the second composite RF signal {right arrow over (ab 2 )} can also be expressed in complex forms, as shown in the equations (Eq. 2.1-2.2) below.
 
{right arrow over ( ab   1 )}= j*a   I   +b   I   =re ( b   I )− im ( a   I )+ j *[ im ( b   I )+ re ( a   I )]  (Eq. 2.1)
 
{right arrow over ( ab   2 )}= j*b   I   +a   I   =re ( a   I )− im ( b   I )+ j *[ im ( a   I )+ re ( b   I )]  (Eq. 2.2)
 
     In the equations (Eq. 2.1-2.2) above, re( ) represents a real part of a complex expression, im( ) represents an imaginary part of the complex expression, a I  represents amplitude of the in-phase component {right arrow over (a I )}, and b I  represents amplitude of the in-phase component {right arrow over (b I )}. 
     The power of the first composite RF signal {right arrow over (ab 1 )} and the second composite RF signal {right arrow over (ab 2 )} can be expressed as |{right arrow over (ab 1 )}| 2  and |{right arrow over (ab 2 )}| 2 , as shown in the equations (Eq. 3.1-3.2) below.
 
|{right arrow over ( ab   1 )}| 2   =|b   I | 2   +|a   I | 2 −[2 *re ( b   I )* im ( a   I )− im ( b   I )* re ( a   I )]  (Eq. 3.1)
 
|{right arrow over ( ab   2 )}| 2   =|b   I | 2   +|a   I | 2 +[2 *re ( b   I )* im ( a   I )− im ( b   I )* re ( a   I )]  (Eq. 3.2)
 
     In this regard, the power of the first composite RF signal {right arrow over (ab 1 )} and the second composite RF signal {right arrow over (ab 2 )} can be generalized as in the equations (Eq. 4.1-4.4) below.
 
|{right arrow over ( ab   1 )}| 2 =Common Power Envelope−Diff RF Envelope  (Eq. 4.1)
 
|{right arrow over ( ab   2 )}| 2 =Common Power Envelope+Diff RF Envelope  (Eq. 4.2)
 
Common Power Envelope=| b   I | 2   +|a   I | 2   (Eq. 4.3)
 
Diff Power Envelope=2 *re ( b   I )* im ( a   I )− im ( b   I )* re ( a   I )  (Eq. 4.4)
 
     The first power amplifier  56  and the second power amplifier  58  are configured to amplify the first composite RF signal {right arrow over (ab 1 )} and the second composite RF signal {right arrow over (ab 2 )} based on a first ET voltage V CCA (t) and a second ET voltage V CCB (t), respectively. In this regard, the first ET voltage V CCA (t) and the second ET voltage V CCB (t) are related to the power of the first composite RF signal {right arrow over (ab 1 )}, namely |{right arrow over (ab 1 )}| 2 , and the second composite RF signal {right arrow over (ab 2 )}, namely |{right arrow over (ab 2 )}| 2 . The first ET voltage V CCA (t) and the second ET voltage V CCB (t) can be determined based on the equations (Eq. 5.1-5.3) below. 
     
       
         
           
             
               
                 
                   
                     
                       
                         
                           
                             
                               V 
                               CCA 
                             
                             ⁡ 
                             
                               ( 
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                           = 
                             
                           ⁢ 
                           
                             
                               R 
                             
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                                         ( 
                                         
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                                           ⁢ 
                                           
                                               
                                           
                                           ⁢ 
                                           Power 
                                           ⁢ 
                                           
                                               
                                           
                                           ⁢ 
                                           Envelope 
                                         
                                         ) 
                                       
                                       - 
                                     
                                   
                                 
                                 
                                   
                                     
                                       ( 
                                       
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                                         ⁢ 
                                         
                                             
                                         
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                                         ⁢ 
                                         Envelope 
                                       
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                     . 
                     
                         
                     
                     ⁢ 
                     5.1 
                   
                   ) 
                 
               
             
             
               
                 
                   
                     
                       
                         
                           
                             
                               V 
                               CCAB 
                             
                             ⁡ 
                             
                               ( 
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                     Eq 
                     . 
                     
                         
                     
                     ⁢ 
                     5.2 
                   
                   ) 
                 
               
             
             
               
                 
                   x 
                   = 
                   
                     
                       [ 
                       
                         
                            
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                         + 
                         
                           
                             
                                
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                     / 
                     
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                     Eq 
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                     5.3 
                   
                   ) 
                 
               
             
           
         
       
     
     In the equations (Eq. 5.1 and 5.2) above, R represents a load impedance seen respectively by the first power amplifier  56  and the second power amplifier  58 . The equations (Eq. 5.1-5.2) can be further approximated by the equations (Eq. 6.1-6.2) below.
 
 V   CCA ( t )≈√{square root over ( R )}*√{square root over ((| b   I | 2   +|a   I | 2 ))}*(1− x/ 2)  (Eq. 6.1)
 
 V   CCB ( t )≈√{square root over ( R )}*√{square root over ((| b   I | 2   +|a   I | 2 ))}*(1+ x/ 2)  (Eq. 6.2)
 
     In the equations (Eq. 6.1-6.2), the x-terms are the same as shown in the equation (Eq. 5.3). According to the equations (Eq. 6.1-6.2), the first ET voltage V CCA (t) and the second ET voltage V CCB (t) can have a same average value √{square root over (R)}*√{square root over ((|b I | 2 +|a I | 2 ))} if the x-terms can be averaged out. Accordingly, the first composite RF signal  42  and the second composite RF signal  44  may have a substantially equal average power that equals the Common Power Envelope |b I | 2 +|a I | 2 , as expressed in the equation (Eq. 4.3). In this regard, the first composite RF signal  42  and the second composite RF signal  44  can have the substantially equal average power |b I | 2 +|a I | 2  regardless of whether the first RF signal  38  and the second RF signal  40  are associated with an identical power envelope (e.g., a I =b I ) or different power envelopes (e.g., a I ≠b I ). As a result, it may be possible to employ fewer numbers of power amplifiers and ETICs in the ET power amplifier apparatus  36 . 
     To average out the x-terms in the equations (Eq. 6.1-6.2), it may be necessary to average out the sin(θ a −θ b ) in the equation (Eq. 5.3). Notably, the sin(θ a −θ b ) can be inherently averaged out when the first RF signal  38  and the second RF signal  40  are uncorrelated signals. For example, when the ET power amplifier apparatus  36  is configured to transmit the first RF signal  38  and the second RF signal  40  concurrently to support MIMO spatial multiplexing, the first RF signal  38  and the second RF signal  40  may be different signals. As such, the first phase term θ a  of the first RF signal  38  and the second phase term θ b  of the second RF signal  40  may be uncorrelated. As a result, the sin(θ a −θ b ) may be averaged out in the equation (Eq. 5.3) to cause the x-terms in the equations (Eq. 6.1-6.2) to become zero. 
     However, when the ET power amplifier apparatus  36  is configured to transmit the first RF signal  38  and the second RF signal  40  concurrently to support MIMO diversity, the first RF signal  38  and the second RF signal  40  may be the same signal. As such, the first phase term θ a  of the first RF signal  38  and the second phase term θ b  of the second RF signal  40  may be correlated to achieve phase coherency. In this regard, it may be necessary to make the first phase term θ a  and the second phase term θ b  uncorrelated by including at least one phase adjuster  66  in the ET power amplifier apparatus  36 . In a non-limiting example, the phase adjuster  66  can be provided between the signal processing circuit  64  and the input circuit  62  and configured to adjust at least one of the first phase term θ a  and the second phase term θ b  such that the first phase term θ a  and the second phase term θ b  can become uncorrelated. For example, the phase adjuster  66  can adjust the first phase term θ a  based on a feedback signal  68  indicative of an average differential between the first ET voltage V CCA (t) and the second ET voltage V CCB (t). The ET power amplifier apparatus  36  may include a measurement circuit  70  configured to measure the average differential between the first ET voltage V CCA (t) and the second ET voltage V CCB (t) and generate the feedback signal  68 . 
     By averaging out the x-terms in the equations (Eq. 6.1-6.2), it may be possible to make the first ET voltage V CCA (t) and the second ET voltage V CCB (t) have the same average value √{square root over (R)}*√{square root over ((|b I | 2 +|a I | 2 ))}, thus making it possible to employ only the ETIC  60  to provide the first ET voltage V CCA (t) and the second ET voltage V CCB (t). In this regard,  FIG. 3  is a schematic diagram providing a further illustration of the ETIC  60  in the ET power amplifier apparatus  36  of  FIG. 2 . Common elements between  FIGS. 2 and 3  are shown therein with common element numbers and will not be re-described herein. 
     The ETIC  60  includes a multi-level charge pump (MCP)  72  and an inductor circuit  74 . The MCP  72  is configured to generate a low-frequency voltage V DC  (e.g., a constant voltage) at multiple levels based on a battery voltage V BAT . In a non-limiting example, the MCP  72  can be configured to generate the low-frequency voltage V DC  at 0 V, V BAT , or 2*V BAT . The inductor circuit  74  is configured to induce a low-frequency current I DC  (e.g., a direct current) based on the low-frequency voltage V DC . The inductor circuit  74  is coupled to the first power amplifier  56  and the second power amplifier  58  to provide the low-frequency IDC to the first power amplifier  56  and the second power amplifier  58 . 
     In one embodiment, the ETIC  60  includes an ET voltage circuit  76 . The ET voltage circuit  76  is configured to generate and provide the first ET voltage V CCA (t) and the second ET voltage V CCB (t) to the first power amplifier  56  and the second power amplifier  58 , respectively. In a specific example, the ET voltage circuit  76  includes a first voltage amplifier  78 A, a first offset capacitor  80 A, a second voltage amplifier  78 B, and a second offset capacitor  80 B. The first voltage amplifier  78 A is configured to generate a first initial ET voltage V′ CCA (t) based on a first ET target voltage V TGTA . The first offset capacitor  80 A is configured to raise the first initial ET voltage V′ CCA (t) by a first offset voltage V OFFA  to generate the first ET voltage V CCA (t) (V CCA (t)=V′ CCA (t)+V OFFA ). Similarly, the second voltage amplifier  78 B is configured to generate a second initial ET voltage V′ CCB (t) based on a second ET target voltage V TGTB . The second offset capacitor  80 B is configured to raise the second initial ET voltage V′ CCB (t) by a second offset voltage V OFFB  to generate the second ET voltage V CCB (t) (V CCB (t)=V′ CCB (t)+V OFFB ). 
     According to the previous discussion, the ET voltage circuit  76  can be configured to generate the first ET voltage V CCA (t) and the second ET voltage V CCB (t) having the same average value √{square root over (R)}*√{square root over ((|b I | 2 +|a I | 2 ))}. Accordingly, the first power amplifier  56  may operate based on a first average power P A  corresponding to the first ET voltage V CCA (t) and the low frequency current I DC  (P A =V CCA (t)*I DC ). Likewise, the second power amplifier  58  may operate based on a second average power P B  corresponding to the second ET voltage V CCB (t) and the low frequency current I DC  (P B =V CCB (t)*I DC ). As such, it may be possible to share the MCP  72  and the inductor circuit  74  between the first power amplifier  56  and the second power amplifier  58 , thus helping to reduce cost and footprint of the ET power amplifier apparatus  36 . 
     Notably, the first ET voltage V CCA (t) and the second ET voltage V CCB (t) can only have the same average value √{square root over (R)}*√{square root over ((|b I | 2 +|a I | 2 ))} if the x-terms in the equations (Eq. 6.1-6.2) can be averaged out. In other words, the first ET voltage V CCA (t) and the second ET voltage V CCB (t) may not be exactly the same if the x-terms in the equations (Eq. 6.1-6.2) are not completely averaged out. In this regard, to make the first average power P A  the same as the second average power P B , the first voltage amplifier  78 A and/or the second voltage amplifier  78 B may be configured to source a first high-frequency current I ACA  (e.g., an alternating current) and/or a second high-frequency current I ACB  (e.g., an alternating current) to the first power amplifier  56  and/or the second power amplifier  58 . Accordingly, the first average power P A  of the first power amplifier  56  can be made to correspond to the first ET voltage V CCA (t), the low frequency current I DC , and the first high-frequency current I ACA , P A =V CCA (t)*(I DC +I ACA ). Similarly, the second average power P B  of the second power amplifier  58  can be made to correspond to the second ET voltage V CCB (t), the low frequency current I DC , and the second high-frequency current I ACB , P A =V CCB (t)*(I DC +I ACB ). As a result, the first average power P A  of the first power amplifier  56  can be kept the same as the second average power P B  of the second power amplifier  58 , even if the x-terms in the equations (Eq. 6.1-6.2) are not completely averaged out. 
     The inductor circuit  74  may be provided based on a number of embodiments, as described next in  FIGS. 4A and 4B . In this regard,  FIG. 4A-4B  are schematic diagrams providing an exemplary illustration of the inductor circuit  74  in the ET power amplifier apparatus  36  of  FIG. 3  configured according to different embodiments of the present disclosure. Common elements between  FIGS. 3, 4A, and 4B  are shown therein with common element numbers and will not be re-described herein. 
       FIG. 4A  is a schematic diagram of an exemplary inductor circuit  74 A, which can be provided as the inductor circuit  74  in the ETIC  60  of  FIG. 3 . The inductor circuit  74 A includes a first power inductor  82  and a second power inductor  84 . The first power inductor  82  is coupled between the MCP  72  and the first power amplifier  56 . The first power inductor  82  is configured to generate the low-frequency current I DC  based on the low-frequency voltage V DC  and provide the low-frequency current I DC  to the first power amplifier  56 . The second power inductor  84  is coupled between the MCP  72  and the second power amplifier  58 . The second power inductor  84  is configured to generate the low-frequency current I DC  based on the low-frequency voltage V DC  and provide the low-frequency current I DC  to the second power amplifier  58 . By employing the first power inductor  82  and the second power inductor  84  in the inductor circuit  74 A, it may be possible to provide isolation between the first power amplifier  56  and the second power amplifier  58 . In a non-limiting example, the first power inductor  82  and the second power inductor  84  can be negatively coupled. 
       FIG. 4B  is a schematic diagram of an exemplary inductor circuit  74 B, which can be provided as the inductor circuit  74  in the ETIC  60  of  FIG. 3 . The inductor circuit  74 B includes a power inductor  86  coupled to the MCP  72  and configured to generate the low-frequency current I DC  based on the low-frequency voltage V DC . 
     As previously described in  FIG. 3 , the first ET voltage V CCA (t) and the second ET voltage V CCB (t) can only have the same average value √{square root over (R)}*√{square root over ((|b I | 2 +|a I | 2 ))} if the x-terms in the equations (Eq. 6.1-6.2) can be averaged out. As such, the first average P A  of the first power amplifier  56  and the second average power P B  of the second power amplifier  58  may be affected if the x-terms in the equations (Eq. 6.1-6.2) are not completely averaged out. Alternative to configuring the first voltage amplifier  78 A and/or the second voltage amplifier  78 B to source the first high-frequency current I ACA  and/or the second high-frequency current I ACB , it may also be possible to adjust the low-frequency current I DC  flowing into the first power amplifier  56  and/or the second power amplifier  58  to make the first average power P A  the same as the second average power P B . 
     In this regard, the inductor circuit  74 B may be configured to include a DC control circuit  88  to couple the power inductor  86  to the first power amplifier  56  and the second power amplifier  58 . In a non-limiting example, the DC control circuit  88  includes a first low-dropout regulator (LDO)  90  and a second LDO  92 . The first LDO  90  is coupled between the power inductor  86  and the first power amplifier  56  to regulate the low-frequency current I DC  flowing into the first power amplifier  56 . The second LDO  92  is coupled between the power inductor  86  and the second power amplifier  58  to regulate the low-frequency current I DC  flowing into the second power amplifier  58 . 
     The DC control circuit  88  may be configured to include a control circuit  94 . The control circuit  94  may be configured to detect a maximum instantaneous voltage differential between the first ET voltage V CCA (t) and the second ET voltage V CCB (t). Accordingly, the control circuit  94  may control the first LDO  90  and/or the second LDO  92  to regulate the low-frequency current I DC  flowing into the first power amplifier  56  and/or the second power amplifier  58  to make the first average power P A  identical to the second average power P B . In a non-limiting example, the control circuit  94  may detect the maximum instantaneous voltage differential between the first ET voltage V CCA (t) and the second ET voltage V CCB (t) based on an indication signal  96 , which may provide feedback of the first ET voltage V CCA (t) and the second ET voltage V CCB (t), or feedback of the first ET target voltage V TGTA  and the second ET target voltage V TGTB . 
     The first LDO  90  and the second LDO  92  may also operate as switches to cut off the low-frequency current I DC  from any of the first power amplifier  56  and the second power amplifier  58 . For example, when the ET power amplifier apparatus  36  is configured to transmit only the first RF signal  38 , the first power amplifier  56  may be configured to amplify the first RF signal  38  directly and the second power amplifier  58  may be deactivated to help conserve energy. As such, the control circuit  94  may control the second LDO  92  to function as a switch to decouple the second power amplifier  58  from the power inductor  86 , thus cutting off the low-frequency current I DC  from the second power amplifier  58 . 
     Alternative to incorporating the ET voltage circuit  76  into the ETIC  60 , as illustrated previously in  FIG. 3 , it may also be possible to provide the ET voltage circuit  76  in a circuit that is separate from the ETIC  60 . For example, the ETIC  60  may be provided in one system-on-chip (SoC) and the ET voltage circuit  76  may be provided in a separate SoC. In this regard,  FIG. 5  is a schematic diagram of an exemplary ET power amplifier apparatus  98  configured according to another embodiment of the present disclosure. Common elements between  FIGS. 3 and 5  are shown therein with common element numbers and will not be re-described herein. 
     As shown in  FIG. 5 , the ET power amplifier apparatus  98  includes an ETIC  100  and a distributed ETIC  102 . The ETIC  100  includes the MCP  72  and the inductor circuit  74 . The distributed ETIC  102  includes the ET voltage circuit  76 . The distributed ETIC  102  may be provided in close proximity to the first power amplifier  56  and the second power amplifier  58  to help reduce trace inductance (e.g., to below 0.1 nH) to mitigate potential distortion in the first ET voltage V CCA (t) and the second ET voltage V CCB (t). 
     The ET power amplifier apparatus  36  of  FIG. 2  can be configured to concurrently transmit additional RF signals via additional antennas. In this regard,  FIG. 6  is a schematic diagram of an exemplary ET power amplifier apparatus  104  configured according to another embodiment of the present disclosure. Common elements between  FIGS. 2 and 6  are shown therein with common element numbers and will not be re-described herein. 
     The signal processing circuit  64  can be configured to generate at least one third RF signal  106  (also denoted as {right arrow over (a X )}) and at least one fourth RF signal  108  (also denoted as {right arrow over (b X )}). The ET power amplifier apparatus  104  may include at least one second input circuit  110  configured to split the third RF signal {right arrow over (a X )} into an in-phase component {right arrow over (a XI )} and a quadrature component {right arrow over (a XQ )}, each having one-half (½) the power of the third RF signal {right arrow over (a X )}. Likewise, the second input circuit  110  can be configured to split the fourth RF signal {right arrow over (b X )} into an in-phase component {right arrow over (b XI )} and a quadrature component {right arrow over (b XQ )}, each having ½ the power of the second RF signal {right arrow over (b X )}. 
     The second input circuit  110  is further configured to generate a third composite RF signal  112  that includes the quadrature component {right arrow over (a XQ )} of the third RF signal {right arrow over (a X )} and the in-phase component {right arrow over (b XI )} of the second RF signal {right arrow over (b X )}. Likewise, the second input circuit  110  can also generate a fourth composite RF signal  114  that includes the in-phase component {right arrow over (a XI )} of the third RF signal {right arrow over (a X )} and the quadrature component {right arrow over (b XQ )} of the fourth RF signal {right arrow over (b X )}. 
     The ET power amplifier apparatus  104  can also include at least one third power amplifier  116  and at least one fourth power amplifier  118  configured to amplify the third composite RF signal  112  and the fourth composite RF signal  114  based on the first ET voltage V CCA (t) and the second ET voltage V CCB (t), respectively. The ET power amplifier apparatus  104  can include at least one second output circuit  120  configured to regenerate the third RF signal  106  and the fourth RF signal  108  from the third composite RF signal  112  and the fourth composite RF signal  114 . The ET power amplifier apparatus  104  can include at least one third signal output  122  coupled to at least one third antenna  124  and at least one fourth signal output  126  coupled to at least one fourth antenna  128 . The second output circuit  120  is further configured to provide the third RF signal  106  and the fourth RF signal  108  to the third signal output  122  and the fourth signal output  126 , respectively. In this regard, the ET power amplifier apparatus  104  can be configured to concurrently transmit the first RF signal  38 , the second RF signal  40 , the third RF signal  106 , and the fourth RF signal  108 . 
     In one example, the first RF signal  38 , the second RF signal  40 , the third RF signal  106 , and the fourth RF signal  108  can be identical RF signals. In this regard, the ET power amplifier apparatus  104  may support four-by-four (4×4) MIMO diversity by concurrently transmitting the first RF signal  38 , the second RF signal  40 , the third RF signal  106 , and the fourth RF signal  108 . In another example, the first RF signal  38 , the second RF signal  40 , the third RF signal  106 , and the fourth RF signal  108  can be different RF signals. In this regard, the ET power amplifier apparatus  104  may support 4×4 MIMO spatial multiplexing by concurrently transmitting the first RF signal  38 , the second RF signal  40 , the third RF signal  106 , and the fourth RF signal  108 . 
     Understandably, the ET power amplifier apparatus  104  may be further configured to include additional input circuits, additional power amplifiers, and additional output circuits to concurrently transmit additional RF signals via additional antennas. As such, the ET power amplifier apparatus  104  can be configured to support massive-MIMO and RF beamforming in a millimeter wave (mmWave) spectrum. 
     Those skilled in the art will recognize improvements and modifications to the preferred embodiments of the present disclosure. All such improvements and modifications are considered within the scope of the concepts disclosed herein and the claims that follow.