Patent Publication Number: US-9432946-B2

Title: Transmission apparatus and transmission method

Description:
CROSS REFERENCE TO RELATED APPLICATIONS 
     This application is a National Stage of International Application No. PCT/JP2013/051724 filed Jan. 28, 2013, claiming priority based on Japanese Patent Application No. 2012-054398, filed Mar. 12, 2012, the contents of all of which are incorporated herein by reference in their entirety. 
     TECHNICAL FIELD 
     The present invention relates to a transmission apparatus and a transmission method, and more particularly to a transmission apparatus and a transmission method that are used for wireless communication and transmit RF (Radio Frequency) signals of a plurality of carrier frequency bands. 
     BACKGROUND ART 
     In the transmission apparatus used for wireless communication, a power amplifier (PA) that amplifies a RF signal to be transmitted consumes power most among the components of the transmission apparatus. Thus, in the development of the transmission apparatus, improving the power efficiency of the power amplifier (PA) is an important challenge. In recent communication standard, linear modulation is mainstream for spectral efficiency improvement. In the linear modulation, requirements concerning signal distortion are strict. 
     Thus, in the power amplifier (PA), to maintain linearity, average output power is set so that instantaneous maximum output (peak) power can be equal to or less than saturated output power. In other words, in the power amplifier (PA), as the ratio of the peak power of the signal to be amplified to average power (Peak-to-Average Ratio, hereinafter abbreviated to PAR) takes a larger value, to maintain the linearity, the average output power must be set lower than the saturated output power. 
     Generally, however, the power amplifier (PA) is characterized in that as the ratio of the average output power to the saturated output power is lower, the ratio (power efficiency) of supply power supplied to the power amplifier (PA) to output power extracted from the power amplifier (PA) is lower. The reduction of the power efficiency runs counter to energy saving. 
     The PAR of the RF signal has a unique value for each communication standard. In recently used high-speed wireless communication such as CDMA (Code Division Multiple Access), WLAN (Wireless Local Area Network), terrestrial digital broadcasting, or LTE (Long Term Evolution), the PAR takes a large value of several dB to tens of dB. Such a size of the PAR is a cause of great reduction of the power efficiency of the power amplifier (PA). 
     In the power amplifier (PA), to solve the problem of the reduction of the power efficiency caused by the low average output power, a polar modulation technology has been actively studied in recent years. 
       FIG. 1  illustrates the example of the power amplifier of an Envelope Tracking (ET) method that is a type of a polar modulation technology. 
     According to the ET method, transmission signal data is input to input terminal  401  of polar modulator  411 , amplitude component signal  403  of the transmission signal data is output to output terminal  402  of polar modulator  411 , and RF modulation signal  408  including the amplitude component and the phase component of the transmission signal data in the carrier wave is output to output terminal  407  of polar modulator  411 . Polar modulator  411  has a function of individually setting the output timings of amplitude component signal  403  and RF modulation signal  408  to desired values. 
     Power supply modulator  404  outputs amplitude component signal  405  obtained by amplifying amplitude component signal  403 , and modulates power supply terminal  409  of RF-PA (Radio Frequency Power Amplifier)  406  based on amplitude component signal  405 . RF modulation signal  408  output to output terminal  407  of polar modulator  411  is input to RF-PA  406 . RF modulation signal  410  that includes the amplitude component and the phase component of the transmission signal data in the carrier wave and that is amplified is output to output terminal  412  of RF-PA  406 . 
     According to the ET method, the voltage of power supply terminal  409  of RF-PA  406  is controlled according to the amplitude of RF modulation signal  410 . Particularly, when RF modulation signal  410  is low output power, the voltage of power supply terminal  409  of RF-PA  406  is accordingly reduced. Thus, wasteful power consumption can be suppressed by limiting the amount of supply power from power supply modulator  404  to RF-PA  406  to a necessary minimum during the low output power. 
     In recent communication standards, to achieve higher-speed wireless communication, as described in Non-patent Literature 1, a Carrier Aggregation (CA) technology collecting a plurality of fragmented bands to utilize has been used. In this CA technology, by bundling the plurality of bands to secure a broadband, a high transmission speed can be achieved. 
     In an inter-band Non-contiguous CA mode in which carrier frequencies are greatly different from each other (difference Δf between carrier frequencies is sufficiently larger than modulation bandwidth f BB  of RF signal of each carrier), communication stability can be improved by simultaneously performing communication at a plurality of carrier frequencies whose propagation characteristics are different. By applying the CA technology, when a plurality of business operators intermittently allocates bands or when the plurality of business operators shares a band, corresponding communication can be performed. 
     In the wireless communication system using the CA technology, a transmission apparatus and a transmission method that transmit the RF signals of a plurality of bands are necessary. In such a transmission apparatus, similarly, improving of power efficiency is required. 
       FIG. 2  is a diagram illustrating the functional configuration of a transmission apparatus disclosed as a wireless communication machine in Patent Literature 1. The transmission apparatus illustrated in  FIG. 2  has a function of transmitting the RF signals of a plurality of bands and a function of improving power efficiency by applying the polar modulation technology. 
     Specifically, in the transmission apparatus illustrated in  FIG. 2 , a modulation signal generated by modulation signal generator  61  is converted from the signal of an orthogonal coordinate system into the signal of a polar coordinate system at polar control unit  62 , and separated into a PM signal having phase information and an AM signal having amplitude information. The separated PM signal is used for phase modulation for frequency generator  11  by PM control unit  63 . Similarly, the AM signal is used for power supply modulation for PA  21  and PA  31  by power supply modulator  64 . In other words, the polar modulation technology, for increasing or decreasing supply power from power supply modulator  64  to PA  21  and PA  31  according to the increase or decrease of the output power of PA  21  and PA  31 , is applied. Thus, the reduction of the power efficiency, even in a high back-off state where average output power is low, can be suppressed. 
     The transmission apparatus illustrated in  FIG. 2  includes path selection switches  14  and  41  for switching GSM (Global System for Mobile Communication) signal path  20  including PA  21  and UMTS (Universal Mobile Telecommunications System) signal path  30  including PA  31 . PA  21  amplifies the RF signal of the carrier frequency f c1  of a wireless communication system (GSM), while PA  31  amplifies the RF signal of the carrier frequency f c2  of a wireless communication system (UMTS). When communication is performed at the wireless communication system of the carrier frequency f c1 , path selection switches  14  and  41  are switched so that PA  21  can input or output a RF signal based on a control signal from controller  15 . When communication is performed at the wireless communication system of the carrier frequency f c2 , path selection switches  14  and  41  are switched so that PA  31  can input or output a RF signal based on a control signal from controller  15 . 
     The transmission apparatus illustrated in  FIG. 2 , which is not compatible with the CA technology for simultaneously outputting two desired frequency components f c1  and f c2 , has a multi-band operation function of operating for one frequency by temporally switching the frequency components f c1  and f c2 . 
     As in the case of the transmission apparatus illustrated in  FIG. 2 , Patent Literatures 2˜5 disclose technologies for maintaining high power efficiency even when average output power is set low by preparing the number of PAs equal to that of used bands, by allocating each PA for each band, by installing band selection switches on the input sides or the output sides of the PAs, by switching the band selection switches so that the PA corresponding to a currently used band can input or output a RF signal, and by applying a polar modulation technology for controlling supply power from a power source to each PA. 
     CITATION LIST 
     Patent Literature 
     
         
         Patent Literature 1: JP2006-324878 A 
         Patent Literature 2: JP2011-512098 A 
         Patent Literature 3: JP2005-244826 A 
         Patent Literature 4: JP2006-270923 A 
         Patent Literature 5: JP2008-205821 A 
       
    
     Non-Patent Literature 
     Non-patent Literature 1: Nobuhiko Mild, et. al., “Carrier Aggregation for achieving Broadband in LTE-Advanced-Advanced”, NTT DoCoMo Technical Journal, Vol. 18, No. 2 
     Non-patent Literature 2: P. Conlantonio, et. al., “A Design technique for Concurrent Dual-Band Harmonic Tuned Power Amplifier, “IEEE Transactions on Microwave Theory and Techniques, Vol. 56, No. 11, pp. 2545 to 2555, 2008 
     Non-patent Literature 3: S. Kousai, et. al., “An Octave-Range, Watt-Level, Fully-Integrated CMOSS Switching Power Mixer Array for Linearization and Back-Off-Efficiency Improvement, “IEEE Journal of Solid-State Circuits, Vol. 44, No. 12, pp. 3376 to 3392, 2009 
     Non-patent Literature 4: P. Saad, et. al., “Design of a Highly Efficient 2-4 GHz Octave Bandwidth GaN-HEMT Power Amplifier, “IEEE Transactions on Microwave Theory and Techniques, Vo. 58, No. 7, pp. 1677 to 1685, 2010 
     Non-patent Literature 5: E Wang, et. al., “An improved Power-Added Efficiency 19-dBm Hybrid Envelope Elimination and Restoration Power Amplifier for 802.11g WLAN Applications, “IEEE Transactions on Microwave Theory and Techniques, Vol. 54, No. 12, pp. 4086 to 4099, 2006 
     Non-patent Literature 6: Shigeru Ando, “Electronic Circuit, from basics to system”, Baifukan 
     SUMMARY OF INVENTION 
     Problems to be Solved 
     However, in the case of technologies described in Patent Literatures 1˜5, the number of power amplifiers equal to that of used bands must be installed. This necessity causes, particularly in a wireless communication system using many bands, the increase of the circuit size and the costs of the transmission apparatus. 
     It is therefore an object of the present invention to provide a transmission apparatus and a transmission method capable of solving the aforementioned problems. 
     Solution to Problems 
     A transmission apparatus according to the present invention includes: 
     a polar modulator that generates a power supply modulation signal and RF (Radio Frequency) signals of a plurality of carrier frequency bands to be transmitted; 
     a power amplifier that amplifies the RF signals from the polar modulator; and 
     a power supply modulator that modulates the power supply terminal of the power amplifier by a signal obtained by amplifying the power supply modulation signal from the polar modulator, 
     wherein the power supply modulation signal is set based on a function using, as an argument, the power of the RF signal of each carrier frequency band output from the power amplifier. 
     A transmission method according to the present invention is a transmission method implemented in a transmission apparatus that generates RF signals of a plurality of carrier frequency bands to transmit the RF signals via a power amplifier, 
     the transmission method comprising: 
     the step of detecting the power of the RF signal of each carrier frequency band output from the power amplifier; 
     the step of setting a power supply modulation signal based on a function using, as an argument, the detected power of the RF signal of each carrier frequency band; and 
     the step of modulating the power supply terminal of the power amplifier by the power supply modulation signal output from a power supply modulator. 
     Effects of Invention 
     According to the transmission apparatus and the transmission method of the present invention, the RF signals of the plurality of carrier frequency bands are simultaneously amplified by the single power amplifier, and the power supply terminal of the power amplifier is modulated by the single power supply modulator. As a result, the circuit size and the costs of the transmission apparatus can be reduced. 
    
    
     
       BRIEF DESCRIPTION OF DRAWINGS 
         FIG. 1  A block diagram illustrating the block configuration of a transmission apparatus including a power amplifier to which a polar modulation technology is applied according to a related art. 
         FIG. 2  A block diagram illustrating the block configuration of a transmission apparatus described in Patent Literature 1. 
         FIG. 3  A block diagram illustrating the block configuration of a transmission apparatus according to the first exemplary embodiment of the present invention. 
         FIG. 4  A characteristic diagram illustrating the input-output power characteristics of a dual-band power amplifier (PA) as the example of a power amplifier illustrated in  FIG. 3 . 
         FIG. 5  A characteristic diagram illustrating the power characteristics of an output signal at the time of saturation when two RF signals of different carrier frequencies are simultaneously input to the dual-band power amplifier (PA) as the example of the power amplifier illustrated in  FIG. 3 . 
         FIG. 6  A characteristic diagram illustrating the power characteristics of the output signal at the time of saturation when the two RF signals of different carrier frequencies are simultaneously input to the dual-band power amplifier (PA) as the example of the power amplifier illustrated in  FIG. 3 . 
         FIG. 7  A characteristic diagram illustrating a relationship between a saturation output and a power-supply voltage when the two RF signals of different carrier frequencies are simultaneously input to the dual-band power amplifier (PA) as the example of the power amplifier illustrated in  FIG. 3 . 
         FIG. 8  A characteristic diagram illustrating the example of setting of a power supply voltage with respect to PA output power when the two RF signals of different carrier frequencies are input to the dual-band power amplifier (PA) as the example of the power amplifier illustrated in  FIG. 3 . 
         FIG. 9  A characteristic diagram illustrating PA output power and power efficiency when the two RF signals of different carrier frequencies are simultaneously input to the dual-band power amplifier (PA) as the example of the power amplifier illustrated in  FIG. 3  and the PA is operated according to the setting of the power supply voltage illustrated in  FIG. 8 . 
         FIG. 10  A characteristic diagram illustrating PA output power and power efficiency when the two RF signals of different carrier frequencies are simultaneously input to the dual-band power amplifier (PA) as the example of the power amplifier illustrated in  FIG. 3  and the PA is operated according to the setting of the power supply voltage illustrated in  FIG. 8 . 
         FIG. 11  A characteristic diagram illustrating PA output power and power efficiency when the two RF signals of different carrier frequencies are simultaneously input to the dual-band power amplifier (PA) as the example of the power amplifier illustrated in  FIG. 3  and the PA is operated under constant power supply voltage. 
         FIG. 12  A characteristic diagram illustrating PA output power and power efficiency when the two RF signals of different carrier frequencies are simultaneously input to the dual-band power amplifier (PA) as the example of the power amplifier illustrated in  FIG. 3  and the PA is operated under constant power supply voltage. 
         FIG. 13  A characteristic diagram illustrating a PA power gain when the two RF signals of different carrier frequencies are simultaneously input to the dual-band power amplifier (PA) as the example of the power amplifier illustrated in  FIG. 3  and the PA is operated according to the setting of the power supply voltage illustrated in  FIG. 8 . 
         FIG. 14  A characteristic diagram illustrating the example of setting of a power supply voltage with respect to PA output power when the two RF signals of different carrier frequencies are input to the dual-band power amplifier (PA) as the example of the power amplifier illustrated in  FIG. 3 . 
         FIG. 15  A characteristic diagram illustrating PA output power and power efficiency when the two RF signals of different carrier frequencies are simultaneously input to the dual-band power amplifier (PA) as the example of the power amplifier illustrated in  FIG. 3  and the PA is operated according to the setting of the power supply voltage illustrated in  FIG. 14 . 
         FIG. 16  A characteristic diagram illustrating a PA power gain when the two RF signals of different carrier frequencies are simultaneously input to the dual-band power amplifier (PA) as the example of the power amplifier illustrated in  FIG. 3  and the PA is operated according to the setting of the power supply voltage illustrated in  FIG. 14 . 
         FIG. 17  A characteristic diagram illustrating the example of setting of a power supply voltage with respect to PA output power when the two RF signals of different carrier frequencies are input to the dual-band power amplifier (PA) as the example of the power amplifier illustrated in  FIG. 3 . 
         FIG. 18  A characteristic diagram illustrating PA output power and power efficiency when the two RF signals of different carrier frequencies are simultaneously input to the dual-band power amplifier (PA) as the example of the power amplifier illustrated in  FIG. 3  and the PA is operated according to the setting of the power supply voltage illustrated in  FIG. 17 . 
         FIG. 19  A characteristic diagram illustrating a PA power gain when the two RF signals of different carrier frequencies are simultaneously input to the dual-band power amplifier (PA) as the example of the power amplifier illustrated in  FIG. 3  and the PA is operated according to the setting of the power supply voltage illustrated in  FIG. 17 . 
         FIG. 20  A characteristic diagram illustrating an output signal at the time of saturation when the two RF signals of different carrier frequencies are simultaneously input to the dual-band power amplifier (PA) as the example of the power amplifier illustrated in  FIG. 3 . 
         FIG. 21  A block diagram illustrating the block configuration of a polar modulator in a transmission apparatus according to the second exemplary embodiment of the present invention. 
         FIG. 22  A block diagram illustrating the block configuration of a controller in the transmission apparatus according to the second exemplary embodiment of the present invention. 
         FIG. 23  A block diagram illustrating the block configuration of an adjacent channel leakage power ratio (ACPR) detector in the transmission apparatus according to the second exemplary embodiment of the present invention. 
         FIG. 24  A block diagram illustrating the block configuration of a polar modulator in a transmission apparatus according to the first modified example or the second modified example of the second exemplary embodiment of the present invention. 
         FIG. 25  A block diagram illustrating the block configuration of a controller in the transmission apparatus according to the first modified example to the fourth modified example of the second exemplary embodiment of the present invention. 
         FIG. 26  A block diagram illustrating the block configuration of a polar modulator in a transmission apparatus according to the third modified example of the second exemplary embodiment of the present invention. 
         FIG. 27  A block diagram illustrating an example of the block configuration of a nonlinear circuit in the transmission apparatus according to the third modified example of the second exemplary embodiment of the present invention. 
         FIG. 28  A block diagram illustrating another example of the block configuration of the nonlinear circuit in the transmission apparatus according to the third modified example of the second exemplary embodiment of the present invention. 
         FIG. 29  A block diagram illustrating the block configuration of a polar modulator in the transmission apparatus according to the fourth modified example of the second exemplary embodiment of the present invention. 
         FIG. 30  A block diagram illustrating the block configuration of a nonlinear circuit in the transmission apparatus according to the fourth modified example of the second exemplary embodiment of the present invention. 
     
    
    
     DESCRIPTION OF EMBODIMENTS 
     Hereinafter, the preferred exemplary embodiments of a transmission apparatus and a transmission method according to the present invention will be described with reference to the accompanying drawings. In the respective drawings referred to below, similar or equivalent portions will be denoted by similar reference numerals, and description thereof will not be repeated. 
     (Overview of Invention) 
     The overview of the present invention will be first given before description of the exemplary embodiments of the invention. 
     The present invention is mainly characterized by achieving a transmission apparatus that includes a power amplifier compatible with a CA (Carrier Aggregation) technology capable of simultaneously amplifying the signals of a plurality of frequencies generated by a signal generator. 
     Specifically, the transmission apparatus according to the present invention is mainly characterized by including a polar modulator that generates a power supply modulation signal and RF (Radio Frequency) signals of a plurality of carrier frequency bands to be transmitted, a power amplifier that amplifies the RF signals from the polar modulator, and a power supply modulator that modulates the power supply terminal of the power amplifier by a signal obtained by amplifying the power supply modulation signal from the polar modulator, and in that the power supply modulation signal is set based on a function using, as an argument, the power of the RF signal of each carrier frequency band output from the power amplifier. 
     Thus, in the transmission apparatus according to the present invention, since the RF signals of the plurality of carrier frequency bands are simultaneously amplified by one power amplifier, the number of power amplifiers can be one, irrespective of the number of RF signals of carrier frequencies to be amplified. In the transmission apparatus according to the present invention, since only one power amplifier is used, only one power supply modulator is necessary. In the transmission apparatus according to the present invention, compared with the transmission apparatuses described in Patent Literatures 1˜5, the transmission apparatus of high power efficiency can be configured by the smaller numbers of power amplifiers and power supply modulators. As a result, a circuit size and costs can be reduced. 
     In the transmission apparatus according to the present invention, since the RF signals of the plurality of carrier frequency bands are simultaneously amplified by one power amplifier, there is no need to install a switch for switching a used frequency band at the input and the output of the power amplifier. As a result, in the transmission apparatus according to the present invention, the increase of the circuit size and the costs caused by the installation of such a switch and the reduction of the power efficiency of the entire transmission apparatus caused by the insertion loss of a switch can be prevented. 
     In the transmission apparatus according to the present invention, the RF signals of the plurality of carrier frequency bands can be simultaneously amplified to be output. Thus, the transmission apparatus according to the present invention is compatible with the CA technology. 
     First Exemplary Embodiment 
       FIG. 3  is a block diagram illustrating the block configuration of a transmission apparatus according to the first exemplary embodiment of the present invention. The transmission apparatus according to the first exemplary embodiment illustrated in  FIG. 3  is configured by including at least polar modulator  601 , power supply modulator  602 , power amplifier  603 , and coupler  604 . Polar modulator  601  and power supply modulator  602  are connected to each other via terminal  607 . Power supply modulator  602  and power amplifier  603  are connected to each other via terminal  608 . Polar modulator  601  and power amplifier  603  are connected to each other via terminal  605 . Coupler  604  is installed on the output side of power amplifier  603 . Coupler  604  and polar modulator  601  are connected to each other via terminal  609 . 
     Polar modulator  601  simultaneously generates RF signals  621   1 ,  621   2 , . . . ,  621   n  having different carrier frequencies f c1 , f c2 , . . . , f cn  to output them to terminal  605 . RF signals  621   1 ,  621   2 , . . . ,  621   n  are input to power amplifier  603  via terminal  605 . Power amplifier  605  amplifies input RF signals  621   1 ,  621   2 , . . . ,  621   n  to output them as RF signals  622   1 ,  622   2 , . . . ,  622   n  of carrier frequencies f c1 , f c2 , . . . , f cn  to terminal  606  via coupler  604 . 
     In the exemplary embodiment, as power amplifier  603 , a multiband power amplifier designed corresponding to the plurality of carrier frequencies f c1 , f c2 , . . . , f cn  is preferably used. For example, for power amplifier  603 , a power amplifier designed for alignment between an input and an output by two or more frequencies, which is similar to that disclosed in Non-patent Literature 2 described in the aforementioned Non-patent Literature Section, can be used. 
     Alternatively, for power amplifier  603 , a broadband power amplifier covering the frequency range of carrier frequencies f c1  to f cn  can be used. For the configuration of the broadband power amplifier, for example, a configuration disclosed in Non-patent Literature 3 or 4 described in the aforementioned Non-patent Literature Section can be employed. 
     Coupler  604  branches RF signals  622   1 ,  622   2 , . . . ,  622   n  output from power amplifier  603  to output them as RF signals  625   1 ,  625   2 , . . . ,  625   n  of carrier frequencies f c1 , f c2 , . . . , f cn  to terminal  609 . To suppress the losses of RF signals  622   1 ,  622   2 , . . . ,  622   n , the powers of RF signals  625   1 ,  625   2 , . . . ,  625   n  branched by coupler  604  are preferably low. RF signals  625   1 ,  625   2 , . . . ,  625   n  are input to polar modulator  601  via terminal  609 . Polar modulator  601  detects the instantaneous powers P OUT1 (t), P OUT2 (t), . . . , P OUTn (t) of RF signals  622   1 ,  622   2 , . . . ,  622   n  based on input RF signals  625   1 ,  625   2 , . . . ,  625   n . 
     Polar modulator  601  outputs power supply modulation signal  623  to terminal  607 . Voltage waveform V AM   _   IN (t) of power supply modulation signal  623  is set based on a function using instantaneous powers P OUT1 (t), P OUT2 (t), . . . , P OUTn (t) of RF signals  622   1 ,  622   2 , . . . ,  622   n  detected by polar modulator  601  as arguments. 
     Power supply modulation signal  623  output to terminal  607  is amplified by power supply modulator  602  to be output as power supply modulation signal  624  to terminal  608 . The power supply voltage of power amplifier  603  is modulated by voltage waveform V AM   _   OUT (t) of power supply modulation signal  624 . Voltage waveform V AM   _   OUT (t) of power supply modulation signal  624  is similarly set based on the function using instantaneous powers P OUT1 (t), P OUT2 (t), . . . , P OUTn (t) of RF signals  622   1 ,  622   2 , . . . ,  622   n  detected as the arguments. 
     Thus, according to the exemplary embodiment, when instantaneous powers P OUT1 (t), P OUT2 (t), . . . , P OUTn (t) of RF signals  622   1 ,  622   2 , . . . ,  622   n  output from power amplifier  603  are reduced, voltage waveform V AM   _   OUT (t) of power supply modulation signal  624  is lowered to suppress a power supply from power supply modulator  602  to power amplifier  603 . As a result, the power consumption of power amplifier  603  and the entire transmission apparatus are suppressed, and power efficiency can be improved. 
     As disclosed in Non-patent Literature 5 described in the aforementioned Non-patent Literature Section, generally, the broader band of the output voltage waveform of the power supply modulator creates problems such as the efficiency reduction of the power supply modulator and the increase of output signal errors. Thus, the operating band of the power supply modulator achievable by a current technology represented by that described in Non-patent Literature 5 is limited to several tens of MHz or lower. 
     In a current wireless communication system including the LTE-Advanced, the modulation bandwidth f BB  of the RF signal of one carrier frequency is 20 MHz at the maximum. On the other hand, for example, in the Inter-band Non-contiguous CA mode used in the LTE-Advanced, a carrier frequency may be set to a band of 800 MHz and 2 GHz. Thus, a difference Δf between carrier frequencies may be 1 GHz or higher. 
     In the exemplary embodiment, as described above, the output voltage waveform V AM   _   OUT (t) of power supply modulation signal  624  is set based on the function using instantaneous powers P OUT1 (t), P OUT2 (t), . . . , P OUTn (t) of RF signals  622   1 ,  622   2 , . . . ,  622   n  as the arguments. The band of instantaneous powers P OUT1 (t), P OUT2 (t), . . . , P OUT  is approximately equal to the modulation bandwidth f BB  of each of RF signals  622   1 ,  622   2 , . . . ,  622   n , and set independently of the difference Δf between the carrier frequencies. Accordingly, in the exemplary embodiment, an operating band necessary for power supply modulator  602  is approximately equal to the modulation bandwidth f BB  of each of RF signals  622   1 ,  622   2 , . . . ,  622   n  without any dependence on the difference Δf between the carrier frequencies. By the current technology represented by that described in Non-patent Literature 5, an operating band (several tens of MHz) higher than that (20 MHz at the maximum) necessary for power supply modulator  602  can be achieved. The power supply modulator based on the current technology represented by that described in Non-patent Literature 5 is a desirable form for power supply modulator  602 . 
     In the polar modulation technology, when there is synchronous deviation between the transmission timing of RF signals  621   1 ,  621   2 , . . . ,  621   n  at input terminal  605  of power amplifier  603  and the transmission timing of power supply modulation signal  624  at power supply terminal  608  of power supply amplifier  603 , signal distortion is generated in RF signals  622   1 ,  622   2 , . . . ,  622   n  at output terminal  606  of power amplifier  603 . Thus, the transmission timings of RF signals  621   1 ,  621   2 , . . . ,  621   n  output from polar modulator  601  and the transmission timings of power supply modulation signal  624  are preferably set so to minimize the signal distortion of RF signals  622   1 ,  622   2 , . . . ,  622   n . 
     Next, a preferable method for setting the output voltage waveform V AM   _   OUT (t) of power supply modulation signal  624  according to the exemplary embodiment will be described. For simpler description, a case where the number of carrier frequencies is two, namely, f c1  and f c2 , will first be described. 
     The setting method will be described by taking an example where a dual-band power amplifier (PA) corresponding to both carrier frequencies of 800 MHz and 2 GHz is used as power amplifier  603 .  FIG. 4  is a characteristic diagram illustrating the input-output power characteristics of the dual-band power amplifier (PA) as the example of power amplifier  603  illustrated in  FIG. 3 . A carrier frequency f c1  is 800 MHz, and a carrier frequency f c2  is 2 GHz. The power supply voltage (=output voltage V AM   _   OUT (t) of power supply modulator  602 ) of power amplifier  603  is set to 1.8 V. 
     The characteristic diagram of  FIG. 4  illustrates the input-output power characteristics of power amplifier  603  when only RF signal  621   1  of the carrier frequency f c1 =800 MHz is input and the input-output power characteristics of power amplifier  603  when only RF signal  621   2  of the carrier frequency f c2 =2 GHz is input. As illustrated in the characteristic diagram of  FIG. 4 , power amplifier  603  is designed to obtain approximately equal saturation output powers between when RF signal  621   1  of the carrier frequency f c1  is input and when RF signal  621   2  of the carrier frequency f c2  is input. 
       FIG. 5  is a characteristic diagram illustrating the power characteristics of an output signal at the time of saturation when two RF signals of different carrier frequencies are simultaneously input to the dual-band power amplifier (PA) as the example of power amplifier  603  illustrated in  FIG. 3 . In other words,  FIG. 5  is a graph plotting output power P out1  of RF signal  622   1  of a carrier frequency f 1  and output power P out2  of RF signal  622   2  of a carrier frequency f 2  at the time of saturation when RF signal  621   1  of the carrier frequency f c1 =800 MHz and RF signal  621   2  of the carrier frequency f c2 =2 GHz are simultaneously input. In the characteristic diagram of  FIG. 5 , the output power of power amplifier  603  at the time of saturation is plotted by changing a power difference ΔP in =P in1 −Pi n2  (dB) between input power P in1  of RF signal  621   1  of the carrier frequency f c1 =800 MHz and input power P in2  of RF signal  621   2  of the carrier frequency f c2 =2 GHz. In the characteristic diagram of  FIG. 5 , the power supply voltage (=output voltage V AM   _   OUT (t) of power supply modulator  602 ) of power amplifier  603  is set to 1.8 V. 
     When the ratio of the input power is changed between RF signal  621   1  of the carrier frequency f c1  and RF signal  621   2  of the carrier frequency f c2  by changing the power difference ΔP in  between the input powers, the output powers of RF signal  622   1  of the carrier frequency f c1  and RF signal  622   2  of the carrier frequency f c2  at the time of saturation also change according to the change of the ratio. Power amplifier  603  in the exemplary embodiment is designed so that the output voltages at the time of saturation of power amplifier  603  can take saturation output powers P sat  of approximately equal values both when only RF signal  621   1  of the carrier frequency f c1  is used and when only RF signal  621   2  of the carrier frequency f c2  is used. 
     Thus, in the case of the power amplifier configured such that the saturation output powers at the time of the input of a single RF signal take equal values P sat , as illustrated in  FIG. 5 , even when both RF signal  621   1  of the carrier frequency f c1  and RF signal  621   2  of the carrier frequency f c2  are simultaneously input, and the input power difference ΔP in  therebetween is changed, a result is obtained, specifically in which the output power total value (P out1 +P out2 ) of the RF signals at the time of saturation is saturation output power P sat , not changed from the time of the input of a single RF signal. 
     This result shows that when the RF signals of a plurality of greatly different carrier frequencies are simultaneously input to the power amplifier (Inter-band Noncontiguous CA mode), the total value of the output powers of the RF signals defines the saturation condition of the power amplifier (PA), irrespective of the input power difference ΔP in  between the RF signals of the carrier frequencies. In other words, the result shows that the power amplifier is saturated when the output power total value (P out1 +P out2 ) of the RF signals reaches the saturation output power P sat . 
       FIG. 6  is a characteristic diagram illustrating the power characteristics of the output signal at the time of saturation when the power supply voltage (=output voltage V AM   _   OUT (t) of power supply modulator  602 ) of power amplifier  603  is set to 0.9, and the two RF signals (f c1 =800 HMz and f c2 =2 GHz) of different carrier frequencies are simultaneously input to power amplifier  603  as in the case illustrated in  FIG. 5 . With V AM   _   OUT (t)=0.9 V illustrated in  FIG. 6 , as in the case of V AM   _   OUT (t)=1.8 V illustrated in  FIG. 5 , irrespective of the input power difference ΔP in  between the RF signals of the carrier frequencies, a result is obtained, specifically in which the power amplifier is saturated when the output power total value (P out1 +P out2 ) of the RF signals reaches the saturation output power P sat . 
     According to the characteristic diagrams of  FIGS. 5 and 6 , the saturation output power P sat  of power amplifier  603  is set to a fixed value not dependent on the input power difference ΔP in  between the RF signals of the carrier frequencies. However, the saturation output power P sat  of power amplifier  603  is dependent on the value of the power supply voltage (=output voltage V AM   _   OUT  of power supply modulator  602 ) of power amplifier  603 . 
       FIG. 7  is a graph plotting a relationship between the saturation output power P sat  of power amplifier  603  and the power supply voltage (=output voltage V AM   _   OUT  of power supply modulator  602 ) of power amplifier  603  when the two RF signals (f c1 =800 MHz and f c2 =2 GHz) of different carrier frequencies are simultaneously input to power amplifier  603  as in the case of those illustrated in  FIGS. 5 and 6 . In  FIG. 7 , the real saturation output power P sat  of power amplifier  603  is indicated by a solid line. In  FIG. 7 , fitting based on the relational expression of Psat∝V AM   _   OUT   2  is indicated by a broken line. It is obvious from the characteristic diagram of  FIG. 7  that the following relationship is established between the saturation output power P sat  of power amplifier  603  and the power supply voltage (=output voltage V AM   _   OUT  of power supply modulator  602 ) of power amplifier  603  when the two RF signals (f c1 =800 MHz and f c2 =2 GHz) of different carrier frequencies are simultaneously input to power amplifier  603 .
 
 P   sat ∝( V   AM   _   OUT ) 2   [Formula 1]
 
     The characteristic diagram of  FIG. 7  illustrates the above relationship. 
     According to the polar modulation technology, by controlling the power supply voltage so that desired output power can always match the saturation power, the saturated state of high power efficiency is always achieved, irrespective of fluctuation in output power. Thus, in the exemplary embodiment, the output voltage V AM   _   OUT (t) of power supply modulator  602  is preferably set so that power amplifier  603  can be always set in a saturated state. According to the result in which the saturation output power P sat  is determined by the output power total value (P out1 +P out2 ) of the RF signals and the result of Formula (1) thus obtained, desirable setting for the output voltage V AM   _   OUT (t) of power supply modulator  602  is given by following Formula (2) using the instantaneous powers P OUT1 (t) and P OUT2 (t) of RF signals  622   1  and  622   2 .
 
 V   AM   _   OUT ( t )= C √{square root over ( P   sat )}= C √{square root over ( P   out1 ( t )+ P   out2 ( t ))}  [Formula 2]
 
     In Formula 2, C is a proportional constant. When a low proportional constant C is taken to set the power supply voltage V AM   _   OUT  of power amplifier  603  low, power efficiency tends to be improved while a gain is lowered. Conversely, when a large proportional constant C is taken to set the power supply voltage V AM   _   OUT  of power amplifier  603  high, a gain tends to be increased while power efficiency is lowered. The proportional constant C is preferably set according to desired characteristics. 
     Hereinafter, the effects of the exemplary embodiment will be described based on, as an example, the characteristics of power amplifier  603  when the RF signal of the carrier frequency f c1 =800 HMz and the RF signal of the carrier frequency f c2 =2 GHz are simultaneously input to power amplifier  603 , and the output voltage V AM   _   OUT (t) of power supply modulator  602  is set by Formula (2). 
     As a condition for obtaining the characteristics of power amplifier  603 , a power difference ΔP in =P in1 −Pi n2  (dB) between the input power P in1  of RF signal  621   1  of the carrier frequency f c1 =800 MHz and the input power P in2  of RF signal  621   2  of the carrier frequency f c2 =2 GHz is set to −6 dB. According to Formula 2, the output voltage V AM   _   OUT (t) of power supply modulator  602  is set as illustrated in  FIG. 8  with respect to the power total value (P out1 +P out2 ) of RF signals  622   1  and  622   2  output from power amplifier  603 . In  FIG. 8 , the proportional constant C (=12.7 VW 1/2 ) is selected so that a gain and power efficiency can be both within permissible ranges. The power efficiency η of power amplifier  603  and the power P out1  and the power P out2  of RF signals  622   1  and  622   2  output from power amplifier  603  under the condition illustrated in  FIG. 8  are illustrated in  FIG. 9 . The power efficiency η is defined by Formula 3 using power P AM  supplied from power modulator  602  to power amplifier  603  and the power P out1  and the power P out2  of RF signals  622   1  and  622   2 .
 
η=( P   out1   +P   out2 )/ P   AM   [Formula 3]
 
     As illustrated in  FIG. 9 , the power efficiency η of power amplifier  603  is maintained almost at a constant value even when the powers P out1  and P out2  of RF signals  622   1  and  622   2  are reduced by about 10 dB. 
       FIG. 10  illustrates the characteristics of power amplifier  603  when the power difference ΔP in =P in1 −Pi n2  (dB) between input power P in1  of RF signal  621   1  and input power P in2  of RF signal  621   2  is changed from −6 dB to +18 dB, from the condition obtaining the result illustrated in  FIG. 9 . As in the case of ΔP in =−6 dB illustrated in  FIG. 9 , in the case of ΔP in =+18 dB illustrated in  FIG. 10 , the power efficiency η of power amplifier  603  is maintained almost at a constant value even when the powers P out1  and P out2  of RF signals  622   1  and  622   2  are reduced by about 10 dB. Thus, in the exemplary embodiment, irrespective of the value of the power difference ΔP in  between the RF signals of the carrier frequencies input to power amplifier  603 , the power efficiency η of power amplifier  603  can be maintained high when the output power of power amplifier  603  is low. 
     As comparison targets,  FIGS. 11 and 12  illustrate the characteristics of power amplifier  603  when the power supply voltage control of power amplifier  603  illustrated in  FIG. 8  is not performed while the output voltage V AM   _   OUT  of power amplifier  603  is set to a fixed value (2.4 V). As a condition for obtaining the characteristics of power amplifier  603 , a power difference ΔP in , between the input power P in1  of RF signal  621   1  of the carrier frequency f c1 =800 MHz and the input power P in2  of RF signal  621   2  of the carrier frequency f c2 =2 GHz, is set to ΔPin=−6 dB in  FIG. 11  and is set to ΔPin=+18 dB in  FIG. 12 . In  FIGS. 11 and 12 , when the powers P out1  and P out2  of RF signals  622   1  and  622   2  are reduced by 10 dB, the power efficiency η is reduced to about ⅓ of a maximum value. As illustrated in  FIGS. 11 and 12 , when no power supply voltage control is performed, the power efficiency η is greatly reduced accompanying the reduction of the RF output powers P out1  and P out2  of power amplifier  603 . The comparison of the power efficiency, when the power supply voltage control according to the exemplary embodiment is used as illustrated in  FIGS. 9 and 10 , with the power efficiency, when no power supply voltage control is used as illustrated in  FIGS. 11 and 12 , clearly shows that the power efficiency at the time of reduction of the RF output powers P out1  and P out2  of power amplifier  603  is improved by the power supply voltage control of the exemplary embodiment. 
       FIG. 13  illustrates power gains G 1  and G 2  at the respective carrier frequencies under the same condition as that for obtaining the result illustrated in  FIG. 10 , specifically, when the power supply voltage control of power amplifier  603  illustrated in  FIG. 8  is performed and the power difference ΔP in , between the input power P in1  of RF signal  621   1  of the carrier frequency f c1 =800 MHz and the input power P in2  of RF signal  621   2  of the carrier frequency f c2 =2 GHz, is set to +18 dB. In the exemplary embodiment, the power supply voltage V AM   _   OUT  of power amplifier  603  is lowered accompanying the reduction of the RF output powers P out1  and P out2  of power amplifier  603 . When the power supply voltage V AM   _   OUT  is lowered, the power gains G 1  and G 2  tend to be reduced. 
     The output voltage V AM   _   OUT (t) of power supply modulator  602  in Formula (2) is desirable setting when two RF signals  621   1  and  621   2  of carrier frequencies are input to power amplifier  603 . Desirable setting of the output voltage V AM   _   OUT (t) of power supply modulator  602  when two or more RF signals  621   1 ,  621   2 , . . . ,  621   n  of carrier frequencies are input to power amplifier  603  is expanded by Formula (4) below using the powers P out1 (t), P out2 (t), . . . , P outn (t) of RF output signals  622   1 ,  622   2 , . . . ,  622   n .
 
 V   AM   _   OUT ( t )∝√{square root over ( P   sat )}=√{square root over ( P   out1 ( t )+ P   out2 ( t )+ . . . + P   outn ( t ))}  [Formula 4]
 
     First Modified Example of First Exemplary Embodiment 
       FIG. 14  illustrates the setting of the power supply voltage V AM   _   OUT  of power amplifier  603  according to the first modified example of the first exemplary embodiment of the present invention. To suppress the reduction of the power gains G 1  and G 2  when the RF output powers P out1  and P out2  of power amplifier  603  are reduced, the power supply voltage V AM   _   OUT  of power amplifier  603  can be set, for example, as illustrated in  FIG. 14 . In  FIG. 14 , the power supply voltage V AM   _   OUT  of power amplifier  603  is set by Formula (5) as shown below. 
     
       
         
           
             
               
                 
                   
                     
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                   [ 
                   
                     Formula 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     5 
                   
                   ] 
                 
               
             
           
         
       
     
     Specifically, the power supply voltage V AM   _   OUT  is set to C √P out1 (t)+P out2 (t) during a period where P out1 (t)+P out2 (t)&gt;(V th /C) 2  is satisfied. The power supply voltage V AM   _   OUT  is set to V th  during a period where P out1 (t)+P out2 (t)&lt;(V th /C) 2  is satisfied. 
     In the case of C √P out1 (t)+P out2 (t)=V th , an upper formula and a lower formula take equal values, and thus any of the two can be used. 
     In the setting of the power supply voltage V AM   _   OUT  illustrated in  FIG. 14  and Formula 5, by preventing power supply voltage V AM   _   OUT  from being lower than the threshold value V th  when the RF output powers P out1  and P out2  of power amplifier  603  are reduced, the reduction of the power gains G 1  and G 2  of power amplifier  603 , caused by the reduction of the power supply voltage V AM   _   OUT , is suppressed. 
       FIGS. 15 and 16  illustrate the characteristics of power amplifier  603  when power supply voltage control is performed according to the setting of the power supply voltage V AM   _   OUT  illustrated in  FIG. 14  and Formula 5. The power supply voltage V AM   _   OUT  is maintained at the fixed value V th  when the RF output powers P out1  and P out2  of power amplifier  603  are reduced. Thus, while the power efficiency η is slightly reduced as illustrated in  FIG. 15 , the reduction of the power gains G 1  and G 2  at the time of a low output can be suppressed as illustrated in  FIG. 16 . 
     Second Modified Example of First Exemplary Embodiment 
       FIG. 17  illustrates the setting of the power supply voltage V AM   _   OUT  of power amplifier  603  according to the second modified example of the first exemplary embodiment of the present invention. To suppress the reduction of the power gains G 1  and G 2  when the RF output powers P out1  and P out2  of power amplifier  603  are reduced, the power supply voltage V AM   _   OUT  of power amplifier  603  can be set, for example, as illustrated in  FIG. 17 . In  FIG. 17 , the power supply voltage V AM   _   OUT  of power amplifier  603  is set by Formula (6) as shown below. 
     
       
         
           
             
               
                 
                   
                     
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                   [ 
                   
                     Formula 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     6 
                   
                   ] 
                 
               
             
           
         
       
     
     A middle formula indicates that C 2 √P th2  and C 1 √P th2  take equal values. 
     In the case of P out1 (t)+P out2 (t)=P th2 , an upper formula and the middle formula take equal values, and thus any of the two can be used. In the case of P out1 (t)+P out2 (t)=P th1 , the middle formula and a lower formula take equal values, and thus any of the two can be used. 
     In the setting of the power supply voltage V AM   _   OUT  illustrated in  FIG. 17  and Formula 6, the value of the proportional constant C 2  at the time of low output power equal to or lower than the threshold value power P th2  is preferably set equal to or higher than the proportional constant C 1  at the time of high output power equal to or higher than the threshold value power P th1 . By such setting of the proportional constants C 1  and C2, the power supply voltage V AM   _   OUT , at the time of low output power equal to or lower than the threshold value power P th2 , is slightly higher than that when a single proportional constant C is used as illustrated in  FIG. 8 , thus a power gain at the time of low output power slightly increases. The supply voltage V AM   _   OUT  is controlled even at the time of low output power equal to or lower than the threshold value power P th2 . Thus, the reduction of the power efficiency η at the time of low output power can be suppressed to a certain extent. 
       FIGS. 18 and 19  illustrate the characteristics of power amplifier  603  when power supply voltage control is performed according to the setting of the power supply voltage V AM   _   OUT  that is illustrated in  FIG. 17  and Formula 6. As illustrated in  FIG. 19 , the reduction of the power gain is suppressed at the time of a low output power equal to or lower than the threshold value P th2  (=9.4 dBm). The reduction of the power gain is achieved by increasing the value of the proportional constant C2, at the time of the low output power equal to or lower than the threshold value P th2 , to increase the power supply voltage V AM   _   OUT  of power amplifier  603 . As illustrated in  FIG. 18 , the proportional coefficient of the power supply voltage V AM   _   OUT  of power amplifier  603  is switched from C 1  (=12.7 V/W 1/2 ) to C 2  (=16.0 VW 1/2 ) with respect to the threshold value power P th1  (=11.4 dBm) to P th2  (=9.4 dB). Accordingly, while the power efficiency η fluctuates within the same power range (=9.4 dBm˜11.4 dBm), generally high power efficiency is maintained within all the power ranges because of the effect of the control of the power supply voltage V AM   _   OUT  of power amplifier  603 . 
     In the setting of the power supply voltage V AM   _   OUT  illustrated in  FIG. 17  and Formula 6, the two proportional coefficients C1 and C2 are switched for each power range. However, three or more proportional coefficients can be switched for each power range. 
     Third Modified Example of First Exemplary Embodiment 
     When a relationship between the saturation output power P sat  of power amplifier  603  and the power supply voltage V AM   _   OUT  of power supply modulator  602  is given by Formula (1), desirable setting for the power supply voltage V AM   _   OUT (t) of power supply modulator  602  is given by Formula (4). More generally, when the relationship between the saturation output power P sat  of power amplifier  603  and the power supply voltage V AM   _   OUT  of power supply modulator  602  is given by a function f of Formula (7), desirable setting for the power supply voltage V AM   _   OUT (t) of power supply modulator  602  is given by Formula (8) using the inverse function h(=f −1 ) of the function f.
 
 P   sat   ∝f ( V   AM )  [Formula 7]
 
 V   AM   _   OUT ( t )∝ h ( P   sat )= h[P   out1 ( t )+ P   out2 ( t )+ . . . + P   outn ( t )]  [Formula 8]
 
     The function h is defined by measuring the relationship between the saturation output power P sat  of power amplifier  603  and the power supply voltage V AM   _   OUT  of power supply modulator  602 . Alternatively, as the function h, the function illustrated in  FIG. 14  and Formula (5) can be used, or the function illustrated in  FIG. 17  and Formula (6) can be used. In other words, the function h can be arbitrarily set so as to obtain desired power efficiency and a desired gain. 
     Fourth Modified Example of First Exemplary Embodiment 
       FIG. 20  is a graph illustrating a relationship, in the dual-band power amplifier (PA) as the example of power amplifier  603  illustrated in  FIG. 3 , between the output power P out1  of RF signal  622   1  of a carrier frequency fc 1  and the output power P out2  of RF signal  622   2  of a carrier frequency fc 2  at the time of saturation when RF signal  621   1  of the carrier frequency f c1 =800 MHz and RF signal  621   2  of the carrier frequency f c2 =2 GHz are simultaneously input. In  FIG. 20 , displaying of the graph is changed while the same data as that illustrated in  FIG. 5  is used. 
     As illustrated in the graph of  FIG. 20 , there is an approximate relationship defined in Formula (9) between the output power P out1  of RF signal  622   1  of the carrier frequency f c1  at the time of saturation and the output power P out2  of RF signal  622   2  of the carrier frequency f c2  at the time of saturation.
 
 P   out1   +P   out2   =P   sat (=const.)  [Formula 9]
 
     However, Formula (9) defines only the approximate relationship. The relationship between the output power P out1  of RF signal  622   1  of the carrier frequency f c1  at the time of saturation and the output power P out2  of RF signal  622   2  of the carrier frequency f c2  at the time of saturation based on real characteristics is represented by Formula (10) using an implicit function u as illustrated in the graph of  FIG. 20 .
 
 u ( P   out1   ,P   out2 )= P   sat (=const.)  [Formula 10]
 
     The implicit function u is defined based on the measured data of the output power P out1  of RF signal  622   1  of the carrier frequency fc 1  at the time of saturation and the measured data of the output power P out2  of RF signal  622   2  of the carrier frequency fc 2  at the time of saturation. 
     More generally, when two or more RF signals  621   1 ,  621   2 , . . . ,  621   n  of carrier frequencies are input to power amplifier  603 , a relationship among the powers P OUT1 (t), P OUT2 (t), . . . , P OUTn (t) of RF output signals  622   1 ,  622   2 , . . . ,  622   n  at the time of saturation is expanded as defined in Formula (11).
 
 u ( P   out1   ,P   out2   , . . . , P   outn )= P   sat (=const.)  [Formula 11]
 
     By combining relational Formula (11) among the powers P OUT1 (t), P OUT2 (t), . . . , P OUTn (t) of RF output signals  622   1 ,  622   2 , . . . ,  622   n  at the time of saturation with relational Formula (7) between the saturation output power P sat  of power amplifier  603  and the output voltage V AM   _   OUT  of power supply modulator  602 , the output voltage V AM   _   OUT  of power supply modulator  602  is set by Formula (12) as shown below.
 
 V   AM   _   OUT ( t )∝ f   −1 ( P   sat )= f   −1   [u ( P   out1 ( t ), P   out2 ( t ), . . . ,  P   outn ( t ))]= w[P   out1 ( t ), P   out2 ( t ), . . . ,  P   outn ( t )]  [Formula 12]
 
     A function w is a composite function of the function f −1  and the function u. As discussed above, by setting the output voltage V AM   _   OUT  of power supply modulator  602  based on the general function w of the powers P OUT1 (t), P OUT2 (t), . . . , P OUTn (t) according to Formula (12), power amplifier  603  always operates in a saturated state, and high power efficiency can be obtained as a result. 
     Second Exemplary Embodiment 
     Next, a transmission apparatus according to the second exemplary embodiment of the present invention will be described with particular attention paid to a polar modulator in the transmission apparatus. 
       FIG. 21  illustrates the block configuration of the transmission apparatus according to the second exemplary embodiment of the present invention. In the transmission apparatus according to the second exemplary embodiment, power supply modulator  602 , power amplifier  603 , and coupler  604  are similar in configuration to those of the transmission apparatus of the first exemplary embodiment, and thus repeated description will be avoided. 
     In the transmission apparatus according to the second exemplary embodiment illustrated in  FIG. 21 , polar modulator  601  includes baseband signal generators  801   1    801   2 , . . . ,  801   n , local oscillation (LO) signal generators  802   1 ,  802   2 , . . . ,  802   n , mixers  803   1 ,  803   2 , . . . ,  803   n , RF signal delay adjusters  804   1 ,  804   2 , . . . ,  804   n , RF signal synthesizer  805 , variable gain amplifiers (VGA)  806   1 ,  806   2 , . . . ,  806   n , controller  807 , branching filter  808 , square root extractor  809 , power modulation signal delay adjuster  810 , and adder  811 . 
     In polar modulator  601 , baseband signal generators  801   1    801   2 , . . . ,  801   n  output baseband signals b in1 (t), b in2 (t), . . . , b inn (t) to mixers  803   1 ,  803   2 , . . . ,  803   n . Local oscillation (LO) signal generators  802   1 ,  802   2 , . . . ,  802   n  output the LO signals of carrier frequencies f c1 , f c2 , . . . , f cn , to mixers  803   1 ,  803   2 , . . . ,  803   n . Mixers  803   1 ,  803   2 , . . . ,  803   n  carries out frequency conversion (up conversion) of baseband signals b in1 (t), b in2 (t), . . . , b inn (t) into carrier frequencies f c1 , f c2 , . . . , f cn  to generate RF signals  621   1 ,  621   2 , . . . ,  621   n  of carrier frequencies f c1 , f c2 , . . . , f cn . RF signals  621   1 ,  621   2 , . . . ,  621   n  are input to RF signal synthesizer  805  via RF signal delay adjusters  804   1 ,  804   2 , . . . ,  804   n , and RF signal synthesizer  805  outputs synthesized RF signals  621   1 ,  621   2 , . . . ,  621   n  to terminal  605 . RF signal synthesizer  805  can include, for example, a broadband hybrid coupler usable within the range of carrier frequencies f c1 , f c2 , . . . , f cn . 
     RF signal delay adjusters  804   1 ,  804   2 , . . . ,  804   n , which are respectively arranged on the output sides of mixers  803   1 ,  803   2 , . . . ,  803   n , can be installed on the input sides of mixers  803   1 ,  803   2 , . . . ,  803   n  instead. 
     Baseband signal generators  801   1    801   2 , . . . ,  801   n  input the powers P in1 (t), P in2 (t), . . . , P inn (t) of baseband signals b in1 (t), b in2 (t), . . . , b inn (t) to variable gain amplifiers (VGA)  806   1 ,  806   2 , . . . ,  806   n . Variable gain amplifiers (VGA)  806   1 ,  806   2 , . . . ,  806   n , which respectively have gains G AM1 , G AM2 , . . . , G AMn , amplify the input powers P in1 (t), P in2 (t), . . . , P inn (t) to G AM1 P in1 (t), G AM2 P in2 (t), . . . , G AMn P inn (t) to output the results to adder  811 . Variable gain amplifiers (VGA)  806   1 ,  806   2 , . . . ,  806   n , which are not always required to have gains of 0 dB or higher, can be replaced with variable attenuators. 
     Variable gain amplifiers (VGA)  806   1 ,  806   2 , . . . ,  806   n  respectively include gain control terminals  814   1 ,  814   2 , . . . ,  814   n . The gains G AM1 , G AM2 , . . . , G AMn  of variable gain amplifiers (VGA)  806   1 ,  806   2 , . . . ,  806   n  are set based on control signals output from controller  807  to gain control terminals  814   1 ,  814   2 , . . . ,  814   n . 
     Adder  811  outputs G AM1 P in1 (t)+G AM2 P in2 (t)+ . . . +G AMn P inn (t) that are additional values of the input signals to square root extractor  809 . Adder  811  can include, for example, an operation amplifier according to a method disclosed in Chapter 5 of Non-patent Literature 6 described in the section of Non-patent Literature. 
     The power gains of the transmission apparatus in paths from baseband signal generators  801   1    801   2 , . . . ,  801   n  to output terminal  606  of power amplifier  603  via input terminal  605  of power amplifier  603  are defined as G RF1 =P out1 /P in1 , G RF2 =P out2 /P in2 , . . . , G RFn =P outn /P inn . Particularly, in an Inter-band Non-contiguous CA mode in which carrier frequencies are greatly different from each other (difference Δf between carrier frequencies is sufficiently larger than modulation bandwidth f BB  of RF signal of each carrier), the influence of the frequency dependency of the power gains is large, and a large difference is generated in value among the power gains G RF1 , G RF2 , . . . , G RFn . 
     At this time, the power gains G RF1 , G RF2 , . . . , G RFn  of the transmission apparatus preferably have a relationship defined by Formula (13) below with the gains G AM1 , G AM2 , . . . , G AMn  of variable gain amplifiers (VGA)  806   1 ,  806   2 , . . . ,  806   n .
 
 G   RF1   :G   RF2   : . . . :G   RFn   =G   AM1   :G   AM2   : . . . :G   AMn   [Formula 13]
 
     Formula (13) is equivalent to following Formula (14).
 
 P   out1   :P   out2   : . . . :P   outn   =G   AM1   P   in1   :G   AM2   P   in2   : . . . :G   AMn   P   inn   [Formula 14]
 
     According to the second exemplary embodiment of the present invention, by controlling the gains of variable gain amplifiers (VGA)  806   1 ,  806   2 , . . . ,  806   n  via controller  807 , the gains G AM1 , G AM2 , . . . , G AMn  are set to satisfy the relationship of Formula 13 or 14. At this time, the signal G AM1 P in1 (t)+G AM2 P in2 (t)+ . . . +G AMn P inn (t) output from adder  811  to square root extractor  809  is proportional to P out1 (t)+P out2 (t)+ . . . +P outn (t). 
     By the aforementioned setting of the gains G AM1 , G AM2 , . . . , G AMn , even when the power gains G RF1 , G RF2 , . . . , G RFn  of the transmission apparatus are frequency-dependent, the sum total P out1 (t)+P out2 (t)+ . . . +P outn (t) of the output powers is correctly calculated from input powers P in1 +P in2 (t)+ . . . +P inn (t). This is particularly effective in the Inter-band Non-contiguous CA mode in which the influence of the frequency dependency of the power gains of the transmission apparatus is large. 
     Square root extractor  809  outputs sqrt[G AM1 P in1 (t)+G AM2 P in2 (t)+ . . . +G AMn P inn (t)] that is a square root of the input signal G AM1 P in1 (t)+G AM2 Pi n2 (t)+ . . . +G AMn P inn (t) as power supply modulation signal  623  to terminal  607  via power supply modulation signal delay adjuster  810 . Square root extractor  809  can include, for example, an IC multiplier according to a method disclosed in Chapter 7 of Non-patent Literature 6 described in the section of Non-patent Literature. 
     As described above, when the gains G AM1 , G AM2 , . . . , G AMn  are set to satisfy the relationship of Formula 13 or 14, power supply modulation signal  623  output to terminal  607  is a signal proportional to sqrt[P out (t)+P out2 (t)+ . . . +P outn (t)]. Power supply modulation signal  623  is amplified by power supply modulator  602  to be output as the output voltage V AM   _   OUT (t) of power supply modulator  602  to terminal  608 . By this operation, in the second exemplary embodiment of the present invention, as in the case of the first exemplary embodiment, the output voltage V AM   _   OUT (t) of power supply modulator  602  is set as defined in Formula (4). 
     Hereinafter, the function of controller  807  will be described in detail. The powers P in1 (t), P in2 (t), . . . , P inn (t) of baseband signals b in1 (t), b in2 (t), . . . , b inn (t) are input to input terminals  812   1 ,  812   2 , . . . ,  81   2n  of controller  807 . 
     RF signals  625   1 ,  625   2 , . . . ,  625   n  of carrier frequencies f c1 , f c2 , . . . , f cn , output to terminal  609  via coupler  604  installed on the output side of power amplifier  603 , are input to branching filter  808 . Branching filter  808  has a function of separately outputting the RF signals of different carrier frequencies to different output terminals. In other words, branching filter  808  separately outputs RF signals  625   1 ,  625   2 , . . . ,  625   n  to different input terminals  813   1 ,  813   2 , . . . ,  813   n . Controller  807  calculates, based on RF signals  625   1 ,  625   2 , . . . ,  625   n  input to different input terminals  813   1 ,  813   2 , . . . ,  813   n , the powers P OUT1 (t), P OUT2 (t), . . . , P OUTn (t) of RF signals  622   1 ,  622   2 , . . . ,  622   n  output from power amplifier  603 . 
     By the aforementioned operation, controller  807  detects the input powers P in1 (t), P in2 (t), . . . , P inn (t) and the output powers P OUT1 (t), P OUT2 (t), . . . , P OUTn (t) of the transmission apparatus. Controller  807  detects the power gains G RF1 =P out1 /P in1 , G RF2 =P out2 /P in2 , . . . , G RFn =P outn /P inn  of the transmission apparatus from the detected input and output powers. Controller  807  calculates desired values of the gains G AM1 , G AM2 , . . . , G AMn  of variable gain amplifiers (VGA)  806   1 ,  806   2 , . . . ,  806   n  based on the power gains G RF1 , G RF2 , . . . , G RFn  of the transmission apparatus detected in the aforementioned operation and Formula (13) or (14). Controller  807  outputs control signals to gain control terminals  814   1 ,  814   2 , . . . ,  814   n  so that the gains G AM1 , G AM2 , . . . , G AMn  of variable gain amplifiers (VGA)  806   1 ,  806   2 , . . . ,  806   n  can be set to the desired values calculated in the aforementioned operation. 
     In the second exemplary embodiment of the present invention, as in the case of the first exemplary embodiment, the transmission timings of RF signals  621   1 ,  621   2 , . . . ,  621   n  output from polar modulator  601  and power supply modulation signal  624  are set so to minimize the signal distortion of RF signals  622   1 ,  622   2 , . . . ,  622   n . In the second exemplary embodiment, the transmission timings of RF signals  621   1 ,  621   2 , . . . ,  621   n  and power supply modulation signal  624  are set based on signal delay time at RF signal delay adjusters  804   1 ,  804   2 , . . . ,  804   n  and power modulation signal delay adjuster  810 . Controller  807  detects the signal distortion of RF signals  622   1 ,  622   2 , . . . ,  622   n  based on RF signals  625   1 ,  625   2 , . . . ,  625   n  input to terminals  813   1 ,  813   2 , . . . ,  813   n . Controller  807  has a function of setting the signal delay time at RF signal delay adjusters  804   1 ,  804   2 , . . . ,  804   n  and power modulation signal delay adjuster  810  so to minimize the detected signal distortion of RF signals  622   1 ,  622   2 , . . . ,  622   n . The signal delay time at RF signal delay adjusters  804   1 ,  804   2 , . . . ,  804   n  is set based on a control signal output from controller  807  to control terminal  815 . The signal delay time at power modulation signal delay adjuster  810  is set based on a control signal output from controller  807  to control terminal  816 . 
     Through the measurement of a given period based on the aforementioned operation, the optimal values of the gains G AM1 , G AM2 , . . . , G AMn  of variable gain amplifiers (VGA)  806   1 ,  806   2 , . . . ,  806   n , and the signal delay time at RF signal delay adjusters  804   1 ,  804   2 , . . . ,  804   n  and power modulation signal delay adjuster  810  are calculated. The gains and the signal delay time can be fixed at the calculated optimal values, or updated again after appropriate time. 
       FIG. 22  is a block diagram illustrating the internal configuration of controller  807 . As illustrated in  FIG. 22 , controller  807  includes at least analog digital converters (ADC)  1001   1 ,  1001   2 , . . . ,  1001   n ,  1002   1 ,  1002   2 , . . . ,  100   2n , and  1005   1 ,  1005   2 , . . . ,  1005   n , digital analog converters (DAC)  1004   1 ,  1004   2 , . . . ,  1004   n ,  1007 , and  1008 , square-law detectors  1003   1 ,  1003   2 , . . . ,  1003   n , adjacent channel leakage power radio (ACPR) detectors  1006   1 ,  1006   2 , . . . ,  1006   n , and micro processor unit (MPU)  1009 . MPU  1009  can be mounted in a digital signal processor (DSP) or a field programmable gate array (FPGA). 
     In controller  807  illustrated in  FIG. 22 , the data of the powers P in1 (t), P in2 (t), . . . , P inn (t) of baseband signals b in1 (t), b in2 (t), . . . , b inn (t) is input to input terminals  812   1 ,  812   2 , . . . ,  812   n . The powers P in1 (t), P in2 (t), . . . , P inn (t) are converted into digital signals at ADCs  1001   1 ,  1001   2 , . . . ,  1001   n , to be input to MPU  1009 . Alternatively, in controller  807 , by omitting ADCs  1001   1 ,  1001   2 , . . . ,  1001   n , the data of the powers P in1 (t), P in2 (t), . . . , P inn (t) can be transferred by digital signals from baseband signal generators  801   1    801   2 , . . . ,  801   n  to MPU  1009 . 
     In controller  807  illustrated in  FIG. 22 , RF signals  625   1 ,  625   2 , . . . ,  625   n  are input to input terminals  813   1 ,  813   2 , . . . ,  813   n . Square-law detectors  1003   1 ,  1003   2 , . . . ,  1003   n  output the powers P OUT1 (t), P OUT2 (t), . . . , P OUTn (t) of RF signals  622   1 ,  622   2 , . . . ,  622   n  calculated based on RF signals  625   1 ,  625   2 , . . . ,  625   n  to ADCs  1002   1 ,  1002   2 , . . . ,  1002   n . The powers P OUT1 (t), P OUT2 (t), . . . , P OUTn (t) are converted into digital signals at ADCs  1002   1 ,  1002   2 , . . . ,  1002   n , to be input to MPU  1009 . 
     MPU  1009  calculates power gains G RF1 =P out1 /P in1 , G RF2 =P out2 /P in2 , . . . , G RFn =P outn /P inn  of the transmission apparatus at carrier frequencies f c1 , f c2 , . . . , f cn  from the aforementioned input power data, in other words, the powers P in1 (t), P in2 (t), . . . , P inn (t) of the baseband signals b in1 (t), b in2 (t), . . . , b inn (t) and the powers P OUT1 (t), P OUT2 (t), . . . , P OUTn (t) of RF signals  622   1 ,  622   2 , . . . ,  622   n . MPU  1009  calculates desired values of the gains G AM1 , G AM2 , . . . , G AMn  of variable gain amplifiers (VGA)  806   1 ,  806   2 , . . . ,  806   n  based on the calculated power gains G RF1 , G RF2 , . . . , G RFn  and Formula (13). 
     MPU  1009  outputs control signals to gain control terminals  814   1 ,  814   2 , . . . ,  814   n  of variable gain amplifiers (VGA)  806   1 ,  806   2 , . . . ,  806   n  via DACs  1004   1 ,  1004   2 , . . . ,  1004   n  so that the gains G AM1 , G AM2 , . . . , G AMn  of variable gain amplifiers (VGA)  806   1 ,  806   2 , . . . ,  806   n  can be set to the desired values calculated in the aforementioned operation. 
     In controller  807  illustrated in  FIG. 22 , each of ACPR detectors  1006   1 ,  1006   2 , . . . ,  1006   n  has a function of calculating and outputting ACPR that is a distortion amount of an input RF signal. RF signals  625   1 ,  625   2 , . . . ,  625   n  input to input terminals  813   1 ,  813   2 , . . . ,  813   n , are respectively input to ACPR detectors  1006   1 ,  1006   2 , . . . ,  1006   n . ACPR detectors  1006   1 ,  1006   2 , . . . ,  1006   n  respectively output the signal distortion amounts ACPR 1 , ACPR 2 , . . . , ACPR n  of RF signals  625   1 ,  625   2 , . . . ,  625   n  to ADCs  1005   1 ,  1005   2 , . . . ,  1005   n . The powers ACPR 1 , ACPR 2 , . . . , ACPR n  are converted into digital signals at ADCs  1005   1 ,  1005   2 , . . . ,  1005   n  to be input to MPU  1009 . 
     In controller  807  illustrated in  FIG. 22 , MPU  1009  outputs the control signals of RF signal delay adjusters  804   1 ,  804   2 , . . . ,  804   n  to control terminal  815  via DAC  1007 . MPU  1009  outputs the control signal of power supply modulation signal delay adjuster  810  to control terminal  816  via DAC  1008 . Alternatively, by omitting DACs  1007  and  1008 , RF signal delay adjusters  804   1 ,  804   2 , . . . ,  804   n  and power supply modulation signal delay adjuster  810  can be directly controlled from MPU  1009  based on digital signals. 
     In controller  807 , MPU  1009  changes the signal delay time at RF signal delay adjusters  804   1 ,  804   2 , . . . ,  804   n  and power supply modulation signal delay adjuster  810  via control terminals  815  and  816 , and simultaneously detects the signal distortion amounts ACPR 1 , ACPR 2 , . . . , ACPR n  of RF signals  625   1 ,  625   2 , . . . ,  625   n . Based on the signal distortion amounts ACPR 1 , ACPR 2 , . . . , ACPR n  of RF signals  625   1 ,  625   2 , . . . ,  625   n , the signal distortion amounts of RF signals  622   1 ,  622   2 , . . . ,  622   n  output from power amplifier  603  are detected. By this operation, MPU  1009  detects the dependency of the signal distortion amounts ACPR 1 , ACPR 2 , . . . , ACPR n  of RF signals  625   1 ,  625   2 , . . . ,  625   n  on the signal delay time at RF signal delay adjusters  804   1 ,  804   2 , . . . ,  804   n  and power supply modulation signal delay adjuster  810 . Then, based on the data of the dependency, MPU  1009  sets the signal delay time at RF signal delay adjusters  804   1 ,  804   2 , . . . ,  804   n  and power supply modulation signal delay adjuster  810  so as to minimize the signal distortion amounts ACPR 1 , ACPR 2 , . . . , ACPR n  of RF signals  625   1 ,  625   2 , . . . ,  625   n . 
       FIG. 23  is a block diagram illustrating the internal configuration of ACPR detector  1006   1 . As illustrated in  FIG. 23 , ACPR detector  1006   1  includes at least local oscillation (LO) signal generator  1201 , amplifiers  1202  and  1205 , mixer  1203 , low-pass filter (LPF)  1204 , a band pass filter (BPF)  1206 , log amplifier  1207 , and detector  1208 . 
     In ACPR detector  1006   1  illustrated in  FIG. 23 , local oscillation (LO) signal generator  1201  outputs a local oscillation (LO) signal. The LO signal output from LO signal generator  1201  is amplified by amplifier  1202  to be output to mixer  1203 . Mixer  1203  mixes the LO signal with RF signal  625   1  input to input terminal  813   1  to output an intermediate frequency (IF) signal to LPF  1204 . LPF  1204  removes an unnecessary high-frequency component included in the IF signal. The IF signal output from LPF  1204  is amplified by amplifier  1205  to be input to BPF  1206 . BPF  1206  passes only a frequency component corresponding to an adjacent channel. The center frequency of BPF  1206  is set to “IF frequency+offset frequency” or “IF frequency-offset frequency”. The offset frequency and the pass-band width of BPF  1206  are defined according to a communication standard. For example, in the case of WCDMA (Wideband-CDMA) Standard, the offset frequency may be set to 5 MHz, and the pass-band width may be set to 3.84 MHz. The frequency component corresponding to the adjacent channel output from BPF  1206  is input to log amplifier  1207 . Log amplifier  1207  subjects the frequency component signal corresponding to the adjacent channel to log scale conversion to output the result to detector  1208 . Detector  1208  includes diode  1209 , capacity  1210 , and resistor  1211 . Detector  1208  down-converts the output signal of log amplifier  1207  from the IF band to a baseband to output it as ACPR 1  to terminal  1010   1 . 
     ACPR detectors  1006   2 , . . . ,  1006   n  are similar in internal configuration and function to ACPR detector  1006   1 . 
     Based on the circuit configuration and the operation described above, in the second exemplary embodiment of the present invention, as in the case of the first exemplary embodiment, in the transmission apparatus that simultaneously transmits the plurality of RF signals having different carrier frequencies, even when the output power of the RF signal is reduced, power efficiency can be maintained high. 
     First Modified Example of Second Exemplary Embodiment 
       FIG. 24  illustrates the block configuration of a transmission apparatus according to the first modified example of the second exemplary embodiment of the present invention. In the transmission apparatus according to the first modified example of the second exemplary embodiment, DC power source  901 , switch  902 , and control terminal  903  of switch  902  are newly added to the transmission apparatus of the second exemplary embodiment illustrated in  FIG. 21 . DC power source  901  outputs a fixed voltage V th . Switch  902  has a function of connecting the input of power supply modulation signal delay adjuster  810  to the output of DC power source  901  or the output of square root extractor  809 . Which of the output of DC power source  901  and the output of square root extractor  809  switch  902  connects to the input of power supply modulation signal delay adjuster  810  is designated by a control signal input to control terminal  903 . 
     Components other than DC power source  901 , switch  902 , and control terminal  903  are similar between the second exemplary embodiment of the present invention illustrated in  FIG. 21  and the first modified example of the second exemplary embodiment of the present invention illustrated in  FIG. 24 . Hereinafter, in the first modified example of the second exemplary embodiment, only operations changed from the second exemplary embodiment will be described. 
       FIG. 25  is a block diagram illustrating the internal configuration of controller  807  according to the first modified example of the second exemplary embodiment of the present invention. Control terminal  903  is connected to MPU  1009 . 
     In the first modified example of the second exemplary embodiment, MPU  1009  in controller  807  calculates the sum total P OUT1 (t)+P OUT2 (t)+ . . . +P OUTn (t) of the powers based on the detected powers P OUT1 (t), P OUT2 (t), . . . , P OUTn (t) of RF signals  622   1 ,  622   2 , . . . ,  622   n . MPU  1009  outputs a control signal to control terminal  903  so that switch  902  can connect the output of square root extractor  809  to the input of power modulation signal delay adjuster  810  during a period where the power sum total is equal to or higher than a set threshold value. MPU  1009  outputs a control signal to control terminal  903  so that switch  902  can connect the output of DC power source  901  to the input of power modulation signal delay adjuster  810  during a period where the power sum total is equal to or higher than the set threshold value. 
     By the aforementioned operation, in the first modified example of the second exemplary embodiment of the present invention, the output voltage V AM   _   OUT (t) of power supply modulator  602  is set to that defined by Formula (15) as shown below. 
     
       
         
           
             
               
                 
                   
                     
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                   [ 
                   
                     Formula 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     15 
                   
                   ] 
                 
               
             
           
         
       
     
     Specifically, the power supply voltage V AM   _   OUT  is set to C √P out1 (t)+P out2 (t)+ . . . +P outn (t) during a period where P out1 (t)+P out2 (t)+ . . . +P outn (t)&gt;(V th /C) 2  is satisfied. The power supply voltage V AM   _   OUT  is set to V th  during a period where P out1 (t)+P out2 (t)+ . . . +P outn (t)&lt;(V th /C) 2  is satisfied. 
     In the case of C √P out1 (t)+P out2 (t)+ . . . +P outn (t)=V th , an upper formula and a lower formula take equal values, and thus any of the two can be used. 
     The output voltage V AM   _   OUT  (t) of power supply modulator  602  given by Formula (15) corresponds to that obtained by expanding Formula (5) to a plurality of bands in the first modified example of the first exemplary embodiment. 
     Thus, in the first modified example of the second exemplary embodiment of the present invention, as in the case of the first modified example of the first exemplary embodiment, in the transmission apparatus that simultaneously transmits the plurality of RF signals having different carrier frequencies, even when the output power of the RF signal is reduced, power efficiency and power gains can be maintained high. 
     Second Modified Example of Second Exemplary Embodiment 
     A transmission apparatus according to the second modified example of the second exemplary embodiment of the present invention has, as in the case of the first modified example of the second exemplary embodiment, the block configuration illustrated in  FIG. 24 . Hereinafter, in the second modified example of the second exemplary embodiment, only operations changed from the first modified example of the second exemplary embodiment will be described. 
     In the second modified example of the second exemplary embodiment of the present invention, the output voltage V AM   _   OUT (t) of power supply modulator  602  is set to that defined by Formula (16) as shown below. 
     
       
         
           
             
               
                 
                   
                     
                       V 
                       
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                         ⁢ 
                         OUT 
                       
                     
                     ⁡ 
                     
                       ( 
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                   [ 
                   
                     Formula 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     16 
                   
                   ] 
                 
               
             
           
         
       
     
     A middle formula indicates that C 2 √P th2  and C 1 √P th2  take equal values. 
     In the case of P out1 (t)+P out2 (t)+ . . . +P outn (t)=P th2 , an upper formula and the middle formula take equal values, and thus any of the two can be used. In the case of P out1 (t)+P out2 (t)+ . . . +P outn (t)=P th1 , the middle formula and a lower formula take equal values, and thus any of the two can be used. 
     The output voltage V AM   _   OUT (t) of power supply modulator  602  given by Formula (16) corresponds to that obtained by expanding Formula (6) to a plurality of bands in the second modified example of the first exemplary embodiment. 
     In the second modified example of the second exemplary embodiment, the output voltage V AM   _   OUT (t) of power supply modulator  602  is set to that defined by Formula (16). Accordingly, the transmission apparatus performs the following operation. During a period where the sum total P OUT1 (t)+P OUT2 (t)+ . . . +P OUTn (t) of the powers of RF signals  622   1 ,  622   2 , . . . ,  622   n  is equal to or higher than a first threshold value P th1 , MPU  1009  outputs the control signal of switch  902  to control terminal  903  so that switch  902  can connect the output of square root extractor  809  to the input of power modulation signal delay adjuster  810 . During a period where the power sum total is equal to or lower than the first threshold value P th1  and equal to or higher than a second threshold value P th2 , MPU  1009  outputs the control signal of switch  902  to control terminal  903  so that switch  902  can connect the output of DC power source  910  to the input of power modulation signal delay adjuster  810 . During a period where the power sum total is equal to or lower than the second threshold value P th2 , MPU  1009  outputs a control signal to control terminal  903  so that switch  902  can connect the output of square root extractor  809  to the input of power modulation signal delay adjuster  810 . By changing the setting values of the gains G AM1 , G AM2 , . . . , G AMn  of variable gain amplifiers (VGA)  806   1 ,  806   2 , . . . ,  806   n  between the period where the power sum total is equal to or higher than the first threshold value P th1  and the period where the power sum total is equal to or lower than the second threshold value P th2 , the proportional coefficients C 1  and C 2  of the output voltage V AM   _   OUT  (t) of power supply modulator  602  are switched. 
     By the aforementioned operation, in the second modified example of the second exemplary embodiment of the present invention, an operation similar to that in the second modified example of the first exemplary embodiment is achieved. Thus, in the second modified example of the second exemplary embodiment of the present invention, as in the case of the second modified example of the first exemplary embodiment, in the transmission apparatus that simultaneously transmits the plurality of RF signals having different carrier frequencies, even when the output power of the RF signal is reduced, power efficiency and power gains can be maintained high. 
     Third Modified Example of Second Exemplary Embodiment 
       FIG. 26  illustrates the block configuration of a transmission apparatus according to the third modified example of the second exemplary embodiment of the present invention. In the transmission apparatus according to the third modified example of the second exemplary embodiment, square root extractor  809  is removed from the transmission apparatus of the second exemplary embodiment illustrated in  FIG. 21 , and nonlinear circuit  904  and terminals  903 ,  905 , and  906  are newly added. In the transmission apparatus according to the third modified example of the second exemplary embodiment, the internal configuration of controller  807  is similar to that illustrated in  FIG. 25 . 
     In the transmission apparatus according to the third modified example of the second exemplary embodiment illustrated in  FIG. 26 , nonlinear circuit  904  has a function of outputting a signal h(x) to terminal  906  with respect to a signal x input to terminal  905 . The sum total P OUT1 (t)+P OUT2 (t)+ . . . +P OUTn (t) of the powers of RF signals  622   1 ,  622   2 , . . . ,  622   n  is input to terminal  905 . Accordingly, a signal h (P OUT1 (t)+P OUT2 (t)+ . . . +P OUTn (t) is output to terminal  906 . In other words, in the transmission apparatus according to the third modified example of the second exemplary embodiment illustrated in  FIG. 26 , by the aforementioned operation, as in the case of the transmission apparatus according to the third modified example of the first exemplary embodiment, the output voltage V AM   _   OUT (t) of power supply modulator  602  is set to that defined by Formula (8). 
     In the transmission apparatus according to the third modified example of the second exemplary embodiment illustrated in  FIG. 26 , a function h indicating the nonlinear characteristics of nonlinear circuit  904  is designated by MPU  1009  of controller  807  via control terminal  903 . As in the case of the transmission apparatus according to the third modified example of the first exemplary embodiment, in the transmission apparatus according to the third modified example of the second exemplary embodiment, the function h can be defined by measuring a relationship between the saturation output power P sat  of power amplifier  603  and the power supply voltage V AM   _   OUT  of power supply modulator  602  or set so as to obtain desired power efficiency and gains at power amplifier  603 . 
       FIG. 27  illustrates the example of nonlinear circuit  904  in the third modified example of the second exemplary embodiment. In  FIG. 27 , nonlinear circuit  904  includes ADC  1021 , lookup table (LUT)  1022 , and DAC  1023 . ADC  1021  converts the signal x input to terminal  905  into a digital signal to output the signal to LUT  1022  via terminal  1024 . LUT  1022  is mounted in MPU, DSP, or FPGA. LUT  1022  stores a function h(x) using the signal x as an argument. The function h(x) is designated by MPU  1009  in controller  807 , and input to LUT  1022  via control terminal  903 . LUT  1022  outputs the digital value of the signal h(x) to DAC  1023  via terminal  1025  by referring to the input signal x and the stored function h. DAC  1023  converts the signal h(x) into an analog value to output it to terminal  906 . 
       FIG. 28  illustrates another example of nonlinear circuit  904  in the third modified example of the second exemplary embodiment. In  FIG. 28 , nonlinear circuit  904  includes m−1 multipliers  1031   1 ,  1031   2 , . . . ,  1031   m−1 , m VGAs  1032   1 ,  1032   2 , . . . ,  1032   m , and adder  1033 . Here, m is a polynomial degree when the function h is represented by a polynomial expression. Multipliers  1031   1 ,  1031   2 , . . . ,  1031   m−1  can be mounted in an analog multiplication circuit disclosed in Chapter 7 of Non-patent Literature 6 described in the section of Non-patent Literature. Adder  1033  can be mounted in an operation amplifier according to the method disclosed in Chapter 5 of Non-patent Literature 6 described in the section of Non-patent Literature. In nonlinear circuit  904  illustrated in  FIG. 28 , the signal x of terminal  905  is input to multiplier  1031   1 , and multiplier  1031   1  outputs a power signal x 2 . The signal x of terminal  905  and the output signal x k  of multiplier  1031   k−1  are input to multiplier  1031   k  (k=2, 3, . . . , m), and a power signal x k+1  that is a product of the signal x and the signal x k  is output. Signals x, x 2 , x 3 , . . . , x m  generated by this operation are respectively input to VGAs  1032   1 ,  1032   2 , . . . ,  1032   m . VGAs  1032   1 ,  1032   2 , . . . ,  1032   m  respectively have gains D 1 , D 2 , D 3 , . . . , D m , and outputs signals D 1 x, D 2 x 2 , D 3 x 3 , . . . D m x m  amplified by the gains to adder  1033 . Adder  1033  adds together input signals from VGAs  1032   1 ,  1032   2 , . . . ,  1032   m  to output a signal h(x)=D 1 x+D 2 x 2 +D 3 X 3 + . . . +D m x m  to terminal  906 . The function h is represented as a polynomial expression of x using coefficients D 1 , D 2 , D 3 , . . . , D m . The gains D 1 , D 2 , D 3 , . . . , D m  of VGAs  1032   1 ,  1032   2 , . . . ,  1032   m  are controlled by MPU  1009  in controller  807  via control terminal  903 . A function h(x) is designated by control of the gains D 1 , D 2 , D 3 , . . . , D m  of VGAs  1032   1 ,  1032   2 , . . . ,  1032   m . 
     Fourth Modified Example of Second Exemplary Embodiment 
       FIG. 29  illustrates the block configuration of a transmission apparatus according to the fourth modified example of the second exemplary embodiment of the present invention. In the transmission apparatus according to the fourth modified example of the second exemplary embodiment, adder  811  is removed from the transmission apparatus of the third modified example of the second exemplary embodiment illustrated in  FIG. 26 , and the output signals of VGAs  806   1 ,  806   2 , . . . ,  806   n  are directly input to nonlinear circuit  904  via terminals  905   1 ,  905   2 , . . . ,  905   n . Signals proportional to the powers P OUT1 (t), P OUT2 (t), . . . , P OUTn (t) of RF signals  622   1 ,  622   2 , . . . ,  622   n  are respectively input to terminals  905   1 ,  905   2 , . . . ,  905   n . Nonlinear circuit  904  has a function of outputting a signal w[P OUT1 (t), P OUT2 (t), . . . , P OUTn (t)] to terminal  906  by using the input signals P OUT1 (t), P OUT2 (t), . . . , P OUTn (t) as arguments. In other words, in the transmission apparatus according to the fourth modified example of the second exemplary embodiment, an operation similar to that in the fourth modified example of the first exemplary embodiment is performed. 
       FIG. 30  illustrates the example of nonlinear circuit  904  in the fourth modified example of the second exemplary embodiment. In  FIG. 30 , nonlinear circuit  904  includes ADCs  1021   1 ,  1021   2 , . . . ,  1021   n , lookup table (LUT)  1022 , and DAC  1023 . In nonlinear circuit  904 , signals x 1 , x 2 , . . . , x n  are respectively input to terminals  905   1 ,  905   2 , . . .  905   n . ADCs  1021   1 ,  1021   2 , . . . ,  1021   n  convert the signals x 1 , x 2 , . . . , x n  of terminals  905   1 ,  905   2 , . . .  905   n  into digital values to output the signals to LUT  1022  via terminals  1024   1 ,  1024   2 , . . . ,  1024   n . LUT  1022  stores a function w(x 1 , x 2 , . . . , x n ) using the signals x 1 , x 2 , . . . , x n  as arguments. The function w(x 1 , x 2 , . . . , x n ) is designated by MPU  1009  in controller  807 , and input to LUT  1022  via control terminal  903 . LUT  1022  outputs the digital value of the signal w(x 1 , x 2 , . . . , x n ) to DAC  1023  via terminal  1025  by referring to the input signals x 1 , x 2 , . . . , x n  and the function w(x 1 , x 2 , . . . , x n ). DAC  1023  converts the signal w(x 1 , x 2 , . . . , x n ) into an analog value to output it to terminal  906 . 
     The transmission apparatus of the present invention has the following effects as compared with those disclosed in Patent Literatures 1 to 5. 
     In the case of the transmission apparatuses described in Patent Literatures 1 to 5, the RF signal of one carrier frequency is amplified by one power amplifier (PA). Thus, when the RF signals of n carrier frequencies are amplified, n power amplifiers (PA) are necessary. Since power supply modulation (polar modulation) is individually applied for each PA, n power supply modulators are necessary. 
     On the other hand, in the case of the transmission apparatuses according to the exemplary embodiments of the present invention, the RF signals of n carrier frequencies are simultaneously amplified by one power amplifier (PA). Thus, the number of PAs is one, irrespective of the number of RF signals of carrier frequencies to be amplified. In the present invention, only one PA is used, and accordingly only one power modulator is necessary. Thus, compared with those disclosed in Patent Literatures 1 to 5, in the transmission apparatuses of the exemplary embodiments, the transmission apparatus of higher power efficiency can be configured by smaller numbers of power amplifiers (PA) and power supply modulators. As a result, a circuit size and costs can be reduced. 
     In the case of the transmission apparatuses described in Patent Literatures 1 to 5, there is a need to install a switch for changing a used band between the input and the output of the power amplifier. The use of such a switch causes the problem of the reduction of the power efficiency of the entire transmission apparatus due to the insertion loss of the switch in addition to the problem of the increase of the circuit size and the costs caused by the increased number of components. 
     On the other hand, in the case of the transmission apparatuses according to the exemplary embodiments of the present invention, there is no need to install any switch for changing a used band between the input and the output of the power amplifier. Thus, the problems of the increase of the circuit size and the costs caused by a switch and the reduction of the power efficiency of the entire transmission apparatus due to the insertion loss of a switch can be solved. 
     In the case of the transmission apparatuses described in Patent Literatures 1 to 5, the method for switching the power amplifiers used in the band changing switch imposes restrictions, namely, inhibition of simultaneous outputting of the RF signals of all bands processable by the transmission apparatus. Because of the restrictions, the transmission apparatuses described in Patent Literatures 1 to 5 have a problem of unsuitability to the CA technology for performing communication by simultaneously using a plurality of bands. 
     On the other hand, in the case of the transmission apparatuses according to the exemplary embodiments of the present invention, the RF signals of an arbitrary number of bands can be simultaneously output, and the CA technology can be employed. 
     The configurations of the preferred exemplary embodiments of the present invention have been described. The contents disclosed in Patent Literatures can be incorporated by reference in the invention. Within the framework of the entire disclosure (including the scope of claims) of the present invention, based on the basic technical ideas, changes and adjustments can be made of the exemplary embodiments. Within the framework of the scope of claims of the present invention, a wide variety of combinations of various disclosed elements or selection can be made. In other words, needless to say, the present invention includes various changes and modifications obtainable by those skilled in the art according to the entire disclosure including the scope of claims and the technical ideas. 
     For example, in the second exemplary embodiment of the present invention, the adjacent channel leakage power (ACPR) is used as a signal distortion index, and the ACPR detector is installed as the signal distortion detector. However, the present invention is not limited to this. The signal distortion detector can use, as a signal distortion index, EVM (Error Vector Magnitude), IMD (Inter-modulation distortion), or MER (Modulation Error Ratio).