Patent Publication Number: US-7902891-B1

Title: Two point modulator using voltage control oscillator and calibration processing method

Description:
BACKGROUND OF THE INVENTION 
     1. Field of the Invention 
     The present invention relates to a two point modulator using a voltage control oscillator and a calibration processing method, and more particularly, to a two-point modulator calibrating a gain and nonlinearity of a voltage control oscillator, and a calibration processing method performed by the two-point modulator. 
     2. Description of the Background Art 
     As generally known, a voltage control oscillator (hereinafter, referred to as VCO) is widely used, as a device for generating a local oscillation signal, for a modulator of a radio communication apparatus. By using the VCO, a frequency modulated signal or a phase-modulated signal can be generated. Moreover, by inputting a modulated signal having a constant envelope, generated by the VCO, to a power amplifier, and controlling a supply voltage of the power amplifier, a modulated signal having a modulated component also on its amplitude can be generated (phase shift keying; PSK, code division multiple access; CDMA, orthogonal frequency division multiplexing; OFDM, etc.). In recent years, there arises a need for enabling an oscillation frequency of the VCO to be adjusted over a wide range of frequencies, in order to adapt the modulator to a communication system using a plurality of different frequency bands. 
     With that, in order to realize a modulator having a wide band, there is suggested a modulation method called two-point modulation.  FIG. 13  shows an example of a configuration of a modulator using a conventional two-point modulation method. 
     As shown in  FIG. 13 , the conventional two-point modulator  501  includes an operation section  521 , a frequency error calculation section  522 , a loop filter  523 , a adding section  525 , a VCO  526 , a frequency detection section  527 , and a buffer  528 . 
     A modulated signal is converted to a signal corresponding to a desired frequency channel by the operation section  521 , and outputted as a low-pass response signal via a frequency error calculation section  522  and a loop filter  523 . Meanwhile, a modulated signal is adjusted by the buffer  528  so as to be a desired signal, and then outputted as a high-pass response signal. The adding section  525  adds the high-pass response signal to the low-pass response signal, and inputs the resultant signal to the VCO  526 . A signal outputted from the VCO  526  is fed back and inputted to the frequency error calculation section  522  via the frequency detection section  527 . The frequency error calculation section  522  detects and outputs a frequency error between the modulated signal outputted from the operation section  521  and the signal outputted from the frequency detection section  527 . This feedback processing stabilizes a frequency of the signal outputted from the VCO  526 . 
     Thus, by using two-point modulation method, modulation characteristics including in a combined manner a frequency gain as a low-pass response via a feedback circuit and a frequency gain as a high-pass response via a feedforward circuit can be obtained, whereby a modulator having a wide band can be realized ( FIG. 14 ). 
     However, even by using the above two-point modulation method, there remains a problem that, if the VCO  526  is a VCO exhibiting nonlinearity, a frequency band in which linear modulation can be performed is narrow, distortion occurs on the output, and, as a result, wideband frequency characteristics cannot be obtained ( FIG. 15 ). Therefore, there arises a need for calibrating a gain and/or nonlinearity of the VCO  526 . 
     U.S. Pat. No. 7,061,341 (Patent Document 1) discloses an invention for solving the above problem.  FIG. 16  shows an example of a configuration of a conventional direct modulator  511  disclosed in Patent Document 1. 
     As shown in  FIG. 16 , the conventional direct modulator  511  includes a PLL circuit having a VCO  1506 , a divide-by-N frequency divider (N counter)  1508 , a phase comparator, a charge pump (CP), and an RC connection filter. A phase signal corresponding to a desired channel is converted to a digital modulated signal by ΔΣ modulator, and the digital modulated signal is supplied to the divide-by-N frequency divider  1508  and the phase comparator. A step signal Δf PM  is converted to an analog signal by a D/A converter  1510 , and is inputted to an auxiliary terminal  1504  of a VCO  1506  via a low-pass filter (hereinafter, referred to as LPF)  1512 . 
     In the above configuration, the PLL circuit is operated in a closed loop state. First, a desired channel frequency fc is inputted and the VCO  1506  is locked up at a division ratio N. A lockup voltage V ctrl  used upon the lockup is held [f REF =f C /N]. Next, the step signal Δf PM  is inputted and the division ratio of the divide-by-N frequency divider  1508  is shifted by ΔN. Moreover, the step signal Δf PM  is adjusted such that the lockup voltage V ctrl  used at this time is the same as the lockup voltage initially used [f REF =(f C +Δf PM )/(N+ΔN)]. By performing the above processing for a plurality of calibration points, the conventional direct modulator  511  calibrates a gain or nonlinearity of the VCO  1506 . 
     However, in the conventional direct modulator  511  disclosed in Patent Document 1, since the PLL circuit is operated in a closed loop state, it takes a long time to perform calibration processing on the VCO  1506 . Therefore, in a communication system in which there is a restriction on lockup time due to the specification thereof, it can occur that the lockup is not completed in time. If calibration processing is started in a state where the lockup is not sufficiently performed (is not completed), frequency offset occurs. 
     In addition, during calibration processing, there is also a problem that the lockup voltage varies by leakage in a filter or a parasitic capacitance included in the apparatus, and thereby frequency drift occurs. 
     SUMMARY OF THE INVENTION 
     Therefore, an object of the present invention is to provide a two-point modulator and a calibration processing method which enable calibration to be performed in short time and optimally, by suppressing signal distortion due to frequency offset and frequency drift, and calibrating a gain and nonlinearity of a VCO in a state where a feedback circuit is in an open loop state. 
     The present invention is directed to a two-point modulator using a voltage control oscillator. In order to achieve the above object, a two-point modulator of the present invention comprises: a modulation section including a feedback circuit for performing feedback control of a signal outputted from the voltage control oscillator based on an inputted modulated signal, and a feedforward circuit for calibrating the modulated signal and outputting the calibrated modulated signal to the voltage control oscillator; a signal output section for, upon calibration processing, outputting a predetermined reference signal in place of the modulated signal, to the modulation section; and a gain correction section for, in a state where the feedback circuit is in an open loop state, calculating a frequency transition amount of the reference signal outputted from the voltage control oscillator, and correcting a gain used for calibration of the modulated signal performed by the feedforward circuit, based on the calculated frequency transition amount. The gain correction section corrects the gain so as to reflect therein influence of signal distortion due to frequency offset and frequency drift. 
     Typically, the reference signal has a pattern in which a positive square pulse representing a frequency f and a negative square pulse representing the frequency f are alternately generated during pulse widths T, respectively, the total number of the generated positive square pulses and negative square pulses being odd. Alternatively, the reference signal has a pattern in which a pulse with a pulse value of 0 having no frequency information, and two or more positive square pulses representing a frequency for two or more negative square pulses representing the frequency f, are generated during pulse widths T, respectively. Still alternatively, the reference signal has a pattern in which, at least, a pulse with a pulse value of 0 having no frequency information, a positive square pulse representing a frequency f 1 , a negative square pulse representing the frequency f 1 , a positive square pulse representing a frequency f 2  different from the frequency f 1 , and a negative square pulse representing the frequency f 2 , are generated during pulse widths T, respectively. In this case, it is preferable that the frequency f 2  is set to a maximum frequency within a range of frequency that the modulated signal can have, and the frequency f 1  is set to a frequency, within the range of frequency that the modulated signal can have, corresponding to a minimum frequency transition amount which can be detected by the feedback circuit. 
     Moreover, if the two-point modulator further comprising the voltage holding section for holding a lockup used for the voltage control oscillator in a state where the feedback circuit is in a closed loop state, the modulation section can bring the feedback circuit into an open loop state by fixing an output voltage for the voltage control oscillator at the lockup voltage. 
     Moreover, it is desirable that the gain correction section calculates a frequency transition amount for each of the square pulses included in the reference signal. Particularly, it is desirable that the gain correction section calculates the frequency transition amount after the square pulses to rise and for an output of the voltage control oscillator is stabilized. 
     Moreover, a calibration processing method performed by a two-point modulator using a voltage control oscillator is realized by the steps of: locking up a feedback circuit for performing feedback control of a signal outputted from the voltage control oscillator based on an inputted modulated signal; applying a voltage used when the lockup is performed, to the voltage control oscillator, and thereby bringing the feedback circuit into an open loop state; outputting a predetermined reference signal to the voltage control oscillator via a feedforward circuit for calibrating the modulated signal; and calculating a frequency transition amount of the reference signal outputted from the voltage control oscillator, and correcting a gain used for calibration of the modulated signal performed by the feedforward circuit, based on the calculated frequency transition amount. 
     According to the present invention, distortion of the reference signal due to frequency offset and frequency drift is reflected in the correction gain value of the VCO. Therefore, calibration of the gain and nonlinearity of the VCO can be performed in short time and appropriately. 
     These and other objects, features, aspects and advantages of the present invention will become more apparent from the following detailed description of the present invention when taken in conjunction with the accompanying drawings. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  shows an example of a configuration of a two-point modulator  1  according to one embodiment of the present invention; 
         FIG. 2  is a flowchart showing a process of a calibration operation performed by the two-point modulator  1 ; 
         FIG. 3  shows an example of a pulse pattern of a reference signal used in a first embodiment; 
         FIG. 4  is a diagram for explaining an example of a distortion occurring in the pulse pattern in  FIG. 3  due to frequency offset and frequency drift; 
         FIG. 5  shows in detail an example of a configuration of the correction gain calculation section  31  used in the first embodiment; 
         FIG. 6  shows an example of a table which a correction gain holding section  32  has in the first embodiment; 
         FIG. 7  shows an example of a pulse pattern of a reference signal used in a second embodiment; 
         FIG. 8  is a diagram for explaining an example of a distortion occurring in the pulse pattern in  FIG. 7  due to frequency offset and frequency drift; 
         FIG. 9  shows in detail an example of a configuration of the correction gain calculation section  31  used in the second embodiment; 
         FIG. 10  shows an example of a pulse pattern of a reference signal used in a third embodiment; 
         FIG. 11  is a diagram for explaining an example of a distortion occurring in the pulse pattern in  FIG. 10  due to frequency offset and frequency drift; 
         FIG. 12  shows an example of a table which a correction gain holding section  32  has in the third embodiment; 
         FIG. 13  shows an example of a configuration of a conventional two-point modulator  501 ; 
         FIG. 14  shows how a modulator having a wide band can be realized with use of a two-point modulation method; 
         FIG. 15  shows nonlinear frequency characteristics of a VCO; and 
         FIG. 16  shows an example of a configuration of a conventional direct modulator  511 . 
     
    
    
     DESCRIPTION OF THE PREFERRED EMBODIMENTS 
     Configuration of Modulator of the Present Invention 
       FIG. 1  shows an example of a configuration of a two-point modulator  1  according to one embodiment of the present invention. The two-point modulator  1  includes a signal output section  10 , a modulation section  20 , and a gain correction section  30 . The signal output section  10  includes a signal selection section  11  and a reference signal generation section  12 . The modulation section  20  includes a operation section  21 , frequency error calculation section  22 , loop filter  23 , voltage holding section  24 , a adding section  25 , a VCO  26 , a frequency detection section  27 , and a gain calibration section  28 . The gain correction section  30  includes a correction gain calculation section  31  and a correction gain holding section  32 . 
     First, an outline of the components of the two-point modulator  1  will be described. 
     The reference signal generation section  12  generates a reference signal used for a calibration operation described later. A modulated signal and the reference signal are inputted to the signal selection section  11 . The signal selection section  11  selects and outputs a modulated signal when normal modulation processing is performed, and selects and outputs the reference signal when calibration processing is performed. For the signal selection section  11 , a multiplexer or the like is used. A signal outputted from the signal selection section  11  is inputted to the operation section  21  and the gain calibration section  28  of the modulation section  20 . 
     The signal outputted from the signal selection section  11  and a desired frequency channel signal are inputted to the operation section  21 . The operation section  21  controls the center frequency of the signal outputted from the signal selection section  11  into the desired value. A signal outputted from the operation section  21  is compared with a frequency signal detected by the frequency detection section  27  in the frequency error calculation section  22 , and thereby an error signal indicating a frequency error between the two signals is calculated. A high-frequency component of the error signal is suppressed by a loop filter  23 , and then the error signal is outputted via the voltage holding section  24  to the adding section  25 . For the loop filter  23 , a low-pass filter or the like is used. The voltage holding section  24  holds the signal outputted from the loop filter  23  as needed. The VCO  26  outputs a signal having a frequency that is based on a signal (control voltage) outputted from the adding section  25 . The frequency detection section  27  detects the frequency of the signal outputted from the VCO  26 , and outputs the detected frequency to the error calculation section  22 . For the frequency detection section  27 , a frequency digital converter (FDC) or the like is used. 
     A feedback circuit having low-pass response is formed by the frequency error calculation section  22 , the loop filter  23 , the voltage holding section  24 , the adding section  25 , the VCO  26 , and the frequency detection section  27 . Owing to the feedback circuit, the error signal calculated by the frequency error calculation section  22  eventually becomes a value substantially equal to 0, and a control voltage is stabilized. The VCO  26  outputs a signal having a frequency corresponding to the desired channel signal, and is locked up. 
     The signal outputted from the signal selection section  11  is inputted to the gain calibration section  28 . The gain calibration section  28  calibrates a gain of the signal outputted from the signal selection section  11 , in accordance with a correction gain value held in the correction gain holding section  32 . The adding section  25  adds a signal outputted from the gain calibration section  28  to a signal outputted from the voltage holding section  24 , and outputs a signal obtained by the addition to the VCO  26 . A feedforward circuit having high-pass response is formed by the gain calibration section  28 , the adding section  25 , and the VCO  26 . 
     On the other hand, the correction gain calculation section  31  calculates a correction gain of the VCO  26  from the frequency detected by the frequency detection section  27 , when a calibration operation is performed. The correction gain holding section  32  holds the correction gain calculated by the correction gain calculation section  31  for each frequency used in the calibration operation. The gain calibration section  28  calibrates a modulated signal passing through the feedforward circuit by using the correction gain held in the correction gain holding section  32 , upon modulation processing. 
     Hereinafter, a characteristic calibration operation performed by the two-point modulator  1  having the above configuration will be described. 
     First Embodiment 
       FIG. 2  is a flowchart showing a process of a first embodiment of a calibration operation performed by the two-point modulator  1  of the present invention. 
     First, signal selection section  11  selects a state where neither a modulated signal nor a reference signal is inputted thereto. A frequency channel signal of a desired frequency f is inputted to the frequency error calculation section  22 , the feedback circuit is brought into a closed loop state (step S 201 ), and then a lockup voltage, which is a voltage used when the VCO  26  is locked up in a state where a non-modulated signal is used, is measured (step S 202 ). The lockup voltage is held in the voltage holding section  24  (step S 203 ). Thereafter, the loop filter  23  is deactivated and the lockup voltage held by the voltage holding section  24  is fixedly supplied as a voltage to be outputted to the adding section  25 , thereby bringing the feedback circuit into an open loop state (step S 204 ). 
     Next, after the feedback circuit becomes an open loop state, the signal selection section  11  performs switching such that an output of the reference signal generation section  12  is selected (step S 205 ). In addition, the gain calibration section  28  sets the correction gain value of the VCO  26  to an initial value (step S 205 ). The reference signal generation section  12  generates a reference signal having a pulse pattern shown in  FIG. 3 , and outputs the reference signal to the correction gain holding section  32  and the gain calibration section  28 . 
       FIG. 3  is a diagram for explaining the reference signal used in the first embodiment for measuring the correction gain value of the VCO  26 . The reference signal shown in  FIG. 3  includes a first pulse having a positive pulse value +A which represents the frequency f, a second pulse having a negative pulse value −A which represents the frequency f, and a third pulse having the positive pulse value +A. The pulse width of each of the first to third pulses is a time period T. The pulse value A and the pulse width T of the reference signal are set to values which allow the correction gain calculation section  31  to calculate a correction gain with sufficient accuracy. For example, if the pulse value A is exceedingly small, a transition amount of an output frequency of the VCO  26  is smaller than a resolution of the frequency detection section  27 . Therefore, the correction gain calculation section  31  cannot precisely calculate the correction gain. On the other hand, if the pulse value A is exceedingly large, the correction gain calculation section  31  cannot precisely calculate the correction gain due to nonlinearity of the VCO  26 . Moreover, if the pulse width T is exceedingly small, the correction gain calculation section  31  cannot sufficiently average an output signal of the frequency detection section  27 , and is influenced by noise. Therefore the correction gain calculation section  31  cannot precisely calculate the correction gain. On the other hand, if the pulse width T is exceedingly large, it takes extra time for the correction gain calculation section  31  to calculate the correction gain. 
     If the two-point modulator  1  is ideal, the reference signal shown in  FIG. 3  is inputted to the VCO  26  without changing, and observed in the frequency detection section  27 . However, in reality, frequency offset and frequency drift can occur. As a result, each of the pulse values ±A of the first to third pulses of the reference signal observed in the frequency detection section  27  varies by a frequency offset B, a frequency drift C 1 , and/or a frequency offset C 2  that is due to the frequency drift as shown by a solid line in  FIG. 4 . Considering the above, in the first embodiment, the correction gain calculation section  31  performs calculation in accordance with the following manner (step S 206 ).  FIG. 5  shows in detail an example of a configuration of the correction gain calculation section  31 . 
     A frequency transition amount measuring section  311  measures frequency of each of the first to third pulses in the period between when a predetermined time period t 0  passes from the rising point of pulse, and when a time period t 1  passes since the predetermined time period t 0  passes, i.e., to the falling point of pulse, thereby obtaining an average frequency transition amount of each pulse. Note that the predetermined time period t 0  is a time period which is needed for the output of the VCO  26  to follow a change of pulse and stabilize, and the length thereof can be set arbitrarily. 
     The obtained frequency transition amounts f meas1  to f meas3  of the first to third pulses are represented by the following equations, respectively.
 
 f   meas1   =+A+B+C 1  [1]
 
 f   meas2   =−A+B+C 1+ C 2  [2]
 
 f   meas3   =+A+B+C 1+2· C 2  [3]
 
     The frequency transition amount correction section  312  obtains a frequency transition amount f comp  of the reference signal distorted due to the frequency offset and the frequency drift, from the frequency transition amounts f meas1  to f meas3  of the first to third pulses measured by the frequency transition amount measuring section  311 , by using an equation [4]. 
     
       
         
           
             
               
                 
                   
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     A calculation result of the equation [4] is f comp =A. Therefore, by reflecting the obtained frequency transition amount f comp  in the reference signal, a signal distortion (B, C 1 , and C 2 ) due to the frequency offset and the frequency drift can be canceled. 
     Accordingly, based on a frequency transition amount f ref  of the reference signal outputted from the reference signal generation section  12  and the frequency transition amount f comp , the operation section  313  obtains, by using the following equation [5], a correction gain value G for calibrating a gain of the VCO  26 , in which the signal distortion due to the frequency offset and the frequency drift is considered. 
     
       
         
           
             
               
                 
                   G 
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                       ref 
                     
                     
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                         comp 
                       
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     The obtained correction gain value G of the VCO  26  is held in the correction gain holding section  32  (step S 207 ). Note that, in the case where a plurality of frequencies (fa, fb, . . . ) are used for the channel signal in the two-point modulator  1 , the correction gain value G of the VCO  26  is obtained for each of the plurality of channel frequencies.  FIG. 6  is an example of a table which the correction gain holding section  32  of the first embodiment has. In the table, the correction gain values G may be held for the plurality of channel frequencies, respectively, as shown in  FIG. 6 , or one correction gain value G may be held and calibrated every time the VCO is locked to each channel frequency. In the latter case, a circuit scale can be reduced in comparison with the former case. Alternatively, since it takes long time for variation such as temperature change or secular change to be caused in comparison with the time during which the communication system performs a communication, the correction gain value G may not necessarily be calibrated every time the VCO is locked to each channel frequency, and may be calibrated at regular time intervals. Thus, lockup time in the case where calibration is not performed can be reduced, and power consumption can be reduced. 
     The calibration processing is completed as described above. The signal selection section  11  switches the system to a state where the modulated signal is selected, and the feedback circuit changes the output of the voltage holding section  24  to an output from the loop filter  23 , thereby returning to a closed loop state (step S 208 ). In modulation processing, the correction gain holding section  32  determines a frequency of the modulated signal, and the correction gain value G of the VCO  26  corresponding to the determined frequency is outputted to the gain calibration section  28 . 
     As described above, according to the first embodiment, an average value of frequency transition amount of each pulse included in the reference signal is reflected in the correction gain value. Thus, even if distortion due to frequency offset and frequency drift occurs on the reference signal, calibration of a gain of the VCO  26  can appropriately be performed. Moreover, since the calibration is performed with the feedback circuit being in an open loop state, the calibration is completed in a short time in comparison with conventional art. 
     In the first embodiment, there is described the reference signal including the first pulse having the pulse value +A, the second pulse having the pulse value −A, and the third pulse having the pulse value +A each of which is generated during the time period T. However, the reference signal is not limited to the pulse pattern described in the first embodiment. The order or the number of pulses can freely be set as long as using a pulse pattern in which a pulse having the pulse value +A and a pulse having the pulse value −A are alternately generated during the pulse widths T, respectively, and the total number of the pulses is odd. 
     Second Embodiment 
     A process of a second embodiment of a calibration operation performed by the two-point modulator  1  of the present invention is basically similar to the process shown in  FIG. 2 , except the processing of step S 206 . Hereinafter, the second embodiment will be described focusing on the processing of step S 206 . 
     When the gain calibration section  28  sets the correction gain value to an initial value (step S 205 ), the reference signal generation section  12  generates a reference signal having a pulse pattern shown in  FIG. 7 , and outputs the generated reference signal to the correction gain holding section  32  and the gain calibration section  28 .  FIG. 7  is a diagram for explaining the reference signal used in the second embodiment for measuring the correction gain value of the VCO  26 . 
     The reference signal shown in  FIG. 7  includes a zero-th pulse which is a null signal representing no frequency information, a first pulse having a positive pulse value +A which represents a frequency f, a second pulse having a negative pulse value −A which represents the frequency f, and a third pulse having the positive pulse value +A. The pulse width of each of the zero-th to third pulses is a time period T. 
     As described above, since frequency offset and frequency drift occur, each of the pulse values ±A of the zero-th to third pulses of the reference signal observed in the frequency detection section  27  varies by a frequency offset B, a frequency drift C 1 , and/or a frequency offset C 2  that is due to the frequency drift as shown by a solid line in  FIG. 8 . Considering the above, in the second embodiment, the correction gain calculation section  31  performs calculation in accordance with the following manner (step S 206 ).  FIG. 9  shows in detail an example of a configuration of the correction gain calculation section  31 . 
     Frequency transition amounts f meas0  to f meas3  of the zero-th to third pulses obtained by the frequency transition amount measuring section  311  are represented by the following equations [6] to [9], respectively.
 
 f   meas0   =+B+C 1  [6]
 
 f   meas1   =+A+B+C 1+ C 2  [7]
 
 f   meas2   =−A+B+C 1+2· C 2  [8]
 
 f   meas3   =+A+B+C 1+3· C 2  [9]
 
     A frequency offset estimation section  314  and a frequency drift estimation section  315  obtain an estimated frequency drift amount f drift  (≈C 2 ), from the frequency transition amount f meas1  of the first pulse and the frequency transition amount f meas3  of the third pulse, by using an equation [10], and in addition, obtain an estimated frequency offset amount f offset  (≈B+C 1 ), from the estimated frequency transition amount f meas0  of the zero-th pulse, by using the following equation [11]. Although C 1  is in fact an error due to frequency drift, C 1  can be treated in the same manner as in an error due to frequency offset B since C 1  is included in all the equations [6] to [9]. Accordingly, +B+C 1  is treated as the estimated frequency offset amount f offset , in the present invention. 
                     f   drift     =         f     meas   ⁢           ⁢   3       -     f     meas   ⁢           ⁢   1         2             [   10   ]               f offset =f meas0   [11]
 
     The frequency transition amount correction section  312  obtains a frequency transition amount f comp  of each pulse of the reference signal, from the estimated frequency offset amount f offset  and the estimated frequency drift amount f drift , by using the following equation [12].
 
 f   comp   =f   measN   −f   offset   −N·f   drift  ( N= 1 to 3)  [12]
 
     Moreover, based on a frequency transition amount f ref  of the reference signal outputted from the reference signal generation section  12  and each frequency transition amount f comp , the operation section  313  obtains a correction gain value G, for each frequency, for calibrating a gain of the VCO  26 , by using the following equation [13]. 
     
       
         
           
             
               
                 
                   
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                     N 
                   
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                         refN 
                       
                       
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     As described above, according to the second embodiment, the estimated frequency offset and estimated frequency drift are obtained and reflected in the correction gain value. Thus, even if distortion due to frequency offset and frequency drift occurs on the reference signal, calibration of a gain of the VCO  26  can appropriately be performed. 
     In the second embodiment, there is described the reference signal including the zero-th pulse having a pulse value of 0, the first pulse having the pulse value +A, the second pulse having the pulse value −A, and the third pulse having the pulse value +A each of which is generated during the time period T. However, the reference signal is not limited to the pulse pattern described in the second embodiment. The order or the number of pulses can freely be set as long as using a pulse pattern in which a pulse having a pulse value of 0 and at least two pulses having the same pulse value (+A or −A) are generated. 
     Third Embodiment 
     A process of a third embodiment of a calibration operation performed by the two-point modulator  1  of the present invention is basically similar to the process shown in  FIG. 2 , except the processing of step S 206 . Hereinafter, the third embodiment will be described focusing on the processing of step S 206 . 
     When the gain calibration section  28  sets the correction gain value to an initial value (step S 205 ), the reference signal generation section  12  generates a reference signal having a pulse pattern shown in  FIG. 10 , and outputs the generated reference signal to the correction gain holding section  32  and the gain calibration section  28 .  FIG. 10  is a diagram for explaining the reference signal used in the third embodiment for measuring the correction gain value of the VCO  26 . 
     The reference signal shown in  FIG. 10  includes a zero-th pulse which is a null signal representing no frequency information, a first pulse having a positive pulse value +A 1  which represents a frequency f 1 , a second pulse having a negative pulse value −A 1  which represents the frequency f 1 , a third pulse having the positive pulse value +A 1 , a fourth pulse having a negative pulse value −A 2  which represents a frequency f 2 , a fifth pulse having a positive pulse value +A 2  which represents the frequency f 2 , a sixth pulse having the negative pulse value −A 3  which represents a frequency f 3 , a seventh pulse having a positive pulse value +A 3  which represents the frequency f 3 , an eighth pulse having a negative pulse value −A 4  which represents a frequency f 4 , and a ninth pulse having a positive pulse value +A 4  which represents a frequency f 4 . The pulse width of each of the zero-th to ninth pulses is a time period T. 
     As described above, since frequency offset and frequency drift occur, the pulse values ±A of the zero-th to ninth pulses of the reference signal observed in the frequency detection section  27  each vary by a frequency offset B, a frequency drift C 1 , and/or a frequency offset C 2  that is due to the frequency drift as shown by a solid line in  FIG. 11 . Considering the above, in the third embodiment, the correction gain calculation section  31  performs calculation in accordance with the following manner (step S 206 ). An example of a detailed configuration of the correction gain calculation section  31  is the same as in  FIG. 9 . 
     Frequency transition amounts f meas0  to f meas9  of the zero-th to ninth pulses obtained by the frequency transition amount measuring section  311  are represented by the following equations [14] to [23], respectively.
 
 f   meas0   =+B+C 1  [14]
 
 f   meas1   =+A 1+ B+C 1+ C 2  [15]
 
 f   meas2   =−A 1+ B+C 1+2· C 2  [16]
 
 f   meas3   =+A 1+ B+C 1+3· C 2  [17]
 
 f   meas4   =−A 2+ B+C 1+4· C 2  [18]
 
 f   meas5   =+A 2+ B+C 1+5· C 2  [19]
 
 f   meas6   =−A 3+ B+C 1+6· C 2  [20]
 
 f   meas7   =+A 3+ B+C 1+7· C 2  [21]
 
 f   meas8   =−A 4+ B+C 1+8· C 2  [22]
 
 f   meas9   =+A 4+ B+C 1+9· C 2  [23]
 
     Moreover, a frequency offset estimation section  314  and a frequency drift estimation section  315  obtain an estimated frequency drift amount f drift  and the estimated frequency offset amount f offset , by using the aforementioned equations [10] and [11]. The frequency transition amount correction section  312  obtains a frequency transition amount f comp  of each pulse of the reference signal by using the aforementioned equation [12]. The operation section  313  obtains a correction gain value G, by using the aforementioned equation [13].  FIG. 12  is an example of a table which the correction gain holding section  32  of the third embodiment has. Other than holding all the correction gain values G corresponding to the pulse values ±A 1 , ±A 2 , ±A 3 , and ±A 4  shown in  FIG. 12 , an average value of the correction gain value G corresponding to the positive pulse value +A and the correction gain value G corresponding to the negative pulse value −A may be held. Upon modulation processing, a correction gain value corresponding to a modulated signal is obtained by using the table. For interpolation among the values on the table, linear interpolation is used, for example. 
     As described above, according to the third embodiment, the estimated frequency offset and estimated frequency drift are obtained and applied to the correction gain value. Thus, even if distortion due to frequency offset and frequency drift occurs on the reference signal, calibration of a gain and nonlinearity of the VCO  26  can appropriately be performed. Moreover, since the calibration is performed with the feedback circuit being in an open loop state, the calibration is performed in a short time in comparison with conventional art even if a reference signal having a plurality of pulses is used. 
     In the third embodiment, the reference signal having square pulses ±A 1 , ±A 2 , ±A 3 , and ±A 4  is used for calibrating nonlinearity of the VCO  26 . However, nonlinearity of the VCO  26  can be calibrated by calculating correction gain values for at least two frequencies in a frequency band of the modulated signal (which corresponds to the range of pulse value from −A 4  to +A 4 , in the third embodiment). In general, when a frequency spectrum of a modulated signal is observed, it is likely that a large number of components are present near DC (near a channel frequency when a frequency spectrum in the RF band is observed). Therefore, only by calculating correction gain values for frequencies (in the third embodiment, the pulse values −A 4  and +A 4 ) corresponding to both ends of the bandwidth of the modulated signal, and frequencies (in the third embodiment, the pulse values ±A 1 ) which are present therebetween, nonlinearity of the VCO 26  can accurately be calibrated. In this case, the pulse values ±A 1  only need to be values which allow the frequency transition amount to be equal to or larger than a minimum resolution of the frequency detection section  27 . Moreover, by calculating correction gain values for other frequencies in the frequency band of the modulated signal, the nonlinearity can more accurately be calibrated. 
     In the first and second embodiments, one correction gain value is obtained through calibration, and, in the third embodiment, eight correction gain values are obtained through calibration. The number of correction gain values to be obtained is determined by the bandwidth of the modulated signal and the nonlinearity of the VCO  26 . In  FIG. 15 , if a linear region is larger than the bandwidth of the modulated signal, one correction gain value is needed. On the other hand, if a linear region is smaller than the bandwidth of the modulated signal, a plurality of correction gain values are needed. 
     In addition, in order to enhance accuracy of calibration, it is desirable that, as shown in  FIG. 10 , a plurality of pulses included in the reference signal are arranged in the order of a square pulse having the lowest frequency (pulse values ±A 1 ) to a square pulse having the highest frequency (pulse values ±A 4 ). The reason will be described below. As shown in  FIG. 11 , square pulses outputted later are more influenced by frequency drift. Therefore, if a square pulse having a low frequency is outputted later, the square pulse is more easily influenced by frequency drift than a square pulse having a high frequency. Accordingly, by outputting square pulses in ascending order of square pulse having the lowest frequency, the square pulses are not extremely influenced by frequency drift, thus enhancing accuracy of calibration. 
     Moreover, in the third embodiment, although the pulse width T is fixed for any reference signals, the pulse value T may be varied depending on pulse values. As previously described, a pulse width of the reference signal is determined by how much influence of noise is reduced by averaging. Considering that an S/N ratio of an average frequency transition amount measured by the correction gain calculation section  31  should be constant, the larger the pulse value of the reference signal is, relatively the smaller influence of noise becomes and therefore the shorter the pulse width can be made. For example, if a pulse width of a reference signal having pulse values ±A 1  is T, a pulse width of a reference signal having a pulse value A 2  (=2×A 1 ) can be set to T/2. Thus, lockup time can be reduced. 
     In the third embodiment, a frequency drift amount is estimated by using the first to third pulses, and then frequency drift of other pulses is corrected by using the estimated frequency drift. However, increased number of square pulses may be outputted as a reference signal, and a frequency drift amount may be estimated for each of the square pulses having pulse values ±A 1 , ±A 2 , ±A 3 , and ±A 4 . That is, each of the square pulses having the pulse value ±A 1 , ±A 2 , ±A 3 , and ±A 4  may be outputted two times, and a frequency drift amount may be estimated and corrected for each of the outputted square pulses. By estimating a frequency drift amount for each of the square pulses, accuracy of calibration is enhanced. However, increasing the number of pulses to be outputted as a reference signal increases time taken for calibration. Therefore, the number of pulse is determined by trade-off between lockup time and accuracy of calibration which are specified in the communication system. 
     Moreover, it is preferable that the zero-th pulse used for estimating frequency offset is used for a start pulse of a reference signal, since the start pulse is hardly influenced by frequency drift. Alternatively, the zero-th pulse may be positioned in mid-stream or at the end of a reference signal. In addition, the first pulse and the third pulse which are used for frequency drift may separately be generated at the beginning and end of a reference signal, or may continuously be generated. 
     While the invention has been described in detail, the foregoing description is in all aspects illustrative and not restrictive. It is understood that numerous other modifications and variations can be devised without departing from the scope of the invention.