Abstract:
A device for compensating for a mismatch of a transmitter and a method of compensating for the mismatch is provided. The device for compensating for a mismatch of an up-converter in a direct conversion transmitter, comprises: a mismatch compensating unit for compensating for an input signal using a first mismatch compensation value to generate a mismatch compensation signal; a down-converter for down-converting a radio frequency (RF) signal to generate an intermediate frequency (IF) signal, the RF signal being generated by up-converting the mismatch compensation signal; a square unit for squaring the IF signal; and a controller for calibrating the first mismatch compensation value to determine a second mismatch compensation value such that a direct current (DC) component of the squared IF signal has a minimum value to compensate for the mismatch of the up-converter using the second mismatch compensation value.

Description:
CROSS-REFERENCE TO RELATED APPLICATION 
   This application claims priority to Korean Patent Application No. 2003-49030 filed on Jul. 18, 2003, the contents of which are incorporated herein by reference. 
   BACKGROUND OF THE INVENTION 
   1. Technical Field 
   The present invention relates to a device for compensating for a mismatch of a transmitter and a method of compensating for the mismatch, and more particularly, to a device and method for compensating for a mismatch of a transmitter that occurs when up-converting a direct conversion transmitter. 
   2. Discussion of the Related Art 
   In a communication device using heterodyne conversion, baseband signals are converted to radio frequency (RF) signals, and vice versa via a plurality of stages of intermediate frequency (IF) signals. The communication device using the heterodyne conversion utilizes a number of RF components such as a SAW (Surface Acoustic Wave) filter and an IF amplifier to reduce the cost and weight of the communication device. 
   In the communication device using direct conversion, baseband signals are converted to RF signals, and vice versa in a single step without an RF to IF conversion step. Thus, in such a communication device, for example, a mobile phone, the mobile phone&#39;s receiver or transmitter may be implemented using a small number of components or in a single chip. In addition, leaked local oscillation signals may be mixed between closely spaced circuit components, and high direct current (DC) offset levels may exist due to a mismatch of the transmitter or the receiver in such communication devices. 
   As a DC offset cancellation circuit for a direct conversion receiver has been disclosed in Korean Laid-Open Patent Publication No. 2003-0034472, there still exists a need for a DC offset cancellation circuit for use with a direct conversion transmitter. 
   SUMMARY OF THE INVENTION 
   According to one aspect of the present invention, a device for estimating a mismatch of a transmitter comprising an up-converter comprises: a mismatch compensating unit for receiving a first in-phase signal and a first quadrature-phase signal to generate a mismatch compensation signal using a mismatch compensation value; a down-converter for mixing a radio frequency (RF) signal with an oscillating signal to generate a second in-phase signal and a second quadrature-phase signal, wherein an up-converter generates the RF signal using the mismatch compensation signal; a first square unit for squaring the second in-phase signal; a second square unit for squaring the second quadrature-phase signal; a first adder for adding an output of the first square unit to an output of the second square unit; and a low pass filter for filtering an output of the first adder to generate an estimated mismatch value, wherein the mismatch compensation value is used to minimize the estimated mismatch value. The up-converter may be a direct up-converter. 
   The down-converter comprises a first local oscillator for generating a first oscillating signal; a first mixer for mixing the RF signal with the first oscillating signal to generate an intermediate frequency (IF) signal; a second low pass filter for filtering an output of the first mixer; a second local oscillator for generating a second oscillating signal; and a second mixer for mixing an output of the second low pass filter with the second oscillating signal to generate a second in-phase signal and a second quadrature-phase signal. 
   According to another aspect of the present invention, a method of compensating for a mismatch of a transmitter having a direct up-converter comprises: adjusting a phase and a gain of a first in-phase signal and a first quadrature-phase signal using a first mismatch compensation value to generate a mismatch compensation signal; up-converting the mismatch compensation signal to generate an RF signal; down-converting the RF signal to generate a second in-phase signal and a second quadrature-phase signal; squaring the second in-phase signal and the second quadrature-phase signal, to add the squared second in-phase signal to the squared second quadrature-phase signal, and to generate an estimated mismatch value; and generating a second mismatch compensation value that is determined such that the estimated mismatch value has a minimum value to compensate for the mismatch of the transmitter using the second mismatch compensation value. 
   According to yet another aspect of the present invention, a method of compensating for a mismatch of an up-converter comprises: compensating for an input signal using a first mismatch compensation value to generate a mismatch compensation signal; up-converting the mismatch compensation signal to generate an RF signal; down-converting the RF signal to generate an IF signal; squaring the IF signal; and repeating the above steps by changing the first mismatch compensation value to determine a second mismatch compensation value such that a direct current (DC) component of the squared IF signal has a minimum value, and to compensate for the mismatch of the up-converter using the second mismatch compensation value. 
   The first mismatch compensation value comprises a phase value or a gain value. The input signal comprises a first in-phase signal and a first quadrature-phase signal. Generating the mismatch compensation signal also comprises shifting a phase value of the first quadrature-phase signal based on a phase value of the first mismatch compensation value to generate a third quadrature-phase signal having a lead phase with respect to the first quadrature-phase signal; shifting the phase of the first quadrature-phase signal based on the phase value of the first mismatch compensation value to generate a fourth quadrature-phase signal having a delay phase with respect to the first quadrature-phase signal; adding the first in-phase signal to the third quadrature-phase signal to generate a first mismatch compensation signal; and obtaining a difference between the first in-phase signal and the fourth quadrature-phase signal to generate a second mismatch compensation signal. Generating the mismatch compensation signal further comprises amplifying the second mismatch compensation signal using the gain value of the first mismatch compensation value. 
   According to yet another aspect of the present invention, a device for compensating for a mismatch of an up-converter comprises: a mismatch compensating unit for compensating for an input signal using a first mismatch compensation value to generate a mismatch compensation signal; a down-converter for down-converting an RF signal to generate an IF signal, the RF signal being generated by up-converting the mismatch compensation signal; a square unit for squaring the IF signal; and a controller for calibrating the first mismatch compensation value to determine a second mismatch compensation value such that a DC component of the squared IF signal has a minimum value in order to compensate for the mismatch of the up-converter using the second mismatch compensation value. 
   The input signal comprises a first in-phase signal and a first quadrature-phase signal. The mismatch compensating unit further comprises: a first phase shifter for shifting a phase of the first quadrature-phase signal based on the phase value of the first mismatch compensation value to generate a third quadrature-phase signal having a lead phase with respect to the first quadrature-phase signal; a second phase shifter for shifting the phase of the first quadrature-phase signal based on the phase value of the first mismatch compensation value to generate a fourth quadrature-phase signal having a delay phase with respect to the first quadrature-phase signal; a first adder for adding the first in-phase signal to the third quadrature-phase signal to generate a first mismatch compensation signal; and a subtractor for obtaining a difference between the first in-phase signal and the fourth quadrature-phase signal to generate a second mismatch compensation signal. 
   The device further comprises an amplifier for amplifying the second mismatch compensation signal using the gain value of the first mismatch compensation value. The down-converter comprises: a first mixer for mixing mix the RF signal with a first oscillating signal to generate a first IF signal; a first low pass filter for filtering the first IF signal; and a second mixer for mixing an output of the second low pass filter with a second oscillating signal to generate a pair of second IF signals, the second IF signals being orthogonal each other. The square unit comprises: a first square unit for squaring one of the second IF signals; a second square unit for squaring one of the second IF signals; a second adder for adding an output of the first square unit to an output of the second square unit; and a second low pass filter for filtering an output of the first adder to extract a DC component from the output of the first adder. 

   
     BRIEF DESCRIPTION OF THE DRAWINGS 
     The features of the present invention will become more apparent by describing in detail exemplary embodiments thereof with reference to the accompanying drawings, in which: 
       FIG. 1  illustrates an up-converter for estimating a mismatch of the up-converter according to an exemplary embodiment of the present invention; 
       FIG. 2  illustrates a mismatch compensating unit according to another exemplary embodiment of the present invention; 
       FIG. 3  is a block diagram showing a direct conversion transmitter having the mismatch compensating unit according to an exemplary embodiment of the present invention; and 
       FIG. 4  is a flowchart showing a method of estimating the mismatch of the up-converter according to an exemplary embodiment of the present invention. 
   

   DETAILED DESCRIPTION OF EXEMPLARY EMBODIMENTS 
     FIG. 1  illustrates an up-converter for estimating a mismatch of the up-converter according to an exemplary embodiment of the present invention,  FIG. 2  illustrates a mismatch compensating unit according to another exemplary embodiment of the present invention, and  FIG. 3  is a block diagram showing a direct conversion transmitter having the mismatch compensating unit according to an exemplary embodiment of the present invention. 
   Referring to  FIG. 1 , an up-converter  10  of a direct conversion transmitter includes a mismatch compensation value inserting unit  20 , a mismatch estimating unit  30  and a compensating unit  49 . The up-converter  10  mixes baseband signals such as an in-phase (I) signal and a quadrature-phase (Q) signal with a local oscillating signal LO, and up-converts the baseband signals to a radio frequency (RF) signal. A mismatch of the up-converter  10  is estimated and the mismatch of the up-converter  10  is compensated based on an estimated mismatch value in order to reduce signal distortion due to the mismatch of the up-converter  10 . 
   A single tone baseband signal, into which a mismatch compensation value (or sweep variable) is inserted, is applied to the up-converter  10  via the mismatch compensation value inserting unit  20 . The up-converter  10  mixes the local oscillating signal LO supplied from a local oscillator with mismatch compensation signals IF 3 _I(t) and IF 3 _Q(t) (shown in  FIG. 2 ) using a mixer, and up-converts the mixed result to generate an RF signal RF(t) (shown in  FIG. 3 ). 
   The mismatch estimating unit  30  down-converts the RF(t) signal, and estimates an estimated mismatch value such as a gain mismatch value and a phase mismatch value. The compensating unit  49  calibrates and compensates for the mismatch of the up-converter  10  based on the estimated mismatch value. 
   As shown in  FIG. 2 , when the up-converter  10  receives the baseband signals such as the in-phase (I) signal and the quadrature-phase (Q) signal, an adder  26  adds the in-phase (I) signal to a quadrature-phase (Q′) signal to provide the added signal to the up-converter  10 , and a subtractor  28  obtains a difference between the in-phase (I) signal and a quadrature-phase (Q″) signal. An output of the subtractor  28  is amplified by an amplifier  29  (having a gain=1+ΔA 2 ) and is provided to the up-converter  10 . In this case, the quadrature-phase (Q′) signal has a lead phase with respect to the Q signal by φ ε2 , and the quadrature-phase (Q″) signal has a delay phase with respect to the Q signal by φ ε2 . ΔA 2  is a gain mismatch compensation value, and φ ε2  is a phase mismatch compensation value. 
   The up-converter  10  receives outputs from the adder  26  and the subtractor  28 , and mixes the outputs of the adder  26  and the subtractor  28  with the local oscillating signal LO to generate the RF signal whose frequency corresponds to the sum of the output signal of the adder  26  (or the subtractor  28 ) and the local oscillating signal LO, or whose frequency corresponds to the frequency difference between the output signal of the adder  26  (or the subtractor  28 ) and the local oscillating signal LO. The RF signal output from the up-converter  10  is passed through a band pass filter and an amplifier (not shown) and is radiated from an antenna (not shown). 
   The RF signal output from the up-converter  10  is input to the mismatch estimating unit  30  to estimate the mismatch of the up-converter  10 . The compensating unit  49  receives the estimated mismatch value and compensates the mismatch of the up-converter  10  using the estimated mismatch value. 
   Referring to  FIG. 3 , a direct conversion transmitter  100  is coupled to a mismatch estimating &amp; compensating unit  200 . The mismatch estimating &amp; compensating unit  200  includes a mismatch compensating unit  210 , a down-converter  220 , a square unit  230  and a control unit  240 . 
   The mismatch compensating unit  210  includes an adder  212 , a subtractor  214 , a first phase shifter  216 , a second phase shifter  218  and an amplifier  219 . The down-converter  220  includes first and second mixers  221  and  224 , first and second local oscillators  222  and  226 , and a low pass filter  223 . 
   The controller  240  receives a direct current (DC) component from the square unit  230  and controls the first and second phase shifters  216  and  218 , the amplifier  219 , and the local oscillator LO 1   120  of the direct conversion transmitter  100 . 
   The first mixer  221  of the down-converter  220  mixes a local oscillating signal ω L03  with the RF signal output from the transmitter  100  to generate an IF signal IF 4 (t). The low pass filter  223  removes unnecessary high frequency signals from the output signals of the first mixer  221 . The second mixer  224  mixes a local oscillating signal ω L04  with the low pass filtered signal output from the low pass filter  223  to generate IF signals IF 2 (t) such as an in-phase (I) signal IF 2 _I(t)  227  and an quadrature-phase (Q) signal IF 2 _Q(t)  228 . 
   A first square unit  232  squares the in-phase (I) signal IF 2 _I(t)  227 , and a second square unit  234  squares the quadrature-phase (Q) signal IF 2 _Q(t)  228 . An adder  236  adds an output of the first square unit  232  to an output of the second square unit  234 . A low pass filter  238  low pass filters an output of the adder  236  to extract a DC component from the output of the adder  236 , and provides the extracted DC component to the controller  240 . 
   The in-phase (I) signal and quadrature-phase (Q) signal input to the direct conversion transmitter  100  are defined as Equation 1.
 
 I ( t )=cos(ω IF3   t ),  Q ( t )=sin(ω IF3   t )  Equation 1
 
   When the in-phase (I) signal and quadrature-phase (Q) signal are treated with the gain mismatch compensation value ΔA 2  and the phase mismatch compensation value φ ε2 , the mismatch compensation signals IF 3 _I(t) and IF 3 _Q(t) are defined as Equation 2. 
   
     
       
         
           
             
               
                 
                   
                     
                       
                         IF3_I 
                         ⁢ 
                         
                           ( 
                           t 
                           ) 
                         
                       
                       = 
                       
                         
                           1 
                           2 
                         
                         ⁡ 
                         
                           [ 
                           
                             
                               cos 
                               ⁡ 
                               
                                 ( 
                                 
                                   
                                     ω 
                                     IF3 
                                   
                                   ⁢ 
                                   t 
                                 
                                 ) 
                               
                             
                             + 
                             
                               sin 
                               ⁡ 
                               
                                 ( 
                                 
                                   
                                     
                                       ω 
                                       IF3 
                                     
                                     ⁢ 
                                     t 
                                   
                                   + 
                                   
                                     ϕ 
                                     ɛ2 
                                   
                                 
                                 ) 
                               
                             
                           
                           ] 
                         
                       
                     
                   
                 
                 
                   
                     
                       
                         IF3_Q 
                         ⁢ 
                         
                           ( 
                           t 
                           ) 
                         
                       
                       = 
                       
                         
                           
                             1 
                             2 
                           
                           ⁡ 
                           
                             [ 
                             
                               
                                 sin 
                                 ⁡ 
                                 
                                   ( 
                                   
                                     
                                       
                                         ω 
                                         IF3 
                                       
                                       ⁢ 
                                       t 
                                     
                                     - 
                                     
                                       ϕ 
                                       ɛ2 
                                     
                                   
                                   ) 
                                 
                               
                               - 
                               
                                 cos 
                                 ⁡ 
                                 
                                   ( 
                                   
                                     
                                       ω 
                                       IF3 
                                     
                                     ⁢ 
                                     t 
                                   
                                   ) 
                                 
                               
                             
                             ] 
                           
                         
                         ⁢ 
                         
                           ( 
                           
                             1 
                             + 
                             
                               Δ 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               
                                 A 
                                 2 
                               
                             
                           
                           ) 
                         
                       
                     
                   
                 
               
             
             
               
                 Equation 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 2 
               
             
           
         
       
     
   
   When ω SP =ω LO1 +ω IF3  and ω data =ω LO1 −ω IF3 , the RF signal RF(t) is defined as Equation 3. 
   
     
       
         
           
             
               
                 
                   
                     
                       
                         RF 
                         ⁡ 
                         
                           ( 
                           t 
                           ) 
                         
                       
                       = 
                         
                       ⁢ 
                       
                         
                           
                             1 
                             4 
                           
                           ⁢ 
                           
                             
                               ( 
                               
                                 1 
                                 + 
                                 
                                   Δ 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   
                                     A 
                                     1 
                                   
                                 
                               
                               ) 
                             
                             ⁡ 
                             
                               [ 
                               
                                 
                                   cos 
                                   ⁡ 
                                   
                                     ( 
                                     
                                       
                                         ω 
                                         SP 
                                       
                                       ⁢ 
                                       t 
                                     
                                     ) 
                                   
                                 
                                 + 
                                 
                                   sin 
                                   ⁡ 
                                   
                                     ( 
                                     
                                       
                                         
                                           ω 
                                           SP 
                                         
                                         ⁢ 
                                         t 
                                       
                                       + 
                                       
                                         ϕ 
                                         ɛ2 
                                       
                                     
                                     ) 
                                   
                                 
                               
                               ] 
                             
                           
                         
                         + 
                       
                     
                   
                 
                 
                   
                     
                         
                       ⁢ 
                       
                         
                           1 
                           4 
                         
                         ⁢ 
                         
                           
                             ( 
                             
                               1 
                               + 
                               
                                 Δ 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 
                                   A 
                                   2 
                                 
                               
                             
                             ) 
                           
                           [ 
                           
                             
                               - 
                               
                                 cos 
                                 ⁡ 
                                 
                                   ( 
                                   
                                     
                                       
                                         ω 
                                         SP 
                                       
                                       ⁢ 
                                       t 
                                     
                                     + 
                                     
                                       ϕ 
                                       ɛ1 
                                     
                                     - 
                                     
                                       ϕ 
                                       ɛ2 
                                     
                                   
                                   ) 
                                 
                               
                             
                             - 
                           
                         
                       
                     
                   
                 
                 
                   
                     
                       
                           
                         ⁢ 
                         
                           sin 
                           ⁢ 
                           
                             ( 
                             
                               
                                 
                                   ω 
                                   SP 
                                 
                                 ⁢ 
                                 t 
                               
                               + 
                               
                                 ϕ 
                                 ɛ2 
                               
                             
                             ) 
                           
                         
                         ] 
                       
                       + 
                     
                   
                 
                 
                   
                     
                         
                       ⁢ 
                       
                         
                           
                             1 
                             4 
                           
                           ⁢ 
                           
                             
                               ( 
                               
                                 1 
                                 + 
                                 
                                   Δ 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   
                                     A 
                                     1 
                                   
                                 
                               
                               ) 
                             
                             ⁡ 
                             
                               [ 
                               
                                 
                                   cos 
                                   ⁡ 
                                   
                                     ( 
                                     
                                       
                                         ω 
                                         data 
                                       
                                       ⁢ 
                                       t 
                                     
                                     ) 
                                   
                                 
                                 - 
                                 
                                   sin 
                                   ⁡ 
                                   
                                     ( 
                                     
                                       
                                         
                                           ω 
                                           data 
                                         
                                         ⁢ 
                                         t 
                                       
                                       - 
                                       
                                         ϕ 
                                         ɛ2 
                                       
                                     
                                     ) 
                                   
                                 
                               
                               ] 
                             
                           
                         
                         + 
                       
                     
                   
                 
                 
                   
                     
                         
                       ⁢ 
                       
                         
                           1 
                           4 
                         
                         ⁢ 
                         
                           
                             ( 
                             
                               1 
                               + 
                               
                                 Δ 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 
                                   A 
                                   2 
                                 
                               
                             
                             ) 
                           
                           [ 
                           
                             
                               cos 
                               ⁡ 
                               
                                 ( 
                                 
                                   
                                     
                                       ω 
                                       data 
                                     
                                     ⁢ 
                                     t 
                                   
                                   + 
                                   
                                     ϕ 
                                     ɛ1 
                                   
                                   - 
                                   
                                     ϕ 
                                     ɛ2 
                                   
                                 
                                 ) 
                               
                             
                             - 
                           
                         
                       
                     
                   
                 
                 
                   
                     
                         
                       ⁢ 
                       
                         sin 
                         ⁢ 
                         
                           ( 
                           
                             
                               
                                 ω 
                                 SP 
                               
                               ⁢ 
                               t 
                             
                             + 
                             
                               ϕ 
                               ɛ1 
                             
                           
                           ) 
                         
                       
                       ] 
                     
                   
                 
               
             
             
               
                 Equation 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 3 
               
             
           
         
       
     
   
   As shown in Equation 3, ΔA 1  is a gain mismatching value of the transmitter  100 , and φ ε1  is a phase mismatching value of the transmitter  100 . 
   Because a mixer of the up-converter  110  outputs the sum frequency (ω LO1 +ω IF3 ) signal and the difference frequency (ω LO1 −ω IF3 ) signal, only the sum frequency (ω LO1 +ω IF3 ) signal is selected by a band pass filter (not shown) and is provided to the down-converter  220  as the RF signal. 
   The IF 4  (t) signal is defined as Equation 4 shown below. When the first mixer  221  uses the local oscillating signal (ω LO3 ), the mixer  221  outputs a sum frequency (ω LO3 +ω SP ) sp) signal and a difference frequency (ω LO3 −ω SP ) signal, and the low pass filter  223  selects the difference frequency (ω LO3 −ω SP ) signal. 
   
     
       
         
           
             
               
                 
                   
                     
                       
                         IF4 
                         ⁡ 
                         
                           ( 
                           t 
                           ) 
                         
                       
                       = 
                         
                       ⁢ 
                       
                         
                           
                             1 
                             8 
                           
                           ⁢ 
                           
                             
                               ( 
                               
                                 1 
                                 + 
                                 
                                   Δ 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   
                                     A 
                                     1 
                                   
                                 
                               
                               ) 
                             
                             ⁡ 
                             
                               [ 
                               
                                 
                                   cos 
                                   ⁡ 
                                   
                                     ( 
                                     
                                       
                                         ω 
                                         IF4 
                                       
                                       ⁢ 
                                       t 
                                     
                                     ) 
                                   
                                 
                                 + 
                                 
                                   sin 
                                   ⁡ 
                                   
                                     ( 
                                     
                                       
                                         
                                           ω 
                                           IF4 
                                         
                                         ⁢ 
                                         t 
                                       
                                       + 
                                       
                                         ϕ 
                                         ɛ2 
                                       
                                     
                                     ) 
                                   
                                 
                               
                               ] 
                             
                           
                         
                         + 
                       
                     
                   
                 
                 
                   
                     
                         
                       ⁢ 
                       
                         
                           1 
                           8 
                         
                         ⁢ 
                         
                           
                             ( 
                             
                               1 
                               + 
                               
                                 Δ 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 
                                   A 
                                   2 
                                 
                               
                             
                             ) 
                           
                           [ 
                           
                             
                               - 
                               
                                 cos 
                                 ⁡ 
                                 
                                   ( 
                                   
                                     
                                       
                                         ω 
                                         IF4 
                                       
                                       ⁢ 
                                       t 
                                     
                                     + 
                                     
                                       ϕ 
                                       ɛ1 
                                     
                                     - 
                                     
                                       ϕ 
                                       ɛ2 
                                     
                                   
                                   ) 
                                 
                               
                             
                             - 
                           
                         
                       
                     
                   
                 
                 
                   
                     
                         
                       ⁢ 
                       
                         sin 
                         ⁢ 
                         
                           ( 
                           
                             
                               
                                 ω 
                                 IF4 
                               
                               ⁢ 
                               t 
                             
                             + 
                             
                               ϕ 
                               ɛ1 
                             
                           
                           ) 
                         
                       
                       ] 
                     
                   
                 
               
             
             
               
                 Equation 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 4 
               
             
           
         
       
     
   
   When the second mixer uses the local oscillating signal (ω LO4 ) and when ω IF4 −ω LO4 =ω IF2 ), the IF 2 _I(t) signal  227  and IF 2 _Q(t) signal  228  are defined as Equation 5. 
   
     
       
         
           
             
               
                 
                   
                     
                       
                         
                           
                             
                               IF2_I 
                               ⁢ 
                               
                                 ( 
                                 t 
                                 ) 
                               
                             
                             = 
                               
                             ⁢ 
                             
                               
                                 
                                   1 
                                   16 
                                 
                                 ⁢ 
                                 
                                   
                                     ( 
                                     
                                       1 
                                       + 
                                       
                                         Δ 
                                         ⁢ 
                                         
                                             
                                         
                                         ⁢ 
                                         
                                           A 
                                           1 
                                         
                                       
                                     
                                     ) 
                                   
                                   ⁡ 
                                   
                                     [ 
                                     
                                       
                                         cos 
                                         ⁡ 
                                         
                                           ( 
                                           
                                             
                                               ω 
                                               IF2 
                                             
                                             ⁢ 
                                             t 
                                           
                                           ) 
                                         
                                       
                                       + 
                                       
                                         sin 
                                         ⁡ 
                                         
                                           ( 
                                           
                                             
                                               
                                                 ω 
                                                 IF2 
                                               
                                               ⁢ 
                                               t 
                                             
                                             + 
                                             
                                               ϕ 
                                               ɛ2 
                                             
                                           
                                           ) 
                                         
                                       
                                     
                                     ] 
                                   
                                 
                               
                               + 
                             
                           
                         
                       
                       
                         
                           
                               
                             ⁢ 
                             
                               
                                 1 
                                 16 
                               
                               ⁢ 
                               
                                 
                                   ( 
                                   
                                     1 
                                     + 
                                     
                                       Δ 
                                       ⁢ 
                                       
                                           
                                       
                                       ⁢ 
                                       
                                         A 
                                         2 
                                       
                                     
                                   
                                   ) 
                                 
                                 [ 
                                 
                                   
                                     - 
                                     
                                       cos 
                                       ⁡ 
                                       
                                         ( 
                                         
                                           
                                             
                                               ω 
                                               IF2 
                                             
                                             ⁢ 
                                             t 
                                           
                                           + 
                                           
                                             ϕ 
                                             ɛ1 
                                           
                                           - 
                                           
                                             ϕ 
                                             ɛ2 
                                           
                                         
                                         ) 
                                       
                                     
                                   
                                   - 
                                 
                               
                             
                           
                         
                       
                       
                         
                           
                               
                             ⁢ 
                             
                               sin 
                               ⁡ 
                               
                                 ( 
                                 
                                   
                                     
                                       ω 
                                       IF2 
                                     
                                     ⁢ 
                                     t 
                                   
                                   + 
                                   
                                     ϕ 
                                     ɛ1 
                                   
                                 
                                 ) 
                               
                             
                             ] 
                           
                         
                       
                     
                   
                 
                 
                   
                     
                       
                         
                           
                             
                               IF2_Q 
                               ⁢ 
                               
                                 ( 
                                 t 
                                 ) 
                               
                             
                             = 
                               
                             ⁢ 
                             
                               
                                 
                                   1 
                                   16 
                                 
                                 ⁢ 
                                 
                                   
                                     ( 
                                     
                                       1 
                                       + 
                                       
                                         Δ 
                                         ⁢ 
                                         
                                             
                                         
                                         ⁢ 
                                         
                                           A 
                                           1 
                                         
                                       
                                     
                                     ) 
                                   
                                   ⁡ 
                                   
                                     [ 
                                     
                                       
                                         sin 
                                         ⁡ 
                                         
                                           ( 
                                           
                                             
                                               ω 
                                               IF2 
                                             
                                             ⁢ 
                                             t 
                                           
                                           ) 
                                         
                                       
                                       + 
                                       
                                         cos 
                                         ⁡ 
                                         
                                           ( 
                                           
                                             
                                               
                                                 ω 
                                                 IF2 
                                               
                                               ⁢ 
                                               t 
                                             
                                             + 
                                             
                                               ϕ 
                                               ɛ2 
                                             
                                           
                                           ) 
                                         
                                       
                                     
                                     ] 
                                   
                                 
                               
                               + 
                             
                           
                         
                       
                       
                         
                           
                               
                             ⁢ 
                             
                               
                                 1 
                                 16 
                               
                               ⁢ 
                               
                                 
                                   ( 
                                   
                                     1 
                                     + 
                                     
                                       Δ 
                                       ⁢ 
                                       
                                           
                                       
                                       ⁢ 
                                       
                                         A 
                                         2 
                                       
                                     
                                   
                                   ) 
                                 
                                 [ 
                                 
                                   
                                     - 
                                     
                                       sin 
                                       ⁡ 
                                       
                                         ( 
                                         
                                           
                                             
                                               ω 
                                               IF2 
                                             
                                             ⁢ 
                                             t 
                                           
                                           + 
                                           
                                             ϕ 
                                             ɛ1 
                                           
                                           - 
                                           
                                             ϕ 
                                             ɛ2 
                                           
                                         
                                         ) 
                                       
                                     
                                   
                                   - 
                                 
                               
                             
                           
                         
                       
                       
                         
                           
                               
                             ⁢ 
                             
                               cos 
                               ⁡ 
                               
                                 ( 
                                 
                                   
                                     
                                       ω 
                                       IF2 
                                     
                                     ⁢ 
                                     t 
                                   
                                   + 
                                   
                                     ϕ 
                                     ɛ1 
                                   
                                 
                                 ) 
                               
                             
                             ] 
                           
                         
                       
                     
                   
                 
               
             
             
               
                 Equation 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 5 
               
             
           
         
       
     
   
   The IF 2 _I(t) signal  227  and IF 2 _Q(t) signal  228  are squared by the square units  232  and  234 , respectively, are added each other by the adder  236 , is low pass filtered by the low pass filter  238 , and the estimated mismatch value is defined as Equation 6. 
   
     
       
         
           
             
               
                 
                   squaring 
                   ⁡ 
                   
                     ( 
                     
                       
                         IF2_I 
                         2 
                       
                       + 
                       
                         IF2_Q 
                         2 
                       
                     
                     ) 
                   
                 
                 = 
                 
                   
                     
                       
                         1 
                         
                           16 
                           2 
                         
                       
                       ⁢ 
                       
                         
                           { 
                           
                             
                               
                                 
                                   [ 
                                   
                                     
                                       
                                         ( 
                                         
                                           1 
                                           + 
                                           
                                             Δ 
                                             ⁢ 
                                             
                                                 
                                             
                                             ⁢ 
                                             
                                               A 
                                               1 
                                             
                                           
                                         
                                         ) 
                                       
                                       ⁢ 
                                       
                                         cos 
                                         ⁡ 
                                         
                                           ( 
                                           
                                             Δ 
                                             ⁢ 
                                             
                                                 
                                             
                                             ⁢ 
                                             ω 
                                             ⁢ 
                                             
                                                 
                                             
                                             ⁢ 
                                             t 
                                           
                                           ) 
                                         
                                       
                                     
                                     - 
                                     
                                       ( 
                                       
                                         1 
                                         + 
                                         
                                           Δ 
                                           ⁢ 
                                           
                                               
                                           
                                           ⁢ 
                                           
                                             A 
                                             2 
                                           
                                         
                                       
                                       ) 
                                     
                                   
                                 
                               
                             
                             
                               
                                 
                                   
                                     
                                       cos 
                                       ⁢ 
                                       
                                         ( 
                                         
                                           
                                             Δ 
                                             ⁢ 
                                             
                                                 
                                             
                                             ⁢ 
                                             ω 
                                             ⁢ 
                                             
                                                 
                                             
                                             ⁢ 
                                             t 
                                           
                                           + 
                                           
                                             ϕ 
                                             ɛ1 
                                           
                                           - 
                                           
                                             ϕ 
                                             ɛ2 
                                           
                                         
                                         ) 
                                       
                                     
                                     ] 
                                   
                                   + 
                                 
                               
                             
                             
                               
                                 
                                   [ 
                                   
                                     
                                       
                                         ( 
                                         
                                           1 
                                           + 
                                           
                                             Δ 
                                             ⁢ 
                                             
                                                 
                                             
                                             ⁢ 
                                             
                                               A 
                                               1 
                                             
                                           
                                         
                                         ) 
                                       
                                       ⁢ 
                                       
                                         sin 
                                         ⁡ 
                                         
                                           ( 
                                           
                                             
                                               Δ 
                                               ⁢ 
                                               
                                                   
                                               
                                               ⁢ 
                                               ω 
                                               ⁢ 
                                               
                                                   
                                               
                                               ⁢ 
                                               t 
                                             
                                             + 
                                             
                                               ϕ 
                                               ɛ2 
                                             
                                           
                                           ) 
                                         
                                       
                                     
                                     - 
                                     
                                       
                                         ( 
                                         
                                           1 
                                           + 
                                           
                                             Δ 
                                             ⁢ 
                                             
                                                 
                                             
                                             ⁢ 
                                             
                                               A 
                                               2 
                                             
                                           
                                         
                                         ) 
                                       
                                       ⁢ 
                                       
                                         sin 
                                         ⁡ 
                                         
                                           ( 
                                           
                                             
                                               Δ 
                                               ⁢ 
                                               
                                                   
                                               
                                               ⁢ 
                                               ω 
                                               ⁢ 
                                               
                                                   
                                               
                                               ⁢ 
                                               t 
                                             
                                             + 
                                             
                                               ϕ 
                                               ɛ1 
                                             
                                           
                                           ) 
                                         
                                       
                                     
                                   
                                   ] 
                                 
                               
                             
                           
                           } 
                         
                         2 
                       
                     
                     + 
                     
                       
                         1 
                         
                           16 
                           2 
                         
                       
                       ⁢ 
                       
                         
                           { 
                           
                             
                               
                                 
                                   [ 
                                   
                                     
                                       
                                         ( 
                                         
                                           1 
                                           + 
                                           
                                             Δ 
                                             ⁢ 
                                             
                                                 
                                             
                                             ⁢ 
                                             
                                               A 
                                               1 
                                             
                                           
                                         
                                         ) 
                                       
                                       ⁢ 
                                       
                                         sin 
                                         ⁡ 
                                         
                                           ( 
                                           
                                             Δ 
                                             ⁢ 
                                             
                                                 
                                             
                                             ⁢ 
                                             ω 
                                             ⁢ 
                                             
                                                 
                                             
                                             ⁢ 
                                             t 
                                           
                                           ) 
                                         
                                       
                                     
                                     - 
                                     
                                       ( 
                                       
                                         1 
                                         + 
                                         
                                           Δ 
                                           ⁢ 
                                           
                                               
                                           
                                           ⁢ 
                                           
                                             A 
                                             2 
                                           
                                         
                                       
                                       ) 
                                     
                                   
                                 
                               
                             
                             
                               
                                 
                                   
                                     
                                       sin 
                                       ⁡ 
                                       
                                         ( 
                                         
                                           
                                             Δ 
                                             ⁢ 
                                             
                                                 
                                             
                                             ⁢ 
                                             ω 
                                             ⁢ 
                                             
                                                 
                                             
                                             ⁢ 
                                             t 
                                           
                                           + 
                                           
                                             ϕ 
                                             ɛ1 
                                           
                                           - 
                                           
                                             ϕ 
                                             ɛ2 
                                           
                                         
                                         ) 
                                       
                                     
                                     ] 
                                   
                                   + 
                                 
                               
                             
                             
                               
                                 
                                   [ 
                                   
                                     
                                       
                                         ( 
                                         
                                           1 
                                           + 
                                           
                                             Δ 
                                             ⁢ 
                                             
                                                 
                                             
                                             ⁢ 
                                             
                                               A 
                                               1 
                                             
                                           
                                         
                                         ) 
                                       
                                       ⁢ 
                                       
                                         cos 
                                         ⁡ 
                                         
                                           ( 
                                           
                                             
                                               Δ 
                                               ⁢ 
                                               
                                                   
                                               
                                               ⁢ 
                                               ω 
                                               ⁢ 
                                               
                                                   
                                               
                                               ⁢ 
                                               t 
                                             
                                             + 
                                             
                                               ϕ 
                                               ɛ2 
                                             
                                           
                                           ) 
                                         
                                       
                                     
                                     - 
                                     
                                       
                                         ( 
                                         
                                           1 
                                           + 
                                           
                                             Δ 
                                             ⁢ 
                                             
                                                 
                                             
                                             ⁢ 
                                             
                                               A 
                                               2 
                                             
                                           
                                         
                                         ) 
                                       
                                       ⁢ 
                                       
                                         cos 
                                         ⁡ 
                                         
                                           ( 
                                           
                                             
                                               Δ 
                                               ⁢ 
                                               
                                                   
                                               
                                               ⁢ 
                                               ω 
                                               ⁢ 
                                               
                                                   
                                               
                                               ⁢ 
                                               t 
                                             
                                             + 
                                             
                                               ϕ 
                                               ɛ1 
                                             
                                           
                                           ) 
                                         
                                       
                                     
                                   
                                   ] 
                                 
                               
                             
                           
                           } 
                         
                         2 
                       
                     
                   
                   ≡ 
                   
                     
                       1 
                       
                         16 
                         2 
                       
                     
                     ⁡ 
                     
                       [ 
                       
                         
                           
                             ( 
                             
                               
                                 Δ 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 
                                   A 
                                   1 
                                 
                               
                               - 
                               
                                 Δ 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 
                                   A 
                                   2 
                                 
                               
                             
                             ) 
                           
                           2 
                         
                         + 
                         
                           
                             ( 
                             
                               
                                 ϕ 
                                 ɛ1 
                               
                               - 
                               
                                 ϕ 
                                 ɛ2 
                               
                             
                             ) 
                           
                           2 
                         
                       
                       ] 
                     
                   
                 
               
             
             
               
                 Equation 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 6 
               
             
           
         
       
     
   
   Equation 6 shows that the gain mismatching value ΔA 1  of the transmitter  100  and the phase mismatching value φ ε1  of the transmitter  100  may be tracked using the mismatch compensation values such as the gain mismatch compensation value ΔA 2  and the phase mismatch compensation value φ ε2 . 
   When ΔA 2  and φ ε2  are set to satisfy the condition in which ΔA 1 =ΔA 2  and φ ε1 =φ ε2  so that the DC component of Equation 6 is minimized, the mismatch of the transmitter  100  is compensated. Therefore, the controller  240  changes the mismatch compensation values ΔA 2  and φ ε2  to determine the final mismatch compensation values ΔA 2 ′ and φ ε2 ′ that minimize the mismatch of the transmitter  100 . The controller  240  provides the final mismatch compensation values ΔA 2 ′ and φ ε2 ′ to the local oscillator LO 1   120 , the phase shifters  216  and  218 , and the amplifier  219 . 
     FIG. 4  is a flowchart showing a method of estimating the mismatch of the up-converter (e.g.,  10  and  110  of  FIGS. 1 and 3 ) according to an exemplary embodiment of the present invention. Referring to  FIG. 4 , mismatch compensation values ΔA 2  and φ ε2  are generated (step S 1 ), and the mismatch compensation values ΔA 2  and φ ε2  are incorporated with a single tone input signals such an in-phase (I) signal and a quadrature-phase (Q) signal, and mismatch compensation signals IF 3 _I(t) and IF 3 _Q(t) are generated (step S 2 ). The mismatch compensation signals IF 3 _I(t) and IF 3 _Q(t) are up-converted into an RF signal by the up-converter  110  of  FIG. 3  (step S 3 ). 
   The RF signal is down-converted by the down-converter  220  of  FIG. 3 , and the IF 2 _I(t) signal  227  and IF 2 _Q(t) signal  228  (both of  FIG. 3 ) are generated (step S 4 ). A DC component corresponding to the mismatch value of the transmitter  100  is obtained using the IF 2 _I(t) signal  227  and IF 2 _Q(t) signal  228  (step S 5 ). The DC component may be changed depending upon the mismatch compensation values ΔA 2  and φ ε2 . 
   The estimated mismatch value is obtained when the mismatch compensation values ΔA 2  and φ ε2  satisfy the condition in which the DC component has minimum value. It is determined if the mismatch compensation values ΔA 2  and φ ε2  satisfy the condition in which the DC component has a minimum value (step S 6 ). When the DC component does not have the minimum value, steps S 1 -S 5  are repeated. When the DC component has the minimum value, the mismatch compensation values ΔA 2  and φ ε2  are set as the estimated mismatch value (step S 7 ). The estimated mismatch value may be stored, for example, in a storage medium such as an electronically erasable programmable read only memory (EEPROM), flash memory, register, etc. 
   It is to be understood that the mismatch estimating &amp; compensating unit  200  may be implemented in the same chip as, for example, the up-converter  10  of  FIG. 1 . Alternately, the mismatch estimating &amp; compensating unit  200  may be implemented in a separate chip as the up-converter  10 . 
   While the present invention has been particularly shown and described with reference to exemplary embodiments thereof, it should be understood by those of ordinary skill in the art that various changes, substitutions and alterations can be made herein without departing from the scope of the invention as defined by appended claims and their equivalents.