Abstract:
A calibration method for radio frequency scattering parameter measurement applying three calibrators and measurement structure thereof, comprising a transmission line segment calibrator, an offset series device calibrator, an offset shunt device calibrator and a tested object measuring instrument, wherein the length of the transmission lines for the offset series device calibrator and the offset shunt device calibrator is equal to the one of the transmission line for the tested object measuring instrument such that the offset series device calibrator, the offset shunt device calibrator and the tested object measuring instrument have the identical error boxes, and after having acquired the scattering parameter matrix of the error box by means of the calibration method, it is possible to connect the tested electronic device onto the tested object measuring instrument and perform operations on uncorrected measurement data thereof thereby obtaining the radio frequency scattering parameter of the tested object.

Description:
BACKGROUND OF THE INVENTION 
       [0001]    1. Field of the Invention 
         [0002]    The present invention relates to a calibration method for radio frequency scattering parameter measurement and measurement structure thereof. In particular, the present invention relates to a calibration method for radio frequency scattering parameter measurement de-embedding and measurement structure thereof suitable for one-tier semiconductor wafer devices or other substrate devices. 
         [0003]    2. Description of Related Art 
         [0004]    Typically, it is difficult to directly measure the voltage and current of a signal in the radio frequency microwave frequency band, thus in such a frequency band, it is necessary to discuss in the form of wave with actions through incidence, reflection and absorption thereby facilitating measurements of scattering parameters thereof. Because the entire measurement system needs to perform a sequence of complicated processes, the measurement calibration is consequently required in order to improve the accuracy of measurements. Herein the measurement errors can be mathematically characterized by using an error matrix, and such errors can be roughly divided into three major categories; i.e., random, drift and system errors, among which the scattering parameter of the system error can be effectively detected by a network analyzer under a stable measurement environment, further obtaining the error thereof, thus completing the measurement calibration. 
         [0005]    In practice, the implementation procedure for such a calibration method is essentially to adjust the initial status of the instrument after startup to a user-defined actual measurement environment so as to eliminate any additional errors other than the tested object; while currently available radio frequency scattering parameter measurement for semiconductor wafer devices typically operates in a two-tier approach, comprising the following steps: 
         [0006]    1. performing calibrations on the system before starting the measurement thereby eliminating the effect caused by the measuring instrument and environment; hence it first uses a probe in conjunction with an Impedance Standard Substrate (ISS) for calibration, whose calibration method can be SOLT (Short-Open-Load-Thru) or LRM (Line-Reflect-Match), and then moves the measurement reference plane to the tip of the probe, but a small segment of connecting line exists between the probe pad and the tested device within the wafer, and the capacitive effect in the probe pad of large area may not be effectively calibrated; 
         [0007]    2. further performing calibrations on the additional dummy structure (e.g., Short, Open, Thru etc.) of the wafer so as to remove the effects caused by the pad and the connecting line, i.e., the de-embedding procedure, thus the major purpose of de-embedding is to remove the effect of the test clamping fixture from the measurement data in raw test results so as to acquire the most primitive characterization of the device. 
         [0008]    However, such a two-tier measurement approach has the following drawbacks: 
         [0009]    1. the high frequency feature of the additional dummy structure on the wafer may not be conveniently appreciated, and in case it is assumed to be an ideal feature, significant errors may be undesirably introduced at high frequency in the de-embedding process; 
         [0010]    2. the two-tier measurement consumes much the wafer probe test time, consequently, as applying to massive tests, it becomes comparatively critical; 
         [0011]    3. since the Impedance Standard Substrate (ISS) is expensive and the feature thereof may degrade after each test due to scratches on its pad caused by the probe, the substrate needs to be replaced after a certain cycles of use, thus adversely elevating the test cost. 
         [0012]    Regarding to the aforementioned drawbacks, a few literatures have proposed certain solutions therefore, including: 
         [0013]    1.  IEEE Trans. Electron Devices,  vol. 54, no. 10, pp. 2706-2714, October 2007, describing the use of a one-tier measurement for de-embedding operation at the cost of five dummy structures (Open, Short, Thru, Left, Right), so the precision thereof may be compromised in comparison with the two-tier approach. 
         [0014]    2.  IEEE Trans. Microwave Theory Tech.,  vol. 51, pp. 2391-2401, December 2003, describing a Multiline Thru-Reflect-Line (TRL) calibration method developed by NIST (National Institute of Standards and Technology), which enables completion of calibration and de-embedding process in a one-tier fashion, but presents a disadvantage of requirement on multiple transmission line segments which significantly occupies valuable wafer area. 
         [0015]    As a result, it would be an optimal solution to provide a calibration method for radio frequency scattering parameter measurement and measurement structure thereof which can perform the de-embedding process in a one-tier radio frequency scattering parameter measurement of semiconductor wafer devices or other substrate devices without using the Impedance Standard Substrate but requiring simply the application of three calibrators for operations. 
       SUMMARY OF THE INVENTION 
       [0016]    The objective of the present invention is to provide a calibration method for radio frequency scattering parameter measurement which improves the accuracy of scattering parameter measurements and uses a one-tier measurement for the de-embedding process. 
         [0017]    Another objective of the present invention is to provide a calibration method for radio frequency scattering parameter measurement which applies the L-OS-OT (Line/Offset-Series/Offset-Shunt) calibration method to perform wideband measurements and uses the known conditions offered by the calibrators to solve the same or more number of the unknown variables thereby achieving the objective of self-calibration. 
         [0018]    To achieve the aforementioned objective, a calibration method for radio frequency scattering parameter measurement and measurement structure thereof, capable of self-calibration, is provided, wherein the measurement structure for radio frequency scattering parameter comprises a transmission line segment calibrator, an offset series device calibrator, an offset shunt device calibrator and a tested object measuring instrument, wherein the length of the transmission lines for the offset series device calibrator and the offset shunt device calibrator is equal to the one of the transmission line for the tested object measuring instrument such that the offset series device calibrator, the offset shunt device calibrator and the tested object measuring instrument have the identical error boxes, and after having acquired the scattering parameter matrix of the error box by means of the calibration method, it is possible to connect the tested electronic device onto the tested object measuring instrument and perform operations on uncorrected measurement data thereof thereby obtaining the radio frequency scattering parameter of the tested object. 
         [0019]    More specifically, said calibration method for radio frequency scattering parameter measurement can remove the introduced errors during measurements, and characteristics of such errors can be expressed by means of mathematical models, in which, after measurements on the transmission line segment calibrator, the offset series device calibrator and the offset shunt device calibrator, it is possible to input into the mathematical model so as to solve all error parameters by calculations, and through repeated operations, the error value required for calibration can be obtained thereby further acquiring the parameter value of the actual tested object. 
         [0020]    More specifically, said transmission line segment calibrator comprises two transmission lines and a transmission line segment, in which the transmission line segment is connected between such two transmission lines. 
         [0021]    More specifically, said offset series device calibrator comprises two transmission lines, an offset transmission line and a series resistor, in which the offset transmission line and the series resistor are connected between the two transmission lines. 
         [0022]    More specifically, said offset shunt device calibrator comprises two transmission lines, an offset transmission line and a shunt resistor, in which the offset transmission line and the shunt resistor are connected between the two transmission lines. 
         [0023]    More specifically, the length of the transmission lines for said offset series device calibrator and offset shunt device calibrator is equal to the one of the transmission line for said tested object measuring instrument such that the offset series device calibrator, the offset shunt device calibrator and the tested object measuring instrument have the identical error boxes. 
         [0024]    More specifically, the length of the offset transmission line for said offset series device calibrator differs from the one of the offset transmission line for said offset shunt device calibrator. 
         [0025]    More specifically, said transmission line segment calibrator, offset series device calibrator, offset shunt device calibrator and tested object measuring instrument can be applied to silicon substrates, compound semiconductor substrates (GaAs, GaN, InP etc.) or ceramic/FR-4 (epoxy glass fiber board) substrates, with the microstrip or coplanar waveguide used as the connecting transmission line. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0026]      FIG. 1A  shows a structure diagram of the microstrip layout used in the calibration method for radio frequency scattering parameter measurement applying three calibrators and measurement structure thereof according to the present invention; 
           [0027]      FIG. 1B  shows a structure diagram of the coplanar waveguide layout used in the calibration method for radio frequency scattering parameter measurement applying three calibrators and measurement structure thereof according to the present invention; 
           [0028]      FIG. 2  shows an equivalent circuit diagram of the calibration method for radio frequency scattering parameter measurement applying three calibrators and measurement structure thereof according to the present invention; 
           [0029]      FIG. 3  shows a calibration operation flowchart of the calibration method for radio frequency scattering parameter measurement applying three calibrators and measurement structure thereof according to the present invention; and 
           [0030]      FIG. 4  shows a two-port network architecture diagram of the calibration method for radio frequency scattering parameter measurement applying three calibrators and measurement structure thereof according to the present invention. 
       
    
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
       [0031]    The aforementioned and other technical contents, aspects and effects in relation with the present invention can be clearly appreciated through the detailed descriptions concerning the preferred embodiments of the present invention in conjunction with the appended drawings. 
         [0032]    Refer initially to  FIGS. 1A ,  1 B and  2 , wherein a structure diagram for the microstrip layout, a structure diagram for the coplanar waveguide layout and an equivalent circuit diagram for the calibrator of the calibration method for radio frequency scattering parameter measurement according to the present invention are respectively shown, and it can be seen that the measurement structure applied in the calibration method for radio frequency scattering parameter measurement according to the present invention uses a microwave probe as the contact interface for microwave signal transmissions, and the microwave probe includes at least a ground  11  and a signal end  12 , in which the measurement structure applied in the calibration method for radio frequency scattering parameter measurement comprises: 
         [0033]    a transmission line segment calibrator  2 , in which the microwave probe (the ground  11  and the signal end  12 ) contacts the transmission line segment calibrator  2 , and the transmission line segment calibrator  2  consists of two transmission lines  21  and a transmission line segment  22 , in which the transmission line segment  22  is connected between the two transmission lines  21 , and the transmission lines  21  are connected to the signal end  12  of the microwave probe thereby performing measurements on the device characteristics of the transmission line segment  22 ; 
         [0034]    an offset series device calibrator  3 , in which the microwave probe (the ground  11  and the signal end  12 ) contacts the offset series device calibrator  3 , and the offset series device calibrator  3  consists of two transmission lines  31 , an offset transmission line  32  and a series resistor  33 , in which the offset transmission line  32  and the series resistor  33  are connected between the two transmission lines  31 , and the transmission lines  31  are connected to the signal end  12  of the microwave probe thereby performing measurements on the characteristics of the offset transmission line  32  and the series resistor  33 ; 
         [0035]    an offset shunt device calibrator  4 , in which the microwave probe (the ground  11  and the signal end  12 ) contacts the offset shunt device calibrator  4 , and the offset shunt device calibrator  4  consists of two transmission lines  41 , an offset transmission line  42  and a shunt resistor  43 , in which the offset transmission line  42  and the shunt resistor  43  are connected between the two transmission lines  41 , and the transmission lines  41  are connected to the signal end  12  of the microwave probe thereby performing measurements on the characteristics of the offset transmission line  42  and the shunt resistor  43 ; 
         [0036]    a tested object measuring instrument  5 , in which the microwave probe (the ground  11  and the signal end  12 ) contacts the tested object measuring instrument  5 , and the tested object measuring instrument  5  consists of two transmission lines  51  and a tested device  52 , in which the tested device  52  is connected between the two transmission lines  51  and the two transmission lines  51  are connected to the signal end  12  of the microwave probe thereby performing measurements on the device characteristics of the tested device  52  (the tested device is shown as an FET device in  FIGS. 1A and 1B ). 
         [0037]    It should be noted that, as shown in  FIG. 2 , the equation for the equivalent circuit of the series device calibrator  3  (where y sp  is a high frequency parasitic effect device) includes: 
         [0000]    
       
         
           
             
               z 
               ≡ 
               
                 Z 
                 
                   Z 
                   C 
                 
               
             
             , 
             
               
                 y 
                 sp 
               
               ≡ 
               
                 
                   Y 
                   sp 
                 
                 
                   Y 
                   C 
                 
               
             
             , 
             
               
                 Y 
                 C 
               
               ≡ 
               
                 1 
                 
                   Z 
                   C 
                 
               
             
             , 
           
         
       
     
         [0000]    and the equation for the equivalent circuit of the shunt device calibrator  4  (where z tp  is a high frequency parasitic effect device) includes: 
         [0000]    
       
         
           
             
               y 
               ≡ 
               
                 Y 
                 
                   Y 
                   C 
                 
               
             
             , 
             
               
                 z 
                 tp 
               
               ≡ 
               
                 
                   Z 
                   tp 
                 
                 
                   Z 
                   C 
                 
               
             
             , 
             
               
                 Y 
                 C 
               
               ≡ 
               
                 
                   1 
                   
                     Z 
                     C 
                   
                 
                 . 
               
             
           
         
       
     
         [0038]    It should be noted that the transmission lines  21  in the transmission line segment calibrator  2 , the transmission lines  31  in the offset series device calibrator  3 , the transmission lines  41  in the offset shunt device calibrator  4  and the transmission lines  51  in the tested object measuring instrument  5  have the same length, such that the transmission line segment calibrator  2 , the offset series device calibrator  3  and the offset shunt device calibrator  4  have the identical error box as the tested object measuring instrument  5 . 
         [0039]    It should be noted that the length of the offset transmission line  32  in the offset series device calibrator  3  differs from the length of the offset transmission line  42  in the offset shunt device calibrator  4 . 
         [0040]    It should be noted that the transmission line segment calibrator  2 , the offset series device calibrator  3 , the offset shunt device calibrator  4  and the tested object measuring instrument  5  can be disposed on a silicon substrate, a compound semiconductor (GaAs, GaN, InP etc.) substrate or a ceramic/FR-4 (epoxy glass fiber board) substrate. 
         [0041]    It should be noted that the transmission line segment calibrator  2 , the offset series device calibrator  3 , the offset shunt device calibrator  4  and the tested object measuring instrument  5  can use the microstrip or the coplanar waveguide as the connection transmission line, as shown in  FIG. 1A , wherein such calibrators (i.e., the transmission line segment calibrator  2 , the offset series device calibrator  3  and the offset shunt device calibrator  4 ) and the tested object measuring instrument  5  use the microstrip as the connection transmission line; and alternatively, as shown in  FIG. 1B , wherein the calibrators  2 ,  3 ,  4  and the tested object measuring instrument  5  apply the coplanar waveguide as the connection transmission line. 
         [0042]    It should be noted that the microwave probe is a high frequency probe and the type thereof can be G-S-G-S-G, G-S-S-G, G-S-G (Ground-Signal-Ground) or G-S (Ground-Signal). 
         [0043]    Refer next to  FIG. 3 , wherein an operation flowchart for the calibration in the calibration method for radio frequency scattering parameter measurement according to the present invention is shown, and it can be seen that, from the chart, the calibration method for radio frequency scattering parameter measurement can apply the known conditions provided by the calibrators to solve the same or more number of the unknown variables, in which the calibration flow for the calibration method for radio frequency scattering parameter measurement comprises the following steps: 
         [0044]    initially, setting the measurement reference impedance of the transmission line to Z C , and setting a self-calibration equation including multiple variables t (e γl ), z, y, z tp , y sp  ( 301 ) (γ indicates the propagation constant of the transmission line, l the length of the transmission line segment in the transmission line segment calibrator, p the ratio of the transmission line lengths for the transmission line segment  22  and the offset transmission line  32 , q the ratio of the transmission line lengths for the transmission line segment  22  and the offset transmission line  42 , z the standardized impedance of the series device calibrator, y the standardized admittance of the shunt device calibrator, and z tp , y sp  the high frequency parasitic effect devices); thus such a self-calibration equation can be expressed as below: 
         [0000]    
       
         
           
             
               
                 
                   
                     f 
                     1 
                   
                   = 
                   
                     
                       
                         [ 
                         
                           1 
                           - 
                           
                             y 
                             sp 
                           
                           - 
                           
                             
                               
                                 z 
                                  
                                 
                                   ( 
                                   
                                     1 
                                     - 
                                     
                                       y 
                                       sp 
                                     
                                   
                                   ) 
                                 
                               
                               2 
                             
                              
                             
                               / 
                             
                              
                             2 
                           
                         
                         ] 
                       
                       · 
                       
                         t 
                         
                           ( 
                           
                             1 
                             - 
                             
                               1 
                                
                               
                                 / 
                               
                                
                               p 
                             
                           
                           ) 
                         
                       
                     
                     + 
                     
                         
                       
                         
                           
                             [ 
                             
                               1 
                               + 
                               
                                 y 
                                 sp 
                               
                               + 
                               
                                 
                                   
                                     z 
                                      
                                     
                                       ( 
                                       
                                         1 
                                         + 
                                         
                                           y 
                                           sp 
                                         
                                       
                                       ) 
                                     
                                   
                                   2 
                                 
                                  
                                 
                                   / 
                                 
                                  
                                 2 
                               
                             
                             ] 
                           
                           · 
                           
                             t 
                             
                               - 
                               
                                 ( 
                                 
                                   1 
                                   - 
                                   
                                     1 
                                      
                                     
                                       / 
                                     
                                      
                                     p 
                                   
                                 
                                 ) 
                               
                             
                           
                         
                         = 
                         
                           trace 
                            
                           
                             { 
                             
                               
                                 
                                   [ 
                                   
                                     M 
                                     
                                       OS 
                                       , 
                                       f 
                                     
                                   
                                   ] 
                                 
                                  
                                 
                                   [ 
                                   
                                     M 
                                     L 
                                   
                                   ] 
                                 
                               
                               
                                 - 
                                 1 
                               
                             
                             } 
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   1 
                   ) 
                 
               
             
             
               
                 
                   
                     f 
                     2 
                   
                   = 
                   
                     
                       
                         [ 
                         
                           1 
                           - 
                           
                             z 
                             tp 
                           
                           - 
                           
                             
                               
                                 y 
                                  
                                 
                                   ( 
                                   
                                     1 
                                     - 
                                     
                                       z 
                                       tp 
                                     
                                   
                                   ) 
                                 
                               
                               2 
                             
                              
                             
                               / 
                             
                              
                             2 
                           
                         
                         ] 
                       
                       · 
                       
                         t 
                         
                           ( 
                           
                             1 
                             - 
                             
                               1 
                                
                               
                                 / 
                               
                                
                               q 
                             
                           
                           ) 
                         
                       
                     
                     + 
                     
                         
                       
                         
                           
                             [ 
                             
                               1 
                               + 
                               
                                 z 
                                 sp 
                               
                               + 
                               
                                 
                                   
                                     y 
                                      
                                     
                                       ( 
                                       
                                         1 
                                         + 
                                         
                                           z 
                                           tp 
                                         
                                       
                                       ) 
                                     
                                   
                                   2 
                                 
                                  
                                 
                                   / 
                                 
                                  
                                 2 
                               
                             
                             ] 
                           
                           · 
                           
                             t 
                             
                               - 
                               
                                 ( 
                                 
                                   1 
                                   - 
                                   
                                     1 
                                      
                                     
                                       / 
                                     
                                      
                                     q 
                                   
                                 
                                 ) 
                               
                             
                           
                         
                         = 
                         
                           trace 
                            
                           
                             { 
                             
                               
                                 
                                   [ 
                                   
                                     M 
                                     
                                       OT 
                                       , 
                                       f 
                                     
                                   
                                   ] 
                                 
                                  
                                 
                                   [ 
                                   
                                     M 
                                     L 
                                   
                                   ] 
                                 
                               
                               
                                 - 
                                 1 
                               
                             
                             } 
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   2 
                   ) 
                 
               
             
             
               
                 
                   
                     f 
                     3 
                   
                   = 
                   
                     
                       - 
                       
                         
                           [ 
                           
                             
                               y 
                               sp 
                             
                             - 
                             
                               
                                 
                                   z 
                                    
                                   
                                     ( 
                                     
                                       1 
                                       - 
                                       
                                         y 
                                         sp 
                                       
                                     
                                     ) 
                                   
                                 
                                 2 
                               
                                
                               
                                 / 
                               
                                
                               2 
                             
                           
                           ] 
                         
                          
                         
                           [ 
                           
                             
                               z 
                               tp 
                             
                             - 
                             
                               
                                 
                                   y 
                                    
                                   
                                     ( 
                                     
                                       1 
                                       - 
                                       
                                         z 
                                         tp 
                                       
                                     
                                     ) 
                                   
                                 
                                 2 
                               
                                
                               
                                 / 
                               
                                
                               2 
                             
                           
                           ] 
                         
                       
                     
                      
                     
                         
                       
                         
                           [ 
                           
                             
                               t 
                               
                                 ( 
                                 
                                   
                                     1 
                                      
                                     
                                       / 
                                     
                                      
                                     p 
                                   
                                   - 
                                   
                                     1 
                                      
                                     
                                       / 
                                     
                                      
                                     q 
                                   
                                 
                                 ) 
                               
                             
                             + 
                             
                               t 
                               
                                 - 
                                 
                                   ( 
                                   
                                     
                                       1 
                                        
                                       
                                         / 
                                       
                                        
                                       p 
                                     
                                     - 
                                     
                                       1 
                                        
                                       
                                         / 
                                       
                                        
                                       q 
                                     
                                   
                                   ) 
                                 
                               
                             
                           
                           ] 
                         
                         + 
                         
                           
                             [ 
                             
                               1 
                               - 
                               
                                 y 
                                 sp 
                               
                               - 
                               
                                 
                                   
                                     z 
                                      
                                     
                                       ( 
                                       
                                         1 
                                         - 
                                         
                                           y 
                                           sp 
                                         
                                       
                                       ) 
                                     
                                   
                                   2 
                                 
                                  
                                 
                                   / 
                                 
                                  
                                 2 
                               
                             
                             ] 
                           
                            
                           
                               
                             
                               
                                 
                                   [ 
                                   
                                     1 
                                     + 
                                     
                                       z 
                                       tp 
                                     
                                     + 
                                     
                                       
                                         
                                           y 
                                            
                                           
                                             ( 
                                             
                                               1 
                                               + 
                                               
                                                 z 
                                                 tp 
                                               
                                             
                                             ) 
                                           
                                         
                                         2 
                                       
                                        
                                       
                                         / 
                                       
                                        
                                       2 
                                     
                                   
                                   ] 
                                 
                                 · 
                                 
                                   t 
                                   
                                     - 
                                     
                                       ( 
                                       
                                         
                                           1 
                                            
                                           
                                             / 
                                           
                                            
                                           p 
                                         
                                         - 
                                         
                                           1 
                                            
                                           
                                             / 
                                           
                                            
                                           q 
                                         
                                       
                                       ) 
                                     
                                   
                                 
                               
                               + 
                               
                                 
                                   [ 
                                   
                                     1 
                                     + 
                                     
                                       y 
                                       sp 
                                     
                                     + 
                                     
                                       
                                         
                                           z 
                                            
                                           
                                             ( 
                                             
                                               1 
                                               + 
                                               
                                                 y 
                                                 sp 
                                               
                                             
                                             ) 
                                           
                                         
                                         2 
                                       
                                        
                                       
                                         / 
                                       
                                        
                                       2 
                                     
                                   
                                   ] 
                                 
                                  
                                 
                                     
                                   
                                     
                                       
                                         [ 
                                         
                                           1 
                                           - 
                                           
                                             z 
                                             tp 
                                           
                                           - 
                                           
                                             
                                               
                                                 y 
                                                  
                                                 
                                                   ( 
                                                   
                                                     1 
                                                     - 
                                                     
                                                       z 
                                                       tp 
                                                     
                                                   
                                                   ) 
                                                 
                                               
                                               2 
                                             
                                              
                                             
                                               / 
                                             
                                              
                                             2 
                                           
                                         
                                         ] 
                                       
                                       · 
                                       
                                         t 
                                         
                                           ( 
                                           
                                             
                                               1 
                                                
                                               
                                                 / 
                                               
                                                
                                               p 
                                             
                                             - 
                                             
                                               1 
                                                
                                               
                                                 / 
                                               
                                                
                                               q 
                                             
                                           
                                           ) 
                                         
                                       
                                     
                                     = 
                                     
                                       trace 
                                        
                                       
                                         { 
                                         
                                           
                                             
                                               [ 
                                               
                                                 M 
                                                 
                                                   OS 
                                                   , 
                                                   f 
                                                 
                                               
                                               ] 
                                             
                                              
                                             
                                               [ 
                                               
                                                 M 
                                                 
                                                   OT 
                                                   , 
                                                   f 
                                                 
                                               
                                               ] 
                                             
                                           
                                           
                                             - 
                                             1 
                                           
                                         
                                         } 
                                       
                                     
                                   
                                 
                               
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   3 
                   ) 
                 
               
             
             
               
                 
                   
                     f 
                     4 
                   
                   = 
                   
                     
                       
                         
                           2 
                            
                           
                             [ 
                             
                               1 
                               - 
                               
                                 y 
                                 sp 
                               
                               - 
                               
                                 
                                   
                                     z 
                                      
                                     
                                       ( 
                                       
                                         1 
                                         - 
                                         
                                           y 
                                           sp 
                                         
                                       
                                       ) 
                                     
                                   
                                   2 
                                 
                                  
                                 
                                   / 
                                 
                                  
                                 2 
                               
                             
                             ] 
                           
                         
                          
                         
                           [ 
                           
                             1 
                             + 
                             
                               y 
                               sp 
                             
                             + 
                             
                               
                                 
                                   z 
                                    
                                   
                                     ( 
                                     
                                       1 
                                       + 
                                       
                                         y 
                                         sp 
                                       
                                     
                                     ) 
                                   
                                 
                                 2 
                               
                                
                               
                                 / 
                               
                                
                               2 
                             
                           
                           ] 
                         
                       
                       + 
                       
                         
                           
                             [ 
                             
                               
                                 y 
                                 sp 
                               
                               - 
                               
                                 
                                   z 
                                    
                                   
                                     ( 
                                     
                                       1 
                                       - 
                                       
                                         y 
                                         sp 
                                         2 
                                       
                                     
                                     ) 
                                   
                                 
                                  
                                 
                                   / 
                                 
                                  
                                 2 
                               
                             
                             ] 
                           
                           2 
                         
                         · 
                         
                           [ 
                           
                             
                               t 
                               
                                 2 
                                  
                                 
                                   / 
                                 
                                  
                                 p 
                               
                             
                             + 
                             
                               t 
                               
                                 
                                   - 
                                   2 
                                 
                                  
                                 
                                   / 
                                 
                                  
                                 p 
                               
                             
                           
                           ] 
                         
                       
                     
                     = 
                     
                       trace 
                        
                       
                         { 
                         
                           
                             
                               [ 
                               
                                 M 
                                 
                                   OS 
                                   , 
                                   f 
                                 
                               
                               ] 
                             
                              
                             
                               [ 
                               
                                 M 
                                 
                                   OS 
                                   , 
                                   r 
                                 
                               
                               ] 
                             
                           
                           
                             - 
                             1 
                           
                         
                         } 
                       
                     
                   
                 
               
               
                 
                   ( 
                   4 
                   ) 
                 
               
             
             
               
                 
                   
                     f 
                     5 
                   
                   = 
                   
                     
                       
                         
                           2 
                            
                           
                             [ 
                             
                               1 
                               - 
                               
                                 z 
                                 tp 
                               
                               - 
                               
                                 
                                   
                                     y 
                                      
                                     
                                       ( 
                                       
                                         1 
                                         - 
                                         
                                           z 
                                           tp 
                                         
                                       
                                       ) 
                                     
                                   
                                   2 
                                 
                                  
                                 
                                   / 
                                 
                                  
                                 2 
                               
                             
                             ] 
                           
                         
                          
                         
                           [ 
                           
                             1 
                             + 
                             
                               z 
                               tp 
                             
                             + 
                             
                               
                                 
                                   y 
                                    
                                   
                                     ( 
                                     
                                       1 
                                       + 
                                       
                                         z 
                                         tp 
                                       
                                     
                                     ) 
                                   
                                 
                                 2 
                               
                                
                               
                                 / 
                               
                                
                               2 
                             
                           
                           ] 
                         
                       
                       + 
                       
                         
                           
                             [ 
                             
                               
                                 z 
                                 tp 
                               
                               - 
                               
                                 
                                   y 
                                    
                                   
                                     ( 
                                     
                                       1 
                                       - 
                                       
                                         z 
                                         tp 
                                         2 
                                       
                                     
                                     ) 
                                   
                                 
                                  
                                 
                                   / 
                                 
                                  
                                 2 
                               
                             
                             ] 
                           
                           2 
                         
                         · 
                         
                           [ 
                           
                             
                               t 
                               
                                 2 
                                  
                                 
                                   / 
                                 
                                  
                                 q 
                               
                             
                             + 
                             
                               t 
                               
                                 
                                   - 
                                   2 
                                 
                                  
                                 
                                   / 
                                 
                                  
                                 q 
                               
                             
                           
                           ] 
                         
                       
                     
                     = 
                     
                       trace 
                        
                       
                         { 
                         
                           
                             
                               [ 
                               
                                 M 
                                 
                                   OT 
                                   , 
                                   f 
                                 
                               
                               ] 
                             
                              
                             
                               [ 
                               
                                 M 
                                 
                                   OT 
                                   , 
                                   r 
                                 
                               
                               ] 
                             
                           
                           
                             - 
                             1 
                           
                         
                         } 
                       
                     
                   
                 
               
               
                 
                   ( 
                   5 
                   ) 
                 
               
             
           
         
       
     
         [0045]    in conjunction with the measurement results from the transmission line segment calibrator, the offset series device calibrator and the offset shunt device calibrator, substituting them into the aforementioned self-calibration equation and using the Newton-Raphson method to acquire the values of t (e γl ), z, y, z tp , y sp  ( 302 ); 
         [0046]    calculating the error boxes and starting the de-embedding process ( 303 ) (the de-embedding process allows to obtain the scattering parameter of the tested object, and in this case the characteristic impedance of the transmission line acts as the reference impedance); 
         [0047]    finally, using γ to figure out Z C  and performing transmission line reference impedance conversion from Z C  to Z 0 , typically 50Ω, thereby acquiring the scattering parameter of the actual tested object based on the reference impedance of Z 0  ( 304 ). 
         [0048]    It should be noted that, in the self-calibration equation illustrated as the Flowchart 1, [M] represents the transmission matrix of the measurement, and subscripts L, OS and OT respectively indicates the three calibrators, Line, Offset-Series and Offset-Shunt; in addition, the subscript f means the forward measurement from the left-side port  1  to the right-side port  2  of the standard device, while the subscript r indicates the reverse measurement from the left-side port  2  to the right-side port  1  of the standard device. 
         [0049]    It should be noted that, referring to  FIG. 4 , an architecture diagram for the two-port network of integral measurement is shown, in which the characteristic impedance of the transmission line in the network is Z C , the characteristic impedance of the network analyzer is Z 0 , and the characteristic impedance can be converted from Z C  to Z 0  by means of a conversion relationship equation thus obtaining the scattering parameter of the actual tested object, wherein the conversion relationship equation can be written as below: 
         [0000]    
       
         
           
             
               
                 
                   
                     [ 
                     
                       D 
                       
                         Z 
                         0 
                       
                     
                     ] 
                   
                   = 
                   
                     
                       
                         1 
                         
                           1 
                           - 
                           
                             Γ 
                             2 
                           
                         
                       
                        
                       
                         [ 
                         
                           
                             
                               1 
                             
                             
                               Γ 
                             
                           
                           
                             
                               Γ 
                             
                             
                               1 
                             
                           
                         
                         ] 
                       
                     
                     · 
                     
                       [ 
                       
                         D 
                         
                           Z 
                           C 
                         
                       
                       ] 
                     
                     · 
                     
                       [ 
                       
                         
                           
                             1 
                           
                           
                             
                               - 
                               Γ 
                             
                           
                         
                         
                           
                             
                               - 
                               Γ 
                             
                           
                           
                             1 
                           
                         
                       
                       ] 
                     
                   
                 
               
               
                 
                   ( 
                   6 
                   ) 
                 
               
             
           
         
       
     
         [0000]    in which [D Z     0   ] and [D Z     C   ] respectively indicates the transmission matrix before and after conversion, with Γ defined as: 
         [0000]    
       
         
           
             
               
                 
                   Γ 
                   = 
                   
                     
                       
                         Z 
                         C 
                       
                       - 
                       
                         Z 
                         0 
                       
                     
                     
                       
                         Z 
                         C 
                       
                       + 
                       
                         Z 
                         0 
                       
                     
                   
                 
               
               
                 
                   ( 
                   7 
                   ) 
                 
               
             
           
         
       
     
         [0050]    It should be noted that, in STEP 4, if it is required to convert the reference impedance to the conventionally used 50Ω (American National Standards Institute (ANSI) has developed the standard measurement base for a transmission line of 50Ω characteristic impedance), then the characteristic impedance of the transmission line is needed so as to get the reference impedance of the transmission line through the following equation by using the direct current resistance measurement value in the offset shunt device calibrator, thus finally acquiring the scattering parameter of the actual tested object with the reference impedance of 50Ω. 
         [0000]        Z   C =γ/( j 2π fC )   (8)
 
         [0000]    
       
         
           
             
               
                 
                   C 
                   = 
                   
                     
                       Re 
                        
                       
                         { 
                         
                           - 
                           
                             
                               
                                 ( 
                                 
                                   1 
                                   + 
                                   
                                     S 
                                     22 
                                   
                                 
                                 ) 
                               
                                
                               γ 
                             
                             
                               j 
                                
                               
                                   
                               
                                
                               4 
                                
                               π 
                                
                               
                                   
                               
                                
                               
                                 fS 
                                 22 
                               
                                
                               
                                 R 
                                 
                                   dc 
                                   , 
                                   shunt 
                                 
                               
                             
                           
                         
                         } 
                       
                     
                      
                     
                       | 
                       
                         f 
                         &lt; 
                         
                           1 
                            
                           
                               
                           
                            
                           GHz 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   9 
                   ) 
                 
               
             
           
         
       
     
         [0051]    It should be noted that the present invention allows to use the direct current resistance measurement values of the offset series device calibrator and the offset shunt device calibrator to figure out the propagation constant of the transmission line thereby eliminating the problem of poor numerical calculations in case of low frequency operations; meanwhile, it is also possible to use the high frequency parasitic effect devices y sp , z tp  of the offset series device calibrator and the offset shunt device calibrator to resolve the problem of poor numerical calculations in self-calibration operations when the LINE phase shift approaches  180  degrees and integer times thereof thereby successfully achieving the effect of wideband calibration measurement. 
         [0052]    Compared with prior art, the calibration method for radio frequency scattering parameter measurement provided by the present invention can offer the following advantages: 
         [0053]    1. the present invention enables improvement in accuracy of scattering parameter measurements and execution of de-embedding process in the one-tier measurement of radio frequency scattering parameter for semiconductor wafer devices or other substrate devices; 
         [0054]    2. the present invention can provide an L-OS-OT calibration method to perform wideband measurements and also use the known conditions offered by the calibrators to solve the same or more number of unknown variables thereby achieving the objective of self-calibration; 
         [0055]    3. the calibration method according to the present invention features convenience in fabrication with simplicity, so it is not required to apply expensive materials, but only exploit the characteristics of series and shunt resistor connections for calibrating to a sufficient frequency bandwidth, and all characteristic parameters can be obtained though the self-calibration process as well. 
         [0056]    By way of the aforementioned detailed descriptions for the preferred embodiments according to the present invention, it is intended to better illustrate the characters and spirit of the present invention rather than restricting the scope of the present invention to the preferred embodiments disclosed in the previous texts. Contrarily, the objective is to encompass all changes and effectively equivalent arrangements within the scope of the present invention as delineated in the following claims of the present application.