Abstract:
A method useful for the characterization of a fixture splits a partially symmetric THRU structure into portions which may then be mathematically removed from both ports of a 2-port measured structure, leaving only the desired device under test (DUT).

Description:
CROSS REFERENCE TO RELATED APPLICATIONS 
       [0001]    The subject application claims priority from U.S. Provisional Patent Application Ser. No. 60/916,872, entitled, CALIBRATION OF A PARTIALLY SYMMETRIC FIXTURE (Kan Tan.), filed 09 May 2007, the entire contents of which are herein incorporated by reference. 
     
    
     FIELD OF THE INVENTION 
       [0002]    The subject application concerns, in general, the field of test and measurement instruments, and in particular, concerns characterizing partially symmetric test fixtures. 
       BACKGROUND OF THE INVENTION 
       [0003]    PCT patent application serial number PCT/US07/75485, CALIBRATION OF A MIRROR-SYMMETRIC FIXTURE (Doubrava, et al.) (hereinafter Doubrava &#39;485), herein incorporated by reference, introduces a method for the characterization of a symmetric fixture, hereinafter called SymmetriCal. The SymmetriCal method (Doubrava &#39;485) splits a symmetric THRU structure into mirrored Half-fixtures which may then be mathematically removed from both ports of a 2-port measured structure, leaving only the probe (i.e., the desired device under test (DUT)). What is needed is a method that can handle partially-symmetric fixtures. 
       SUMMARY OF THE INVENTION 
       [0004]    A partial symmetric fixture is characterized with a single 2-port S-parameter measurement. The mathematical process splits the fixture into two partially symmetric half-fixtures, completely describing each half in terms of 2-port S-parameters. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWING 
         [0005]      FIG. 1  shows an example of a partially symmetric fixture. 
           [0006]      FIG. 2  shows another example of a partially symmetric fixture. 
       
    
    
     DETAILED DESCRIPTION OF THE EMBODIMENTS 
       [0007]    The subject invention is an enhanced method which can handle partially symmetric fixtures. One example of partially symmetric fixture  100  is shown in  FIG. 1 , where the fixture is mostly symmetric, except for the inter-connectors  110 ,  120  and  116 ,  126  which are of two different types. The different connectors at the two sides may facilitate the through (THROU) calibration. Test fixture  100  includes a first trace  112  extending from a first connector  110  through a connection pad  114  to a second connector  116 , and a second trace  122  extending from a third connector  120  through a second connection pad  124  to a fourth connector  126 . 
         [0008]    The second example of partially symmetric fixture  200  is shown in  FIG. 2 , where the fixture is less symmetric than the one in  FIG. 1 . Elements in  FIG. 2  bearing similar reference numerals to those of  FIG. 1  serve the same purpose, and need not be described again. In  FIG. 2 , only the connection pads  214 ,  224  and their neighboring area are symmetric. 
         [0009]    The extended method of the subject invention, called Partial SymmetriCal, can handle fixtures satisfying the partial symmetry requirement. The term “partial symmetry”, as used herein means that the junction section between two half sides (LEFT and RIGHT Portions) is symmetric. 
         [0010]    The pad areas shown in  FIG. 1  and  FIG. 2  are symmetric, so the test fixtures in  FIG. 1  and  FIG. 2  satisfy partial symmetry requirements. But they are not completely symmetric as required by Doubrava &#39;485 (i.e., SymmetriCal™). 
         [0011]    Less strict requirements in accordance with the method of the subject invention (which may be called, Partial SymmetriCal) provide more flexibility for fixture designs. For test fixtures that are supposed to be symmetric, the Partial SymmetriCal provides a means to check how good the symmetry assumption is. 
       Calibration of Partially Symmetric Fixtures 
       [0012]    A partial symmetric fixture is characterized with a single 2-port S-parameter measurement. The mathematical process splits the fixture into two partially symmetric half-fixtures, completely describing each half in terms of 2-port S-parameters. 
         [0013]    Measurement of a device under test (DUT) embedded between the half-fixtures can be easily de-embedded using the Half-fixture 
         [0014]    S-parameters, or equivalently, T-parameters. 
         [0015]    The partially symmetric fixture F and its components X and Y can be characterized in terms of S-parameters: 
         [0000]    
       
         
           
             
               
                 
                   Sx 
                   = 
                     
                    
                   
                     ( 
                     
                       
                         
                           
                             Sx 
                             11 
                           
                         
                         
                           
                             Sx 
                             12 
                           
                         
                       
                       
                         
                           
                             Sx 
                             21 
                           
                         
                         
                           
                             Sx 
                             22 
                           
                         
                       
                     
                     ) 
                   
                 
               
             
             
               
                 
                   Sy 
                   = 
                     
                    
                   
                     ( 
                     
                       
                         
                           
                             Sy 
                             11 
                           
                         
                         
                           
                             Sy 
                             12 
                           
                         
                       
                       
                         
                           
                             Sy 
                             21 
                           
                         
                         
                           
                             Sy 
                             22 
                           
                         
                       
                     
                     ) 
                   
                 
               
             
             
               
                 
                   Sf 
                   = 
                     
                    
                   
                     ( 
                     
                       
                         
                           
                             Sf 
                             11 
                           
                         
                         
                           
                             Sf 
                             12 
                           
                         
                       
                       
                         
                           
                             Sf 
                             21 
                           
                         
                         
                           
                             Sf 
                             22 
                           
                         
                       
                     
                     ) 
                   
                 
               
             
           
         
       
     
         [0000]    
       
         
               
             
           
               
                   
               
             
             
               
                 
                   
                             
                     
                         
                         
                     
                   
                 
               
               
                   
               
             
          
         
       
     
         [0016]    The partial symmetric constraints is reflected in the model as 
         [0000]      Sx 22 =Sy 11    (1) 
         [0017]    The reciprocity constraints applied to each component X, Y as well as whole fixture F yields: 
         [0000]      Sx 12 =SX 21    
         [0000]      Sy 12 =SY 21    
         [0000]      Sf 12 =Sf 21    (2) 
         [0018]    The S-parameters of X, Y and F are related by 
         [0000]    
       
         
           
             
               
                 
                   
                     [ 
                     
                       
                         
                           
                             Sf 
                             11 
                           
                         
                         
                           
                             Sf 
                             12 
                           
                         
                       
                       
                         
                           
                             Sf 
                             21 
                           
                         
                         
                           
                             Sf 
                             22 
                           
                         
                       
                     
                     ] 
                   
                   = 
                   
                     [ 
                     
                       
                         
                           
                             
                               Sx 
                               11 
                             
                             + 
                             
                               
                                 
                                   Sx 
                                   12 
                                 
                                 · 
                                 
                                   Sy 
                                   11 
                                 
                                 · 
                                 
                                   Sx 
                                   21 
                                 
                               
                               
                                 1 
                                 - 
                                 
                                   
                                     Sx 
                                     22 
                                   
                                   · 
                                   
                                     Sy 
                                     11 
                                   
                                 
                               
                             
                           
                         
                         
                           
                             
                               
                                 Sx 
                                 12 
                               
                               · 
                               
                                 Sy 
                                 12 
                               
                             
                             
                               1 
                               - 
                               
                                 
                                   Sx 
                                   22 
                                 
                                 · 
                                 
                                   Sy 
                                   11 
                                 
                               
                             
                           
                         
                       
                       
                         
                           
                             
                               
                                 Sy 
                                 21 
                               
                               · 
                               
                                 Sx 
                                 21 
                               
                             
                             
                               1 
                               - 
                               
                                 
                                   Sx 
                                   22 
                                 
                                 · 
                                 
                                   Sy 
                                   11 
                                 
                               
                             
                           
                         
                         
                           
                             
                               Sy 
                               22 
                             
                             + 
                             
                               
                                 
                                   Sy 
                                   21 
                                 
                                 · 
                                 
                                   Sx 
                                   22 
                                 
                                 · 
                                 
                                   Sy 
                                   12 
                                 
                               
                               
                                 1 
                                 - 
                                 
                                   
                                     Sx 
                                     22 
                                   
                                   · 
                                   
                                     Sy 
                                     11 
                                   
                                 
                               
                             
                           
                         
                       
                     
                     ] 
                   
                 
               
               
                 
                   ( 
                   3 
                   ) 
                 
               
             
           
         
       
     
         [0019]    In the equation (3), Sf 11 , Sf 12 , Sf 22  can be obtained through two port measurements using a Vector Network Analyzer (VNA) or a Time Domain Reflectometer (TDR) on the whole fixture F; Sx 11  and Sy 22  can be obtained using the time domain gating method described in Doubrava &#39;489. 
         [0020]    Only three independent variables Sx 12 , Sy 12 , Sx 22  are unknown in (3). These three unknown variables can be resolved from three independent equations in (3) as following, 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       
                         Sx 
                         12 
                       
                       · 
                       
                         Sy 
                         11 
                       
                       · 
                       
                         Sx 
                         21 
                       
                     
                     
                       1 
                       - 
                       
                         
                           Sx 
                           22 
                         
                         · 
                         
                           Sy 
                           11 
                         
                       
                     
                   
                   = 
                   
                     
                       Sf 
                       11 
                     
                     - 
                     
                       Sx 
                       11 
                     
                   
                 
               
               
                 
                   ( 
                   4 
                   ) 
                 
               
             
             
               
                 
                   
                     
                       
                         Sx 
                         12 
                       
                       · 
                       
                         Sy 
                         12 
                       
                     
                     
                       1 
                       - 
                       
                         
                           Sx 
                           22 
                         
                         · 
                         
                           Sy 
                           11 
                         
                       
                     
                   
                   = 
                   
                     Sf 
                     12 
                   
                 
               
               
                 
                   ( 
                   5 
                   ) 
                 
               
             
             
               
                 
                   
                     
                       
                         Sy 
                         21 
                       
                       · 
                       
                         Sx 
                         22 
                       
                       · 
                       
                         Sy 
                         12 
                       
                     
                     
                       1 
                       - 
                       
                         
                           Sx 
                           22 
                         
                         · 
                         
                           Sy 
                           11 
                         
                       
                     
                   
                   = 
                   
                     
                       Sf 
                       22 
                     
                     - 
                     
                       Sy 
                       22 
                     
                   
                 
               
               
                 
                   ( 
                   6 
                   ) 
                 
               
             
           
         
       
     
         [0021]    Multiplying (4) with (6) and dividing square of (5) yields 
         [0000]    
       
         
           
             
               
                 
                   
                     Sx 
                     22 
                   
                   = 
                   
                     ± 
                     
                       
                         
                           
                             ( 
                             
                               
                                 Sf 
                                 11 
                               
                               - 
                               
                                 Sx 
                                 11 
                               
                             
                             ) 
                           
                            
                           
                             ( 
                             
                               
                                 Sf 
                                 22 
                               
                               - 
                               
                                 Sy 
                                 22 
                               
                             
                             ) 
                           
                         
                         
                           Sf 
                           12 
                           2 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   7 
                   ) 
                 
               
             
           
         
       
     
         [0022]    Plugging (7) into (4) and (6) respectively to get 
         [0000]    
       
         
           
             
               
                 
                   
                     Sx 
                     12 
                   
                   = 
                   
                     ± 
                     
                       
                         
                           
                             ( 
                             
                               
                                 Sf 
                                 11 
                               
                               - 
                               
                                 Sx 
                                 11 
                               
                             
                             ) 
                           
                            
                           
                             ( 
                             
                               1 
                               - 
                               
                                 Sx 
                                 22 
                                 2 
                               
                             
                             ) 
                           
                         
                         
                           Sx 
                           22 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   8 
                   ) 
                 
               
             
             
               
                 
                   
                     Sy 
                     12 
                   
                   = 
                   
                     ± 
                     
                       
                         
                           
                             ( 
                             
                               
                                 Sf 
                                 22 
                               
                               - 
                               
                                 Sy 
                                 22 
                               
                             
                             ) 
                           
                            
                           
                             ( 
                             
                               1 
                               - 
                               
                                 Sx 
                                 22 
                                 2 
                               
                             
                             ) 
                           
                         
                         
                           Sx 
                           22 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   9 
                   ) 
                 
               
             
           
         
       
     
         [0023]    The signs in (7) (8) and (9) affect phase of S parameters. They can be resolved from time domain measurement and continuity of phase. 
         [0024]    If Sx 22 =0, then Sx 12 , Sy 12  can not be computed from (8) and (9). Instead, they need to be resolved from 
         [0000]        Sx   12   ·SY   12 =Sf 12    (10) 
         [0025]    Extra knowledge of relation between Sx 12  and Sy 12  are needed to resolve them: for example, if THRU are symmetric, then 
         [0000]      Sx 12 =SY 12    
         [0026]    Or, if traces on left and right are uniform, but the trace in X side is twice as long as the trace in Y side, then 
         [0000]    
       
      
       Sx 
       12 
       =Sy 
       12 
       ·Sy 
       12  
      
     
         [0027]    Combining the relation between Sx 12  and Sy 12  with (10), Sx 12  and Sy 12  can be resolved. 
         [0028]    For a completely symmetric fixture, which is considered in Doubrava &#39;485, (1) will have two extra symmetric terms 
         [0000]      Sx 12 =Sy 12    
         [0000]      Sx 11 =Sy 22    
         [0029]    It can be verified that equations (3)-(10) with these two extra symmetric terms yield the same results as in Doubrava &#39;485. 
         [0030]    The subject invention (Partial SymmetriCal) can handle fixtures satisfying partial symmetry requirement, which is less strict than completely symmetric required by the SymmetriCal (Doubrava &#39;485) method. For completely symmetric fixture, the Partial SymmetriCal yields the same result as SymmetriCal. For fixtures that are very close to symmetric, the Partial SymmetriCal provides a check on how symmetry it is, and can calibrate out asymmetry. The subject method (Partial SymmetriCal) is the super set of SymmetriCal; the Partial SymmetriCal involves more steps to gain more accurate calibration results. For the fixtures that are almost completely symmetric, if calibration efficiency is preferred over accuracy, then the SymmetriCal should be used; if accuracy is preferred over efficiency, then the Partial SymmetriCal should be used. 
         [0031]    It is noted that the subject invention is also useful in combination with the teaching of U.S. patent application Ser. No. 12/117461 CALIBRATED S-PARAMETER MEASUREMENTS OF A HIGH IMPEDANCE PROBE (Hagerup, et al.), herein incorporated by reference.