Patent Publication Number: US-2015084656-A1

Title: Two port vector network analyzer using de-embed probes

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This application claims the benefit of U.S. Provisional Patent Application No. 61/882,283 titled Two Port System Network Analysis Using De-embed Probes filed on Sep. 25, 2013, which application is hereby incorporated herein by reference. 
    
    
     TECHNICAL FIELD 
     The disclosed technology relates generally to signal acquisition systems and, more particularly, to a system for measuring the scattering parameters (S-parameters) of a device under test. 
     BACKGROUND 
     Typical probes used for signal acquisition and analysis devices such as digital storage oscilloscopes (DSOs) and the like have an impedance associated with them which varies with frequency. For example, a typical probe may have an impedance of 100K to 200K Ohms at DC, which impedance drops towards 200 ohms at 1.5 GHz. Higher bandwidth probes drop to even lower impedance values. This drop in impedance as frequency increases, coupled with the fact that many devices under test being probed have an output impedance in the range of 25-150 ohms, results in a significant loading of the device under test by the probe. As such, an acquired waveform received via a probe loading such a device under test may not accurately represent the voltage of the device under test prior to the introduction of the probe. 
     Traditionally, a vector network analyzer or a time-domain reflectometer (TDR) system with a sampling oscilloscope have been required to measure the scattering parameters (S-parameters) for a two-port network characterization of a device under test in order to de-embed the effects of the probes. However, vector network analyzers and TDR systems are expensive. 
     What is needed is a more cost effective system that allows a user to view fully de-embedded representations of waveforms at the probe tip. 
     SUMMARY 
     Certain embodiments of the disclosed technology include a method for determining an S-parameter set of a device under test using a test and measurement instrument including measuring an impedance of a signal generator with a first de-embed probe, measuring an input voltage to the device under test with the first de-embed probe connected to the input of the device under test, measuring an output voltage from the device under test with a second de-embed probe connected to the output of the device under test, measuring three loads of the device under test with the first de-embed probe connected to the input of the device under test and the second de-embed probe connected to the output of the device under test; and calculating the S-parameter set of the device under test based on the impedance of the signal generator, the input voltage to and the output voltage from the device under test, and the measured three loads of the device under test. 
     Certain embodiments of the disclosed technology include a test and measurement system for measuring an S-parameters set of a device under test, including a signal generator, the device under test, a first de-embed probe configured to measure an impedance of the signal generator and an input voltage of the device under test, a second de-embed probe configured to measure an output voltage of the device under test and an impedance of the device under test, wherein the first de-embed probe and the second de-embed probe are configured to measure at least three loads when both the first de-embed probe and the second de-embed probe are connected to the device under test, and a processor configured to calculate the S-parameter set of the device under test based on the impedance of the signal generator, the input voltage and the output voltage of the device under test, and the measured three loads of the device under test. 
     Certain embodiments of the disclosed technology also include a test and measurement system including a device under test, two de-embed probes connected to the device under test and configured to take measurements of the device under test, and a processor configured to receive the measurements taken by the two de-embed probes and to determine the S-parameter set of the device under test based on the measurements of the device under test. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIGS. 1-4  illustrates block diagrams of a test and measurement system used to determine S-parameter sets of a device under test according to embodiments of the disclosed technology. 
         FIG. 5  illustrates an alternative block diagram of a test and measurement system used to determine S-parameter sets of a device under test according to embodiments of the disclosed technology. 
         FIGS. 6-7  illustrates another alternative block diagram of a test and measurement system used to determine S-parameter sets of a device under test according to other embodiments of the disclosed technology. 
         FIG. 8  illustrates a signal flow graph according to the test and measurement system shown in  FIGS. 1-4 . 
         FIG. 9  illustrates a signal flow graph according to other embodiments of the test and measurement instrument. 
     
    
    
     DETAILED DESCRIPTION 
     In the drawings, which are not necessarily to scale, like or corresponding elements of the disclosed systems and methods are denoted by the same reference numerals. 
       FIG. 1  depicts a test and measurement system including a test and measurement instrument  100 , such as a digital storage oscilloscope, connected to two de-embed probes  102  and  104  to measure the S-parameters of a device under test  114 . The test and measurement system shown in  FIGS. 1-4  allows a test and measurement instrument, such as a digital storage oscilloscope, to act as a calibrated vector network analyzer measurement system. That is, the test and measurement system is capable of measuring all four S-parameters of a two-port device under test  114 . The test and measurement instrument  100  includes a processor (not shown) to calculate the various computations discussed below. 
     De-embed probes are described in U.S. Patent Application Publication No. 2005/0185768 A1 titled CALIBRATION METHOD AND APPARATUS, U.S. Patent Application Publication No. 2005/0094746 A1 titled CHARACTERISTIC MEASUREMENT SYSTEM FOR A DIGITAL MODULATION SIGNAL TRANSMISSION CIRCUIT, U.S. Patent Application Publication No. 2007/0276614 A1 titled DE-EMBED METHOD FOR MULTIPLE PROBES COUPLED TO A DEVICE UNDER TEST, and U.S. Pat. No. 7,405,575 B2 titled SIGNAL ANALYSIS SYSTEM AND CALIBRATION METHOD FOR MEASURING THE IMPEDANCE OF A DEVICE UNDER TEST, each of which is herein incorporated by reference in its entirety. 
     The de-embed probes  102  and  104  contain loads that can be placed across the inputs of each probe under control of the test and measurement instrument  100 . This allows for a fully calibrated and de-embedded measurement at the probe inputs. Although not shown, probes  102  and  104  contain controllers that interact with a processor or controller (not shown) of the test and measurement instrument  100  to control the various switches (not shown) within probes  102  and  104  so that different loads can be placed across the inputs of each probe. 
     The test and measurement system of  FIG. 1  also includes a signal generator  106 . As shown in  FIG. 1 , the signal generator  106  may be an external signal generator. However, as shown in  FIG. 5 , the signal generator  106  may also be internal to the test and measurement instrument  100 . Preferably, the signal generator  106  is a step signal generator. However, other types of signal generators  106  may be used. For example, a sine wave generator could be used and stepped through each frequency of interest. The sine wave generator may provide a better signal-to-noise ratio. 
     A test fixture  108  provides connection ports, port one  110  and port two  112 , for connection to the device under test  114 , the signal generator  106  and the de-embed probes  102  and  104 . The test fixture  108  can be custom to the type of device under test  110  used. For example, if the device under test  114  is a cable, the test fixture  108  would contain connectors to connect to the cable device under test. The text fixture  108  could also contain a switching arrangement to move the test signal from one cable pair to another cable pair as the testing progresses. 
       FIGS. 1-4  illustrate the calibration process to determine the S-parameters of the device under test  114 . The below described calibration procedure may be manual, partially automated or fully automated. 
     Initially, probe  102  and signal generator  106  are connected to port one  110  so the probe  102  may measure the impedance of the signal generator  106  as a function of frequency. The probe  102  is connected to the signal generator  106  at the reference plane of the signal generator  106 , which is the point at which the S-parameters of the device under test  114  are measured at the signal generator  106  end. An external trigger  120  is connected to an external trigger input of the test and measurement instrument  100 . External trigger  120  is also connected to the signal generator  106 . The external trigger  120  triggers the signal generator  106  via a signal from the test and measurement instrument  100 , or vice versa. 
     When probe  102  and signal generator  106  are connected to port one  110  as shown in  FIG. 1 , two acquisitions are taken with two different de-embed probe loads in probe  102 , and test and measurement instrument  100  can calculate the reflection coefficient parameter Γ s  for the signal generator  106  based on these acquisitions. As seen in  FIG. 1 , the device under test  114  is not connected to port one  110  during this measurement. However, a cable connector mounted on the test fixture  108  may be attached and therefore the S-parameters must have been previously measured and stored. Its effects can then be de-embedded out of the signal generator reflection coefficient parameter Γ s . 
     The input voltage, V1, to the device under test  114  from signal generator  106  is measured by connecting the input port  116  of the device under test  114  to port one  110  and connecting the output port  118  of the device under test  114  to port two  112 . Probe  102  is connected to port one  110 . Probe  104  remains unconnected to port two  112  for this measurement. In this configuration shown in  FIG. 2 , the de-embed acquisitions are taken to compute the de-embedded input voltage, V1, into the input port  116  of the device under test  114 . 
     To acquire the output voltage, V2, at the output port  118  of the device under test  114  probe  102  from port one  110  of the test fixture  108  is removed and probe  104  is connected to port two  112  of the test fixture  108 . Again, the necessary de-embed acquisitions are acquired and V2 is computed. 
     As shown in  FIG. 4 , both probes  102  and  104  are connected to port one  110  and port two  112 , respectively, while the device under test  114  is also connected. In this configuration, three different loads on probe  104  at port two  112  are switched in by the test and measurement instrument  100  while acquisitions by probe  102  into port one  110  are acquired. The three measured loads by probe  102  on port one  110  are represented by Γ m1 , Γ m2 , and Γ m3 . 
     The measurements of Γ s , V1, V2, Γ m1 , Γ m2 , and Γ m3  can be obtained in any order as long as the probes  102  and  104  and the device under test  114  are configured as discussed above for the acquisitions. In some embodiments, both probes  102  and  104  may stay connected for most of the measurements, as will be discussed in further detail below. 
     Once, Γ s , V1, V2, Γ m1 , Γ m2 , and Γ m3  have been measured, the S-parameters of the device under test  114  can then be computed based on the measurements of Γ s , V1, V2, Γ m1 , Γ m2 , and Γ m3 . 
       FIG. 8  illustrates a signal flow graph to represent the test and measurement system discussed above in  FIGS. 1-4 . The signal generator is represented by b s  and Γ s . The load value Γ L  is either part of the de-embed probe used or a load in the test fixture. The remaining parameters S 11 , S 12 , S 21 , S 22  represent the two port device under test  114 . The signal flow graph of  FIG. 8  is used to derive some of the following equations. 
     The value of input voltage to the device under test is V1 and the output voltage from the device under test  114  is V2. Both can be measured directly using de-embed probes  102  and  104  as discussed above. Equations (1) and (2) are derived from the signal flow graph shown in  FIG. 8 . 
         V 1 =a 1 +b 1  (1)
 
         V 2 =a 2 +b 2  (2)
 
     The following equations (3), (4), and (5) describe the relationship of S-parameters in the two port network: 
     
       
         
           
             
               
                 
                   
                     Γ 
                     
                       m 
                        
                       
                           
                       
                        
                       1 
                     
                   
                   = 
                   
                     
                       Ss 
                       11 
                     
                     + 
                     
                       
                         
                           S 
                           12 
                         
                         · 
                         
                           S 
                           21 
                         
                         · 
                         
                           Γ 
                           
                             c 
                              
                             
                                 
                             
                              
                             1 
                           
                         
                       
                       
                         1 
                         - 
                         
                           
                             S 
                             22 
                           
                           · 
                           
                             Γ 
                             
                               c 
                                
                               
                                   
                               
                                
                               1 
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   3 
                   ) 
                 
               
             
             
               
                 
                   
                     Γ 
                     
                       m 
                        
                       
                           
                       
                        
                       2 
                     
                   
                   = 
                   
                     
                       Ss 
                       11 
                     
                     + 
                     
                       
                         
                           S 
                           12 
                         
                         · 
                         
                           S 
                           21 
                         
                         · 
                         
                           Γ 
                           
                             c 
                              
                             
                                 
                             
                              
                             2 
                           
                         
                       
                       
                         1 
                         - 
                         
                           
                             S 
                             22 
                           
                           · 
                           
                             Γ 
                             
                               c 
                                
                               
                                   
                               
                                
                               2 
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   4 
                   ) 
                 
               
             
             
               
                 
                   
                     Γ 
                     
                       m 
                        
                       
                           
                       
                        
                       3 
                     
                   
                   = 
                   
                     
                       Ss 
                       11 
                     
                     + 
                     
                       
                         
                           
                             S 
                             12 
                           
                           · 
                           
                             S 
                             21 
                           
                           · 
                           
                             Γ 
                             
                               c 
                                
                               
                                   
                               
                                
                               3 
                             
                           
                         
                         
                           1 
                           - 
                           
                             
                               S 
                               22 
                             
                             · 
                             
                               Γ 
                               
                                 c 
                                  
                                 
                                     
                                 
                                  
                                 3 
                               
                             
                           
                         
                       
                       . 
                     
                   
                 
               
               
                 
                   ( 
                   5 
                   ) 
                 
               
             
           
         
       
     
     These equations represent the measured loads when the device under test  114  and probes  102  and  104  are all connected to port one  110  and port two  112  of the test fixtures as seen in  FIG. 4 . 
     The three equations, (3), (4), and (5) may be written to solve for Ss 11 , S 22 , and S 12 ·S 21 . The values of Γ c1 , Γ c2 , and Γ c3  are known from the stored S-parameters in the de-embed probe  104  and test and measurement instrument. These parameters are measured at manufacturing of the test and measurement instrument and the probes and would be stored in the memories of the test and measurement instruments and the probes. The value of Ss 11  is the parameter for both the signal generator  106  and the device under test  114  input port  116  in parallel. 
     Equations (3), (4), and (5) can be solved by starting with their general form and multiplying out the denominator on the right side of the equal sign to obtain (6): 
     Let: 
       Γ m   −S   22 ·Γ m ·Γ c   =Ss   11   −Ss   11   ·S   22 ·Γ c   +S   12   ·S   21 ·Γ c   (6).
 
     Then rearrange (6) to obtain (7): 
       Γ m   =Ss   11   −Ss   11   ·S   22 ·Γ c   +S   12   ·S   21 ·Γ c   +S   22 ·Γ m ·Γ c   (7).
 
     Then rearrange (7) to obtain (8): 
       Γ m =Γ m ·Γ c   ·S   22   +SS   11 +( S   12   ·S   21   −Ss   11   ·S   22 )·Γ c   (8).
 
     Some immediate variables are defined as follows in equations (9), (10), and (11): 
         x   1   =S   22   (9).
 
         x   2   =SS   11   (10).
 
         x   3   =S   12   ·S   21   −Ss   11   ·S   22   (11).
 
     Now the intermediate variable in (9), (10), and (11) are substituted into (8) to obtain equations (12), (13), and (14): 
       Γ m1 =Γ m1 ·Γ c1   ·x   1   +x   2   +x   3 ·Γ c1   (12).
 
       Γ m2 =Γ m2 ·Γ c2   ·x   1   +x   2   +x   3 ·Γ c2   (13).
 
       Γ m3 =Γ m1 ·Γ c3   ·x   1   +x   2   +x   3 ·Γ c3   (14).
 
     The system of equations (12), (13), and (14) may then be put into matrix notation and solved for x 1 , x 2 , and x 3  as shown in (15). 
     
       
         
           
             
               
                 
                   
                     [ 
                     
                       
                         
                           
                             Γ 
                             
                               m 
                                
                               
                                   
                               
                                
                               1 
                             
                           
                         
                       
                       
                         
                           
                             Γ 
                             
                               m 
                                
                               
                                   
                               
                                
                               2 
                             
                           
                         
                       
                       
                         
                           
                             Γ 
                             
                               m 
                                
                               
                                   
                               
                                
                               3 
                             
                           
                         
                       
                     
                     ] 
                   
                   = 
                   
                     
                       
                         [ 
                         
                           
                             
                               
                                 
                                   
                                     Γ 
                                     
                                       m 
                                        
                                       
                                           
                                       
                                        
                                       1 
                                     
                                   
                                   · 
                                 
                               
                             
                             
                               
                                 
                                   
                                     Γ 
                                     
                                       m 
                                        
                                       
                                           
                                       
                                        
                                       2 
                                     
                                   
                                   · 
                                 
                               
                             
                             
                               
                                 
                                   
                                     Γ 
                                     
                                       m 
                                        
                                       
                                           
                                       
                                        
                                       3 
                                     
                                   
                                   · 
                                 
                               
                             
                           
                            
                           
                             
                               
                                 
                                   Γ 
                                   
                                     c 
                                      
                                     
                                         
                                     
                                      
                                     1 
                                   
                                 
                               
                               
                                 1 
                               
                               
                                 
                                   Γ 
                                   
                                     c 
                                      
                                     
                                         
                                     
                                      
                                     1 
                                   
                                 
                               
                             
                             
                               
                                 
                                   Γ 
                                   
                                     c 
                                      
                                     
                                         
                                     
                                      
                                     2 
                                   
                                 
                               
                               
                                 1 
                               
                               
                                 
                                   Γ 
                                   
                                     c 
                                      
                                     
                                         
                                     
                                      
                                     2 
                                   
                                 
                               
                             
                             
                               
                                 
                                   Γ 
                                   
                                     c 
                                      
                                     
                                         
                                     
                                      
                                     3 
                                   
                                 
                               
                               
                                 1 
                               
                               
                                 
                                   Γ 
                                   
                                     c 
                                      
                                     
                                         
                                     
                                      
                                     3 
                                   
                                 
                               
                             
                           
                         
                         ] 
                       
                        
                       
                         [ 
                         
                           
                             
                               
                                 x 
                                 1 
                               
                             
                           
                           
                             
                               
                                 x 
                                 2 
                               
                             
                           
                           
                             
                               
                                 x 
                                 3 
                               
                             
                           
                         
                         ] 
                       
                     
                     . 
                   
                 
               
               
                 
                   ( 
                   15 
                   ) 
                 
               
             
           
         
       
     
     The solution of x from b=Ax is simply x=A −1 b. Accordingly, from x 1 , x 2 , and x 3  variables Ss 11 , S 22 , and S 12 ·S 21  can be computed from equations (9)-(11). 
     As mentioned above, Ss 11  is the parameter for both the signal generator  106  and the device under test  114  input port  116  in parallel. Removing the signal generator  106  impedance from Ss 11  to get the actual value for S 11  can be performed through the following equations. Equation (10) above is used and Ss 11  is replaced with the combination for the generator and the DUT and equation (16) is then solved for y dut . 
     The value of Ss 11  includes the generator as shown in the following equation (16) where the admittance of the generator is added in parallel to the admittance of the device under test  114 . 
     
       
         
           
             
               
                 
                   
                     x 
                     2 
                   
                   = 
                   
                     
                       Ss 
                       11 
                     
                     = 
                     
                       
                         
                           1 
                           - 
                           
                             ( 
                             
                               
                                 y 
                                 s 
                               
                               + 
                               
                                 y 
                                 dut 
                               
                             
                             ) 
                           
                         
                         
                           1 
                           + 
                           
                             ( 
                             
                               
                                 y 
                                 s 
                               
                               + 
                               
                                 y 
                                 dut 
                               
                             
                             ) 
                           
                         
                       
                       . 
                     
                   
                 
               
               
                 
                   ( 
                   16 
                   ) 
                 
               
             
           
         
       
     
     Equation (16) can be solved for y dut  since the measured value of generator admittance, y s , is known when signal generator  106  is characterized and Ss 11  was calculated above. 
     As discussed above, Γ s  is the reflection coefficient of the signal generator  106  and the test fixture  108 . The value of impedance when Γ s  is measured can be computed from the following equation (18), where Z 0  is a reference impedance, which is typically 50 ohms. 
     
       
         
           
             
               
                 
                   
                     
                       Z 
                       s 
                     
                     = 
                     
                       
                         
                           
                             Z 
                             0 
                           
                            
                           
                             ( 
                             
                               1 
                               + 
                               
                                 Γ 
                                 s 
                               
                             
                             ) 
                           
                         
                         
                           1 
                           - 
                           
                             Γ 
                             s 
                           
                         
                       
                       . 
                       
                         
 
                       
                        
                       Then 
                     
                   
                   , 
                 
               
               
                 
                   ( 
                   17 
                   ) 
                 
               
             
             
               
                 
                   
                     y 
                     s 
                   
                   = 
                   
                     
                       1 
                       
                         Z 
                         s 
                       
                     
                     . 
                   
                 
               
               
                 
                   ( 
                   18 
                   ) 
                 
               
             
           
         
       
     
     Then y dut  is substituted into (19) to compute S 11 . 
     
       
         
           
             
               
                 
                   
                     S 
                     11 
                   
                   = 
                   
                     
                       
                         1 
                         - 
                         
                           y 
                           dut 
                         
                       
                       
                         1 
                         + 
                         
                           y 
                           dut 
                         
                       
                     
                     . 
                   
                 
               
               
                 
                   ( 
                   19 
                   ) 
                 
               
             
           
         
       
     
     At this point the value of S 11 , S 22 , and S 12 ·S 21  have all been computed. The remaining task is to use these values and some additional measurement to compute S 21 . If the device under test  114  is a passive system, then S 12 =S 21 . However, if the device under test  114  is active, then S 21  can be solved for as shown below. 
     The following equations for the transfer function of V2/V1 are derived from the signal flow graph using Mason&#39;s rule, as is known in the art. This is the transfer function of the device under test  114  since V2 is the voltage at the output port and V1 is the voltage at the input port. 
     
       
         
           
             
               
                 
                   
                     A 
                     v 
                   
                   = 
                   
                     
                       
                         V 
                          
                         
                             
                         
                          
                         2 
                       
                       
                         V 
                          
                         
                             
                         
                          
                         1 
                       
                     
                     = 
                     
                       
                         
                           
                             
                               S 
                               21 
                             
                             · 
                             
                               Γ 
                               L 
                             
                           
                           + 
                           
                             S 
                             21 
                           
                         
                         
                           1 
                           - 
                           
                             
                               S 
                               22 
                             
                             · 
                             
                               Γ 
                               L 
                             
                           
                           + 
                           
                             S 
                             11 
                           
                           - 
                           
                             
                               S 
                               11 
                             
                             · 
                             
                               S 
                               22 
                             
                             · 
                             
                               Γ 
                               L 
                             
                           
                           + 
                           
                             
                               S 
                               12 
                             
                             · 
                             
                               S 
                               21 
                             
                             · 
                             
                               Γ 
                               L 
                             
                           
                         
                       
                       . 
                     
                   
                 
               
               
                 
                   ( 
                   20 
                   ) 
                 
               
             
           
         
       
     
     Equation (18) can be solved for S 21 : 
     
       
         
           
             
               
                 
                   
                     S 
                     21 
                   
                   = 
                   
                     
                       ( 
                       
                         1 
                         - 
                         
                           
                             S 
                             22 
                           
                           · 
                           
                             Γ 
                             L 
                           
                         
                         + 
                         
                           S 
                           11 
                         
                         - 
                         
                           
                             S 
                             11 
                           
                           · 
                           
                             S 
                             22 
                           
                           · 
                           
                             Γ 
                             L 
                           
                         
                         + 
                         
                           
                             S 
                             12 
                           
                           · 
                           
                             S 
                             21 
                           
                           · 
                           
                             Γ 
                             L 
                           
                         
                       
                       ) 
                     
                     · 
                     
                       
                         
                           A 
                           v 
                         
                         
                           
                             Γ 
                             L 
                           
                           + 
                           1 
                         
                       
                       . 
                     
                   
                 
               
               
                 
                   ( 
                   21 
                   ) 
                 
               
             
           
         
       
     
     After solving for S 21  from equation (21) use the value of S 12 ·S 21  from equation (11) above to solve for S 12 : 
     
       
         
           
             
               
                 
                   
                     S 
                     12 
                   
                   = 
                   
                     
                       
                         
                           S 
                           12 
                         
                         · 
                         
                           S 
                           21 
                         
                       
                       
                         S 
                         21 
                       
                     
                     . 
                   
                 
               
               
                 
                   ( 
                   22 
                   ) 
                 
               
             
           
         
       
     
     Accordingly, from using the above equations, the complete set of S-parameters, S 11 , S 12 , S 21 , and S 22 , for the device under test  114  have been computed from the measured data. The test and measurement instrument  100  includes a processor and a memory (not shown) to store executable instructions for implementing the above discussed process for determining the S-parameter set of a device under test and for otherwise controlling the test and measurement instrument  100 . The processor can also be external to the test and measurement instrument. 
     The above-discussed process for determining the S-parameter set of the device under test  114  only works if S 21  is generally not zero at all frequencies. If S 21  is zero at certain frequencies, as is nominally the case with an amplifier, then a modified procedure would be required. The modified procedure is shown in  FIGS. 6 and 7 . Initially, as shown in  FIG. 6 , the signal generator  106  is connected to port two  112  and the necessary acquisitions are taken to measure V2 without probe  104  connected to port two  112 . As seen in  FIG. 7 , signal generator  106  and probe  104  are connected to port two  112  to measure V1 from probe  104 . The formulas are modified as follows: 
     
       
         
           
             
               
                 
                   
                     A 
                     v 
                   
                   = 
                   
                     
                       
                         V 
                          
                         
                             
                         
                          
                         2 
                       
                       
                         V 
                          
                         
                             
                         
                          
                         1 
                       
                     
                     = 
                     
                       
                         
                           
                             
                               S 
                               12 
                             
                             · 
                             
                               Γ 
                               L 
                             
                           
                           + 
                           
                             S 
                             12 
                           
                         
                         
                           1 
                           - 
                           
                             
                               S 
                               11 
                             
                             · 
                             
                               Γ 
                               L 
                             
                           
                           + 
                           
                             S 
                             22 
                           
                           - 
                           
                             
                               S 
                               22 
                             
                             · 
                             
                               S 
                               11 
                             
                             · 
                             
                               Γ 
                               L 
                             
                           
                           + 
                           
                             
                               S 
                               21 
                             
                             · 
                             
                               S 
                               12 
                             
                             · 
                             
                               Γ 
                               L 
                             
                           
                         
                       
                       . 
                     
                   
                 
               
               
                 
                   ( 
                   23 
                   ) 
                 
               
             
           
         
       
     
     Equation (23) can be solved for S 12 : 
     
       
         
           
             
               
                 
                   
                     S 
                     12 
                   
                   = 
                   
                     
                       ( 
                       
                         1 
                         - 
                         
                           
                             S 
                             11 
                           
                           · 
                           
                             Γ 
                             L 
                           
                         
                         + 
                         
                           S 
                           22 
                         
                         - 
                         
                           
                             S 
                             22 
                           
                           · 
                           
                             S 
                             11 
                           
                           · 
                           
                             Γ 
                             L 
                           
                         
                         + 
                         
                           
                             S 
                             21 
                           
                           · 
                           
                             S 
                             12 
                           
                           · 
                           
                             Γ 
                             L 
                           
                         
                       
                       ) 
                     
                     · 
                     
                       
                         
                           A 
                           v 
                         
                         
                           
                             Γ 
                             L 
                           
                           + 
                           1 
                         
                       
                       . 
                     
                   
                 
               
               
                 
                   ( 
                   24 
                   ) 
                 
               
             
           
         
       
     
     After solving for S 12  from equation (24) use the value of S 12 ·S 21  from equation (11) above to solve for S 21 : 
     
       
         
           
             
               S 
               21 
             
             = 
             
               
                 
                   S 
                   12 
                 
                 · 
                 
                   S 
                   21 
                 
               
               
                 S 
                 12 
               
             
           
         
       
     
     In some embodiments of the disclosed technology, probes  102  and  104  can stay connected to the device under test  114 , as shown in  FIG. 4  for each device under test  114  tested. Such an embodiment would be less timing consuming for a user and there would be less chance of damage to the test fixture  108  and the device under test  114  during the probing process. This is especially advantageous for high performance probes that typically must be soldered into place. 
     Initially, the signal generator  106  for the system is characterized as discussed above. That is, signal generator  106  is still characterized without the device under test  114  connected to port one  110  and port two  112 , as shown in  FIG. 1 . 
     Probe  104  is then connected to the test fixture at port two  112  and the device under test  114  and signal generator  106  are also connected to port one  110  and port two  112 , as shown in  FIG. 4 . As discussed above, three different loads from the probe on port two  112  will be switched in from probe  104  while de-embed probe  102  on port one  110  makes a measurement of Γ m1 , Γ m2 , and Γ m3 . These three sets of measurements are used to solve for Ss 11 , S 22 , and S 12 ·S 21  of the device under test  114 , as discussed above with respect to equations (3)-(15). S 11  can be determined by removing the known Γ s  of the signal generator  106  from the parallel combination, as discussed above with respect to equations (16) and (19). 
     Rather than measuring V1 and V2 as discussed above, that is, with only a single probe connected at a time, V1 and V2 can be measured with both de-embed probes  102  and  104  and the device under test  114  connected to port one  110  and port two  112 . These voltages, however, include the loading effects of each probe  102  and  104  on the opposite port  110  and  112 . Equation (20) above, therefore, has to be modified to include the reflection coefficient of port two  112 , Γ P2 , replacing Γ L . It will be assumed that the de-embed probes  102  and  104  have some known load. 
     The signal flow graph shown in  FIG. 8  would be modified as shown in  FIG. 9  to include the effects of the de-embed probes  102  and  104  loading on each port. The value of Γ P2  is for the de-embed probe  104  connected to port two  112  of the device under test  114 . 
     Equation (25) can be used to compute the value of S 21 . The values of S 12 ·S 21 , S 11 , A v , and Γ P2  are known based on the above discussed equations and measurements. 
     
       
         
           
             
               
                 
                   
                     
                       
                         
                           A 
                           v 
                         
                         = 
                           
                          
                         
                           
                             V 
                              
                             
                                 
                             
                              
                             2 
                           
                           
                             V 
                              
                             
                                 
                             
                              
                             1 
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           
                             
                               
                                 
                                   S 
                                   21 
                                 
                                 · 
                                 
                                   Γ 
                                   
                                     P 
                                      
                                     
                                         
                                     
                                      
                                     2 
                                   
                                 
                               
                               + 
                               
                                 S 
                                 21 
                               
                             
                             
                               1 
                               - 
                               
                                 
                                   S 
                                   22 
                                 
                                 · 
                                 
                                   Γ 
                                   
                                     P 
                                      
                                     
                                         
                                     
                                      
                                     2 
                                   
                                 
                               
                               + 
                               
                                 S 
                                 11 
                               
                               - 
                               
                                 
                                   S 
                                   11 
                                 
                                 · 
                                 
                                   S 
                                   22 
                                 
                                 · 
                                 
                                   Γ 
                                   
                                     P 
                                      
                                     
                                         
                                     
                                      
                                     2 
                                   
                                 
                               
                               + 
                               
                                 
                                   S 
                                   12 
                                 
                                 · 
                                 
                                   S 
                                   21 
                                 
                                 · 
                                 
                                   Γ 
                                   
                                     P 
                                      
                                     
                                         
                                     
                                      
                                     2 
                                   
                                 
                               
                             
                           
                           . 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   25 
                   ) 
                 
               
             
           
         
       
     
     Equation (22) can be solved for S 21 : 
     
       
         
           
             
               
                 
                   
                     S 
                     21 
                   
                   = 
                   
                     
                       ( 
                       
                         1 
                         - 
                         
                           
                             S 
                             22 
                           
                           · 
                           
                             Γ 
                             
                               P 
                                
                               
                                   
                               
                                
                               2 
                             
                           
                         
                         + 
                         
                           S 
                           11 
                         
                         - 
                         
                           
                             S 
                             11 
                           
                           · 
                           
                             S 
                             22 
                           
                           · 
                           
                             Γ 
                             
                               P 
                                
                               
                                   
                               
                                
                               2 
                             
                           
                         
                         + 
                         
                           
                             S 
                             12 
                           
                           · 
                           
                             S 
                             21 
                           
                           · 
                           
                             Γ 
                             
                               P 
                                
                               
                                   
                               
                                
                               2 
                             
                           
                         
                       
                       ) 
                     
                     · 
                     
                       
                         
                           A 
                           v 
                         
                         
                           
                             Γ 
                             
                               P 
                                
                               
                                   
                               
                                
                               2 
                             
                           
                           + 
                           1 
                         
                       
                       . 
                     
                   
                 
               
               
                 
                   ( 
                   26 
                   ) 
                 
               
             
           
         
       
     
     Once S 21  has been determined, then S 12  can be determined by using equation (20) above. Then, the S-parameter set of the device under test  114  have been determined while leaving both probes  102  and  104  and the input  116  and output  118  of the device under test  114  connected to port one  110  and port two  112 . 
     Although standard de-embed probes have been discussed above with respect to de-embed probes  102  and  104 , the de-embed probes  102  and  104  can also alternatively be subminiature version A (SMA) input de-embed probes. A standard de-embed probe allows the reference plane for the device under test S-parameter measurement to be established directly at the connector point as desired. However, if an SMA input de-embed probe is used, the S-parameters of the portion of the test fixture  108  between the SMA probe input and up to the reference plane must be measured separately and then de-embedded out of the final measurements. 
     The disclosed technology is not limited to two port devices under test. That is, the disclosed technology can be used to provide S-parameter measurements for devices under test with more than two ports. This is done in a similar manner as vector network analyzers. For example, to measure the S-parameters for a three-port device under test, several two port measurements, as discussed above, are performed between any two ports while the remaining port(s) are terminated with a reference impedance, Z ref . After all combinations of two ports have been measured through the above method, the technique is known to compute out the parameters of the three port system using the two port system parameters. 
     The test and measurement instrument  100  may be an oscilloscope, as discussed above. However, the test and measurement instrument  100  may also be a spectrum analyzer. Further, the test and measurement instrument  100  may include a user interface to allow a user to setup control and initiate the required processes for the test and measurement instrument to act as the vector network analyzer. As mentioned above, the test and measurement instrument  100  includes a processor and a memory (not shown) to store executable instructions for implementing the above discussed process for determining the S-parameter set of a device under test and for otherwise controlling the test and measurement instrument  100 . Computer readable code embodied on a computer readable medium, when executed, causes the computer to perform any of the above-described operations. As used here, a computer is any device that can execute code. Microprocessors, programmable logic devices, multiprocessor systems, digital signal processors, personal computers, or the like are all examples of such a computer. In some embodiments, the computer readable medium can be a tangible computer readable medium that is configured to store the computer readable code in a non-transitory manner. 
     Having described and illustrated the principles of the disclosed technology in a preferred embodiment thereof, it should be apparent that the disclosed technology can be modified in arrangement and detail without departing from such principles. We claim all modifications and variations coming within the spirit and scope of the following claims.