Abstract:
A method and apparatus for calibrating a vector network analyzer for use with a test system using a mathematical model of, for example, a slotted line. Voltage and displacement data sampled along the slotted line, used with the mathematical model, creates a plurality of equations which may be solved to generate a reflection coefficient which may be used as an impedance standard of known accuracy and used to calibrate a VNA thereby, without actual use of precision impedance standards.

Description:
BACKGROUND  
         [0001]    1. Field of the Invention  
           [0002]    The invention generally relates to a method and apparatus for calibration of a vector network analyzer (VNA). Specifically, the invention relates to VNA calibration using, for example, a slotted line and voltage measurements taken from multiple points along the slotted line. Alternatively, a uniform transmission line may be used and the voltage measurements take from discrete points along the uniform transmission line.  
           [0003]    2. Description of Related Art  
           [0004]    VNAs may be used to measure the electrical characteristics of an electrical component/structure, referred to as a device under test (DUT). Measurement accuracy using a VNA is increased if the VNA is calibrated prior to use. Calibration may be performed each time the VNA is energized, exposed to environmental changes or has changes made to the test frequency(s) or test system, i.e. the associated jumpers, connectors/adapters and or couplers used to couple the DUT with the VNA.  
           [0005]    A VNA is calibrated by identifying and quantifying systemic errors present in the test system. VNA&#39;s are generally designed for use with several different methods of calibration to account for the different forms of test system errors. Each method removes one or more of the systematic errors through vector error correction. Vector error correction may characterize the systematic errors by measuring, for example, calibration standards (devices with known s-parameters) then mathematically removing the effects of the systematic errors from subsequent measurements on the DUT.  
           [0006]    A common method of calibration involves the alternate use of shorts, opens, loads, and a thru (direct connection of VNA test ports) using a known high precision standard in place of the DUT. This method may be time consuming and expensive, requiring a range of different standards and or adapters to approximate a range of desired DUTs. Further, each time the test system is assembled with a different standard or configuration, the interconnections between components may become worn or damaged, introducing further errors into the calibration. Also, the connections and reconnections themselves may cause erroneous calibrations due to variances in the torque, contact surface area, contact pressure and or alignment between the various connectors. In many cases, no standard similar to the DUT exists. Further, it may be impossible to connect available standards to each other, the VNA and or the DUT.  
           [0007]    Another calibration method may include a series of test system electrical models loaded into the VNA. The test system electrical model closest to the one actually used to couple the VNA to the DUT is selected and a stored series of error factors applied. The calibration accuracy may be only as accurate as the electrical model used. For maximum accuracy, a separate electrical model may be required for every conceivable test system which might arise and errors may again occur as test system components become worn or damaged, modifying the actual electrical characteristics of the test system from those expected by the chosen model.  
           [0008]    Other VNA calibration methods exist. Some methods are optimized for determining a single form of error systemic to a specific test system and test parameter configuration. For high precision DUT measurement, several calibration methods may be used and the resulting error factors combined. However, multiple calibration methods create additional calibration time and expense.  
           [0009]    It is an object of the present invention to solve these and other problems that will become clear to one skilled in the art upon review of the following specification. 
       
    
    
     BRIEF DESCRIPTION OF THE FIGURES  
       [0010]    The accompanying drawings, which are incorporated in and constitute a part of this specification, illustrate embodiments of the invention and, together with a general description of the invention given above, and the detailed description of the embodiments given below, serve to explain the principles of the invention.  
         [0011]    [0011]FIG. 1 is a diagram showing one embodiment of a test system according to the invention.  
         [0012]    [0012]FIG. 2 is a flow chart showing a typical Calibration and DUT testing sequence, according to the invention. 
     
    
     DETAILED DESCRIPTION  
       [0013]    A VNA test system is shown in FIG. 1. A source signal generated by the VNA is coupled to the test system by an input jumper  10 . A reflected signal is coupled from the test system back to the VNA by an output jumper  20 . The input jumper  10  and output jumper  20  send and receive their respective signals through a directional coupler  30 . The directional coupler  30  is coupled via any required connectors, adapters and or jumpers to a slotted line  40  that is coupled in-line with the DUT, for example an antenna. Alternatively, the directional coupler  30  may be built into the VNA, eliminating the need for input jumper  10 , output jumper  20  and their associated connectors by internalizing them in a hard wired configuration within the body of the VNA. A voltage measurement probe  50 , coupled to the VNA by a sample jumper  60 , may be introduced at a known location along the slotted line  40  to sample the voltage. A position encoder  70  indicates the position of the voltage measurement probe  50  along the slotted line  40 .  
         [0014]    A complex voltage standing wave may be modeled as shown in equation 1:  
           V=V   o ( e   jβx   +ρe   −jβx )   Eq. 1  
         [0015]    In equation 1, x is a position along a conductor, β is the propagation constant, ρ is the voltage reflection coefficient and V o  is the source voltage magnitude.  
         [0016]    If the standing wave is measured by applying the voltage measurement probe  50  along the slotted line  40 , the measured voltage is modeled as shown in equation 2:  
           V   m   =C ( e   jβx   +ρe   −jβx ) e   −jβy Eq.  2  
         [0017]    In equation 2, y is the length of the coupling probe line and C is a constant representing the product of the source voltage and coupling coefficient. Phase shift in the coupling probe may be incorporated into the βy term.  
         [0018]    Multiple equations, generated by taking voltage measurement probe  50  samples at N different positions (x 1 , x 2 , . . . , x N ) along the slotted line  40  at a common frequency, may be described in matrix form by equation 3:  
               {           V     m                 1                 V     m                 2               ⋮             V   mN           }     =       [                j                 β                   x   1                      -   j                   β                   x   1                        j                 β                   x   2                      -   j                   β                   x   2                 ⋮       ⋮                  j                 β                   x   N                      -   j                   β                   x   N               ]          {           C                          -   j                   β                 y                   ρ                 C                          -   j                   β                 y               }               Eq   .              3                               
 
         [0019]    As the slotted line  40  sample voltage measurements are made, some errors are introduced, which may be modeled as shown in equation 4:  
               {           ɛ   1               ɛ   2             ⋮             ɛ   N           }     =         [                j                 β                   x   1                      -   j                   β                   x   1                        j                 β                   x   2                      -   j                   β                   x   2                 ⋮       ⋮                  j                 β                   x   N                      -   j                   β                   x   N               ]          {           C                          -   j                   β                 y                   ρ                 C                          -   j                   β                 y               }       -     {           V     m                 1                 V     m                 2               ⋮             V   mN           }               Eq   .              4                               
 
         [0020]    In matrix notation, equation 4 may be written as shown in equation 5.  
         {tilde over (ε)}= {overscore (B)}{tilde over (p)}−{tilde over (α)}   Eq. 5  
         [0021]    Using parameter estimation, the error may be minimized by selecting for {tilde over (p)} the parameter vector {circumflex over (p)} that is the solution to the following complex matrix equation 6:  
         {overscore (B)} *T {overscore (B)}{circumflex over (p)}={overscore (B)} *T {tilde over (α)}  Eq. 6  
         [0022]    The parameter vector {circumflex over (p)} contains the best estimate of the voltage reflection coefficient of the load. Error statistics, for example the variance, may be computed to indicate how well the set of measurements fit the analytical model (equation 2). For higher accuracy, equation 2 may be enhanced to include known systematic errors in the slotted line. Similar error minimization techniques may be employed to produce the best estimate of the reflection coefficient.  
         [0023]    The reflection coefficient obtained through this method may be considered an impedance standard of known accuracy. One skilled in the art will recognize that this impedance standard may be used in the various error correction/calibration schemes of a VNA.  
         [0024]    For example, the “Response” calibration technique models the VNA system as a complex proportionality constant (the calibration coefficient) as shown in equation 7:  
         ρ c =Aρ m    Eq. 7  
         [0025]    In equation 7, ρ c  is the calibrated reflection coefficient and ρ m  is the measured reflection coefficient. During calibration, the impedance standard provides a known reflection coefficient. Equation 7 may then be easily solved for the calibration coefficient. More elaborate calibration routines may require multiple impedance standard measurements, which may be acquired by making multiple slotted line  40  measurements and processing the data as described above.  
         [0026]    The required calculations/data manipulation may be performed manually or various levels of computer processing may be utilized. The VNA may have embedded data processing circuits and a numeric processor. Alternatively, the VNA may be coupled with an external processor, for example a personal computer (PC) or other well known computing means. Data acquisition/transfer links between the selected computing means, the VNA and or the position encoder  70  may be used to minimize requirements for manual data translation between the devices.  
         [0027]    The position encoder  70  may range in complexity from a simple series of graduated markings along the slotted line  40  to an electromechanical or optical position sensor or a plurality of hardwired switches each coupled to discrete, fixed probes, coupled directly to the, for example, PC.  
         [0028]    The slotted line  40  may be, for example, a coaxial conductor with a slot or a series of spaced apart apertures through which the voltage measurement probe  50  may be inserted to contact the center conductor of the coaxial cable. Alternatively, the voltage measurement probe  50  may be a series of switches each coupled to discrete, fixed probes, coupled by a common sample jumper  60  to the VNA, the switches controlled by the PC and known systemic errors caused by the different switches added depending upon the switch in use, to enable an automated VNA calibration test system.  
         [0029]    Any electrical disturbances, for example connectors between the DUT and the slotted line  40  will not be captured by measurements upon the slotted line  40 . These disturbances may be estimated and added to the calculation manually or the electrical model enhanced to include these effects. Alternatively, the slotted line  40  may be formed with a direct lead to the DUT, minimizing systemic errors that are not accounted for in the calibration. For example, the slotted line may be formed in a section of antenna mast. In this embodiment, the device under test may be an antenna or antenna element, for example a radiating slot or radiator element. Errors due to connector wear and improper connector assembly may be reduced by attaching the directional coupler  30  directly to the slotted line  40 , thereby removing one set of connectors and their associated systemic errors.  
         [0030]    In a micro circuit embodiment, the slotted line  40  may be formed in a, for example CMOS, integrated circuit with different voltage measurement probe  50  sample points switchable by semiconductor based switches coupled to fixed probes, and taken off to an array of leads from the CMOS package. In this form, measurements upon a micro circuit and or micro strip antenna may be made without requiring the insertion of circuit testing clips/jumpers and their associated systemic errors, in-line. In the analysis of an integrated circuit, it may be impossible to attach standards. However, by the method described above, fixed probes may be integrated into the design of the integrated circuit to enable circuit analysis according to the invention.  
         [0031]    In other embodiments, the slotted line  40  may be replaced with other structures providing independent measurements of complex voltage standing wave ratios and or complex reflection coefficients. Multiple measurements generating a plurality of equations solvable for the, for example, reflection coefficient as described above.  
         [0032]    The measurements and data processing described herein may be used as part of a calibration method as shown in FIG. 2. Calibration data acquisition and processing, calibration coefficient generation, error statistical handling, DUT impedance generation and VNA calibration coefficient generation may be used to calibrate the VNA. The calibrated VNA being regularly checked and updated as necessary to ensure that the DUT measurements obtained from the calibrated VNA are as accurate as possible.  
         [0033]    As decribed, the invention provides a reflection calibration method using a simplified test apparatus that does not use the previously required series of precision impedance standards and repeated modifications to the test system interconnections. If desired, the calibration calculations may be fully automated by the use of a position encoder  70  which cooperates with the VNA to feed test system slotted line  40  voltage measurement and position data to a processor which may be external or internal to the VNA.  
                                             Table of Parts                                    10   input jumper           20   output jumper           30   directional coupler           40   slotted line           50   voltage measurement probe           60   sample jumper           70   position encoder                      
 
         [0034]    Where in the foregoing description reference has been made to ratios, integers, components or modules having known equivalents then such equivalents are herein incorporated as if individually set forth.  
         [0035]    While the present invention has been illustrated by the description of the embodiments thereof, and while the embodiments have been described in considerable detail, it is not the intention of the applicant to restrict or in any way limit the scope of the appended claims to such detail. Additional advantages and modifications will readily appear to those skilled in the art. Therefore, the invention in its broader aspects is not limited to the specific details, representative apparatus, methods, and illustrative examples shown and described. Accordingly, departures may be made from such details without departure from the spirit or scope of applicant&#39;s general inventive concept. Further, it is to be appreciated that improvements and/or modifications may be made thereto without departing from the scope or spirit of the present invention as defined by the following claims.