Abstract:
A method of calibrating a measurement path of a vector network analyzer having at least two reference receivers, and a total of 2N measurement ports, where N is an integer comprises the steps of presenting a high reflect calibration standard at each measurement port and measuring a reflection characteristic for each measurement port. The method further comprises the steps of presenting a line calibration standard and a through calibration standard is presented between N direct pairs of the measurement ports and measuring reflection and transmission responses to each standard. From these measurements, the method calculates directivity, source match, and reflection tracking error coefficients for each one of the measurement ports.  
     An apparatus for calibrating a measurement path comprises a VNA having at least two reference receivers, two test channels, and a total of 2N measurement ports, wherein N is an integer. The apparatus further comprises a means for measuring and storing reflection and transmission characteristics for each measurement port when a high reflect, a line, and a through calibration standard is connected thereto. The apparatus further comprises a means for calculating directivity, source match, reflection tracking, load match, forward transmission tracking, and reverse transmission tracking for each one of the measurement ports.

Description:
BACKGROUND  
         [0001]    A vector network analyzer (“VNA”) is used to characterize the behavior of an electrical device over a band of frequencies. Because of mismatches and leakage, it is not currently possible to directly measure a device under test (“DUT”) at high frequencies without calibration of the VNA. Errors exist in any measurement using a VNA. These measurement errors contribute to the uncertainty of the measurement attributable only to the DUT. By quantifying these measurement errors, their effects can be mathematically removed from the measurement to yield characterization parameters for the device itself. As one of ordinary skill in the art can appreciate, the better the quantification of the measurement errors, the better the ability to remove their effects on the device characterization. Measurement errors in the VNA can be separated into two categories: random errors and systematic errors. Random errors are non-repeatable measurement variations due to noise and temperature changes. Random errors are unpredictable and are difficult to adequately quantify. Systematic errors are repeatable measurement variations in the VNA test-set hardware. Systematic errors are predictable and are possible to quantify and mathematically remove. Systematic errors are the most significant source of VNA measurement uncertainty in the characterization of a device. Therefore, it is beneficial to quantify and remove the systematic errors from the VNA measurements. Conventionally, quantification of the systematic errors is achieved through a VNA calibration. By connecting a number of known calibration artifacts to ports of the VNA, one can measure the calibration artifacts, compare the measured results against known results, and then algorithmically extract systematic error coefficients from the contribution made to the measurement from the known calibration device. Measurements of an unknown device, thereafter, use the systematic error coefficients to mathematically extract the characteristics attributable only to the DUT.  
           [0002]    There are a number of calibration procedures available for a 2-port VNA. Calibration methods are named after the group of calibration standards used to extract systematic error coefficients. Some of the more common methods use short, open, load and through calibration standards (“SOLT”), through, reflect, and line calibration standards (“TRL”) and a series of electronic loads used as calibration standards (“electronic calibration” or “Ecal”).  
           [0003]    A preferred method in metrology laboratories is the TRL calibration. It is preferred because it achieves the most accurate assessment of the systematic errors. This is due to the use of an airline standard that can be manufactured very precisely. Additionally, there is no need to know the magnitude of the reflection coefficient of the “reflect” calibration artifact and no need to know the delay of the “line” calibration artifact. Better measurement accuracy in a manufacturing environment provides better feedback in product process control as well as more accurate statistical models for the product cost analysis. Better measurement accuracy in a research and engineering environment provides a more accurate device model permitting simulators to more accurately predict behavior of the product in the context of a circuit.  
           [0004]    U.S. patent application Ser. No. 10/098,040 having priority date Sep. 18, 2000 entitled “Method and Apparatus for Linear Characterization of Multiterminal Single-ended or Balanced Devices” (herein “the &#39;040 patent application Ser. No. ”), and other U.S. Patent Applications claiming priority from the same Provisional Application, disclose a method and apparatus for an SOLT calibration applicable to multiport devices. With specific reference to FIG. 1 of the drawings, there is shown a system block diagram of a 4-port VNA  100  connected to a device under test  101  (“DUT”) as described by the &#39;040 patent application Ser. No. in which a single reference channel  102  and two test channels, first test channel  111  (“A”) and second test channel  112  (“B”), are deployed. The reference channel  102  samples the incident signal, generated by signal generator  105 , through a reference channel sampler  110  placed in series between the signal generator  105  and source transfer switch  106 . The source transfer switch  106  electrically connects the signal generator  105  to a first signal path  107  or a second signal path  108 . The source transfer switch  106  terminates the signal path  107  or  108  that is not connected to the signal generator  105  in a source transfer characteristic impedance  109 . A switching network  150  provides for a connection of the first or second test channel  111 ,  112  to one of 2N measurement ports  103   1 , through  103   2N . The switching network  150  is taught in the &#39;040 patent application Ser. No., the teachings of which are hereby incorporated by reference.  
           [0005]    The first and second test channels  111 ,  112  measure the scattered reflected and transmitted signals from one of the measurement ports  103  connected to the DUT  101  in response to the stimulus from the signal generator  105 . The test set-up of FIG. 1 provides for a complete SOLT calibration methodology. There is a need, however, for a more accurate method of device characterization. Under the prior art, the TRL calibration method provides for improved calibration accuracy, but is applicable only to 2 port devices. There is a need, therefore, for a method and apparatus for more accurate calibration and measurement of multiport devices.  
         SUMMARY  
         [0006]    A method of calibrating a measurement path of a vector network analyzer comprises the steps of providing a vector network analyzer having at least two reference receivers, and a total of 2N measurement ports, where N is an integer. A high reflect calibration standard is presented at each measurement port and the VNA measures a reflection characteristic for each measurement port. A line calibration standard is presented between N direct pairs of the measurement ports. The VNA then measures forward and reverse reflection and transmission characteristics for each one of the N direct pairs. A through calibration standard is presented between each one of the N direct pairs and forward and reverse reflection and transmission characteristics for each one of the N pairs is measured. The method then calculates directivity, source match, and reflection tracking error coefficients for each one of the measurement ports.  
           [0007]    An apparatus for calibrating a measurement path of a vector network analyzer (“VNA”) comprises a vector network analyzer having at least two reference receivers, two test channels, and a total of 2N measurement ports, wherein N is an integer. The system further comprises a means for measuring and storing high reflect characteristics for each measurement port when a high reflect calibration standard is connected thereto, line forward and reverse reflection and transmission characteristics for each one of N direct pairs of the measurement ports when a line calibration standard is connected therebetween, direct through forward and reverse reflection and transmission characteristics for each one of the N direct pairs when a through calibration standard is connected therebetween, and indirect through forward and reverse reflection and transmission characteristics for each one of said N−1 indirect pairs of said measurement ports when said through calibration standard is connected therebetween. The system further comprises a means for calculating directivity, source match, and reflection tracking for each one of the measurement ports based upon the high reflect characteristics, said line forward and reverse reflection and transmission characteristics, and said through forward and reverse reflection and transmission characteristics, load match for each measurement port and forward transmission tracking and reverse transmission tracking for each one of the N direct pairs and N−1 indirect pairs. 
       
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS  
       [0008]    [0008]FIG. 1 illustrates a prior art test set-up and VNA.  
         [0009]    [0009]FIG. 2 shows an apparatus according to the teachings of the present invention.  
         [0010]    [0010]FIGS. 3 through 16 show steps for measuring direct pairs of measurement ports in an embodiment of a method according to the present teachings.  
         [0011]    [0011]FIGS. 17 and 18 show steps for measuring indirect pairs of measurement ports in an embodiment of a method according to the present teachings.  
         [0012]    [0012]FIG. 19 shows a flow graph of error coefficients for X and Y error adapters.  
         [0013]    [0013]FIGS. 20 and 21 show steps for measuring proximal pairs of measurement ports in an embodiment of a method according to the present teachings.  
         [0014]    [0014]FIGS. 22 through 26 illustrate a flow chart of an embodiment of a method according to the present teachings. 
     
    
     DETAILED DESCRIPTION OF INVENTION  
       [0015]    With specific reference to FIG. 2 of the drawings, there is shown a system block diagram of a 4-port VNA  200  that deploys first and second reference channels  201 ,  202 , respectively, and first and second reference channel samplers  110 ,  210 , respectively. In the test set-up shown in FIG. 2, the samplers  110 ,  210  in a specific example may be bridges or directional couplers. The reference channel samplers  110 ,  210  are placed in the first and second signal paths  107 ,  108  on an opposite side of a signal transfer switch  106  from signal generator  105 . The samplers  110 ,  210  extract in one direction a small and predictable portion of the signal present on the first and second signal paths  107 ,  108  for measurement by the first and second reference channels  201 ,  202 , respectively. The sampled portion is typically −10 dB to −20 dB relative to the signal level on the signal path  107  or  108 . The source transfer switch  106  connects either the signal generator  105  to the first signal path  107  and a signal transfer switch terminating load  109  to the second signal path  108  or connects the signal generator  105  to the second signal path  108  and connects the signal transfer switch terminating load  109  to the first signal path  107 . In a specific embodiment, there are only two switch positions for the signal transfer switch  106 .  
         [0016]    A system for measuring a multiple port DUT  101  has as many measurement ports  103   1  through  103   2N  as there are DUT ports. The illustrative example shown in the drawings includes a 4-port DUT  101  connected to measurement ports  103   1 ,  103   2 ,  103   3 , and  103   4 . The teachings of the present invention, however, may be applied to a multiport test set-up for measuring DUTs having more than four device connections. A switch network  150  permits connection of each measurement port  103   1  through  103   2N  to a first or second signal path  107 ,  108  or to a local terminating impedance,  104   1  through  104   2N . Certain switch network configurations connect one of the measurement ports  103  to the first signal path  107  or/and a different one of the measurement ports  103  to the second signal path  108  while the remaining paths are terminated in the local terminating impedance  104 . The switch network  150  also has sampling arms  113 , sampling arms  113   1  through  113   4  in the illustrated embodiment. The sampling arms  113   1  through  113   4  each comprise a sampler  114  that samples a small and predictable portion of the signal level present at the respective measurement port  103 . The sampler  113  may be a coupler or a bridge that takes somewhere between −10 dB and −20 dB of the signal level from the signal level present on the respective measurement port  103 . In a specific embodiment according to the present teachings, the portion sampled from the measurement ports  103  is substantially the same portion sampled from the signal paths  107 ,  108 . The sampled signal may then be connected to either a first or second test channel  111 ,  112  through a respective sampling switch  115  or may be connected to a sampling arm terminating load  116 . A switch network  150  of this configuration may connect a reflection path from the measurement ports  103  to one of first and second test channels  111 ,  112  while terminating the reflection paths from measurement ports  103  not connected to a test channel in a local sampling arm terminating impedance  116 .  
         [0017]    In a method according to the teachings of the present invention, a TRL calibration on a multi-port DUT having 2N device connections is performed by conducting a conventional 2-port TRL calibration first on each one of N direct pairs of the measurement ports. A user may define the N direct pairs by representing all measurement ports  103  in groupings of two measurement ports  103 , where a first port in the direct pair is capable of connection to the first test channel  111  and a second, port in the direct pair is capable of connection to the second test channel  112 . As an example, if there are 2N measurement ports, the direct pairs of measurement ports are measurement ports  103   1  and  103   N+1 , measurement ports  103   2  and  103   N+2 , et seq. up to the direct pair of measurement ports  103   N  and  103   2N  where measurement ports  103   1  through  103   N  are capable of connection to the first test channel  111  and measurement ports  103   N+1  through  103   2N  are capable of connection to the second test channel  112 .  
         [0018]    The method according to the present teachings then performs a through measurement on N−1 indirect pairs of the measurement ports  103  for a 2N port DUT. The N−1 indirect pairs are defined as those groupings of two measurement ports  103  that are not represented in the set of direct pairs of measurement ports where a first measurement port in the indirect pair is capable of connection to the first test channel  111  and the second measurement port in the indirect pair is capable of connection to the second test channel  112 . In the illustrated example, there are two direct pairs; first direct pair comprising measurement ports  103   1  and  103   3  and second direct pair comprising measurement ports  103   2  and  103   4 . Also in the specific example, there are two indirect pairs; first indirect pair comprising measurement ports  103   1  and  103   4  and second indirect pair comprising measurement ports  103   2  and  103   3 .  
         [0019]    With specific reference to FIG. 3 of the drawings, there is shown a high reflect calibration standard  301  (“the reflect  301 ”) connected to the measurement port  103  of the first direct pair that is capable of connection to the first test channel  111 . In the illustrated embodiment, this is measurement port  103   1 . The switching network  150  is then set so the measurement port  103   1  is connected to the first signal path  107  and the respective sampling arm  113   1  is connected to the first test channel  111 . All remaining unused measurement ports  103   2 ,  103   3  and  103   4  are terminated in their respective local terminating loads  104  and their respective sampling arms  113  are connected to the sampling arm terminating loads  116   2 ,  116   3 , and  116   4 . As one of ordinary skill in the art appreciates, for measurement of the measurement port  103   1  only the switch network configuration that terminates in a characteristic impedance those measurement ports  103  that are capable of connection to the first test channel  111  are important to the results. Because the isolation of the switches that comprise the switch network  150  is so high, the measurement ports  103  capable of connection to the second test channel  112  do not figure in the high reflect measurement. The reflect  301  may have an unknown magnitude, but its phase charcateristics must be known. The signal generator  105  is then swept through a desired frequency range as programmed by an operator and measurements are taken at specific frequencies across the range. During the frequency sweep the VNA  200  measures and stores a ratio of the measured signal level at the first test channel  111  over the measured signal level at the first reference receiver  201 . The resulting ratio is a frequency dependant reflection coefficient, herein referred to as a high reflect characteristic for measurement port  103   1 .  
         A reflect     —     1 /R1 reflect     —     1    
         [0020]    With specific reference to FIG. 4 of the drawings, the same reflect  301  is disconnected from measurement port  103   1  and is connected to the remaining measurement port in the first direct pair, measurement port  103   3  in the specific example. The switch network  150  is then configured so that the measurement port  103   3  is in the second signal path  108 , the first signal path  107  is terminated in a characteristic impedance  109 , and the sampling arm  113   3  is connected to the second test port  112 . The unused measurement ports  103  capable of connection to the second test port  112 , the measurement port  103   4  in the specific example, are terminated in the local characteristic impedance  104  in the switching network  150 . The sampling arms  113  of the unused measurement ports  103  are also terminated in the respective sampling arm terminating loads  116 . The signal generator  105  stimulates the second signal path  108  with a signal that is swept over the same desired frequency range as in the reflection measurement of measurement port  103   1 . The VNA  200  measures and stores a measurement of a ratio of the measured signal level at the second test channel  112  over measured signal level of the second signal path  108  as presented to the second reference receiver  202  yielding a frequency dependent array of reflected signal level, herein referred to as a high reflect characteristic for measurement port  103   3 :  
         B reflect     —     3 /R2 reflect     —     3    
         [0021]    With specific reference to FIG. 5 of the drawings, a next step in the calibration process is to connect a low-loss delay line calibration standard  401  (“the line  401 ”) between the first direct pair, measurement port  103   1  and measurement port  103   3  in the illustrated example. In a preferred embodiment, the line  401  is an airline i.e. a delay line having an air dielectric, which is commonly used in metrology laboratories. For on-wafer measurements, a delay line is used. The delay of the line  401  is unknown, but the physical dimensions of the line  401  relate to a range of calibration frequencies. Additional delay line calibration standards can be used to cover a broader frequency range as desired. The delay of the line  401  is defined over a range of frequencies bounded by approximately more than 20 degrees phase shift at a lowest specified frequency and less than 160 degrees phase shift at a highest specified frequency. At frequencies around 500 MHz and below, coaxial airline dimensions become very large and not practical. In this case, and with specific reference to FIG. 6, two high-quality matched loads  501  (“the matched loads  501 ”) are connected to each measurement port  103  of the direct pair. The matched loads  501  are used for calibrating the VNA in a frequency range down to the lowest VNA frequency. The resulting calibration values of the line  401  and the matched loads  501  are different, but the algorithmic formulations using the measured ratios are the same.  
         [0022]    With specific reference to FIG. 5 of the drawings in which the line  401  is measured, the transfer switch  106  is set so that the signal generator  105  stimulates the first signal path  107  and the second signal path  108  is terminated at the characteristic impedance  109 . The switch network  150  is configured so that the measurement port  103   1  accepts the stimulus signal from the first signal path  107  and the signal from the sampling arm  113   1  is presented to the first test port  111 . The switch network  150  is further configured so that the measurement port  103   3  is terminated in the transfer switch characteristic impedance  109  through second signal path  108  and a transmitted signal is presented to the second test port  112  through sampling arm  113   3 . The signal generator  105  sweeps the desired frequency range and the VNA  200  measures signal level from the first and second test channels  111 ,  112  and the first and second reference receivers  201 ,  202  and stores the results in a data array. For purposes of clarity and consistency only, when the signal generator  105  is connected to the first signal path  107 , all resulting measurements are considered forward direction measurements. Accordingly, the measurements made of the line  401  in the forward direction are represented as the data arrays:  
         [0023]    A f     —     line     —     13 ,  
         [0024]    B f     —     line     —     13 ,  
         [0025]    R1 f     —     line     —     13 , and  
         [0026]    R2 f     —     line     —     13 .  
         [0027]    where each array comprises a series of measured points at specific frequencies along the desired frequency range.  
         [0028]    The transfer switch  106  is then reconfigured (not shown in the drawings) so that the signal generator  105  stimulates the second signal path  108  and the first signal path  107  is terminated in the transfer switch characteristic impedance  109 . The configuration of the switch network  150  is not changed from the forward direction measurements. The signal generator  105  again sweeps the desired frequency range and the VNA  200  measures signal level from the first and second test channels  111 ,  112  and the first and second reference receivers  201 , 202  and stores them in data arrays. For purposes of clarity and consistency only, when the signal generator  105  is connected to the second signal path  108 , all resulting measurements are considered reverse direction measurements. Accordingly, the measurements made of the line  401  in the reverse direction are represented as the data arrays:  
         [0029]    A r     —     line     —     13 ,  
         [0030]    B r     —     line     —     13 ,  
         [0031]    R1 r     —     line     —     13 , and  
         [0032]    R2 r     —     line     —     13 .  
         [0033]    where each array comprises a series of measured points at specific frequencies along the desired frequency range.  
         [0034]    If a broader frequency range is necessary, the same measurement procedure is performed on the first direct pair, measurement ports  103   1  and  103   3  in the specific embodiment, with a different airline covering a different frequency band. In addition, the matched loads  501  as shown in FIG. 6 of the drawings may be used to simulate a high loss line having a perfect match in order to take measurements at lower frequencies than are practical with an airline calibration standard. Depending upon the matched load, the quality of the match at higher frequencies, and the desired frequency range, the matched loads may be used in place of the airline calibration standard. As new measurements are made for the different frequency ranges using the appropriate calibration standards, the results are stored in the forward and reverse direction arrays with each data point corresponding to a specific stimulus signal frequency. Accordingly, the calibration frequency band can extend over more frequencies than is possible with a single airline calibration standard.  
         [0035]    With specific reference to FIG. 7 of the drawings, a next step in the calibration process is to connect a through calibration standard  601  (“the thru  601 ”) between the first direct pair, measurement port  103   1  and measurement port  103   3  in the illustrated embodiment. The thru  601  may have either a zero length or a non-zero length. In either case, an electrical length of the thru  601  must be a known value. For on-wafer measurements, it is not possible to obtain a high quality zero thru calibration standard. Accordingly, for on-wafer measurements, the non-zero thru calibration standard is used.  
         [0036]    To measure the thru  601 , the transfer switch  106  is set so that the signal generator  105  stimulates the first signal path  107  and the second signal path  108  is terminated in the transfer switch characteristic impedance  109 . The switch network  150  is configured so that the measurement port  103   1  accepts the stimulus signal from the first signal path  107  and the sampling arm  113   1  is connected to the first test port  111 . The switch network  150  is further configured so that the measurement port  103   3  is terminated in the transfer switch characteristic impedance  109  through second signal path  108  and the sampling arm  113   3  is connected to the second test port  112 . The unused measurement ports  103 , which in the specific embodiment comprise measurement ports of the second direct pair, measurement port  103   2  and measurement port  103   4 , are terminated in the local characteristic impedances  104   2  and  104   4 , respectively. The sampling arms  113   2  and  113   4  are also terminated in local sampling arm terminating loads  116   2  and  116   4 . The signal generator  105  sweeps the desired frequency range and the VNA  200  measures signal level from the first and second test channels  111 ,  112  and the first and second reference receivers  201 ,  202  and stores the results in memory. According to the nomenclature used for purposes of the present disclosure, because the signal generator  105  is connected to the first signal path  107 , the resulting measurements are considered forward direction measurements. Accordingly, the measurements made of the thru  601  in the forward direction are represented as the arrays:  
         [0037]    A f13     —     thru ,  
         [0038]    B f13     —     thru ,  
         [0039]    R1 f13     —     thru , and  
         [0040]    R2 f13     —     thru .  
         [0041]    where each array comprises a series of measured points at specific frequencies along the desired frequency range.  
         [0042]    The transfer switch  106  is then set (not shown) so that the signal generator  105  stimulates the second signal path  108  and the first signal path is terminated in the transfer switch characteristic impedance  109 . The switch network  150  is not changed. The signal generator  105  again sweeps the desired frequency range and the VNA  200  measures signal level from the first and second test channels  111 ,  112  and the first and second reference receivers  201 ,  202  and stores them in memory. Because the signal generator  105  is connected to the second signal path  108 , the resulting measurements are considered reverse direction measurements. Accordingly, the measurements made of the thru  601  in the reverse direction are represented as the arrays:  
         [0043]    A r13     —     thru ,  
         [0044]    B r13     —     thru ,  
         [0045]    R1 r13     —     thru , and  
         [0046]    R2 r13     —thru   .  
         [0047]    where each array comprises a series of measured points at specific frequencies along the desired frequency range.  
         [0048]    With specific reference to FIG. 8 of the drawings and with the thru  601  still connected, the transfer switch  106  is configured so that the signal generator  105  is in the first signal path  107  and the second signal path  108  is terminated in the characteristic impedance  109 . Measurements of the first direct pair are still being made. Accordingly, the switch network  150  is configured so that the measurement port  103   1  is connected to the first signal path  107  and the respective sampling arm  113   1  is connected to the first test channel  111 . The remaining unused measurement ports  103  capable of connection to the first test channel  111 , measurement port  103   2  in the specific example, are terminated at respective local characteristic impedances  104 , local characteristic impedance  104   2  in the specific example. In addition, the sampling arm  113   2  of the unused measurement port  103   2  is terminated in local sampling arm characteristic impedance  116   2 . The switch network  150  is further configured so that the measurement port capable of connection to the second test channel  112  in the first direct pair, specifically measurement port  103   3 , is terminated at the respective local characteristic impedance,  104   3  in the specific example, and the respective sampling arm,  113   3  is connected to the second test channel  112 . The measurement ports  103  of the direct pairs not being measured are also terminated in local characteristic impedances, local characteristic impedance  104   2  and  104   4  in the specific example, and the respective sampling arms  113   2  and  113   4  are terminated in local sampling arm terminating load  116   2  and  116   4 . The signal generator  105  is again swept through the desired frequency range and for each frequency point in the range, the VNA  200  measures a ratio of the reflection response over the stimulus and a ratio of the transmission response over the stimulus of the terminated thru  601  and stores the data in the following arrays:  
         [0049]    A f13     —     termthru /R1 f13     —     termthru    
         [0050]    B f13     —     termthru /R1 f13     —     termthru .  
         [0051]    With specific reference to FIG. 9 of the drawings, the thru  601  is still connected between the measurement ports  103  of the first direct pair and the transfer switch  106  is then re-configured so that the signal generator  105  is in the second signal path  108  and the first signal path  107  is terminated in the characteristic impedance  109 . The switch network  150  is also reconfigured so that the measurement port  103  in the first direct pair that is capable of connection to the second test channel  112 , measurement port  103   3  in the illustrated example, is connected to the second signal path  108  and the respective sampling arm  113   3  is connected to the second test channel  112 . The measurement port  103  in the first direct pair that is capable of connection to the first test channel  111 , measurement port  103   1  in the illustrated example, is terminated in the respective local characteristic impedance  104   1  and the respective sampling arm  113   1  is connected to the first test channel  111 . The measurement ports  103  of the direct pairs not being measured are locally terminated in their characteristic impedances,  104   2  and  104   4  in the illustrated example. Additionally, the sampling arms  113  of the unused measurement ports  103 , sampling arms  113   2  and  113   4  in the illustrated example, are terminated in their respective local sampling arm terminating loads  116   2  and  116   4 . The signal generator  105  is swept through the desired frequency range and for each frequency point in the range, the VNA  200  measures a ratio of the signal level of the reflection response of the terminated thru  601  over the signal level of the stimulus signal as measured at the reference channel  201 , and a ratio of the signal level of the transmission response of the terminated thru  601  over the signal level of the stimulus signal. The measured values are stored in data arrays:  
         [0052]    A r13     —     termthru /R1 r13     —     termthru , and  
         [0053]    B r13     —     termthru /R2 r13     —     termthru .  
         [0054]    With specific reference to FIGS. 10 through 16 of the drawings, the same calibration steps and measurements described in reference to FIGS. 3 through 9 of the drawings, are carried out for the measurement ports that comprise the second direct pair, measurement port  103   2  and measurement port  103   4  in the illustrated example. Accordingly, the resulting data gathered through the process for the second direct pair is measured and stored in the data arrays:  
         [0055]    A reflect     —     2 ,  
         [0056]    R1 reflect     —     2 ,  
         [0057]    B reflect     —     4 ,  
         [0058]    R2 reflect     —     4 ,  
         [0059]    A f24     —     line ,  
         [0060]    B f24     —     line ,  
         [0061]    R1 f24     —     line ,  
         [0062]    R2 f24     —     line ,  
         [0063]    A r24     —     line ,  
         [0064]    B r24     —     line ,  
         [0065]    R1 r24     —     line ,  
         [0066]    R2 r24     —     line ,  
         [0067]    A f24     —     thru ,  
         [0068]    B f24     —     thru ,  
         [0069]    R1 f 24     —     thru ,  
         [0070]    R2 f24     —     thru ,  
         [0071]    A r24     —     thru ,  
         [0072]    B r24     —     thru ,  
         [0073]    R1 r24     —     thru ,  
         [0074]    R2 r24     —     thru ,  
         [0075]    A f24     —     termthru /R1 f24     —     termthru ,  
         [0076]    B f24     —     termthru /R1 f24     —     termthru ,  
         [0077]    B r24     —     termthru /R2 r24     —     termthru ,  
         [0078]    A r24     —     termthru /R2 r24     —     termthru .  
         [0079]    where all of the data arrays having a single point of measurement for each frequency measured in the desired frequency range. It is best practice to measure the same frequency points along the range so that each array has a measured value for each frequency point. It is acceptable, however, to interpolate the data to obtain a value for a specific frequency value as long as the frequency value is within the boundary of the lowest measured frequency and the highest measured frequency in the desired frequency range and the interval between measured frequencies is small enough to fully characterize the DUT including any resonances thereof. If multiple line calibration standards are used to obtain a broader frequency range, the measurements taken by the VNA  200  are stored in appropriate array elements in a larger array having an element for each frequency along the frequency range of interest. Accordingly, multiple steps of connecting calibration standards and making measurements may be performed to completely populate a single data array.  
         [0080]    In a multiport calibration according to an aspect of an embodiment of the present invention, the same calibration steps and measurements described in FIGS. 3 through 9 of the drawings are carried out for the measurement ports of all of the direct pairs. The general description of a set of direct pairs for a DUT having 2N ports comprises the set where m is a set of integers between 1 and N, and the direct pairs are the measurement port  103   m  and measurement port  103   N+m . Measurements of each direct pair yield a  22  data arrays that are stored and maintained in an embodiment of a system according to the teachings of the present invention.  
         [0081]    With specific reference to FIG. 17 of the drawings, the next step of the process is to connect the thru  601  between the first indirect pair of measurement ports, which in the illustrated embodiment comprises measurement port  103   1  and measurement port  103   4 . The signal transfer switch  106  is configured so that the signal generator  105  stimulates the first signal path  107  and the second signal path  108  is terminated in the characteristic impedance  109 . The switch network  150  is configured so that the measurement port  103  of the first indirect pair that is capable of connection to the first test channel  111 , measurement port  103   1  in the illustrated example, is connected to the first signal path  107  and the respective sampling arm  113   1  is connected to the first test channel  111 . The switch network  150  is further configured so that the measurement port  103  of the first indirect pair that is capable of connection to the second test channel  112 , measurement port  103   4  in the illustrated example, is terminated at the respective local terminating load  104   4  and the respective sampling arm  113   4  is connected to the second test channel  112 . All unused measurement ports, measurement port  103   2  and measurement port  103   3  in the specific example, are terminated in the respective local terminating load  104   2  and  104   3  and their respective sampling arms  113   2  and  113   4  are terminated in respective local sampling arm terminating loads  116   2  and  116   3 . The signal generator  105  is then swept over the desired frequency range and the ratio of the signal level at the first test channel  111  over the signal level at the first reference receiver  201  is measured and stored as additional data arrays:  
         [0082]    A f14     —     thruterm /R1 f14     —     thruterm , and  
         [0083]    B f14     —     thruterm /R1 f14     —     thruterm .  
         [0084]    The transfer switch  106  is then reconfigured (not shown) so that the signal generator  105  stimulates the second signal path  108  and the first signal path  107  is terminated in the characteristic impedance  109 . The switch network  150  is configured so that the measurement port in the first indirect pair that is capable of connection to the first test channel  111 , measurement port  103   1 , is terminated in the local terminating load  104   1 . The measurement port in the first indirect pair that is capable of connection to the second test channel  112 , measurement port  103   4  in the illustrated example, is connected to the second signal path  108 . The signal generator  105  is then swept over the desired frequency range and the ratio of the signal level at the second test channel  112  over the signal level at the second reference receiver  202  is measured and stored as a additional arrays:  
         [0085]    A r14     —     thruterm /R2 r14     —     thruterm ,  
         [0086]    B r14     —     thruterm /R2 r14     —     thruterm .  
         [0087]    Similarly, and with specific reference to FIG. 18 of the drawings, the same measurement and storage steps made for the first indirect pair, measurement port  103   1  and measurement port  103   4  in the illustrated example, are performed for the second indirect pair, measurement port  103   2  and measurement port  103   3  in the illustrated example. Briefly, the thru  601  is connected between the measurement ports  103  of the second indirect pair. In a first step, the thru  601  is terminated in a local terminating impedance at  104   3 , is stimulated in a forward direction, while the ratio of the signal level present at the first test channel  111  over the first reference receiver  201  is measured and stored and the ratio of the signal level present at the second test channel  112  over the first reference receiver  201  is measured and stored to yield the frequency dependent data arrays:  
         [0088]    A f23     —     thruterm /R1 f23     —     thru     —     term , and  
         [0089]    B f23     —     thruterm /R1 f23     —     thruterm .  
         [0090]    The switch network  150  is then reconfigured so that the signal generator  105  stimulates the second signal path  108 , the measurement port  103  of the indirect pair capable of connection to the second test channel  112  is connected to the second signal path  108  and the measurement port  103  of the indirect pair capable of connection to the first test channel  111  is terminated in a local terminating load  104 . The signal generator  105  is swept over the desired frequency range and the ratios are measured and stored to yield the frequency dependent arrays:  
         [0091]    A r23     —     thruterm /R2 r23     —     thruterm , and  
         [0092]    B r23     —     thruterm /R2 r23     —     thruterm .  
         [0093]    In a multiport embodiment of a method according to the teachings of the present invention, additional similar measurements are taken for each direct pair and each indirect pair of the measurement ports  103 .  
         [0094]    With specific reference to FIG. 19 of the drawings, there is shown a TRL calibration flow graph between any first port and any second port of the VNA  200 . A multiport embodiment has a different calibration flow graph to represent the directivity  1901 , source match  1902 , and reflection tracking error coefficients  1903  for the X error adapter  1910  and directivity  1904  source match  1905 , and reflection tracking error coefficients  1906  for the Y error adapter  1920  An embodiment of a method according to the present teachings determines the X error adapter  1910  and the Y-error adapter  1920  for each direct pair. The flow graph represents an S-parameter matrix for the X error adapter  1910 , S x , which corresponds to the error artifacts for a first measurement port  103  in the direct pair, and an S-parameter matrix for the Y error adapter  1920 , S y , which corresponds to the error artifacts for a second measurements port  103  in the direct pair.  
         [0095]    S-parameter matrix S act  represents the S-parameters of an actual calibration standard without the contribution of the X and Y error adapters. The S-parameter matrices of the X error adapter may be expressed as T-parameters using the following known conversion where port  1  is on the left and port  2  is on the right when looking at the DUT  101 :  
             Tx   =       [           Tx   11           Tx   12               Tx   21           Tx   22           ]     =     [           1     Sx   21               -     Sx   22         Sx   21                   Sx   11       Sx   21                   Sx   12          Sx   21       -       Sx   11          Sx   22           Sx   21             ]               (   1   )                               
 
         [0096]    Accordingly, the matrix Sx may be converted into corresponding T-parameters expressed as Tx. If the matrix T act     —     thru  expresses the T-parameters of just the thru  601  and T meas     —     thru  expresses the T-parameters of the thru  601  as measured in context with the X and Y error adapters, then the following relationship holds true:  
           T   x   T   act     —     thru   T   y   =T   meas     —     thru    (2)  
         [0097]    Similarly, if the matrix T act     —     line  expresses the T-parameters of just the line  401  and T meas     —     line  expresses the T-parameters of the line  401  as measured in context with the X and Y error adapters, then the following relationship holds true:  
           T   x   T   act     —   line T   y   =T   meas     —     line    (3)  
         [0098]    If the following relationships are defined:  
           T   act x   =T   act     —     line   T   act     —     thru   −1    (4)  
         [0099]    and  
           T   meas     —     x   =T   meas     —     line   T   meas     —     thru   −1    (5)  
         [0100]    then the following equation can be written  
           T   x   T   act     —     x   =T   meas     —     x   T   x    (6)  
         [0101]    The thru  601  and the line  401  are each assumed to be perfectly matched. Therefore, the value of their reflection coefficient in the respective actual S-parameter matrix is set to zero. If the thru  601  has a non-zero length transmission coefficient, it is defined by S 21     —     thru =S 12     —     thru . The line  401  has a transmission coefficient defined by S 21     —     line     —     S   12     —     line . From equation (4), therefore T act     —     x  may be expressed as:  
               T   act_x     =     [             S     21      _thru         S     21      _line             0           0           S     21      _line         S     21      _thru               ]             (   7   )                               
 
         [0102]    Measurements of the unterminated thru  601  and the line  401 , each provide eight frequency dependent arrays of measured and stored results. There are four thru forward reflection and transmission arrays and four thru reverse reflection and transmission arrays. The arrays of measured data for the thru  601  are used in an algorithmic formulation in the S-parameter domain to compensate for the presence of the signal transfer switch  106  prior to calculation of the T meas     —     x  matrix. Both the S meas     —     line  and S meas     —     thru  are corrected by the formulation given by:  
               S   corrected     =     [       (                 A   f       R1   f       -         A   r       R2   r              R2   f       R1   f             1   -         R2   f       R1   f              R1   r       R2   r                             B   f       R1   f       -         B   r       R2   r              R2   f       R1   f             1   -         R2   f       R1   f              R1   r       R2   r                   )          (                 A   r       R2   r       -         A   f       R1   f              R1   r       R2   r             1   -         R2   f       R1   f              R1   r       R2   r                             B   r       R2   r       -         B   f       R1   f              R1   r       R2   r             1   -         R2   f       R1   f              R1   r       R2   r                   )       ]             (   8   )                               
 
         [0103]    where A f , B f , R1 f  and R2 f  are the forward direction raw measurement data, i.e. when the signal transfer switch  106  is directing the signal generator  105  to the first signal path  107 , and A r , B r , R1 r  and R2 r  are the reverse direction raw measurement data, i.e. when the signal transfer switch  106  is directing the signal generator  105  to second signal path  108 .  
         [0104]    Referring now to the measurements of the first direct pair, meaurement ports  103   1  and  103   3 , a corrected S-parameter matrix of the thru  601  measured in cascaded combination with the X and Y error adapters for the first direct pair is expressed herein as S meas13     —     thru     —     corrected . The correction formulation shown in equation (8) uses the arrays; A f13     —     thru , B f13     —     thru , R1 f13     —     thru , R2 f13     —     thru , A r13     —     thru , B r13     —     thru , R1 r13     —     thru , and R2 r13     —     thru  to calculate S meas13     —     thru     —     corrected . Converting the S meas13     —     thru     —     corrected  matrix to the corresponding T-parameters using equation (1) yields matrix T meas13     —     thru     —     corrected . To obtain the S meas13     —     line      —     corrected  matrix for the first direct pair, the correction formulation shown in equation (8) uses the arrays; A f13     —     line , B f13     —     line , R1 f13     —     line , R2 f13     —     line , A r13     —     line , B r13     —     line , R1 r13     —     line , and R2 r13     —     line . Converting the corrected S meas13     —     line     —     corrected  matrix to the corresponding T-parameters, yields matrix T meas13     —     line     —     corrected . The T meas13     —     thru     —     corrected  and T meas13     —     line     —     corrected  matrices are used in equations (4) and (5) to calculate T act     —     x  and T meas     —     x .  
         [0105]    Referring now to the general case, T x  is the T-parameter matrix for the X error adapter and is defined by its matrix elements as:  
             Tx   =     [           Tx   11           Tx   12               Tx   21           Tx   22           ]             (   9   )                               
 
         [0106]    T meas     —     x  is also defined by its matrix elements, and is represented as:  
               T   meas_x     =     [           T   meas_x11           T   meas_x12               T   meas_x21           T   meas_x22           ]             (   10   )                               
 
         [0107]    From equation (5), T meas     —     x  for measurement ports  103   1  and  103   3 , which is expressed as T meas13     —     x , is calculated using the T meas13     —     thru     —     corrected  and T meas13     —     line     —     corrected  matrices. Accordingly:  
         
       T 
       meas13 
       
         — 
       
       x 
       =T 
       meas13 
       
         — 
       
       line 
       
         — 
       
       corrected 
       T 
       meas13 
       
         — 
       
       thru 
       
         — 
       
       corrected 
       −1  
     
         [0108]    Using the relationship in equations (4), substituting the terms in equation (6), and eliminating the S 21     —     thru /S 21     —     line  term, the following general equation can be written:  
                 Tx   21       Tx   11       =       (       -     T   meas_x11       +         4        T   meas_x12          T   meas_x21       +       (       T   meas_x11     -     T   meas_x22       )     2         +     T   meas_x22       )       2        T   meas_x12                 (   11   )                               
 
         [0109]    and  
                 Tx   22       Tx   12       =       (       -     T   meas_x11       +         4        T   meas_x12          T   meas_x21       +       (       T   meas_x11     -     T   meas_x22       )     2         +     T   meas_x22       )       2        T   meas_x12                 (   12   )                               
 
         [0110]    Based upon the T-parameter to S-parameter conversion, Tx 21 /Tx 11  and Tx 22 /Tx 12  in terms of the corresponding S-parameter error adapter matrix may also be expressed as:  
                 Tx   21       Tx   11       =       Sx   11     =   B             (   13   )                               
 
         [0111]    and  
                 Tx   22       Tx   12       =         Sx   11     -         Sx   12          Sx   21         Sx   22         =   A             (   14   )                               
 
         [0112]    As one of ordinary skill in the art can appreciate, equations (11) and (12) are equal. Because there is a square root in the solution, there are two possible mathematical solutions. The smaller valued solution, defined by B, corresponds to the directivity error coefficient  1901  of error adapter X. The larger valued solution, defined by A, is a mathematical combination of source match  1902  and reflection tracking  1903 .  
         [0113]    As mentioned before, at frequencies around 500 MHz and below, the dimensions of the line  401  become very large and not practical. Calculation of the directivity  1901  and the solution represented by A for the lower frequencies uses the measurements taken of the two high-quality matched loads  501  instead of the line  601 . It is assumed that the matched loads  501  are perfectly matched to the measurement port and have a zero reflection coefficient. The same algorithmic formulations shown in equations (5) through (14) are used. To understand the usage of the measurement results from the two matched loads, note that the thru  601  has a non-zero-length transmission coefficient defined by S 12thru =S 12thru . The matched loads  501  have a transmission isolation coefficient defined by S 21load =S 12load . Due to the high isolation between the matched loads  501 , S 21load  is close to a zero value. Accordingly, S21load is set to a very small, non-zero value, such as 10 −10  in order to avoid division by zero ambiguity in the S-parameter to T-parameter conversion. From this, T act     —     x  at the lower frequencies can be calculated and is given by:  
               T   act_x     =     [             S     21      _thru         10     -   10             0           0           10     -   10         S     21      _thru               ]             (   15   )                               
 
         [0114]    As shown before, by using equations (4) and (5), substituting results into equation (6) and eliminating the S 21     —     thru /10 −10  term, equations (11) and (12) are derived. The S-parameters from the matched loads  501  are corrected using equation (8) to yield S meas13     —     load     —     corrected , which is then converted using equation (1) to yield T meas13     —     load     —     corrected . The T meas13     —     load     —     corrected  term is used to calculate T meas13     —     x  in place of the terms measuring the line  401 . The calculations in equations (11) and (12), therefore, are the same as for the line  401 .  
         [0115]    A similar process is performed to calculate terms in the error adapter Y. Beginning with equations (2) and (3) and defining the following relationships:  
           T   act     —     y   =T   act     —     thru   −1   T   act     —     line    (16)  
         [0116]    and  
           T   meas     —     y   =T   meas     —     thru   −1   T   meas     —     line    (17)  
         [0117]    then the following equation can be written:  
           T   act     —     y   T   y   =T   y T meas     —     y    (18)  
         [0118]    With specific reference to FIG. 19 of the drawings, the known conversion for T-parameter matrix for the error adapter Y in terms of the S-parameters where port  1  is on the right and port  2  is on the left when looking at the DUT  101  is:  
             Ty   =       [           Ty   11           Tx   12               Ty   21           Ty   22           ]     =     [           1     Sy   12               -     Sy   11         Sy   12                   Sy   22       Sy   12                   Sy   12          Sy   21       -       Sy   11          Sy   22           Sy   12             ]               (   19   )                               
 
         [0119]    Accordingly, the matrix Sy may be converted into corresponding T-parameters expressed as Ty. The T meas13     —     thru     —     corrected  and T meas13     —     line     —     corrected  matrices have already been calculated and are used in equation (17) to calculate T meas13     —     y , where:  
               T   meas13_y     =     [           T   meas13_y11           T   meas13_y12               T   meas13_y21           T   meas13_y22           ]             (   20   )                               
 
         [0120]    Using equation (18), substituting the relationships in equations (16) and (17) and eliminating the S 21thru /S 21line  term, the following equation for the first direct pair can be written:  
                 Ty   12       Ty   11       =       (       -     T   meas13_y11       +         4        T   meas13_y12          T   meas13_y21       +       (       T   meas13_y11     -     T   meas13_y22       )     2         +     T   meas13_y22       )       2        T   meas13_y21                 (   21   )                               
 
         [0121]    and  
                 Ty   22       Ty   21       =       (       -     T   meas13_y11       +         4        T   meas13_y12          T   meas13_y21       +       (       T   meas13_y11     -     T   meas13_y22       )     2         +     T   meas13_y22       )       2        T   meas13_y21                 (   22   )                               
 
         [0122]    From equation (19),  
                     Ty   12       Ty   11           and           Ty   22       Ty   21                                   
 
         [0123]    in terms of the corresponding the S-parameters for the error adapter Y is also given by:  
                 Ty   12       Ty   11       =       -     Sy   11       =   D             (   23   )                               
 
         [0124]    and  
                 Ty   22       Ty   21       =             Sy   12          Sy   21         Sy   22       -     Sy   11       =   C             (   24   )                               
 
         [0125]    As one of ordinary skill in the art can appreciate, equations (21) and (22) are equal and because of the square root have two solutions. The smaller value or the first solution, defined by Sy 11 , corresponds to the directivity error of the Y error adapter. The larger value or the second solution, defined by C, corresponds to the error coefficient,  
               Sy   12          Sy   21         Sy   22       -     Sy   11       ,                         
 
         [0126]    for the Y error adapter.  
         [0127]    With reference to the portion of the calibration procedure that measures the high reflect calibration standard as illustrated in FIGS. 3 and 4 of the drawings, the high reflect standard  301 , is connected to one measurement port  103   1  of the first direct pair and the same high reflect standard  301  is disconnected from the measurement port  103   1  and is then connected to the other measurement port  103   3  of the direct pair. With specific reference to FIG. 19 of the drawings the following equation can be written:  
               Γ     meas_reflect      _x       =       Sx   11     +         Sx   12          Sx   21          Γ     act_reflect      _x           1   -       Sx   22          Γ     act_reflect      _x                       (   25   )                               
 
         [0128]    where Γ meas     —     reflect     —     x  is the measured reflection coefficient of the high reflect standard  301  at the measurement port capable of connection to the first test channel, measurement port  103   1  in the first direct pair, and Γ act     —     reflect     —     x  is the actual reflection coefficient of the high reflect standard at the same measurement port  103   1 . The same high reflect calibration standard  301  is connected to the opposite port in the first direct pair, measurement port  103   3  in the specific example. With respect to the error adapter Y, the following equation can also be written:  
               Γ     meas_reflect      _y       =       Sy   11     +         Sy   12          Sy   21          Γ     act_reflect      _y           1   -       Sy   22          Γ     act_reflect      _y                       (   26   )                               
 
         [0129]    where Γ meas     —     reflect     —     y  is the measured reflection coefficient of the high reflect standard  301  at measurement port  103   3  and Γ act     —     reflect     —     y  is the actual reflection coefficient of the high reflect standard at the measurement port  103   3 . A value for the measured reflection coefficient of the high reflect standard, Γ meas     —     reflect     —     x , for the measurement port  103   1  may be obtained from the following measured and stored arrays A reflect     —     1 /R1 reflect     —     1 . Similarly, a value for the measured reflection coefficient of the high reflect standard, Γ meas     —     reflect     —     y , for the measurement port  103   3  may be obtained from the following measured and stored arrays B reflect     —     3 /R2 reflect     —     3 . Because the same high reflect standard is connected to measurement ports  103   1  and  103   3 , it is possible to solve for Γ act     —     reflect     —     x  in equation (25) and Γ act     —     reflect     —     y  in equation (26), and set the r terms equal to each other. From the resulting relationship and equations (13), (14), (23), (24), (25) and (26), the following relationship can be written:  
               Sx   22     =         (     B   -     Γ     meas_reflect      _x         )          (     C   -     Γ     meas_reflect      _y         )          Sy   22           (     A   -     Γ     meas_reflect      _x         )          (     D   -     Γ     meas_reflect      _y         )                 (   27   )                               
 
         [0130]    As one of ordinary skill in the art appreciates, equation (27) has two unknown terms, but permits the expression of Sx 22  in terms of Sy 22 . Accordingly, another relationship is necessary in order to solve for these two unknown terms.  
         [0131]    With specific reference to FIGS. 7 and 19, the following equation can also be written:  
               Γ   meas_thru11     =       Sx   11     +         Sx   12          Sx   21          Sy   22         1   -       Sx   22          Sy   22                     (   28   )                               
 
         [0132]    where Γ meas     —     thru11  is measured as A f13     —     thru /R1 f13     —     thru  for the measurement port of the first direct pair that is capable of connection to the first test channel  111 . From (13), (14), (23) and (24), the following can be written  
               Sx   22     =           (     B   -     Γ     meas_reflect      _x         )          (     C   -     Γ     meas_reflect      _y         )          (     B   -     Γ   meas_thru11       )           (     A   -     Γ     meas_reflect      _x         )          (     D   -     Γ     meas_reflect      _y         )          (     A   -     Γ   meas_thru11       )                   (   29   )                               
 
         [0133]    and Sx 22 may  be calculated. Sx 22  is the source match error coefficient at the first measurement port  103   1 . Due to the square root in equation (29), there are 2 solutions for Sx 22 . Having an approximate value of the argument of the high reflect calibration standard, however, the correct choice can be made. For example a short circuit calibration standard should have an argument of 180 degrees and an open circuit calibration standard should have an argument of zero degrees. If a non-zero thru  601  is used, then the phase rotation of the reflect  301  is calculated from the electrical length of the non-zero through. From this calculation, a correct solution for Sx 22  from equation (29) is apparent. Accordingly, the type of reflect  301 , whether a short circuit or an open circuit, and an electrical length of the non-zero thru must be known. If the reflect  301  is an offset short, it is also necessary to know the phase of the offset.  
         [0134]    When a value for Sx 22  is known, a value for Sy 22  may be calculated from equation (27). Sy 22  is the source match error coefficient of error adapter Y at the measurement port capable of connection to the second test channel  112 , which is measurement port  103   3  in the specific example.  
         [0135]    Because a definite value for Sx 22  is known, equations (13), (14) and (29) permit calculation of a reflection tracking coefficient for the error adapter X and is given by:  
           Sx   12   Sx   21 =( B−A ) Sx   22    (30)  
         [0136]    Similarly, a definite value for Sy 22  and equations (23), (24) and (27) permit calculation of a reflection tracking for the error adapter Y and is given by:  
           Sy   12   Sy   21 =( D−C ) SY   22    (31)  
         [0137]    At this point in the process, the directivity, source match and reflection tracking for the error adapter X and the error adapter Y are determined. The X error adapters are defined as the error artifacts presented in series with the measurement ports  103  capable of connection to the first test channel  111 . Similarly, the Y error adapters are defined as the error artifacts presented in series with the measurement ports  103  capable of connection to the second test channel  112 .  
         [0138]    In the specific four-port embodiment, the measurements and calculations described herein for measurement ports  103   1  and  103   3  yield directivity, source match and reflection tracking for the error adapter X related to measurement port  103   1  and directivity, source match, and reflection tracking for the error adapter Y related to measurement port  103   3 . The same measurements and calculations described herein for measurement ports  103   1  and  103   3  are performed for the second direct pair. Specifically, measurements and calculations are made for measurement ports  103   2  and  103   4  to yield directivity, source match and reflection tracking for the error adapter X related to measurement port  103   2  and directivity, source match, and reflection tracking for the error adapter Y related to measurement port  103   4 . In a multiport embodiment, the same measurements and calculations are made for each direct pair to yield directivity, source match and reflection tracking for the error adapter X related to the measurement port of the direct pair capable of connection to the first test channel  111  and directivity, source match, and reflection tracking for the error adapter Y related to the measurement port of the direct pair capable of connection to the second test channel  112 . Accordingly, a 2N port DUT  100  has N different X error adapter and N different Y error adapter associated therewith.  
         [0139]    Using the forward reflection and transmission measurements made on the terminated thru  601 , which in a specific example of the first direct pair are the A f13     —     termthru /R1 f13     —     termthru  and B f13     —     termthru /R1 f13     —     termthru  arrays, it is possible to solve for a load match error coefficient presented at the measurement port capable of connection to the second test channel  112  and a forward transmission tracking error coefficient for the first direct pair. The load match for the measurement port  103   3 ,Γ L3 , and forward transmission tracking for the first direct pair,τ 13 , are given by:  
               Γ   L3     =         Sx   11     -     (       A   f13_termthru     /     R1   f13_termthru       )             Sx   11          Sx   22       -       Sx   12          Sx   21       -       Sx   22          (       A   f13_termthru     /     R1   f13_termthru       )                   (   32   )                               
 
         [0140]    and  
         τ 13 =( B   f13     —     termthru   /R 1 f13     —     termthru )(1 −SX   22 Γ L3 )   (33)  
         [0141]    Using the reverse reflection and transmission measurements made on the terminated thru  601 , which in a specific example of the first direct pair are the A r13     —     termthru /R2 r13     —     termthru  and B r13     —     termthru /R2 f13     —     termthru  arrays, it is possible to solve for a load match error coefficient presented at the measurement port capable of connection to the first test channel  111  and a reverse transmission tracking error coefficient for the first direct pair. The load match for the measurement port  103   1 ,Γ L1 , and the reverse transmission tracking coefficient,τ 31 , are given by:  
               Γ   L1     =         Sy   11     -     (       B   r13_termthru     /     R2   r13_termthru       )             Sy   11          Sy   22       -       Sy   12          Sy   21       -       Sy   22          (       B   r13_termthru     /     R2   r13_termthru       )                   (   34   )                               
 
         [0142]    and  
         τ 31=(   A   r13     —     termthru   /R 2 r13     —     termthru )(1 −SY   22 Γ L1 )   (35)  
         [0143]    In the specific illustrated embodiment, using the measurements made of the terminated thru for the second direct pair, the same algorithmic formulations shown in equations (32) through (35) as described for measurement ports  103   1  and  103   3  are applied to the measurement ports  103   2  and  103   4 . Accordingly, directivity, source match, reflection tracking and load match error coefficients for each measurement port in the first and second direct pairs and forward and reverse transmission tracking error coefficients for the first and second direct pairs are determined. In a multiport embodiment of a method according to the teachings of the present invention, the directivity, source match, reflection tracking and load match error coefficients for each measurement port in all of the direct pairs and forward and reverse transmission tracking error coefficients for all of the direct pairs are similarly determined.  
         [0144]    Using the measurements of the thru  601  using the first indirect pair, measurement ports  103   1  and  103   4 , the forward and reverse transmission tracking error coefficients,τ 14  and τ 41 , is determined. The measured and stored arrays, A f14     —     thruterm /R1 f14     —     thru     —     term and B   f14     —     thruterm /R1 f14     —     thruterm , are inserted into an equation similar to equation (33) and the measured and stored arrays, A r14     —     thruterm /R2 r14     —     thru     —     term  and B r14     —     thruterm /R2 r14     —     thruterm , are inserted in an equation similar to equation (35). Using the load match error coefficients already calculated for each of the measurement ports  103 , the forward and reverse transmission tracking for the indirect pair comprising measurement ports  103   1  and  103   4  is calculated as follows:  
         τ 14 =( B   f14     —     termthru   /R 1 f14     —     termthru )(1 −SX   22 Γ L4 )   (36)  
         [0145]    and  
         τ 41 =( A   r4l     —     termthru   /R 2 r41     —     termthru )(1 −SX   22 Γ L1 )   (37)  
         [0146]    Similar calculations are made for the remaining indirect pairs. In the specific embodiment illustrated, the measured and stored arrays, A f23     —     thruterm /R1 f23     —     thru     —     term  and B f23     —     thruterm /R1 f23     —     thruterm , are used to calculate the forward transmission tracking error coefficient for the indirect pair comprising measurement ports  103   2  and  103   3  and the measured and stored arrays, A r23     —     thruterm /R2 r23     —     thruterm  and B r23     —     thruterm /R2 r23     —     thruterm , are used to calculate the reverse transmission tracking error coefficient for the same indirect pair.  
         [0147]    Forward and reverse transmission tracking error coefficients between the measurement ports  103  capable of connection to the same test channel, either the first test channel  111  or the second test channel  112 , are herein referred to as “proximal pairs”. In the specific illustrated embodiment the proximal pairs are measurement ports  103   1  and  103   2 , measurement ports  103   3  and  103   4 . The related forward and reverse transmission tracking error coefficients of the proximal pairs are; τ 12 , τ 21 , τ 34 , and τ 43 , which may be determined either through measurement and calculation or through pure calculation. The method for pure calculation of the forward and reverse transmission tracking error coefficients is taught in the &#39;040 patent application Ser. No.  
         [0148]    The forward transmission tracking error coefficient for each proximal pair where both measurement ports  103  of the proximal pair are capable of connection to the first test channel  111  is measured and calculated by connecting the thru  601  between the measurement ports  103  of the proximal pair, connecting the signal generator  105  to a first one of the measurement ports  103  of the proximal pair and terminating the sampling arm  113  in a local terminating impedance  116 . For purposes of nomenclature, the first measurement port  103  of the proximal pair is designated as “port F”. The other measurement port  103  of the proximal pair, which for purposes of nomenclature is designated as “port G”, is terminated in a local terminating impedance  104 , and the respective sampling arm  113  is connected to the first test channel  111 . The VNA  200  measures and stores a ratio of a transmission response over the reference signal, A fFG     —     termthru /R1 fFG     —     termthru . The ratio is used in the transmission tracking error coefficient equation where:  
         τ FG =( A   fFG     —     termthru   /R 1 fFG     —     termthru )(1 Sx   22     —     portF Γ portF )   (38)  
         [0149]    The reverse transmission tracking error coefficient for the same proximal pair, ports F&amp;G, where both measurement ports  103  of the proximal pair are capable of connection to the first test channel  111  is measured and calculated by keeping the connection of the thru  601  between the measurement ports  103  of the proximal pair, connecting the signal generator  105  to the second one of the measurement ports  103  of the proximal pair and terminating the sampling arm  113  in a local terminating impedance  116 . The first one of the measurement ports  103  of the proximal pair is terminated in the local terminating impedance  104 , and the respective sampling arm  113  is connected to the first test channel  111 . The VNA  200  measures and stores a ratio of a transmission response over the reference signal, A rFG     —     termthru /R1 rFG     —     termthru . The ratio is used in the transmission tracking error coefficient equation where:  
         τ=( A   rFG     —     termthru   /R 1 rFG     —     termthru )(1 −Sx   22     —     portG Γ portG )   (39)  
         [0150]    For purposes of illustration and with specific reference to FIG. 20, there is shown connection diagrams for the determination of the forward and reverse transmission tracking error coefficients for the proximal pair comprising measurement ports  103   1  and  103   2 . The forward transmission measurement is made by connecting the signal generator  105  to the first signal path  107 . The switch network  150  is configured so that the first signal path  107  is connected to the measurement port  103   1  and the respective sampling arm  113   1  is terminated in the local sampling arm impedance  116   1 . The switch network  150  is further configured so that the measurement port  103   2  is terminated in the local terminating impedance  104   2  and the sampling arm  113   2  is connected to the first test channel  111 . The signal generator  105  sweeps through the plurality of frequencies that define the desired frequency range and measures the ratio A f12     —     termthru /R1 f12     —     termthru . Using equation (37) the forward transmission tracking error coefficient for the proximal pair is calculated as:  
         Γ 12 =( A   f12     —     termthru   /R 1 f12     —     termthru )(1 −SX   22     —     port1 Γ port1 )  
         [0151]    The thru  601  connection and the signal transfer switch  106  configuration are maintained. With specific reference to FIG. 21 of the drawings, the switch network  150  is reconfigured so that the measurement port  103   2  is connected to the first signal path  107  and the respective sampling arm  113   2  is terminated in the local sampling terminating impedance  116   2 . Additionally, the switch network  150  is configured so that the measurement port  103   1  is terminated in the local terminating impedance  104   1  and the sampling arm  113   1  is connected to the first test channel  111 . The signal generator  105  sweeps through the plurality of frequencies that define the desired frequency range and measures the ratio A r12     —     termthru /R1 r12     —     termthru . Using equation (38) the reverse transmission tracking error coefficient for the proximal pair is calculated as:  
         τ 21 =( A   r12     —     termthru   /R 1 r12     —     termthru )(1 −SX   22     —     port2 Γ port2 )  
         [0152]    The same measurement and calculation process is repeated for the remaining proximal pairs, which in the illustrated embodiment is the proximal pair comprising measurement ports  103   3  and  103   4 . As one of ordinary skill in the art appreciates, the measurements for the proximal pair capable of connection to the second test channel  112  are carried out using the same process, but with the second test channel  112  and the second reference channel  202  as measurement devices. In a multiport embodiment, the measurement and calculation process is repeated for all of the proximal pairs.  
         [0153]    With specific reference to FIGS. 22 through 26 of the drawings, there is shown a flow chart of a method according to the teachings of the present invention in which a reflect standard  301  is connected  2201  to one port of a first direct pair and the switch network  150  is configured for measurement  2202  by the VNA  200  of a ratio of the reflection response over the stimulus. See FIG. 3 of the drawings. The ratio yields a value for a number of frequencies in a desired frequency range. The numbers are stored in a data array where each element of the data array holds the measured ratio at a single frequency. The reflect  301  is then disconnected and reconnected  2203  to the other port in the direct pair, the switch network  150  is reconfigured, and the other port in the direct pair is stimulated and the ratio of the reflection response over the stimulus is measured and stored  2204  in another data array. See FIG. 4 of the drawings. In a preferred embodiment, the desired frequency range for which all measurements are taken is the same. In this case, each element in the data arrays represents measured results at the same frequency point along the desired frequency range.  
         [0154]    The flow chart continues with step of connecting  2301  and configuring  2302  the switch network  150  for measurement of the line  401  between ports of the same direct pair. The VNA  200  measures  2302  a forward direction reflection and transmission response at the measurement ports  103  of the direct pair at the first and second test channels  111 ,  112  as well as the first and second reference channels  201 ,  202 . The switch network  150  is then reconfigured  2303  for the reverse direction measurement and the VNA  200  then measures  2303  a reverse direction reflection and transmission response at the measurement ports  103  of the direct pair at the first and second test channels  111 ,  112  as well as the first and second reference channels  201 ,  202 . Not shown in the flow chart is the connection and measurement of the matched loads  501  as shown in FIG. 6 of the drawings to extend the calibration to the lower frequency range.  
         [0155]    With specific reference to FIGS. 23, 7, and  8  of the drawings, the flow chart continues with the step of connecting  2401  the thru  601  to the measurement ports  103  of the same direct pair. The switch network  150  is configured  2402  for forward direction measurement of the thru  601 , and the forward direction reflection and transmission responses and the reference channel signals are measured and stored in data arrays. The switch network  150  is then reconfigured  2403  for the reverse direction measurements and the reverse direction reflection and transmission responses and the reference channel signals are measured and stored in data arrays.  
         [0156]    With specific reference to FIGS. 23 and 9 of the drawings, the thru  601  remains connected and the switch network  150  is reconfigured  2501  for a forward direction measurement, where the thru  601  is locally terminated in a local impedance  104  within the switch network  150 . The forward direction reflection and transmission responses of the locally terminated thru  601  are measured and stored as well as the reference channel signals. The switch network  150  is then reconfigured  2502  for a reverse direction measurement of the locally terminated thru  601 , the reverse reflection and transmission responses and the reference channel signals are measured and stored. The process repeats  2503  for all direct pairs of measurement ports. The indices n and m as shown in the flow chart represent that the process increments through all of the direct pairs. As one of ordinary skill in the art appreciates, the direct pairs may be defined in another way than is illustrated herein in which case, the step of incrementing through the direct pairs as shown by reference numeral  2504  uses a different convention. After incrementing to the next direct pair, the process steps repeat (See connector E in FIG. 22 of the drawings) until all direct pairs are measured. See FIGS. 10 through 16 for an illustrative representation of the measurements made on the second direct pair.  
         [0157]    With specific reference to FIGS. 24 and 19 of the drawings, the directivity  1901 , source match  1902  and reflection tracking  1903  error coefficients for the X error adapter  1910  are calculated  2601  from the stored data arrays. The directivity  1904 , source match  1905  and reflection tracking  1906  error coefficients for the Y error adapter  1920  are also calculated  2602  from the stored data arrays. Using the results of the calculations, the load match and transmission tracking error coefficients are then calculated for both the X and Y error adapters. The calculation process is repeated  2604  for all direct pairs.  
         [0158]    With specific reference to FIGS. 24, 17, and  18 , the thru  601  is connected  2701  between the measurement ports  103  of the first indirect pair. The switch network  150  is configured  2702  for a forward direction measurement with the thru  601  locally terminated in the switch network  150 . The forward reflection and transmission responses and the first and second reference channels are measured. The measured results are stored in additional data arrays. The switch network  150  is reconfigured  2703  for a reverse direction measurement with the thru  601  locally terminated in the switch network  150 . The reverse reflection and transmission responses and the first and second reference channels are measured. The measured results are stored in data arrays. This process is repeated  2704  for all indirect pairs. As one of ordinary skill in the art appreciates, the indirect pairs may be defined in many different ways. The flow chart illustrates one method where the measurement port  103  capable of connection to the first test channel  111  is incremented from 1 to N−1 and while the measurement port  103  capable of connection to the second test channel  112  is incremented from N+2 to 2N. The last indirect pair is between measurement ports  103  N and N+1. Other methods depending upon the definition of the measurement ports  103  that make up the indirect pairs differ from the one illustrated herein.  
         [0159]    With specific reference to FIG. 25 of the drawings, the flow chart continues with the steps of calculating  2801  a transmission tracking coefficient for each indirect pair. The process increments  2802  through all of the indirect pairs in the same way as for the measurement portion of the indirect pairs.  
         [0160]    With specific reference to FIGS. 25, 20, and  21 , the process then continues with the steps of connecting the thru  601  between the measurement ports  103  that comprise proximal pairs. In the illustrated embodiment, the proximal pairs are the measurement ports  103  that are adjacent to each other. The thru  601  is connected  2803  between a first proximal pair as shown in FIG. 20 and the switch network  150  is configured  2804  for a forward direction measurement of the thru  601  in a locally terminated condition. See FIG. 20 of the drawings. A ratio of the forward transmission response over the stimulus as measured by the first reference channel is measured and stored  2804  in a data array. The switch network  150  is reconfigured  2805  for a reverse direction measurement. See FIG. 21 of the drawings. A ratio of the reverse transmission response over the stimulus as measured by the first reference channel is measured and stored  2805  in a data array. The steps for the proximal pairs are repeated  2806  for each proximal pair. As one of ordinary skill in the art appreciates, the method of incrementing the measurement ports  103  in the loop  2806  for repetition of the process for each proximal pair begins with measurement ports  103   n  and  103   m  where n=1 and m=n+1. Both n and m are incremented through the process, although there is one condition where n and m actually define an indirect pair. In that case, the process steps are not performed.  
         [0161]    With specific reference to FIG. 26 of the drawings, the flow chart continues with the steps of calculating  2901  the transmission tracking error coefficients for each one of the proximal pairs.  
         [0162]    When all of the systematic error coefficients are determined, the DUT  101  is inserted for measurement  2902 . The measured DUT data is then corrected  2903  according to the teachings of the &#39;040 patent application Ser. No. by using all of the systematic error coefficients calculated as taught herein. Advantageously, a method and apparatus according to the teachings herein provides an improved characterization of the error artifacts present in measurements made of the DUT  101  with the VNA  200 . This provides for a more accurate characterization of the frequency response of the DUT  101  as distinct from the frequency response contributions of the error artifacts that are part of the measurement system.