Abstract:
In one embodiment, a method of operating a network analyzer, comprises applying a stimulus signal on at least one port of the network analyzer for provision to a device under test (DUT) within a test fixture coupled to the network analyzer; generating measurement data from the DUT in response to the stimulus signal on at least one port of the network analyzer; and generating an amplitude response of the DUT across a frequency range, wherein a port extension module of the network analyzer automatically applies loss compensation to the amplitude response in a manner that is non-linearly related to frequency according to at least one controllable parameter.

Description:
TECHNICAL FIELD 
   The present application is generally related to calibrating network analyzers to perform measurements using test fixtures. 
   BACKGROUND OF THE INVENTION 
   Network analyzers are devices that are used to determine the radio frequency (RF) characteristics of various devices under test (DUTs). In many situations, a DUT is a relatively small component designed to interface with a trace contact point on a printed circuit board (PCB). Many network analyzers typically utilize an interface adapted to receive a coaxial coupling. To test a DUT designed to be employed on a PCB using such a network analyzer, a test fixture is often employed. A test fixture is generally a specialized device that is adapted to readily accept a DUT and that electrically couples the DUT to one or several ports of a network analyzer. 
   For many DUTs (such as balanced filters, baluns, balanced amplifiers, etc.), the pertinent performance measurements depend upon both the magnitude and phase of the signals applied to and received at each port. In the case of balanced devices, it is quite important that the loss of each port be identical between the balanced pairs of ports. However, the use of network analyzers and test fixtures to perform such measurements presents difficulties. Specifically, it is common to experience different path lengths on different ports using test fixture/network analyzer configurations. The variations may result from PCB layout constraints, manufacturing process limitations, and/or other reasons. The variations between ports may cause the loss to vary between the port thereby reducing the accuracy of the measurements of a DUT using the test fixture. The amplitude loss in the test fixture may cause a properly functioning part to fail insertion loss tests. The amplitude loss can also make matching measured results to model predictions difficult. 
   De-embedding an S-parameter description of the test fixture has been used to address loss in the text fixture. In known implementations, de-embedding requires a network analyzer to be operated in an error correction mode and involves multiple analyzer sweeps to generate measurement data to be corrected. The measurement data is then processed on an off-line basis by applying one or several error correction arrays using matrix operations. Also, known error correction arrays are statically defined in error correction files. Furthermore, the error correction arrays involve a one-to-one relationship between error terms and the spectral data. Accordingly, it is often the case that the requirements for de-embedding a test fixture are difficult and are often not practical in normal manufacturing environments. 
   SUMMARY 
   Some representative embodiments provide port extension functionality of a network analyzer to compensate for the loss introduced by a test fixture. The port extension functionality may involve multiple parameters per port to model the non-linear loss response associated with a network analyzer. After the various parameters of a given port are calibrated, the network analyzer automatically provides amplitude correction to measurement data on a non-linear frequency dependent basis. 
   Additional representative embodiments are directed to systems and methods for automatically calibrating a network analyzer that includes loss compensation port extension functionality. Specifically, S11 measurements of a known reflection are made from which phase and amplitude references can be generated. “S11 measurements” refer to measurements made by a network analyzer using a scattering parameter model where “S11” refers to the ratio of a reflected signal to an incident signal on the same port. The known reflection may result from an open circuit (e.g., omitting the DUT from the test fixture) and/or a short circuit. Processing of the measurement data may be performed to account for errors in the amplitude response that result from poor source/PCB match of the test set-up. The processing enables a greater degree of accuracy in the calculation of the loss presented by the various port connections to the test fixture. 

   
     BRIEF DESCRIPTION OF THE DRAWINGS 
       FIG. 1  depicts a flowchart according to one representative embodiment. 
       FIG. 2  depicts an amplitude response, a phase response, and a delay response of a test fixture using the open standard according to one representative embodiment. 
       FIG. 3  depicts a graph of measurement data and a polynomial fitted to the measurement data according to one representative embodiment. 
       FIG. 4  depicts a flowchart for automatically calibrating a network analyzer and using the calibrated network analyzer to perform measurements of a DUT according to one representative embodiment. 
       FIG. 5  depicts a block diagram of a network analyzer according to one representative embodiment. 
       FIG. 6  depicts a graphical user interface for controlling loss compensation applied by port extension functionality according to one representative embodiment. 
   

   DETAILED DESCRIPTION 
   Known port extension functionality refers to processing performed by a network analyzer to correct the delay resulting from the extension of a port of the network analyzer to a DUT using, for example, a test fixture. Known port extension applies a relatively simple linear model of phase response of a test fixture to correct measurement data in real-time during operation of a network analyzer. Known port extension functionality does not account for loss introduced by the test fixture. Specifically, the amplitude response of a test fixture is substantially more complicated than the linear model used for phase compensation and, hence, known port extensions are not capable of applying known amplitude correction techniques to measurement data in real-time. 
   Some representative embodiments provide port extension functionality in a network analyzer to correct for the amplitude response of a test fixture. Specifically, some representative embodiments employ a formula that models loss introduced by a test fixture as a function of frequency. After measurement data is obtained by the network analyzer, the port extension functionality applies a gain to an S-parameter in proportion to the loss defined by the formula and parameters associated with the respective port connection(s) to the test fixture. Because a suitable formula can be employed to generate the gain, the port extension functionality can apply the loss compensation in real-time. Specifically, numerically intensive error matrices need not be applied. Accordingly, the loss compensation can be applied concurrently with the occurrence of analyzer sweeps and the display of resulting spectral data. 
   The particular fitting formula is preferably selected to represent the expected loss function of the transmission line used to model the characteristics of the test fixture. In one representative embodiment, the following formula is used to model the loss associated with a network analyzer/test fixture set-up:
 
Loss( f )= a·f   1/2   +b·f+c,   equation (1)
 
where f is frequency and a, b, and c are constants. The parameter c is the loss at DC and the parameters a and b can be determined by suitably processing measurement data associated with the test fixture. For pure coaxial lines in air, this loss function follows almost ideally a square-root loss curve. For cables with dielectrics, the loss curve is steeper than a square-root function and, for microstrip lines, the loss versus frequency characteristic can be nearly a linear function. Accordingly, the preceding formula follows each of the transmission line models relatively closely.
 
   In another representative embodiment, the following formula is used to model the loss associated with a network analyzer/test fixture set-up:
 
Loss( f )= a·f   b   +c,   equation (2)
 
where f is frequency and a, b, and c are constants. The parameter c is the DC loss and parameters a and b may be determined by suitably processing measurement data associated with the test fixture.
 
   In some representative embodiments, the loss compensation is directly controlled by the user. For example, the user may directly input values for parameters a, b, and c using a graphical user interface (GUI). Alternatively, the user may enter the loss at one or several frequency points into GUI  600 , as shown in  FIG. 6 , via controls  601  and  602 . Software operating on the network analyzer may automatically calculate parameters a and b algebraically as will be discussed herein below. One benefit of enabling a user to change the loss compensation applied through port extension functionality is that the user may view the effect of changes as measurement data is obtained and displayed by the network analyzer in real-time. 
   In other representative embodiments, the parameters of the formula used to calculate the gain factors are determined in an autonomous manner by the network analyzer. Specifically, a stimulus signal is successively provided to multiple ports of a network analyzer and reflection measurements are made on each of the multiple ports. The reflection measurements are used to estimate the loss associated with the test fixture through each port. Additionally, the coaxial-to-PCB connection of the test fixtures frequently exhibits relatively poor impedance matching. A poor impedance match will result in significant ripples when the open standard is used to obtain the reflection measurements. Also, coupler/bridge directivity may introduce ripples in reflection measurements. Accordingly, some representative embodiments estimate the losses associated with multiple ports of a network analyzer coupled to a test fixture by suitably processing amplitude response values associated with multiple frequencies. 
   Referring now to the drawings,  FIG. 1  depicts a flowchart for operation of a network analyzer according to one representative embodiment. In one representative embodiment, the flowchart is implemented using suitable software instructions or code executed by a processor of the network analyzer. In other embodiments, integrated circuitry may be alternatively or additionally employed to implement a portion of the flowchart or the entire flowchart. 
   In step  101 , a short standard or an open standard is selected for subsequent measurements. The short standard refers to an ideal electrical connection having unity reflection with 180 degrees of phase shift. Measurements under the short standard typically obtain the response of the test fixture set-up when a suitable test kit component is inserted within the test fixture. The open standard refers to an unterminated transmission line. The open standard is measured by omitting placement of any element within the test fixture and, hence, the circuit path is “open.” The selection of the standard may occur by receiving suitable input from the user of a network analyzer through a graphical user interface (GUI) or other interface. Any other suitable reflection standard can be used if the amplitude versus frequency response of the fixture is known or can be assumed. 
   In step  102 , a port of the network analyzer is selected for calibration. In one representative embodiment, a suitable software loop selects a respective port by iteratively stepping through each port available on the device. Alternatively, the user may manually select the port through a GUI or other interface. 
   In step  103 , a signal is generated on the selected port. In step  104 , reflection measurements are made on the selected port. In step  105 , the measurements are processed to determine the response across a frequency span. In step  106 , the response data is stored for subsequent processing. 
   In step  107 , a logical comparison is made to determine whether there are additional ports to be tested. If so, the process flow returns to step  102 . In step  108 , a logical comparison is made to determine whether to repeat the process for the other standard. If the logical comparison is true, the process flow returns to step  102  to perform the process using the other standard. In step  109 , the parameters of the loss formula are calculated and used to calibrate the port extension functionality of the network analyzer. 
   In some representative embodiments, the parameters a, b, and c associated with equations (1) and (2) are determined algebraically using a relatively small number of measurement points. For example, for equation (1), the parameter c is determined from the measurement data as the loss at DC and the parameters a and b are determined as follows:
 
 a =( L   1   f   2   −L   2   f   1 )/( f   2   f   1   1/2   −f   1   f   2   1/2 ),  equation (3)
 
 b =( L   1   f   2   1/2   −L   2   f   1   1/2 )/( f   1   f   2   1/2   −f   2   f   1   1/2 ),  equation (4)
 
where L 1 , f 1 , and L 2 , f 2  are the first and second losses and frequencies associated with the losses, respectively. In equations (3) and (4), the loss is represented in dB. If there is a DC offset (c is non-zero), then L1=Loss1−c and L2=Loss2−c, where Loss1 and Loss2 are the losses determined by the measurement data at the respective frequencies.
 
   For equation (2), the parameter c is determined from the measurement data as the loss at DC and the parameters a and b are determined as follows:
 
 a =exp{(ln( f   2 )ln( L   1 )−ln( f   1 )ln( L   2 ))/(ln( f   2 )−ln( f   1 )}  equation (5)
 
 b =ln( L   1   /L   2 )/ln( f   1   /f   2 )  equation (6)
 
where L 1 , f 1 , and L 2 , f 2  are the first and second losses and frequencies associated with the losses, respectively.
 
   In another embodiment, equation (2) is used to generate the loss compensation values while only values a and c are calculated using equation (5) and the DC loss respectively. Parameter b is set to 0.5. This produces gain compensation that changes with the square root of frequency which closely models the loss of an ideal, lossy air-filled transmission line in which the loss is caused primarily by the “skin effect.” In another representative embodiment, the DC loss is assumed to be negligible and parameter c is omitted or set to zero. 
   In alternative embodiments, the loss parameters may be stored as a factor to be multiplied by a delay term. Specifically, a standard delay or custom delay is selected through an interface of the network analyzer. The loss factors are then scaled by the selected delay thereby making the loss a function of the delay. The benefit of relating the loss to the delay in this manner is to adapt the loss between multiple test fixtures that have common properties and differ only in the length from ports to the DUT interface(s). 
     FIG. 2  depicts amplitude response  201 , phase response  202 , and delay response  203  associated with reflection measurements of a test fixture using the open standard according to one representative embodiment. The responses associated with the open standard may be used as a directed normalization of the correct trace when testing of DUTs occurs. However, as seen in  FIG. 2 , responses  201 – 203  exhibit ripple. The ripples in responses  201 – 203  are indicative of errors caused by the poor source match (the coaxial-to-PCB connection) of the measurement system and the open response. 
   It is possible to appreciably mitigate the source match contribution by employing an average of the open standard and the short standard. However, in some test situations, it is not readily practical to perform measurements using the short standard and only open standard measurements are applied. Some representative embodiments process the measurement data obtained from the open standard to mitigate the errors generated by the poor source match of the test system. In some embodiments, a polynomial curve fitting algorithm or a line fitting algorithm may be applied to the amplitude response obtained from the measurement data to model the loss presented by a test fixture. The use of a polynomial or other suitable formula results in less sensitivity to ripple caused by the poor source match associated with the test fixture. 
   For example, the measurement data associated with a test fixture and generated using the open standard can be fitted to equation (1) by taking a change of variables such that g=f 1/2  thereby giving: Loss(g 2 )=a·g+b·g 2 +c. After transforming the equation through the change in variables, a polynomial fitting algorithm may be applied to determine appropriate values for a and b. Typically, polynomial fitting algorithms calculate values a and b to minimize an error metric between the resulting polynomial and the measurement data. Such polynomial fitting algorithms are known in the art. 
   In another embodiment, equation (2) can be transformed into a form that enables an application of a line fitting method to be applied. The log of each side can be taken as follows: log(Loss(f)−c)=log(a)+b·log(f). The fitting method may be applied by taking the log of the loss data (after offsetting by c) and the log of frequency. The Y-intercept of the fitted line can be mapped to a and the slope to b. Typical line fitting methods may be employed such as the least squares method. 
     FIG. 3  depicts a graph of measurement data  301  and polynomial fitted curve  302  to the measurement data according to one representative embodiment. The measurement data  301  was obtained by measurements of a test fixture using the open standard. Curve  302  results from fitting equation (1) to the measurement data  301  using a polynomial fitting algorithm. As seen in  FIG. 3 , curve  302  closely approximates the measurement data  301  while omitting ripples. Accordingly, when curve  302  is used to generate amplitude compensation values for measurements of DUTs, the processed measurement values will exhibit a relatively high degree of accuracy. 
   Because a function is used to model the loss presented by the test fixture, it is possible that a particular frequency may be scaled by a factor that is greater than the loss presented by the test fixture. Accordingly, it is possible that the amplitude response associated with that frequency may be greater than one for certain testing procedures. Some known tests are used to determine whether a device is unstable by detecting whether the amplitude response at certain frequencies is greater than one. To prevent the loss compensation from causing a properly functioning device from failing such a test, a relatively small offset may be applied to ensure that the amplitude response of the test fixture after application of loss compensation is always less than one. 
     FIG. 4  depicts a flowchart for automatically calibrating a network analyzer and using the calibrated network analyzer to perform measurements of a DUT according to one representative embodiment. In one representative embodiment, the flowchart is implemented using suitable software instructions or code executed by a processor of the network analyzer. In other embodiments, integrated circuitry may be alternatively or additionally employed to implement a portion of or the entire flowchart. 
   In step  401 , measurement data of a test fixture using the open standard is obtained for the ports of the network analyzer. In step  402 , a line fitting method or a polynomial fitting method is applied to the measurement data to calculate parameters for the loss formula. In step  403 , the network analyzer is calibrated by storing the calculated loss parameters. In step  404 , measurement data of a DUT is obtained. In step  405 , gain values are calculated using the appropriate parameters. For example, suppose that the measurement values of interest are S 12  measurements (i.e., a stimulus signal is applied to port one and the output signal from port two is measured). The parameters for port one and for port two are retrieved. For each frequency of interest, a first gain value is calculated using the parameters for port one and a second gain value is calculated using the parameters for port two. The gain values are then applied to the measurement data. Using the S 12  example, the amplitude measurement values are multiplied by the previously mentioned first and second gain values. In step  407 , the processed measurement values are stored and/or output as appropriate (e.g., used to display an amplitude response of the DUT on the screen of the network analyzer). 
     FIG. 5  depicts a block diagram of network analyzer  500  according to one representative embodiment. Network analyzer  500  includes typical elements common to network analyzers. For example, network analyzer  500  includes processor  504  to control the operations of network analyzer  500 . Network analyzer  500  further includes memory  505  to store measurement data for processing. Network analyzer  500  includes display  501  for presenting measurement data, user interfaces, and/or the like and user controls  502  to enable user control over the operations of network analyzer  500 . Network analyzer  500  includes multiple coaxial or other ports  503  to generate signals for application to a DUT and to receive signals from a DUT during test operations. 
   Network analyzer  500  includes suitable logic to apply port extension functionality to compensate for loss associated with a test fixture and logic for automatically calibrating the port extension functionality. For example, non-volatile memory  506  may be used to store software instructions or code that define the operations of network analyzer  500 . Non-volatile memory  506  includes signal processing algorithms  509  that perform spectral analysis of measurement data. Signal processing algorithms  509  include loss compensation module  510  according to one representative embodiment. Loss compensation module  510  implements the application of gain to measurement data according to port extension functionality. Specifically, loss compensation module  510  retrieves appropriate parameters from port extension settings  507 . Compensation module  510  uses the retrieved parameters to calculate gain values on a frequency dependent basis. Non-volatile memory  506  further includes port extension calibration module  508  that measures reflection signals from ports  503  and automatically calculates port extension settings  507  after processing of the measurement data.