Effective calibration is paramount to accurate vector network analyzer (VNA) measurements. Since the introduction of the VNA around 1970, a number of different calibration routines have been created for VNAs, based on the types of circuit standards used, such as short-openload- reflect (SOLR) to augment the classic short-open-load-thru (SOLT) calibrations. Both of these types of calibrations have a high dependence on the load model and this report introduces a flexible VNA calibration program called VersiCal that enables the use of improved calibration load models for SOLR and SOLT calibrations using loads with complex electrical behavior. The software provides an improved thru model for SOLT calibrations with non-zero-length thru standards, and helps deliver excellent broadband calibration accuracy comparable to a multiline thru-reflect-line (TRL) VNA calibration at higher frequencies, without the low-frequency inaccuracies often associated with TRL calibrations. In addition, filebased descriptions of calibration standards are facilitated so that the test engineer can use eiher measured descriptions, EM analyses, or alternative models for the calibration standard to be used.

Calibration algorithms such as TRL and line-reflect-match (LRM) approaches have been widely adopted for RF/microwave VNAs,1,2 relegating traditional SOLT calibrations to lower-frequency measurements.3 The main reason for this is the lack of accurate models to characterize the behavior of the lumped short, open and load calibration standards at higher frequencies, especially the load and in some cases the thru standard. Despite the acuracy of TRL and LRM calibrations, TRL will always lose accuracy at some low frequency or at frequencies where delay-line phase shift becomes too close to a multiple of 180 deg. LRM calibrations also generally assume idealized load models.

The behavior of current load and thru standards can differ significantly from the ideal at higher frequencies, degrading the accuracy of a calibration. However, a more exhaustive modeling of the load and thru standards will provide improved calibration results that are comparable to those achieved with multiline TRL calibrations using an algorithm called a complex openshort- load-thru (cSOLT) calibration.4 As an extension to this approach, a complex short-open-load-reciprocal (cSOLR) algorithm was developed5 based on an extension of the original SOLR method.6 These new cSOLT and cSOLR solutions are embodied in the VersiCal software, allowing users to achieve excellent calibration integrity across a broadband frequency range. The software uses LabView software from National Instruments and supports most RF/microwave VNAs.

A SOLT algorithm extracts the error terms used for calibration from uncorrected measurements of the four standards and computes the error terms needed to correct the raw data. It requires three reflection standards (usually a short, open, and matching load) to obtain the reflection error terms and a fourth (a direct thru connection between the reference planes) to determine transmission tracking and load match errors. While open and short standards are usually well behaved and can be easily modeled, it is sometimes difficult to find a load for a given testfixture environment that will provide a good impedance match over a wide frequency range. An example of a difficult setup would be using a surfacemount or on-wafer load for calibrations with a hybrid microstrip fixture. Another example is found in commercial coaxial calibration kits whereby the use of a sliding load is available to overcome the difficulty in fabricating a sufficiently low reflection broadband (e.g. > 4 GHz) coaxial load. Unfortunately, the sliding-load approach requires about five additional measurements, adding to the calibration time and complexity. It also requires a precision air-line-based sliding load standard that is not available for onboard or on-wafer calibrations and is too fragile to meet the needs of many calibration environments. As implemented in most VNAs, the load is assumed to be nonreflecting or modeled with a simple series resistive-inductive (RL) network, and the thru standard is modeled with an ideal transmission line model, typically with zero length or as a pure time delay.

A complex load model (Fig. 1) can overcome limitations in traditional SOLT calibrations and yield improved broadband accuracy. 4 It may also reduce cost. With the new model, any surface-mount resistor may be used as the load standard, avoiding the laser-trimmed loads of more expensive calibration boards.

Improved VNA calibrations may in some cases also result from use of an enhanced model for the thru standard, when it must be of finite length. In cases where, for example, a probe-tip calibration or a shift in the reference place is necessary, a user must account for the length of the thru standard and some of its physical parameters as part of the calibration. VersiCal provides a model for an imperfect thru standard that will account for conductor losses, does not assume a real and constant characteristic impedance, and can use either the loss tangent or the dielectric conductivity to model dielectric losses along with a magnetic tangent and the conductor self inductance.7 This model is very flexible since it does not require any of the physical characteristics of the line. VersiCal also uses the advanced thru model to account for possible offset lengths (with losses) in the reflection standards.

Even with this detail in modeling the thru standard, there will be cases where the behavior of a given thru standard does not fit a model. This can happen when a measurement setup does not allow for a straight connection between reference planes, as with a 90-deg. orientation between input and output connectors. Versi- Cal's cSOLR algorithm combines the original SOLR method6 with more accurate modeling of the load standard. In addition, the SOLR as originally implemented requires an estimate of the electrical length of the device used as reciprocal standard. VersiCal implements an automatic root selection algorithm, which is a variation of that proposed earlier that enables the code to automatically select the right solution for the calibration without any estimation of the length.8

VersiCal supports the following calibration algorithms:

SOLT,3 which is the classical shortopen- load-thru algorithm based on a system of three equations obtained over three measurements of three well-known standards. To obtain transmission error terms, a fourth measurement of a known through standard is required. Typically, the load is assumed to be nonreflecting or modeled with a simple series RL network, and the thru standard is modeled with an ideal transmission line model (typically zero length).
SOLR,6 which was developed by Ferrero and Pisani2 and follows the same procedure as SOLT but allows any reciprocal device as a thru standard for calibration purposes.
cSOLT,4 which was developed at USF and provides a more accurate and complex model for the load and thru standards.
cSOLR,5 which implements the SOLR algorithm combined with more accurate/complex models for the load standards to mak cSOLT.
mSOLT,9 which allows the use of standard definitions of any of the models from a measurement (or simulated) file. This allows a user to skip the modeling stage and use any .s2p file as a standard definition.

The VersiCal 3.2 calibration software supports a wide range of VNAs, including the 37xxxD ("Lightning") and MS446XX ("Scorpion") series from Anritsu Co., the 87XX and PNA analyzers from Agilent Technologies, the ZVA, ZVB, and ZBT series of VNAs from Rohde & Schwarz, and the older 8510 VNA from Agilent and 360B from Wiltron Co. (now Anritsu). VersiCal is capable of measuring the switch error in order to be able to perform cSOLR. From the previous list only those VNAs with four samplers will support the cSOLR option.

The various algorithms listed earlier can be combined in any form to achieve a VNA calibration. VersiCal supports all the classical frequency-dependent capacitance and inductance models used for open and short standards, respectively, and offset lengths (which can account for possible losses). The software features an intuitive graphical user interface (GUI) for control and data entry (Fig. 2).

VersiCal is structured on three main columns corresponding to the three basic functions of the program: acquire raw data, specify a model, and compute and send error coefficients to the VNA. The first column contains the controls that allow a user to obtain raw data corresponding to standard calibrations from a VNA. Once measured, this data is stored in text files in a disk-drive directory specified by a user. An online VNA is not needed for this step if raw data is already available as an .sp2 file; a user simply provides the name for the .sp2 file.

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VersiCal's second column shows the information needed to describe a calibration standard model and the algorithm used for the calibration. Models include short, open, and load standards (Fig. 3). The short and open models are classical models of frequency-dependent inductance and capacitance for the short. The load is represented by a complex model of Fig. 1. An offset is included for the three reflection standards, using the same characteristics as the model used for the thru standard presented in Fig. 4. A variety of options are available in VersiCal with respect to the thru/ reciprocal standard in which a physical model can be selected for the thru standard or the unknown reciprocal option for a SOLR calibration. A SOLR calibration in VersiCal will also accept an estimate for the length of the thru standard, or can automatically estimate its length.

VersiCal's menus and options provide a great deal of flexibility when performing a VNA calibration. For example, a user can measure calibration standards in any order with the option of measuring one port at a time or both ports at the same time. If raw data was measured with another software tool or generated from a simulator, a user can select the associated .s2p file containing that data. Versi- Cal allows a user to move a calibration reference plane simply by providing the delay length required for the shift. Error terms, once computed, are stored in a text file. A user can generate a variety of text files with different error terms and send them to a VNA as needed. This capability makes it possible to compare the results of different calibration approaches and make adjustments as necessary.

The CalCompare function in VersiCal (Fig. 5) implements algorithms10 that allow calculating the maximum vector difference in S-parameters as a result of different calibration approaches. This general approach to calibration comparison has become a standard for benchmarking calibration algorithms. CalCompare can use a file with error terms generated by VersiCal and perform a comparison with another file or with a calibration loaded in the VNA, even if it was performed with different software and/or a different calibration algorithm.

To illustrate the effectiveness of the VersiCal software, it was used to perform comparisons between cSOLT and TRL calibrations using standards fabricated on 20-mil-thick dielectric material from Rogers Corp. Surface-mount resistors served as load standards. Opens were achieved with open-ended transmission lines, and shorts were realized with plated viaholes. The calibration ran from 40 MHz to 20 GHz and was compared to a calibration based on the National Institute of Science and Technology (NIST) multiline TRL algorithm. For comparison, a regular SOLT calibration with RL load model was performed. A model 37369A VNA from Anritsu was used throughout.

The first step in the calibration involved obtaining models for the calibration standards. An initial calibration using the NIST Multical software was followed by measurements of the short, open, and load standards to be modeled. The load modeling emphasizes fitting the high-frequency TRLcalibrated S-parameter data and also makes sure that the low-frequency extrapolation trends to the DC value of the load resistor, Fitting the models can be done with commercial circuitsimulation software. In the case of this example, the Advanced Design System (ADS) simulation software from Agilent Technologies was used for model fitting.

For the load standard fabricated on this test board, a significant difference was found when fitting TRL-calibrated load data using the complex load model and the classical RL model (Fig. 6). The same procedure was applied for fitting data for the short and open with their respective models. The thru standard was assumed ideal in order to obtain a center of the thru reference plane in the calibration.

Once models were obtained for the calibration standards, the calibration is performed and the error terms obtained with the calibration were entered into CalCompare for comparison. When comparing the maximum vector differences of cSOLT and TRL calibrations as well as SOLT and TRL calibrations (Fig. 7), and a comparison between the reference TRL and a second TRL as a repeatability test, the level of improvement obtained with the cSOLT comparison is clear.

VersiCal provides a versatile solution for VNA calibrations with improved models and flexible calibration algorithms. Integrated as a full LabView application, it includes useful tools such as CalCompare and supports a wide range of commercial VNAs. A trial version of VersiCal is available from Modelithics, Inc.. Contact the company by e-mail at support@modelithics.com for more information.

ACKNOWLEDGMENTS
VersiCal was developed initially at the University of South Florida's Center for Wireless and Microwave Information (WAMI) Systems Center through a series of student projects directed by Drs. Thomas Weller and Lawrence Dunleavy. The list of students making contributions to this software in various ways includes, but is not necessarily limited to, Michael Imparato, Peter Kirby, Sathya Padmanabhan, John Daniels, Alberto Rodriguez, and Daniel Sosa-Martin. Previous research projects at the University of South Florida directly or indirectly related to this software was funded by Modelithics, M/A-COM, and Anritsu Co.

REFERENCES
1. H. J. Eul and B. Schiek, "Thru-match-reflect: One result of a rigorous theory for de-embedding and network analyzer calibration," in Proceedings of the 18th European Microwave Conference, Stockholm, Sweden, September 1988, pp. 909-914.
2. R. Marks, "A multiline method of network analyzer calibration," IEEE Microwave Theory & Techniques, Vol. 39, No. 7, July 1991, pp. 1205-1215.
3. J. Fitzpatrick, "Error models for system measurements," Microwave Journal, Vol. 21, No. 5, May 1978, pp. 63-66.
4. S. Padmanabhan, L. Dunleavy, J.E. Daniel, A. Rodriguez, and P.L. Kirby, "Broadband Space Conservative On-Wafer Network Analyzer Calibrations with More Complex Load and Thru Models," IEEE Journal, Vol. 54, No. 9, September, 2006, pp. 3583-3593.
5. J. E. Daniels, "Development of Enhanced Multiport Network Analyzer CalibrationsUsing Non-Ideal Standards," 2005, unpublished.
6. A. Ferrero and U. Pisani, "Two-port network analyzer calibration using an unknown thru,'" Microwave and Guided Wave Letters, 1992, pp. 505-507.
7. Alberto Rodriguez, University of South Florida, Tampa, FL, personal communication, Jan. 9, 2007.
8. J. Stenarson and K. Yhland, "Automatic root selection for the unknown thru algorithm," presented at the Automatic RF Techniques Group 67th Microwave Measurements Conference, June 16, 2006.
9. M. Imparato, T. Weller, and L." 1999 IEEE MTT-S International Microwave Symposium Digest, Anaheim, CA, June 1999, pp. 1643-1646.
10. R. B. Marks, J. A. Jargon, and John R. Juroshek, "Calibration Comparison Method for Vector Network Analyzers," 48th ARFTG Conference Digest, Dec. 5-6, 1996, pp. 38-45.
11. VersiCal's User's Manual, Modelithics, Inc., 3650 Spectrum Blvd., Tampa, FL 33612; www.modelithics.com.