@article{Williams2001a, abstract = {We develop analytic expressions for the impulse response and kickout pulses of a simple sampling circuit that incorporate the nonlinear junction capacitance of the sampling diode. We examine the effects of both the time-varying junction capacitance and conductance on the impulse response and kickout pulses, and discuss their impact on the accuracy of the nose-to-nose calibration technique}, author = {Williams, D.F. and Remley, K.A.}, doi = {10.1109/22.925484}, journal = {IEEE Transactions on Microwave Theory and Techniques}, keywords = {large-signal and nonlinear measurement hardware}, number = {6}, pages = {1013--1019}, title = {{Analytic sampling-circuit model}}, url = {http://ieeexplore.ieee.org/search/srchabstract.jsp?tp=&arnumber=925484}, volume = {49}, year = {2001} } @article{Cappy1988, abstract = {The high electron mobility transistor's (HEMT's) noise behavior is presented from theoretical and experimental points of view. The general method used in the high-frequency noise analysis is described and the different approximations commonly used in the derivation of the noise parameter expressions are discussed. A comparison between the noise performance of both MESFETs and HEMTs is carried out. The measurement techniques providing the noise figure and the other noise parameters are then described and compared.}, author = {Cappy, A.}, doi = {10.1109/22.3475}, journal = {IEEE Transactions on Microwave Theory and Techniques}, keywords = {noise 50 ohms measurement methods}, number = {1}, pages = {1--10}, title = {{Noise modeling and measurement techniques [HEMTs]}}, url = {http://ieeexplore.ieee.org/search/srchabstract.jsp?tp=&arnumber=3475}, volume = {36}, year = {1988} } @article{Kasa1974, abstract = {A general evaluation procedure is described for calibration of a linear complex reflectometer (network analyzer) and for two-port measurements. New closed-form formulas and procedures are given for two practical cases: 1) calibration or measurement with two known standards and a sliding termination; 2) calibration or measurement by one standard and two different sliding terminations. The reflection coefficient magnitudes and phases of these sliding terminations need not be known. The closed-form formulas make it possible to determine calibration constants by direct calculation without approximations or complicated multivariable iterations.}, author = {Kasa, I.}, doi = {10.1109/TIM.1974.4314321}, journal = {IEEE Transactions on Instrumentation and Measurement}, keywords = {VNA measurements}, number = {4}, pages = {399 -- 402}, title = {{Closed-Form Mathematical Solutions to Some Network Analyzer Calibration Equations}}, url = {http://ieeexplore.ieee.org/xpl/freeabs all.jsp?arnumber=4314321}, volume = {23}, year = {1974} } @article{Williams2007, abstract = {Most of the equipment required is readily available in most microwave labs: a vector network analyzer, a microwave signal generator, and, of course, a sampling oscilloscope. In this paper, the authors summarize many of the corrections discussed in " Terminology for high-speed sampling-oscilloscope calibration" [Williams et al., 2006] and "Magnitude and phase calibrations for RF, microwave, and high-speed digital signal measurements" [Remley and Hale, 2007] that are necessary for metrology-grade measurements and Illustrate the application of these oscilloscopes to the characterization of microwave signals.}, author = {Williams, D. and Hale, P. and Remley, K.A.}, doi = {10.1109/MMW.2007.383954}, journal = {IEEE Microwave Magazine}, keywords = {large-signal and nonlinear measurement hardware}, number = {4}, pages = {59--68}, title = {{The Sampling Oscilloscope as a Microwave Instrument}}, url = {http://ieeexplore.ieee.org/search/srchabstract.jsp?tp=&arnumber=4271280}, volume = {8}, year = {2007} } @techreport{EURAMET:EuropeanAssociationofNationalMetrologyInstitutes2011, author = {{EURAMET : European Association of National Metrology Institutes}}, keywords = {uncertainty specific to RF measurement}, title = {{Guidelines on the evaluation of Vector Network Analysers (VNA)}}, url = {http://www.euramet.org/fileadmin/docs/Publications/calguides/EURAMET cg-12 v 2.0 Guidelines on Evaluation.pdf}, year = {2011} } @article{Ferrero1992a, abstract = {A generalized multiport network analyzer implemented using commercially available hardware is presented. Measurement calibration is accomplished through a novel calibration procedure which requires only conventional standards used for two-port calibrations. The calibration theory accounts for the errors due to the signal switching network but does not systematically remove errors due to signal switching leakage between port pairs. The approach is verified on a three-port test set implementation, and the measuring system can be expanded to n ports with additional hardware in a straightforward manner. Experimental verification was carried out through measurement of one-, two-, and three-port devices connected to the test set ports in several different ways. Excellent agreement of the same corrected S-parameters measured at different test set ports was observed, and confidence in system accuracy is established through measurement of two-port verification standards}, author = {Ferrero, A. and Pisani, U. and Kerwin, K.J.}, doi = {10.1109/22.168766}, journal = {IEEE Transactions on Microwave Theory and Techniques}, keywords = {signal integrity and multiport measurements}, number = {11}, pages = {2078 -- 2085}, title = {{A new implementation of a multiport automatic network analyzer}}, url = {http://ieeexplore.ieee.org/search/srchabstract.jsp?tp=&arnumber=168766}, volume = {40}, year = {1992} } @article{Hall2004, abstract = {This paper explores a recent suggestion to use a bivariate form of the Gaussian 'error propagation law' to propagate uncertainty in the measurement of complex-valued quantities (Ridler N M and Salter M J 2002 Metrologia 39 295–302). Several alterative formulations of the law are discussed in which the contributions from individual input terms are more explicit. The calculation of complex-valued sensitivity coefficients is discussed and a matrix generalization of the notion of a 'component of uncertainty' in a measurement result is introduced. A form of a 'chain rule' is given for the propagation of uncertainty when several intermediate equations are involved.}, author = {Hall, B.D.}, doi = {10.1088/0026-1394/41/3/010}, journal = {Metrologia}, keywords = {uncertainty specific to RF measurement}, number = {3}, pages = {173--177}, title = {{On the propagation of uncertainty in complex-valued quantities}}, url = {http://iopscience.iop.org/0026-1394/41/3/010/pdf/0026-1394 41 3 010.pdf}, volume = {41}, year = {2004} } @article{Ku2002, abstract = {This paper proposes a system-level behavioral model for RF power amplifiers (PAs), which exhibit memory effects, that is based on the parallel Wiener system. The model extraction is performed using two-tone intermodulation distortion (IMD) measurements with different tone frequency spacings and power levels. It is found that by using such a model, more accurate adjacent-channel power-ratio levels may be predicted for high PAS close to the carrier frequency. This is validated using IS-95B CDMA signals on a low-power (0.5 W) class-AB PA, and on a high-power (45 W) class-B PA. The model also provides a means to quantify memory effects in terms of a figure-of-merit that calculates the relative contribution to the IMD of the memoryless and memory portion of the PA nonlinearity. This figure-of-merit is useful in providing an estimate of the amount of correction that a memoryless predistortion system may have on PAS that exhibit memory effects.}, author = {Ku, H. and McKinley, M.D. and Kenney, J.S.}, doi = {10.1109/TMTT.2002.805196}, journal = {IEEE Transactions on Microwave Theory and Techniques}, keywords = {nonlinear measurements and test signals}, number = {12}, pages = {2843--2849}, title = {{Quantifying memory effects in RF power amplifiers}}, url = {http://ieeexplore.ieee.org/search/srchabstract.jsp?tp=&arnumber=1098003}, volume = {50}, year = {2002} } @article{Sipila1998, abstract = {A system is presented for the accurate measurement of high-frequency periodic time-domain voltage and current waveforms of a nonlinear microwave device. The measurements are performed in the time domain using a high-speed sampling oscilloscope. The results are Fourier-transformed into the frequency domain for error correction and then back into the time domain. An error-correction algorithm is presented that makes it possible to obtain accurate waveforms in spite of nonideal system components. Practical difficulties in measurement-system characterization are also discussed. An accurate circuit model for the measurement fixture is developed and its element values are determined. Measurement results are given showing the waveforms in a microwave transistor operated in the nonlinear region. The errors caused by signal processing are discussed}, author = {Sipila, M. and Lehtinen, K. and Porra, V.}, doi = {10.1109/22.6087}, journal = {IEEE Transactions on Microwave Theory and Techniques}, keywords = {large-signal and nonlinear measurement hardware}, number = {10}, pages = {1397 -- 1405}, title = {{High-frequency periodic time-domain waveform measurement system}}, url = {http://ieeexplore.ieee.org//xpls/abs all.jsp?arnumber=6087}, volume = {36}, year = {1998} } @techreport{UKAS2007, address = {Feltham, UK}, author = {UKAS}, institution = {United Kingdom Accreditation Service (UKAS)}, keywords = {general measurement uncertainty}, title = {{The Expression of Uncertainty and Confidence in Measurement}}, url = {http://www.ukas.com/library/Technical-Information/Pubs-Technical-Articles/Pubs-List/M3003.pdf}, year = {2007} } @inproceedings{Demmler1994, abstract = {A high power on-wafer measurement system based on the new microwave transition analyzer (MTA) HP 71500A has been developed for the complete characterization of the large signal behavior of transistors. One key feature of the MTA based measurement system is that during power sweeps the harmonic behavior, up to 40 GHz, can be measured. To improve the accuracy of power measurements the vector measurement capability of the MTA is also utilized to allow full vector calibration of the measurement system. In addition, this vector measurement feature allows both the input reflection and the transmission coefficients of a device under test (DUT) to be measured as a function of frequency and input power. The input and output voltage waveforms at the transistor terminals are also calculated from the measurement data. This improved capability is possible since the vector calibrated measurement system allows both the measurement of the fundamental and the higher harmonics with respect to magnitude and phase.}, address = {Cannes, France}, author = {Demmler, M. and Tasker, P. J. and Schlechtweg, M.}, booktitle = {European Microwave Conference (EuMC)}, doi = {10.1109/EUMA.1994.337406}, keywords = {large-signal and nonlinear measurement hardware}, pages = {1367--1372}, title = {{A Vector Corrected High Power On-Wafer Measurement System with a Frequency Range for the Higher Harmonics up to 40 GHz}}, url = {http://ieeexplore.ieee.org/search/srchabstract.jsp?tp=&arnumber=4138452}, year = {1994} } @article{Dambrine1993, abstract = {A method for measuring the noise parameters of MESFETs and HEMTs is presented. It is based on the fact that three independent noise parameters are sufficient to fully describe the device noise performance. It is shown that two noise parameters, Rn and |YOPT|, can be directly obtained from the frequency variation of the noise figure F50 corresponding to a 50 $\Omega$ generator impedance. By using a theoretical relation between the intrinsic noise sources as additional data, the F50 measurement only can provide the four noise parameters. A good agreement with more conventional techniques is obtained.}, author = {Dambrine, G. and Happy, H. and Danneville, F. and Cappy, A.}, doi = {10.1109/22.223734}, journal = {IEEE Transactions on Microwave Theory and Techniques}, keywords = {noise 50 ohms measurement methods}, number = {3}, pages = {375--381}, title = {{A new method for on wafer noise measurement}}, url = {http://ieeexplore.ieee.org/search/srchabstract.jsp?tp=&arnumber=223734}, volume = {41}, year = {1993} } @inproceedings{Davidson1990, abstract = {Two new techniques are presented in an effort to achieve greater accuracy and better repeatability in the on-wafer calibration of vector network analyzers. The first is a method of determining an inductance value for the match standard during the calibration process so that only its resistance, not its reactance, needs to be known. The second is a new type of calibration, LRRM (line-reflect-reflect-match),which is a variation of LRM with several possible advantages. Also, a simple series resistance-inductancemodel for a coplanar load is experimentally investigated to 40 GHz and found to provide a good description of the load behavior.}, author = {Davidson, Andrew and Jones, Keith and Strid, Eric}, booktitle = {ARFTG Conference Digest}, doi = {10.1109/ARFTG.1990.323996}, keywords = {VNA measurements}, pages = {57 -- 63}, title = {{LRM and LRRM Calibrations with Automatic Determination of Load Inductance}}, url = {http://ieeexplore.ieee.org/search/srchabstract.jsp?tp=&arnumber=4119568}, year = {1990} } @article{Rehnmark1974, abstract = {Formulas are presented for the direct calculation of the scattering parameters of a linear two-port, when it is measured by an imperfect network analyzer. Depending on the hardware configuration of the test set, the measurement system is represented by one of two flowgraph models. In both models presented, leakage paths are included. The error parameters, i.e., the scattering parameters of the measuring system, are six respective ten complex numbers for each frequency of interest. A calibration procedure, where measurements are made on standards, will determine the error parameters. One of many possible calibration procedures is briefly described. By using explicit formulas instead of iterative methods, the computing time for the correction of the scattering parameters of the unknown two-port is significantly reduced. The addition of leakage paths will only have a minor effect on computational complexity while measurement accuracy will increase.}, author = {Rehnmark, S}, doi = {10.1109/TMTT.1974.1128250}, issn = {0018-9480}, journal = {IEEE Transactions on Microwave Theory and Techniques}, keywords = {VNA measurements}, number = {4}, pages = {457--458}, title = {{On the Calibration Process of Automatic Network Analyzer Systems (Short Papers)}}, url = {http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=1128250}, volume = {22}, year = {1974} } @inproceedings{Rytting1982, author = {Rytting, D K}, booktitle = {Hewlett-Packard RF \& Microwave Measurement Symposium and Exhibition}, keywords = {VNA measurements}, title = {{An analysis of vector measurement accuracy enhancement techniques}}, year = {1982} } @article{Woods1977, abstract = {Network analysis, in terms of S-parameters, is invariably carried out in modern textbooks by employing the power-wave concept. It is shown that this approach is not relevant to practical measurement; furthermore, the complication of square roots, real parts, conjugates, moduli and conjugate transpose matrices is carried throughout the mathematics. These difficulties are overcome by employing the voltage-wave concept with complex normalisation, whereby the analysis is carried out in terms of port-voltage and port-current relationships, from which, power flow relationships are readily obtained in a straightforward manner. The new method of network analysis presented is not only completely general and rigorous, but simple to apply and faster than any other known technique. It is based on a once-for-all solution of the most general problem of all in 3-port analysis, namely, a 3 \~{A}— 3 renormalising matrix, each element of which embodies three renormalising factors. Examples are given of the derivation of some 2-port and 3-port network equations, but in a more general form in which the port normalising impedances are not only different but complex. It is concluded that the voltage-wave S-parameter approach, with complex normalisation, should not only be revived and taught in academic institutions, but that it should take precedence over the power-wave approach which has a very restricted application. In a companion paper, a reappraisal is made of computer-corrected network analyser design and calibration.}, author = {Woods, D.}, doi = {10.1049/piee.1977.0037}, journal = {Proceedings of the Institution of Electrical Engineers}, keywords = {signal integrity and multiport measurements}, number = {3}, pages = {198 -- 204}, title = {{Multiport-network analysis by matrix renormalisation employing voltage-wave S-parameters with complex normalisation}}, url = {http://ieeexplore.ieee.org/search/srchabstract.jsp?tp=&arnumber=5253889}, volume = {124}, year = {1977} } @article{IRE1959, author = {-}, doi = {10.1109/JRPROC.1960.287380}, journal = {Proceedings of the IRE}, keywords = {noise theoretical bases}, number = {1}, pages = {60--68}, title = {{IRE Standards on Methods of Measuring Noise in Linear Twoports, 1959}}, url = {http://ieeexplore.ieee.org/search/srchabstract.jsp?tp=&arnumber=4065915}, volume = {48}, year = {1960} } @inproceedings{VandenBroeck1994, abstract = {The vectorial nonlinear-network analyzer concept is introduced and realized in practice. A vectorial nonlinear-network analyzer excites a nonlinear microwave device-under-test with a combination of sinewaves of different frequencies and accurately detects the phase and amplitude of all frequency components of the incident and the scattered waves. A new, statistic efficient, absolute calibration procedure is developed based on a row crest factor multisine reference generator characterized by a broadband sampling oscilloscope. This makes the calibration traceable to the accuracy of a so-called nose-to-nose measurement}, address = {San Diego, CA}, author = {{Van den Broeck}, T. and Verspecht, J.}, booktitle = {IEEE MTT-S International Microwave Symposium Digest}, doi = {10.1109/MWSYM.1994.335170}, keywords = {large-signal and nonlinear measurement hardware}, pages = {1069--1072}, title = {{Calibrated vectorial nonlinear-network analyzers}}, url = {http://ieeexplore.ieee.org/search/srchabstract.jsp?tp=&arnumber=335170}, year = {1994} } @techreport{Agilent2010, author = {Agilent}, institution = {Agilent}, keywords = {noise theoretical bases}, title = {{Noise figure measurement accuracy}}, url = {http://cp.literature.agilent.com/litweb/pdf/5952-3706E.pdf}, year = {2010} } @article{Bauer1974, abstract = {De-embedding is the process of deducing the impedance of a device under test from measurements made at a distance, when the electrical properties of the intervening structure are known. Unterminating is the process of deducing the electrical properties of the intervening structure from a series of measurements with known embedded devices. The mathematical steps necessary for de-embedding and unterminating are reviewed, and a technique is presented for unterminating with theoretically redundant measurements in order to minimize the effect of experimental errors.}, author = {Bauer, R.F. and Penfield, P.}, doi = {10.1109/TMTT.1974.1128212}, journal = {IEEE Transactions on Microwave Theory And Techniques}, keywords = {uncertainty specific to RF measurement,VNA measurements}, number = {3}, pages = {282--288}, title = {{De-embedding and Unterminating}}, url = {http://ieeexplore.ieee.org/search/srchabstract.jsp?tp=&arnumber=1128212}, volume = {22}, year = {1974} } @article{Engen1979, abstract = {In an earlier paper, the use of a "thru-short-delay" (TSD) technique for calibrating the dual six-port automatic network analyzer was described. Another scheme required only a length of precision transmission line and a "calibration circuit." The better features of these two somewhat different approaches have now been combined and the requirement for either a known short, or a "calibration circuit" eliminated. This paper will develop the theory for this new procedure.}, author = {Engen, G.F. and Hoer, C.A.}, doi = {10.1109/TMTT.1979.1129778}, journal = {IEEE Transactions on Microwave Theory and Techniques}, keywords = {VNA measurements}, number = {12}, pages = {987 -- 993}, title = {{Thru-Reflect-Line: An Improved Technique for Calibrating the Dual Six-Port Automatic Network Analyzer}}, url = {http://ieeexplore.ieee.org/search/srchabstract.jsp?tp=&arnumber=1129778}, volume = {27}, year = {1979} } @article{Fukui1966, abstract = {The expressions for available power gain and noise measure of linear two-ports are introduced in terms of the two-port parameters and the gain and the noise parameters, respectively. Their graphical representations on the source admittance plane with rectangular coordinates are also shown. Furthermore, it is shown that the behavior of available power gain, noise figure, and noise measure can be represented on the Smith-chart or the complex reflection coefficient plane of the source admittance. It is more convenient to investigate the gain and noise performance of amplifiers over a wide range of source admittance in this representation than with rectangular coordinates. As an example of the graphical representation the gain and noise performance of a microwave transistor is illustrated on the Smith-chart.}, author = {Fukui, H.}, doi = {10.1109/TCT.1966.1082556}, journal = {IEEE Transactions on Circuit Theory}, keywords = {noise theoretical bases}, number = {12}, pages = {137--142}, title = {{Available Power Gain, Noise Figure, and Noise Measure of Two-Ports and Their Graphical Representations}}, url = {http://ieeexplore.ieee.org/search/srchabstract.jsp?tp=&arnumber=1082556}, volume = {13}, year = {1966} } @article{Harris1981, abstract = {The mismatch uncertainty associated with a simple microwave power measurement is precisely defined and shown, under certain assumptions, to have a U-shaped probability density distribution. Earlier expressions for the mismatch error when measuring microwave attenuation receive further mathematical development; and, when all the phase angles are unknown, it is shown that there are six independent contributions to the mismatch error, each with a U-shaped distribution. When the phase angles of the scattering parameters of the device under test are known, the mismatch error expression contains three independent contributions cach with a U-shaped distribution. The combination of U-shaped distributions is discussed in detail and new expressions are presented for the standard deviations of the mismatch uncertainties in the above two cases. The uncertainties yielded by these new expressions are in closer agreement with experience than those obtained by using methods based on maximum limits.}, author = {Harris, I.A. and Warner, F.L.}, doi = {10.1049/ip-h-1:19810007}, journal = {IEE Proceedings H}, keywords = {uncertainty specific to RF measurement}, number = {1}, pages = {35--41}, title = {{Re-examination of mismatch uncertainty when measuring microwave power and attenuation}}, url = {"http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=?arnumber=4644837}, volume = {128}, year = {1981} } @article{Hillbrand1976, abstract = {A method for computer aided noise analysis is presented which is based on a description of noise by means of correlation matrices. The method is a two-port analysis and it is, therefore, applicable to circuits which are composed of simple two-ports with known noise performance. The correlation matrix concept holds two main advantages over other methods of noise analysis. Partially correlated noise sources can be treated without any loss of efficiency and information concerning minimum noise figure and noise matching conditions is obtained.}, author = {Hillbrand, H. and Russer, P.}, doi = {10.1109/TCS.1976.1084200}, journal = {IEEE Transactions on Circuits and Systems}, keywords = {noise theoretical bases}, number = {4}, pages = {235--238}, title = {{An efficient method for computer aided noise analysis of linear amplifier networks}}, url = {http://ieeexplore.ieee.org/search/srchabstract.jsp?tp=&arnumber=1084200}, volume = {23}, year = {1976} } @article{Pasquet2008, abstract = {The noise power wave formalism is used to extract the noise parameters from the noise power measurement. A first step consists of calibrating the measurement setup. We only assume that the receiver is unidirectional. The noise parameters are then deduced from power measurements with analytical relations with no further assumptions.}, author = {Pasquet, D. and Bourdel, E. and Quintanel, S. and Ravalet, T. and Houssin, P.}, doi = {10.1109/TMTT.2008.2002235}, journal = {IEEE Transactions on Microwave Theory and Techniques}, keywords = {noise general measurement methods}, number = {9}, pages = {2136--2142}, title = {{New method for noise-Parameter measurement of a mismatched linear two-port using noise power wave formalism}}, url = {http://ieeexplore.ieee.org/search/srchabstract.jsp?tp=&arnumber=4599243\&isnumber=4616565}, volume = {56}, year = {2008} } @article{Schreurs2003, abstract = {Behavioral models for microwave devices from time domain large-signal measurements are developed. For the presented examples, the model is defined by representing the terminal currents as a function of the terminal voltages and their derivatives. When using these models as building blocks of higher level designs, the simulation speed is significantly improved.}, author = {Schreurs, D. and Wood, J. and Tufillaro, N. and Barford, L. and Root, D. E.}, doi = {10.1002/mmce.10062}, issn = {1096-4290}, journal = {International Journal of RF and Microwave Computer-Aided Engineering}, keywords = {nonlinear modeling starting from large-signal measurements}, month = jan, number = {1}, pages = {54--61}, title = {{Construction of behavioral models for microwave devices from time domain large-signal measurements to speed up high-level design simulations}}, url = {http://doi.wiley.com/10.1002/mmce.10062}, volume = {13}, year = {2003} } @inproceedings{Blockley2005, abstract = {We describe an instrument that uses directional bridges and a five-channel, mixer-based receiver to make vector-corrected measurements of signals from 0.3MHz to 20GHz. This instrument yields voltage, current or travelling waves in either time-domain or frequency-domain with ≈85dB SFDR and with phase accuracy that can be traced to national standards laboratories. The instrument is used to characterize the effect of an amplifier on a wideband complex-modulated signal. Results are compared with data gathered using a calibrated sampling oscilloscope equipped to capture long records with timebase correction. We show effects such as input-impedance induced distortion that can be seen only with this new instrument.}, address = {Long Beach, CA}, author = {Blockley, P. and Gunyan, D. and Scott, J.B.}, booktitle = {IEEE MTT-S International Microwave Symposium Digest}, doi = {10.1109/MWSYM.2005.1516977}, keywords = {large-signal and nonlinear measurement hardware}, title = {{Mixer-based, vector-corrected, vector signal/network analyzer offering 300kHz-20GHz bandwidth and traceable phase response}}, url = {http://ieeexplore.ieee.org/search/srchabstract.jsp?tp=&arnumber=1516977}, year = {2005} } @techreport{JCGM2008a, author = {JCGM}, institution = {Joint Committee for Guides in Metrology (JCGM)}, keywords = {general measurement uncertainty}, title = {{Evaluation of measurement data — Supplement 1 to the “Guide to the expression of uncertainty in measurement” — Propagation of distributions using a Monte Carlo method}}, url = {http://www.bipm.org/utils/common/documents/jcgm/JCGM 101 2008 E.pdf}, year = {2008} } @article{Lazaro1999, abstract = {A novel method for measuring the four noise parameters of a field-effect transistor (FET) is presented. It is based on the determination of its intrinsic noise matrix elements [C11INT, C22INT, Re(C12 INT), Im(C12INT)] by fitting the measured device noise figure for a matched source reflection coefficient (F50) at a number of frequency points, thus, a tuner is not required. In contrast to previous works, no restrictive assumptions are made on the intrinsic noise sources. The receiver full-noise calibration is easily performed by using a set of coaxial and on-wafer standards that are commonly available in a microwave laboratory, thus, an expensive broad-band tuner is not required for calibration either. On-wafer experimental verification up to 26 GHz is presented and a comparison with other F50-based and tuner-based methods is given. As an application, the dependence of the FET intrinsic noise sources as a function of the bias drain-current and gate-length is obtained.}, author = {Lazaro, A. and Pradell, L. and O'Callaghan, J.M.}, doi = {10.1109/22.750233}, journal = {IEEE Transactions on Microwave Theory and Techniques}, keywords = {noise 50 ohms measurement methods}, number = {3}, pages = {315--324}, title = {{FET noise-parameter determination using a novel technique based on 50-$\Omega$ noise-figure measurements}}, url = {http://ieeexplore.ieee.org/search/srchabstract.jsp?tp=&arnumber=750233}, volume = {47}, year = {1999} } @article{Marks1991, abstract = {The author presents a method for the calibration of network analyzers. The essential feature is the use of multiple, redundant transmission line standards. The additional information provided by the redundant standards is used to minimize the effects of random errors, such as those caused by imperfect connector repeatability. The resulting method exhibits improvements in both accuracy and bandwidth over conventional methods. The basis of the statistical treatment is a linearized error analysis of the TRL (thru-reflect-line) calibration method. The analysis presented is useful in the assessment of calibration accuracy. It also yields results relevant to the choice of standards.}, author = {Marks, R.B.}, doi = {10.1109/22.85388}, journal = {IEEE Transactions on Microwave Theory and Techniques}, keywords = {VNA measurements}, number = {7}, pages = {1205 -- 1215}, title = {{A multiline method of network analyzer calibration}}, url = {http://ieeexplore.ieee.org/search/srchabstract.jsp?tp=&arnumber=85388}, volume = {39}, year = {1991} } @article{Marks1992, abstract = {This work generalizes and extends the classical circuit theory of electromagnetic waveguides. Unlike the conventional theory, the present formulation applies to all waveguides composed of linear, isotropic material, even those involving lossy conductors and hybrid mode fields, in a fully rigorous way. Special attention is given to distinguishing the traveling waves, constructed with respect to a well-defined characteristic impedance, from a set of pseudo-waves, defined with respect to an arbitrary reference impedance. Matrices characterizing a linear circuit are defined, and relationships among them, some newly discovered, are derived. New ramifications of reciprocity are developed. Measurement of various network parameters is given extensive treatment.}, author = {Marks, R.B. and Williams, D.F.}, journal = {Journal of Research of the National Institute of Standards and Technology}, keywords = {VNA measurements}, number = {5}, pages = {533 -- 561}, title = {{A general waveguide circuit theory}}, url = {http://www.eeel.nist.gov/dylan papers/GeneralWaveguideCricuitTheory.pdf}, volume = {97}, year = {1992} } @article{Root2005, abstract = {We present an optimal experiment design methodology and a superior and fully automated model generation procedure for identifying a class of broad-band multiharmonic behavioral models in the frequency domain. The approach reduces the number of nonlinear measurements needed, minimizes the time to generate the data from simulations, reduces the time to extract the model functions from data, and when used for simulation-based models, takes maximum advantage of specialized simulation algorithms. The models have been subject to extensive validation in applications to real microwave integrated circuits. The derived model is valid for both small and large amplitude drive signals, correctly predicts even and odd harmonics through cascaded chains of functional blocks, simulates accurately load-pull behavior away from 50 $\Omega$, and predicts adjacent channel power ratio and constellation diagrams in remarkably close agreement to the circuit model from which the behavioral model was derived. The model and excitation design templates for generating them from simulations are implemented in Agilent Technologies' Advanced Design System.}, author = {Root, D.E. and Verspecht, J. and Sharrit, D. and Wood, J. and Cognata, A.}, doi = {10.1109/TMTT.2005.855728}, journal = {IEEE Transactions on Microwave Theory and Techniques}, keywords = {nonlinear modeling starting from large-signal measurements}, number = {11}, pages = {3656--3664}, title = {{Broad-band poly-harmonic distortion (PHD) behavioral models from fast automated simulations and large-signal vectorial network measurements}}, url = {http://ieeexplore.ieee.org/search/srchabstract.jsp?tp=&arnumber=1528820}, volume = {53}, year = {2005} } @article{Woods1975, abstract = {It is shown that a typical network anlayser can be characterised in terms of three standards and five residual parameters, provided that all mismatches are invariant between the reflection and transmission modes of operation. The five residuals are expressed in terms of 22 internal parameters and the detector mismatches. Source mismatch does not contribute to systematic error, as is generally believed.}, author = {Woods, D.}, doi = {10.1049/el:19750311}, issn = {00135194}, journal = {Electronics Letters}, keywords = {VNA measurements}, number = {17}, pages = {403}, title = {{Rigorous derivation of computer-corrected network-analyser calibration equations}}, url = {http://link.aip.org/link/?ELL/11/403/1}, volume = {11}, year = {1975} } @inproceedings{Verspecht1995, abstract = {A measurement setup and calibration procedure are described allowing the accurate on wafer measurement of phases and amplitudes of the spectral components of incident and scattered voltage waves at the signal ports of a nonlinear microwave device. A comparison is made between measurements performed with the setup and simulations based on a Root-model}, address = {Orlando, FL}, author = {Verspecht, J. and Debie, P. and Barel, A. and Martens, L.}, booktitle = {IEEE MTT-S International Microwave Symposium Digest}, doi = {10.1109/MWSYM.1995.406147}, keywords = {large-signal and nonlinear measurement hardware}, pages = {1029--1032}, title = {{Accurate on wafer measurement of phase and amplitude of the spectral components of incident and scattered voltage waves at the signal ports of a nonlinear microwave device}}, url = {http://ieeexplore.ieee.org/search/srchabstract.jsp?tp=&arnumber=406147}, year = {1995} } @article{Bockelman1995, abstract = {A theory for combined differential and common-mode normalized power waves is developed in terms of even and odd mode impedances and propagation constants for a microwave coupled line system. These are related to even and odd-mode terminal currents and voltages. Generalized s-parameters of a two-port are developed for waves propagating in several coupled modes. The two-port s-parameters form a 4-by-4 matrix containing differential-mode, common-mode, and cross-mode s-parameters. A special case of the theory allows the use of uncoupled transmission lines to measure the coupled-mode waves. Simulations verify the concept of these mixed-mode s-parameters, and demonstrate conversion from mode to mode for asymmetric microwave structures}, author = {Bockelman, D.E. and Eisenstadt, W.R.}, doi = {10.1109/22.392911}, journal = {IEEE Transactions on Microwave Theory and Techniques}, keywords = {signal integrity and multiport measurements}, number = {7}, pages = {1530 -- 1539}, title = {{Combined differential and common-mode scattering parameters: theory and simulation}}, url = {http://ieeexplore.ieee.org/search/srchabstract.jsp?tp=&arnumber=392911}, volume = {43}, year = {1995} } @article{BorgesdeCarvalho2002, abstract = {This paper presents a comprehensive study of intermodulation-distortion response asymmetries often observed in microwave nonlinear systems subject to a two-tone or multitone test. The reasons for the different amplitudes of the two adjacent tones are first investigated under small- and large-signal regimes, using a general circuit with frequency-dependent embedding impedances and resistive and reactive nonlinearities. It is shown that this intriguing phenomenon can be mainly attributed to the terminating impedances at the baseband or difference frequencies. Multitone behavior is also addressed and its main differences from the two-tone case explained. Those theoretical conclusions are then extrapolated for real circuits and validated by measured results obtained from microwave power amplifiers of two different technologies, i.e., a GaAs MESFET and an Si bipolar junction transistor.}, author = {{Borges de Carvalho}, N. and Pedro, J.C.}, doi = {10.1109/TMTT.2002.802321}, journal = {IEEE Transactions on Microwave Theory and Techniques}, keywords = {nonlinear measurements and test signals}, number = {9}, pages = {2090--2101}, title = {{A comprehensive explanation of distortion sideband asymmetries}}, url = {http://ieeexplore.ieee.org/search/srchabstract.jsp?tp=&arnumber=1028948}, volume = {50}, year = {2002} } @article{Brinkhoff2003, abstract = {The intermodulation performance of an FET in the common-source configuration is dependent on the impedance presented to its gate and drain terminals, not only at fundamental, but also at harmonic and baseband frequencies. At baseband frequencies, these terminating impedances are usually determined by the bias networks, which may have varying impedance over the frequencies involved. This can give rise to asymmetry in two-tone intermodulation levels, and changing intermodulation levels with tone spacing, as previous studies have shown. In this paper, an FET is analyzed to gain an understanding, useful to the circuit designer, of the contributing mechanisms, and to enable the prediction of bias points and the design of networks that can minimize or maximize these effects. Compact formulas are given to facilitate this. An amplifier was tested, showing good agreement between the theoretical and measured results.}, author = {Brinkhoff, J. and Parker, A.E.}, doi = {10.1109/TMTT.2003.808704}, journal = {IEEE Transactions on Microwave Theory and Techniques}, keywords = {nonlinear measurements and test signals}, number = {3}, pages = {1045--1051}, title = {{Effect of baseband impedance on FET intermodulation}}, url = {http://ieeexplore.ieee.org/search/srchabstract.jsp?tp=&arnumber=1191766}, volume = {51}, year = {2003} } @article{Clark2002, abstract = {An accurate nonlinear model is necessary to optimize the tradeoff between efficiency and linearity in power amplifiers. Gain compression (AM/AM) and amplitude-phase (AM/PM) distortion are the two primary model inputs used to characterize the nonlinearity. The amplifier's AM/AM and AM/PM characteristics are typically measured statically using a vector network analyzer. Since the input is typically a modulated signal, it is desirable to characterize the amplifier dynamically. This paper describes and demonstrates a dynamic AM/AM and AM/PM measurement and modeling technique involving a spectrum analyzer and two-tone input signals. A complete analysis of the measurement technique is presented, along with the data processing needed for the identification of a new three-box model. The test configuration and procedure are presented with special precautions to minimize measurement error. Results for a solid-state amplifier are used to accurately predict intermodulation distortion, while those for a traveling-wave tube amplifier show good agreement with that obtained dynamically using a 16 quadrature-amplitude-modulation signal}, author = {Clark, C.J. and Silva, C.P. and Moulthrop, A.A. and Muha, M.S.}, doi = {10.1109/TMTT.2002.1006421}, journal = {IEEE Transactions on Microwave Theory and Techniques}, keywords = {nonlinear measurements and test signals}, number = {6}, pages = {1590--1602}, title = {{Power-amplifier characterization using a two-tone measurement technique}}, url = {http://ieeexplore.ieee.org/search/srchabstract.jsp?tp=&arnumber=1006421}, volume = {50}, year = {2002} } @article{Eul1991, abstract = {A general theory for performing network analyzer calibration is presented. Novel calibration procedures are derived which allow for partly unknown standards. The most general procedure derived is called TAN and allows for five unknown parameters in the three calibration standards. The values of the unknown parameters are determined during the calibration procedure via eigenvalue conditions. The good performance of all the procedures has been shown experimentally. This wide spectrum of procedures using different calibration standards makes it possible to choose an optimal algorithm for any environment}, author = {Eul, H.-J. and Schiek, B.}, doi = {10.1109/22.76439}, journal = {IEEE Transactions on Microwave Theory and Techniques}, keywords = {VNA measurements}, number = {4}, pages = {724 -- 731}, title = {{A generalized theory and new calibration procedures for network analyzer self-calibration}}, url = {http://ieeexplore.ieee.org/search/srchabstract.jsp?tp=&arnumber=76439}, volume = {39}, year = {1991} } @article{Ferrero1992, abstract = {A procedure performed by using a genuine two-port reciprocal network instead of a standard `thru' in a full two-port error correction of an automatic network analyzer is presented. Although it can be applied to any type of waveguide system, the proposed technique is particularly useful with noninsertable coaxial or one-wafer devices. Experimental comparisons show that the suggested procedure provides a great degree of accuracy}, author = {Ferrero, A. and Pisani, U.}, doi = {10.1109/75.173410}, journal = {IEEE Microwave and Guided Wave Letters}, keywords = {VNA measurements}, number = {12}, pages = {505 -- 507}, title = {{Two-port network analyzer calibration using an unknown `thru'}}, url = {http://ieeexplore.ieee.org/search/srchabstract.jsp?tp=&arnumber=173410}, volume = {2}, year = {1992} } @article{Hall2002, abstract = {A method of uncertainty analysis based on classical statistical principles is presented for a measurand that is a linear combination of multidimensional input quantities. The method assigns the measurand a combined standard uncertainty matrix and an effective degrees of freedom, which allows the measurand to be estimated by an ellipsoidal confidence region in the multidimensional space. Simulations for a 95 \% nominal confidence level show the ellipsoids to contain the measurand with probability approximately 0.95, as required. The derivation of the method assumes all input uncertainties to be evaluated by the Type A method. So the method is analogous to the Welch-Satterthwaite formula for one-dimensional data, a derivation of which is given in an appendix.}, author = {Hall, B.D. and Willink, R.}, doi = {10.1088/0026-1394/39/4/5}, journal = {Metrologia}, keywords = {uncertainty specific to RF measurement}, number = {4}, pages = {361--369}, title = {{A classical method for uncertainty analysis with multidimensional data}}, url = {http://iopscience.iop.org/0026-1394/39/4/5/pdf/0026-1394 39 4 5.pdf}, volume = {39}, year = {2002} } @article{Kruppa1971, abstract = {FormuIas are derived for the direct calculation of the scattering parameters of a linear two-port, using measurements made on a test set having residual, tracking, and mistermination errors. The problem is formulated by representing the measuring system in terms of scattering parameters. Solutions using this formulation have previously been obtained only in an implicit manner using an iterative approach. The associated calibration procedure is included.}, author = {Kruppa, W. and Sodomsky, K.F.}, doi = {10.1109/TMTT.1971.1127466}, journal = {IEEE Transactions on Microwave Theory and Techniques}, keywords = {VNA measurements}, number = {1}, pages = {122--123}, title = {{An Explicit Solution for the Scattering Parameters of a Linear Two-Port Measured with an Imperfect Test Set (Correspondence)}}, url = {http://ieeexplore.ieee.org/xpls/abs all.jsp?arnumber=1127466\&tag=1}, volume = {19}, year = {1971} } @article{Martens2005, abstract = {An increasing number of multiport devices, whether they be multiband wireless phone components, backplane balanced transmission lines, or classical devices such as power dividers, are being characterized in the RF, microwave, and millimeter-wave frequency bands. S-parameter measurements are often required, and ordinary vector network analyzer (VNA) measurements must be modified to perform these measurements quickly and accurately. This article explores a number of hardware architectures and calibration procedures for multiport measurements and their impacts on flexibility and uncertainties.}, author = {Martens, J. and Judge, D. and Bigelow, J.}, doi = {10.1109/MMW.2005.1580339}, journal = {IEEE Microwave Magazine}, keywords = {signal integrity and multiport measurements}, number = {4}, pages = {72 -- 81}, title = {{Multiport vector network analyzer measurements}}, url = {http://ieeexplore.ieee.org/search/srchabstract.jsp?tp=&arnumber=1580339}, volume = {6}, year = {2005} } @article{Mitama1979, abstract = {Conventional methods for noise parameter measurement for linear noisy two-ports have been improved by introducing a computational method for evaluating measured admittance errors. Derivation and comparison with a conventional method are given. Noise parameters of a packaged 0.5-mu m gate-length GaAs MESFET (NE38806) were successfully measured using the proposed technique.}, author = {Mitama, M. and Katoh, H.}, doi = {10.1109/TMTT.1979.1129680}, journal = {IEEE Transactions on Microwave Theory and Techniques}, keywords = {noise extraction methods}, number = {6}, pages = {612 -- 615}, title = {{An improved computational method for noise parameter measurement}}, url = {http://ieeexplore.ieee.org/search/srchabstract.jsp?tp=&arnumber=1129680}, volume = {27}, year = {1979} } @article{Randa2007, abstract = {The National Institute of Standards and Technology has developed the capability to measure noise parameters on a wafer in the 1-12.4-GHz range. The authors describe the measurement method and the uncertainty analysis and present results of measurements on a highly reflective transistor. Typical standard uncertainties are within the range of 20-25 K in Tmin, which is the minimum transistor noise temperature, and about 0.03 in the magnitude of Gammaopt, which is the reflection coefficient for which Tmin occurs}, author = {Randa, J. and Walker, D.K.}, doi = {10.1109/TIM.2007.891145}, journal = {IEEE Transactions on Instrumentation and Measurement}, keywords = {noise general measurement methods}, number = {2}, pages = {551--554}, title = {{On-Wafer measurement of transistor noise parameters at NIST}}, url = {http://ieeexplore.ieee.org/search/srchabstract.jsp?tp=&arnumber=4126905}, volume = {56}, year = {2007} } @techreport{Taylor1994, address = {Gaithersburg, MD}, author = {Taylor, B.N. and Kuyatt, C.E.}, institution = {National Institute of Standards and Technology (NIST)}, keywords = {general measurement uncertainty}, title = {{Guidelines for Evaluating and Expressing the Uncertainty of NIST Measurement Results}}, url = {http://www.physics.nist.gov/Pubs/guidelines/TN1297/tn1297s.pdf}, year = {1994} } @article{Tippet1982, abstract = {A new measurement technique is described that eliminates the mismatched-induced errors that occur when the scattering matrix of a multiport device is measured with a 2-port network analyzer. These errors arise from neglecting the finite reflections from the imperfect auxiliary loads terminating the unused ports of the device under test in each of the required 2-port measurements. It is shown how a systematic application of the generalized scattering matrix renormalization transform completely eliminates these errors. This new method is completely general and can therefore be applied to measurements of the scattering matrix of an n-port device with an m-port network analyzer (m