The metrology of electrical impedance at high frequency: a review

The measurement of electrical impedance in the high-frequency range (loosely speaking, from 100 kHz to 100 MHz) is a common characterization technique in research and applications concerning condensed matter physics, engineering and biology. Commercial instruments for impedance measurement have specifications, including frequency range and base accuracy, continuously improving. The calibration of impedance instruments and standards in the high-frequency range represents a tough challenge for metrology laboratories; measurement methods and traceability paths are not as firmly established as those employed for lower (audio) or higher (microwave) frequencies. In the last few years, the problem has received increased attention from the metrology community. The paper gives a review of recent results in the field.

[1]  Enis Turhan,et al.  Four-terminal-pair capacitance characterization at frequencies up to 30 MHz using resonance frequencies , 2007 .

[2]  R. D. Cutkosky.  Four-terminal-pair networks as precision admittance and impedance standards , 1964, IEEE Transactions on Communication and Electronics.

[3]  B. Hall.  Monte Carlo uncertainty calculations with small-sample estimates of complex quantities , 2006 .

[4]  R. Lapuh,et al.  Evaluation of capacitance and resistance standards at higher frequencies , 2000, Conference on Precision Electromagnetic Measurements. Conference Digest. CPEM 2000 (Cat. No.00CH37031).

[5]  Z. Svetik,et al.  Simplified high accuracy high bandwidth calibration of dielectric capacitors , 2001, IMTC 2001. Proceedings of the 18th IEEE Instrumentation and Measurement Technology Conference. Rediscovering Measurement in the Age of Informatics (Cat. No.01CH 37188).

[6]  A. Sproul,et al.  Impedance analysis: A powerful method for the determination of the doping concentration and built-in potential of nonideal semiconductor p‐n diodes , 2005 .

[7]  K. Yokoi,et al.  A calibration method for four-terminal-pair high-frequency resistance standards , 1993 .

[8]  L. Oberto,et al.  Estimation of the modulus of a complex-valued quantity , 2006 .

[9]  H.P. Hall,et al.  How electronics changed impedance measurements , 2004, Proceedings of the 21st IEEE Instrumentation and Measurement Technology Conference (IEEE Cat. No.04CH37510).

[10]  F. J. Wilkins,et al.  Resistors having a calculable performance with frequency , 1969 .

[11]  Nile M. Oldham,et al.  Uncertainty analysis for four terminal-pair capacitance and dissipation factor characterization at 1 and 10 MHz , 2000, IEEE Trans. Instrum. Meas..

[12]  Luca Callegaro,et al.  A remotely controlled coaxial switch for impedance standard calibration , 2002, IEEE Trans. Instrum. Meas..

[13]  Raymond Nelson Jones,et al.  Evaluation of Three-Terminal and Four-Terminal Pair Capacitorsat High Frequencies | NIST , 1980 .

[14]  J. Melcher.  Systematic errors of long thin coaxial cables for the connection of four-terminal-pair devices , 1994 .

[15]  Nicola Bowler,et al.  Electrical conductivity measurement of metal plates using broadband eddy-current and four-point methods , 2005 .

[16]  S. A. Awan,et al.  Calibration of IVDs at frequencies up to 1 MHz by permuting capacitors , 2000 .

[17]  R. D. Cutkosky.  Techniques for comparing four-terminal-pair admittance standards , 1970 .

[18]  G. Hein,et al.  The ac quantum Hall effect as a primary standard of impedance , 2007 .

[19]  Digby D. Macdonald,et al.  Application of Kramers‐Kronig Transforms in the Analysis of Electrochemical Impedance Data II . Transformations in the Complex Plane , 1986 .

[20]  Luca Callegaro,et al.  CALIBRATION OF IMPEDANCES BY THE SUBSTITUTION METHOD: NUMERICAL UNCERTAINTY EVALUATION , 2001 .

[21]  Giovanni Mana,et al.  A Universal Geometry for Calculable Frequency-Response Coefficient of LCR Standards and New 10-MHz Resistance and 1.6-MHz Quadrature-Bridge Systems , 2007, IEEE Transactions on Instrumentation and Measurement.

[22]  J. Q. Shields,et al.  Phase-Angle Characteristics of Cross Capacitors , 1972 .

[23]  A. M. Thompson,et al.  An Absolute Determination of Resistance Based on a Calculable Standard of Capacitance , 1968 .

[24]  T. Aoki,et al.  Capacitance scaling system , 1996 .

[25]  I. Youngs.  Dielectric measurements and analysis for the design of conductor/insulator artificial dielectrics , 2000 .

[26]  Luca Callegaro,et al.  Four-terminal-pair impedances and scattering parameters , 2003 .

[27]  Nile M. Oldham,et al.  The sensitivity of a method to predict a capacitor's frequency characteristic , 1999, IMTC/99. Proceedings of the 16th IEEE Instrumentation and Measurement Technology Conference (Cat. No.99CH36309).

[28]  L. Callegaro.  Four terminal-pair impedance comparisons at high frequency , 2004, Proceedings of the 21st IEEE Instrumentation and Measurement Technology Conference (IEEE Cat. No.04CH37510).

[29]  Wuliang Yin,et al.  A multi-frequency impedance analysing instrument for eddy current testing , 2006 .

[30]  J. J. Hill,et al.  Theory, design and measurement of inductive voltage dividers , 1968 .

[31]  Luca Callegaro,et al.  Resonance frequency of four-terminal-pair air-dielectric capacitance standards and closing the metrological impedance triangle , 2004 .

[32]  B P Kibble.  Proposals for extending traceable impedance measurements to higher frequencies , 1998 .

[33]  Dongxue Dai,et al.  Calibration Theory and Measurement Method of Four-Terminal-Pair Standard Capacitor Frequency Characteristic , 2004, 2004 Conference on Precision Electromagnetic Measurements.

[34]  Marian Kampik,et al.  High-frequency thin-film multijunction thermal converter on a quartz crystal chip , 2002, Conference Digest Conference on Precision Electromagnetic Measurements.

[35]  Shakil A. Awan,et al.  A new four terminal-pair bridge for traceable impedance measurements at frequencies up to 1 MHz , 2001, IEEE Trans. Instrum. Meas..

[36]  B D Hall,et al.  Calculating measurement uncertainty for complex-valued quantities , 2003 .

[37]  S.A. Awan,et al.  Towards accurate measurement of the frequency dependence of capacitance and resistance standards up to 10 MHz , 2004, CPEM 2004.

[38]  J. Bohacek,et al.  Octofilar resistors with calculable frequency dependence , 2001 .

[39]  Thomas J. Witt,et al.  Electrical resistance standards and the quantum Hall effect , 1998 .

[40]  B D Hall,et al.  Some considerations related to the evaluation of measurement uncertainty for complex-valued quantities in radio frequency measurements , 2007 .

[41]  R. Clarke,et al.  Dielectric metrology with coaxial sensors , 2007 .

[42]  Joachim Fischer,et al.  Determination of the Boltzmann constant—status and prospects , 2006 .

[43]  L. Callegaro,et al.  Progresses toward capacitance measurements at ultra-acoustic frequencies , 2004, 2004 Conference on Precision Electromagnetic Measurements.

[44]  M. Elia,et al.  Bioelectrical impedance analysis-part II: utilization in clinical practice. , 2004, Clinical nutrition.

[45]  S. K. Basu,et al.  A Direct-Reading Current-Comparator Bridge for Scaling Four-Terminal Impedances at Audio Frequencies , 1966 .

[46]  Y. Semenov,et al.  Determination of the frequency dependence of capacitance standards with ceramic dielectrics , 2002, Conference Digest Conference on Precision Electromagnetic Measurements.

[47]  R. Cole,et al.  A Wide Range Capacitance‐Conductance Bridge , 1949 .

[48]  Andrew D. Koffman,et al.  Evaluation of a Capacitance Scaling System , 2007, IEEE Transactions on Instrumentation and Measurement.

[49]  A Millea,et al.  A Class of Double-Balance Quadrature Bridges for the Intercomparison of Three-Terminal Resistance, Inductance and Capacitance Standards , 1969 .

[50]  Brian J. Simonds,et al.  An upper bound to the frequency dependence of the cryogenic vacuum-gap capacitor , 2006 .

[51]  Luca Callegaro.  On strategies for automatic bridge balancing , 2004, CPEM 2004.

[52]  Luca Callegaro,et al.  Automated system for inductance realization traceable to AC resistance with a three-voltmeter method , 2001, IEEE Trans. Instrum. Meas..

[53]  A. M. Thompson,et al.  A New Theorem in Electrostatics and its Application to Calculable Standards of Capacitance , 1956, Nature.

[54]  Chih-Ming Wang,et al.  Uncertainty analysis for vector measurands using fiducial inference , 2006 .

[55]  B. P. Kibble.  Four terminal-pair to anything else! , 1999 .

[56]  T. Aoki,et al.  A new universal calibration method for four-terminal-pair admittance standards , 1990 .

[57]  N. Oldham,et al.  Overview of bioelectrical impedance analyzers. , 1996, The American journal of clinical nutrition.

[58]  R. Hanke,et al.  An improved straddling method with triaxial guards for the calibration of inductive voltage dividers at 1592 Hz , 1989 .

[59]  N. F. Astbury.  The design, contruction, and use of resistors of calculable reactance , 1935 .

[60]  R. N. Jones,et al.  Lumped parameter impedance measurements , 1967 .

[61]  E. Barsoukov,et al.  Impedance spectroscopy : theory, experiment, and applications , 2005 .

[63]  Randolph E. Elmquist.  Calculable coaxial resistors for precision measurements , 2000, IEEE Trans. Instrum. Meas..

[64]  Blaise Jeanneret,et al.  The quantized Hall resistance: towards a primary standard of impedance , 2006 .

[65]  D.L.H. Gibbings,et al.  A design for resistors of calculable a.c./d.c. resistance ratio , 1963 .

[66]  M J Salter,et al.  An approach to the treatment of uncertainty in complex S-parameter measurements , 2002 .

[67]  K. Suzuki,et al.  Calibration method for four-terminal-pair capacitance standards: Progress report , 1998, 1998 Conference on Precision Electromagnetic Measurements Digest (Cat. No.98CH36254).

[68]  C. Davis,et al.  Impedance spectroscopy of human erythrocytes: system calibration, and nonlinear modeling , 1993, IEEE Transactions on Biomedical Engineering.

[69]  Klaus Grohmann.  A step-up method for calibrating inductive voltage dividers up to 1 MHz , 1976, IEEE Transactions on Instrumentation and Measurement.

[70]  Jack C. M. Wang,et al.  An optimal vector-network-analyzer calibration algorithm , 2003 .

[71]  V. D'Elia,et al.  High-accuracy voltage and current transmission by a four-coaxial cable , 2000, Conference on Precision Electromagnetic Measurements. Conference Digest. CPEM 2000 (Cat. No.00CH37031).

[72]  B. C. Waltrip,et al.  Digital impedance bridge , 1995 .

[73]  B. D. Hall,et al.  A classical method for uncertainty analysis with multidimensional data , 2002 .

[74]  R. Kronig.  On the Theory of Dispersion of X-Rays , 1926 .

[75]  B D Hall,et al.  On the propagation of uncertainty in complex-valued quantities , 2004 .

[76]  R N Clarke,et al.  Traceable measurements of the static permittivity of dielectric reference liquids over the temperature range 5–50 °C , 2005 .

[77]  Yicheng Wang.  Frequency dependence of capacitance standards , 2003 .

[78]  J. Melcher,et al.  Inductance calibration in the frequency range from 50 Hz to 1 MHz at PTB , 2002, Conference Digest Conference on Precision Electromagnetic Measurements.

[79]  Nick M. Ridler,et al.  Generalized adaptive calibration schemes for precision RF vector network analyzer measurements , 2003, IEEE Trans. Instrum. Meas..

[80]  D. Tarach,et al.  High-accuracy N-port impedance measurement by means of modular digital AC compensators , 1993 .

[81]  Harald Moser,et al.  From the calculable AC resistor to capacitor dissipation factor determination on the basis of time constants , 2001, IEEE Trans. Instrum. Meas..

[82]  M. Elia,et al.  Bioelectrical impedance analysis--part I: review of principles and methods. , 2004, Clinical nutrition.

[83]  V. D'Elia,et al.  A new architecture for high-accuracy admittance measuring systems , 2002, Conference Digest Conference on Precision Electromagnetic Measurements.

[84]  Peter M. Harris,et al.  Evolution of the ‘Guide to the Expression of Uncertainty in Measurement’ , 2006 .

[85]  R. D. Cutkosky,et al.  The Precision Measurement of Transformer Ratios , 1960 .

[86]  Klaus Grohmann,et al.  Self-Calibrating Cryo Current Comparators for AC Applications , 1984, IEEE Transactions on Instrumentation and Measurement.

[87]  Ulrich Stumper,et al.  Uncertainty of VNA S-parameter measurement due to nonideal TRL calibration items , 2005, IEEE Transactions on Instrumentation and Measurement.