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Electromagnetic Reverberation Chambers

Book Description

Dedicated to a complete presentation on all aspects of reverberation chambers, this book provides the physical principles behind these test systems in a very progressive manner. The detailed panorama of parameters governing the operation of electromagnetic reverberation chambers details various applications such as radiated immunity, emissivity, and shielding efficiency experiments.

In addition, the reader is provided with the elements of electromagnetic theory and statistics required to take full advantage of the basic operational rules of reverberation chambers, including calibration procedures. Comparisons with other testing systems (TEM cells, anechoic chambers) are also discussed.

Table of Contents

  1. Cover
  2. Title Page
  3. Copyright
  4. Preface
  5. Foreword
  6. Introduction
  7. Chapter 1. Position of the Reverberation Chambers in Common Electromagnetic Tests
    1. 1.1 Introduction
    2. 1.2 Electromagnetic fields and plane waves
      1. 1.2.1 Definition and properties of plane waves
        1. Waves equations
        2. Relations linking the electric and magnetic fields
        3. Plane waves animated by continuous harmonic variations
        4. Resolution of the waves equation
        5. Wavelength
        6. Impedance of the plane wave
      2. 1.2.2 General plane wave representation
      3. 1.2.3 Assimilation of the far-field to a local plane wave
      4. 1.2.4 Induction phenomena produced by plane waves
        1. Calculation by induction of the magnetic field vector H
        2. Calculation by interaction of the electric field vector E
    3. 1.3 Electromagnetic tests in confined areas
      1. 1.3.1 Emission of a small rectangular loop
        1. Near-field Formulas
        2. Far-field formulas
      2. 1.3.2 Tests carried out in a TEM cell
        1. Carrying out an immunity test
        2. Measurement of the emission in a TEM cell
      3. 1.3.3 Measurements carried out in an anechoic shielded chamber
      4. 1.3.4 Position of the reverberation chambers in tests carried out in a confined space
        1. Immunity test confined in a reverberation chamber
        2. Brief description of a mode stirred reverberation chamber
    4. 1.4 Discussion
      1. 1.4.1 On the use of the plane wave concepts
      2. 1.4.2 On the uncertainty margin of the measurements carried out in a reverberation chamber
    5. 1.5 Bibliography
  8. Chapter 2. Main Physical Features of Electromagnetic Cavities
    1. 2.1 Introduction
    2. 2.2 Reduction of the modes in a 1D cavity
      1. 2.2.1 Description of the 1D cavity
      2. 2.2.2 Solutions of the 1D waves equation
        1. General waves equation
        2. Waves equation for the harmonic steady state
        3. Waves equation solutions
      3. 2.2.3 Eigenmodes computation
      4. 2.2.4 Comparison of a cavity to a network of LC resonators
      5. 2.2.5 Contribution of the quality factor to the cavity
      6. 2.2.6 Optimal coupling of the energy on an eigenmode
      7. 2.2.7 Deviation of the modal frequencies produced by an obstacle
      8. 2.2.8 Implementation of mode stirring
    3. 2.3 Physical features of an empty rectangular cavity
      1. 2.3.1 Geometrical description of the reverberation chamber
      2. 2.3.2 Calculation of the eigenmodes’ frequencies
      3. 2.3.3 The first eigenmode
      4. 2.3.4 Higher order modes
      5. 2.3.5 Mode spacing and mode density
      6. 2.3.6 Quality factor of the 3D cavity
      7. 2.3.7 Regarding the excitation conditions of the cavity
      8. 2.3.8 Plane wave spectrum
      9. 2.3.9 Influence of the energy losses on the plane wave spectrum
    4. 2.4 The 3D cavity operating in stirred modes
      1. 2.4.1 Role given to mode stirring
      2. 2.4.2 Mechanical mode stirring
      3. 2.4.3 Experimental proof of the modal excursion
    5. 2.5 Discussion
      1. 2.5.1 On the geometry of reverberation chambers
      2. 2.5.2 On the use of the RLC resonators
      3. 2.5.3 On the contribution of the modal interferences
    6. 2.6 Bibliography
  9. Chapter 3. Statistical Behavior of Stirred Waves in an Oversized Cavity
    1. 3.1 Introduction
    2. 3.2 Descriptions of the ideal random electromagnetic field
      1. 3.2.1 The electromagnetic field assumed as a random variable
      2. 3.2.2 Statement of the postulate of an ideal random field
      3. 3.2.3 Presentation conventions of the random variables
        1. Absolute amplitude of the electric field
        2. Power collected on an antenna
        3. Normalized field and power variable
        4. The x2 variable
        5. Normalized absolute amplitude of the electric field
      4. 3.2.4. x2 probability distribution
      5. 3.2.5 Probability density function of the absolute field amplitude
      6. 3.2.6 Probability density function of the power variable
    3. 3.3 Simulation of the properties of an ideal random field
      1. 3.3.1 Construction of the plane wave spectrum
      2. 3.3.2 Construction of the interferences by random trials
      3. 3.3.3 Use of the central limit theorem
    4. 3.4 Contribution of the statistical tests
      1. 3.4.1 Role given to the size N of the statistical sampling
      2. 3.4.2 Assessment of the experimental data to the probability distributions
        1. Power data collected on a receiver
        2. Voltage data collected on an electric field probe
      3. 3.4.3 Estimate of the variances and means
        1. Search for the estimator giving the likelihood maximum
        2. Evaluation of the bias error
      4. 3.4.4 Kolmogorov-Smirnov test
        1. Introduction to the KS test approach
        2. Construction of Massey’s table
        3. Simulation of the KS test
    5. 3.5 Balance of power in a reverberation chamber
      1. 3.5.1 Review of the main features of antennas
        1. Antenna efficiency
        2. Directivity of an antenna
        3. Gain of an antenna
      2. 3.5.2 Receiving antenna immersed in an ideal random field
      3. 3.5.3 Measurement of the power radiated by a device in a reverberation chamber
    6. 3.6 Discussion
      1. 3.6.1 On the hypothesis of the ideal random field
      2. 3.6.2 On the simulation of the disordered field by plane waves trials
    7. 3.7 Bibliography
  10. Chapter 4. Impact of the Physical and Technological Parameters of a Reverberation Chamber
    1. 4.1 Introduction
    2. 4.2 Main parameters for reverberation chamber design
      1. 4.2.1 List of the main building parameters
      2. 4.2.2 Impact of the geometrical and physical parameters of the chamber
      3. 4.2.3 Factors influencing the quality factor of a chamber
        1. The Q1 quality factor associated with the losses in the walls
        2. The Q2 quality factor attached to the receiving antenna
        3. The Q3 quality factor attached with the devices under test
        4. Behavior of the composite quality factor versus the excitation frequency
        5. Role given to the transmitting antenna
      4. 4.2.4 Space correlation of an ideal random electromagnetic field distribution
    3. 4.3 The usual techniques of mode stirring
      1. 4.3.1 Mechanical mode stirring
        1. The mode stirring procedure
        2. The mode tuning procedure
        3. Measurement of the efficiency of a mode stirrer
        4. Mixed mode stirring
      2. 4.3.2 Frequency agitation of the modes or electronic stirring
        1. Stirring by frequency hopping
        2. Continuous frequency agitation
        3. Combination of frequency agitation with the mechanical stirring
      3. 4.3.3 Stirring by switching the transmitting antennas
      4. 4.3.4 Mode stirring by dimensional modulation of the chamber
    4. 4.4 The characterization of reverberation chambers
      1. 4.4.1 Aims of the characterization of reverberation chambers
      2. 4.4.2 Characterization of the efficiency of mode stirring
        1. Measurement of the modal dislocation
        2. Measurement of the stirring ratio
        3. Estimate of the correlation angle of the mode stirrer
      3. 4.4.3 Test of the stationary random electromagnetic field distribution
        1. Estimator of the mean amplitude of the field
        2. Estimate of the σν standard deviation
        3. Measurement of the uncertainty attached to the mean field amplitude
        4. Nth order statistic
        5. Estimate of the maximum field amplitude
        6. Discussion on the ratio of the maximum and mean amplitudes
      4. 4.4.4 Measurements of the quality factor
        1. Method of modal selection
        2. Power balance method
        3. The damping time-constant method
      5. 4.4.5 Localization of the lowest usable frequency of the chamber
    5. 4.5 Discussion
      1. 4.5.1 Regarding the law of large numbers
      2. 4.5.2 On the impact of the volume of the large devices under test
    6. 4.6 Bibliography
  11. Chapter 5. Radiated Immunity Tests in a Reverberation Chamber
    1. 5.1 Introduction
    2. 5.2 The calibration process
      1. 5.2.1 Measurement methods of the statistical uniformity of the field distribution
        1. Nature of the statistical estimate
        2. The Smax(f) limit
        3. Selection of the measurement points and of the stirrer positions for the calibration. EN 61000-4-21 and DO 160 section 20.6 standards
    3. 5.3 Examples of calibration results
    4. 5.4 Implementing of the immunity test for a piece of equipment
      1. 5.4.1 The loading effect of the device under test
      2. 5.4.2 Incidence on the statistical uniformity of the field
      3. 5.4.3 Observation of possible malfunctioning of the device under test
      4. 5.4.4 An example of immunity tests
    5. 5.5 Immunity test in reverberation and anechoic chambers
      1. 5.5.1 The conventional approach of illumination in an anechoic chamber
      2. 5.5.2 Illumination in a reverberation chamber
    6. 5.6 Rectangular components of the electric field and the total electric field
    7. 5.7 Discussion
      1. 5.7.1 The limits of statistical uniformity from one standard to another
      2. 5.7.2 The choice of the number of stirrer positions from one standard to another
      3. 5.7.3 The nature of immunity tests in reverberation chambers
    8. 5.8 Bibliography
  12. Chapter 6. Emissivity Tests in Reverberation Chambers
    1. 6.1 Introduction
    2. 6.2 A few notions on electromagnetic radiation and antennas
      1. 6.2.1 Origin of electromagnetic radiation
      2. 6.2.2 Properties of the electromagnetic field at a distance from the radiation source
      3. 6.2.3 Intensity and directivity of the electromagnetic radiation
      4. 6.2.4 Polarization and partial directivities
      5. 6.2.5 Efficiency and gain of an antenna
      6. 6.2.6 Effective area of an antenna
      7. 6.2.7 Transmission balance between two antennas — Friis expression
      8. 6.2.8 Formulation and properties of the radiation in a spherical graph
        1. General expression of the electromagnetic field
        2. Properties of electromagnetic radiation
        3. Spherical waveguide and truncation of series expansion of spherical harmonics
    3. 6.3 Measurement of the total radiated power in free space
      1. 6.3.1 Definitions
      2. 6.3.2 Conventional measurement methods of the total radiated power
    4. 6.4 Measurement of the unintentional emission of a device under test
      1. 6.4.1 Calibration and evaluation of the total radiated power in reverberation chambers
        1. Configuration of the calibration measurement
        2. Calculation of the total radiated power
        3. Operating mode of the measurement of the total radiated power in reverberation chambers
          1. Calibration check
          2. Determination stage of the total radiated power in reverberation chambers
          3. Global statistical uncertainty
        4. Evaluation of the insertion losses on a very large frequency band
        5. Measurements based on the estimation of the maximum received power
    5. 6.5 Measurement examples of the total radiated power
      1. 6.5.1 The calibration phase
      2. 6.5.2 The measurement phase of the device under test
    6. 6.6 Total radiated power and radiated emissivity
    7. 6.7 Measurement of the efficiency and of the diversity gain of the antennas
      1. 6.7.1 Measurement of the antenna efficiency
      2. 6.7.2 Measurement of the diversity gain of the antennas
    8. 6.8 Discussion
      1. 6.8.1 On the measurement of the radiated emissivity of a device in a reverberation chamber
      2. 6.8.2 On the measurements of radiofrequency devices in a reverberation chamber
    9. 6.9 Bibliography
  13. Chapter 7. Measurement of the Shielding Effectiveness
    1. 7.1 Introduction
    2. 7.2 Definitions of the shielding effectiveness
      1. 7.2.1 Shielding effectiveness of cables and connectors
      2. 7.2.2 Attenuation of the shielded enclosures
      3. 7.2.3 Shielding effectiveness of the materials
    3. 7.3 Measurement of the effectiveness of shielded cables and connectors in reverberation chambers
      1. 7.3.1 Electromagnetic coupling on wires placed in a reverberation chamber
      2. 7.3.2 The effective area of a cable or a shielded connector
        1. Configuration of the devices under test, in the context of a calculation or a measurement
        2. Calculation of the effective area of the shielded cable
      3. 7.3.3 Relationship between the reference power and the current induced on a device under test
      4. 7.3.4 Conversion of the shielding attenuation into a transfer impedance
      5. 7.3.5 Examples of the measurements of the shielding effectiveness of the connectors
        1. Description of the device under test
        2. Physical properties of the device under test
        3. Comparison of the theoretical laws and measurements
    4. 7.4 Measurement of the attenuation of the shielded enclosures
      1. 7.4.1 Expected electromagnetic coupling mechanisms
      2. 7.4.2 Example of attenuations measured on a shielded enclosure
    5. 7.5 Measurement of the shielding effectiveness of the materials
      1. 7.5.1 On the size of the devices under test with respect to the wavelength
        1. Method of the coupled rooms
        2. Method of the shunted shielded enclosure
      2. 7.5.2 Examples of attenuation measurements carried out on a material
        1. Brief description of the material
        2. Practical configuration of the sample under test
    6. 7.6 Discussion
      1. 7.6.1 The accuracy of the measurement of the shielding attenuation of the materials
      2. 7.6.2 The recorded curves of shielding attenuation
    7. 7.7 Bibliography
  14. Chapter 8. Mode Stirring Reverberation Chamber: A Research Tool
    1. 8.1 Introduction
    2. 8.2 A non-ideal random electromagnetic field
      1. 8.2.1 An estimate of the statistics of a rectangular component of an electric field in an effective reverberation chamber
        1. Estimate of the Rayleigh distribution parameter
        2. The goodness of-fit test for a Rayleigh distribution with an a priori unknown parameter
        3. Example of the Kolmogorov-Smirnov test according to the Massey and Stephens criteria from measurements carried out in a reverberation chamber
      2. 8.2.2 Resorting to a replacement distribution: the Weibull distribution
        1. The Weibull distribution with two parameters
        2. Estimate of the parameters of the Weibull distribution
        3. Goodness-of-fit test of the Weibull distribution and associated critical values
        4. The Weibull distribution applied to measurement data in reverberation chambers
    3. 8.3 Studying the correlation of a set of measurements
      1. 8.3.1 Outline of the link between correlation and statistical uncertainty
      2. 8.3.2 Measurement of the correlation
      3. 8.3.3 Study of the linear correlation during experimental estimates
      4. 8.3.4 Statistical distribution of the coefficient of linear correlation
      5. 8.3.5 Approximation of a normal distribution for the estimate of the first order correlation function
      6. 8.3.6. Residual correlation and impact on the reproducibility of the measurements in reverberation chambers
    4. 8.4 Quantization of the scattered and coherent fields in a reverberation chamber
      1. 8.4.1 Coherent residual field in a reverberation chamber and the Rice statistics
      2. 8.4.2 Goodness-of-fit test of a Rice distribution in a reverberation chamber
      3. 8.4.3 Example of evaluation of a Rice channel in a reverberation chamber
    5. 8.5 Discussion
    6. 8.6 Bibliography
    1. Appendix 1. Notion of Probability
      1. A1.1. The random variable concept
      2. A1.2. Probability concept from intuition
      3. A1.3. Probability density function (pdf)
      4. A1.4. Computation of moments
        1. A1.4.1. Computation of the moment of the x random variable
        2. A1.4.2. Computation of the moment of the x squared random variable
      5. A1.5. Centered and normalized variables
        1. A1.5.1. Centered variables
        2. A1.5.2. Normalized variables
      6. A1.6. Computation of the variance and standard deviation
        1. A1.6.1. Definition of the variance
        2. A1.6.2. Definition of the standard deviation
      7. A1.7. Probability distributions
        1. A1.7.1. Uniform probability distribution
        2. A1.7.2. Normal probability distribution
      8. A1.8. The cumulative distribution function (cdf)
      9. A1.9. The ergodism notion
        1. A1.9.1. Intuitive definition of the ergodic property
        2. A1.9.2. Use of ergodism to the calculation of the autocorrelation function
      10. A1.10. Features of the random stationary variables
      11. A1.11. The characteristic function
      12. A1.12. Summary of the main probability distributions
        1. A1.12.1. Uniform distribution
        2. A1.12.2. Normal distribution
        3. A1.12.3. Chi-squared distribution
        4. A1.12.4. Weibull distribution
        5. A1.12.5. Exponential distribution
        6. A1.12.6. Rayleigh distribution
      13. A1.13. Tables of numerical values of the normal distribution integrals
        1. A1.13.1. Calculation of the integral
        2. A1.13.2. Solution to the integral equation
      14. A1.14. Bibliography
    2. Appendix 2. Formulas of the Quality Factor of a Rectangular Cavity
      1. A2.1. Quality factor of the TMm n p mode
      2. A2.2. Calculation of the average Q quality factor
      3. A2.3. Bibliography
    3. Appendix 3. Total Field and Total Power Variables
      1. A3.1. Total field variables
      2. A3.2. x2 variable attached to the total field
      3. A3.3. Total field probability density function
        1. A3.3.1. The pdf related to the total “et” normalized field variable
        2. A3.3.2. The pdf related to the absolute amplitude of the total field “Et”
      4. A3.4. Calculation of the mean of the total field
        1. A3.4.1. Mean of the normalized “et” amplitude
        2. A3.4.2. Mean of the absolute “Et” amplitude
      5. A3.5. The pdf of the total power
        1. A3.5.1. Variables of total power “pt” variable
        2. A3.5.2. Computation of the pdf related to the total power
        3. A3.5.3. The pdf of the normalized total power variable “ptr”
        4. A3.5.4. Computation of the pdf of the total normalized power
      6. A3.6. Calculation of the mean total powers
        1. A3.6.1. Mean of the total normalized power “ptr”
        2. A3.6.2. Mean of the total power “ptr”
    4. Appendix 4. Calculation of the Variances of υφ, υη, υθ
      1. A4.1. Variance of the υφ and υη variables
      2. A4.2. Variance of the υθ variable
    5. Appendix 5. Electric Dipole Formulas
      1. A5.1. Complete formulas of the electric dipole
      2. A5.2. Near-field formulas of the electric dipole
      3. A5.3. Far-field formulas of the electric dipole
      4. A5.4. Bibliography
  16. Index