## Focused Beam Methods: Measuring Microwave Materials in Free SpaceDetermining the intrinsic microwave properties of materials is important for a variety of applications ranging from antenna and electronic circuit design to remote sensing to electromagnetic interference mitigation. A number of methods exist for characterizing intrinsic properties of materials at microwave frequencies, including transmission lines, resonant cavities, and impedance analysis. The use of free-space measurement methods has become commonplace among microwave material characterization laboratories due to its ease of use and reasonable accuracy. While some free-space facilities exist that can characterize down to 500 MHz, the method is most useful for characterizing materials from 2 GHz through millimeter waves. This book is designed to acquaint engineers and scientists with the theory and practice of using microwave focused beam systems for free-space characterization of materials. |

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### Contents

INTRODUCTION | 1 |

THEORY IMPLEMENTATION | 18 |

INVERTING INTRINSIC PROPERTIES 44 | 44 |

4 MEASUREMENT EXAMPLES | 60 |

MEASUREMENT UNCERTAINTY | 72 |

MEASURING DIFFUSE SCATTER | 88 |

ADVANCED METHODS | 110 |

REFERENCES 124 | 124 |

### Common terms and phrases

ABCD matrix angle aperture approximately backscatter beam waist calculated calibration standard characterization complex components Debye Debye model defined dielectric permittivity dielectric relaxation diffraction dihedral dipole dispersion echo width edge effects electric field electromagnetic energy Equation 𝑓 FDTD feed antenna fixture focused beam system four-parameter free space free-space measurement function Gaussian beam geometrical optics geometry horn antennas illuminating beam imaginary permittivity inhomogeneity intrinsic properties inversion algorithm iterative lens lenses 𝑀 magnetic permeability material measurement material specimen measured data measurement system metal plate microwave 𝑛 network analyzer normal incidence over-illumination paraxial approximation permittivity and permeability phase drift phase error plane wave polarization propagation 𝑅 R-matrix radar radius reflection coefficient relative response and isolation Rexolite 𝑆 sample scattering parameters shown in Figure signal slab specimen position specimen thickness specular surface target time-domain transmission coefficient transmission line uncertainty voltage wavelength 𝑍 𝜀 𝜇 𝜎 𝜔