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  1. Università “La Sapienza”, Roma Study of propagative and radiative behavior of printed dielectric structures using the finite difference time domain method (FDTD) Fabrizio Frezza Paolo Nocito 24th February 2005

  2. Introduction Purposes of this work: - high performance flexible finite difference time domain (FDTD) simulator programming; - application of the described method to study printed dielectric structures, particularly microstrip leaky wave antennas, verifying FDTD implementation limits, with regards to accuracy; - synthesis of novel methods to change propagative and radiative behavior of microstrip leaky wave antennas. Study of propagative and radiative behavior of printed dielectric structures using the finite difference time domain method (FDTD)

  3. Letting: LOSSES IN DIELECTRIC LEAKY WAVE Dispersion parameters Assuming kx=0, at the air-dielectric interface: (separability condition) Study of propagative and radiative behavior of printed dielectric structures using the finite difference time domain method (FDTD)

  4. Leaky waves Leaky waves are an analytical prolongation of discreet guided modes; the dominant mode may become leaky when asymmetries are present. Electromagnetic field can be expressed as a linear combination of guided and leaky modes, avoiding slowly convergent improper integrals. For a 90% efficient leaky wave antenna, whose length is L, from diffraction theory: where qM is the main beam direction (with respect to aperture’s perpendicular direction) and Dq is the width of the first lobe. Study of propagative and radiative behavior of printed dielectric structures using the finite difference time domain method (FDTD)

  5. Simulator programming Simulation program features: - software entirely coded in C language (~8000 lines) using its advanced features to speed-up simulation, limiting memory usage; - meta-language definition to describe and simulate different types of electromagnetic devices; - tested with: - electromagnetic problems whose solution is known in closed form; - leaky wave antennas, both air (stub-loaded) and partially filled (slot e microstrip) ones, verifying the obtained results with other numerical methods. Study of propagative and radiative behavior of printed dielectric structures using the finite difference time domain method (FDTD)

  6. Simulation procedure Simulation steps: 1 computational domain build-up; 2 recurrent application of the impressed magnitudes and a numerical implementation of Maxwell’s equations obtained with a second order accurate finite difference algorithm; 3 steady condition reach check; 4 results analysis and dispersion parameters extraction using the matrix-pencil algorithm. Study of propagative and radiative behavior of printed dielectric structures using the finite difference time domain method (FDTD)

  7. Computational domain build-up 1 The feeder and the microstrip are wrapped in Bérenger’s PML. 2 PML is covered by a PEC layer. 3 The strip, PEC surfaces and dielectric touching the PML are stretched to the outer PEC. Study of propagative and radiative behavior of printed dielectric structures using the finite difference time domain method (FDTD)

  8. where: PML parameters Bérenger’s PML electric conductivity profile used: Magnetic conductivity profile satisfies the impedance matching condition: For dielectric structures, adopting 18¸36 PML layers: Study of propagative and radiative behavior of printed dielectric structures using the finite difference time domain method (FDTD)

  9. Supposing that the x-component of electric field should be measured on plane P, in both time and frequency domain: Steady condition On the same surfaces where the electromagnetic field it to be measured, steady condition is tested after 8 consecutive time intervals, whose length is related to the minimum frequency to be simulated. 1 [s] movie ~3x10-11 [s] real. Study of propagative and radiative behavior of printed dielectric structures using the finite difference time domain method (FDTD)

  10. Stub-loaded antenna The antenna was studied: - varying the d/a ratio; - changing the impressed electromagnetic field frequency; - using stub whose height is not infinite; - adding flanges. Study of propagative and radiative behavior of printed dielectric structures using the finite difference time domain method (FDTD)

  11. Stub-loaded antenna Antenna parameters: a=4.8 [mm] a’=2.4 [mm] d=0.0÷1.2 [mm] b=2.4 [mm] Feeded by a TE10 @ f=50 [GHz]. Study of propagative and radiative behavior of printed dielectric structures using the finite difference time domain method (FDTD)

  12. Stub-loaded antenna Study of propagative and radiative behavior of printed dielectric structures using the finite difference time domain method (FDTD)

  13. Stub-loaded antenna Study of propagative and radiative behavior of printed dielectric structures using the finite difference time domain method (FDTD)

  14. Slot antenna The antenna was studied: - changing the impressed electromagnetic field frequency; - using lateral walls whose height is not infinite; Study of propagative and radiative behavior of printed dielectric structures using the finite difference time domain method (FDTD)

  15. Slot antenna Antenna parameters: a=2.2 [mm] a’=1.0 [mm] d=0.1 [mm] b=1.6 [mm] er=2.56 Feeded by a TE10 @ f=5¸100 [GHz], with 5 [GHz] intervals Study of propagative and radiative behavior of printed dielectric structures using the finite difference time domain method (FDTD)

  16. Slot antenna Study of propagative and radiative behavior of printed dielectric structures using the finite difference time domain method (FDTD)

  17. Slot antenna Study of propagative and radiative behavior of printed dielectric structures using the finite difference time domain method (FDTD)

  18. Microstrip antenna The antenna was studied (two values for d): - varying the w/d ratio; - changing the impressed electromagnetic field frequency; - altering the distance between the microstrip and the right lateral wall; - modifying the relative dielectric constant profile; • introducing an air-gap between the dielectric and the ground floor. Study of propagative and radiative behavior of printed dielectric structures using the finite difference time domain method (FDTD)

  19. |Ex (f)| for the symmetric mode. |Ex (f)| for the asymmetric mode. Microstrip antenna To determine simulation parameters, the device was studied using a feeding TE10 mode which, after convergence had been verified, was replaced by an asymmetric mode. Following this procedure, an assessment of the minimum measurable leaky field is obtained, getting an evaluation of simulation accuracy. Study of propagative and radiative behavior of printed dielectric structures using the finite difference time domain method (FDTD)

  20. Microstrip antenna Antenna parameters: w=0.3¸3.9 [mm] d=4.5 [mm] h=1.5 [mm] h1=0.265¸1.3125 [mm] er=2.56 Feeded by two Ey modes @ f=50 [GHz] with a p phase difference. Study of propagative and radiative behavior of printed dielectric structures using the finite difference time domain method (FDTD)

  21. Microstrip antenna Study of propagative and radiative behavior of printed dielectric structures using the finite difference time domain method (FDTD)

  22. Microstrip antenna Study of propagative and radiative behavior of printed dielectric structures using the finite difference time domain method (FDTD)

  23. Microstrip antenna Antenna parameters: w=2.7 [mm] d=4.5 [mm] h=1.59 [mm] n=0, 1, 2, 4 Feeded by a TE10 mode @ f=50 [GHz] Study of propagative and radiative behavior of printed dielectric structures using the finite difference time domain method (FDTD)

  24. Microstrip antenna Study of propagative and radiative behavior of printed dielectric structures using the finite difference time domain method (FDTD)

  25. Microstrip antenna Study of propagative and radiative behavior of printed dielectric structures using the finite difference time domain method (FDTD)

  26. Microstrip antenna • Antenna parameters: • w=2.54 [mm] (2h) • d=12.7 [mm] (10h) • h=1.27 [mm] • er=8.875 • Feeded by two Ey modes, with a p phase difference: • f=5÷25 [GHz], • 2.5 [GHz] intervals; • f=13.0÷14.5 [GHz], • .1 [GHz] intervals. Study of propagative and radiative behavior of printed dielectric structures using the finite difference time domain method (FDTD)

  27. Microstrip antenna Study of propagative and radiative behavior of printed dielectric structures using the finite difference time domain method (FDTD)

  28. Microstrip antenna Study of propagative and radiative behavior of printed dielectric structures using the finite difference time domain method (FDTD)

  29. Microstrip antenna Observations: - accuracy assessment and simulation parameters choice was implemented substituting the impressed asymmetric magnitude with a symmetric one (original approach); - an evaluation of method accuracy is given by confined superficial waves, too. They can be generated in air-dielectric devices; - for low values of normalized phase constant, when high losses take place, dispersion parameters extraction from simulation output by matrix-pencil algorithm could lead, sometimes, to unreliable results. Study of propagative and radiative behavior of printed dielectric structures using the finite difference time domain method (FDTD)

  30. Conclusions 1. An accurate high performance time domain simulator has been successfully programmed. 2. FDTD helps predicting experimental results, furnishing eventual disadvantages generated by side effects, which were not accounted for. 3. Dispersion curves, thus far field, can be controlled modulating microstrip width, changing impressed magnitude frequency, inserting an air-gap under the dielectric or introducing asymmetry. Study of propagative and radiative behavior of printed dielectric structures using the finite difference time domain method (FDTD)

  31. Conclusions 4. An inhomogeneous dielectric profile heavily affects normalized attenuation constant; if there were a method to control such profile, for example electrically, a variation of leakage constant could be obtained without changing the antenna structure, a desirable feature to be added to the scanning angle property that characterizes leaky wave antennas. 5. Previous studies which deal with air-gap or variable dielectric profile microstrip antennas were not found. Probably, they can be considered for further analysis. 6. Considering the performed simulations, a two dimensional implementation of matrix-pencil algorithm could be a valid tool to post-process FDTD results. Study of propagative and radiative behavior of printed dielectric structures using the finite difference time domain method (FDTD)

  32. Conclusions 4. An inhomogeneous dielectric profile heavily affects normalized attenuation constant; if there were a method to control such profile, for example electrically, a variation of leakage constant could be obtained without changing the antenna structure, a desirable feature to be added to the scanning angle property that characterizes leaky wave antennas. 5. Previous studies which deal with air-gap or variable dielectric profile microstrip antennas were not found. Probably, they can be considered for further analysis. 6. Considering the performed simulations, a two dimensional implementation of matrix-pencil algorithm could be a valid tool to post-process FDTD results. Study of propagative and radiative behavior of printed dielectric structures using the finite difference time domain method (FDTD)