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

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

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

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

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

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. PML parameters Bérenger’s PML electric conductivity profile used: Magnetic conductivity profile satisfies the impedance matching condition: where: 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 , 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. Study of propagative and radiative behavior of printed dielectric structures using the finite difference time domain method (FDTD) 1 [s] movie ~3x10 -11 [s] real.

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

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 TE 10 @ 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 Study of propagative and radiative behavior of printed dielectric structures using the finite difference time domain method (FDTD) The antenna was studied: - changing the impressed electromagnetic field frequency; - using lateral walls whose height is not infinite;

15. Slot antenna Antenna parameters: a=2.2 [mm] a’=1.0 [mm] d=0.1 [mm] b=1.6 [mm]  r =2.56 Feeded by a TE 10 @ 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 Study of propagative and radiative behavior of printed dielectric structures using the finite difference time domain method (FDTD) The antenna was studied (two values for d): - changing the impressed electromagnetic field frequency; - varying the w/d ratio; - modifying the relative dielectric constant profile; - altering the distance between the microstrip and the right lateral wall; -introducing an air-gap between the dielectric and the ground floor.

19. Microstrip antenna To determine simulation parameters, the device was studied using a feeding TE 10 mode which, after convergence had been verified, was replaced by an asymmetric mode. Study of propagative and radiative behavior of printed dielectric structures using the finite difference time domain method (FDTD) Following this procedure, an assessment of the minimum measurable leaky field is obtained, getting an evaluation of simulation accuracy. |E x (f)| for the symmetric mode. |E x (f)| for the asymmetric mode.

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]  r =2.56 Feeded by two E y modes @ f=50 [GHz] with a  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 TE 10 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]  r =8.875 Feeded by two Ey modes, with a  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 Study of propagative and radiative behavior of printed dielectric structures using the finite difference time domain method (FDTD) 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.

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)