User`s Manual
Contents
1. g e VY In this structure two metal wires along x and y directions are mounted on the top surface of a grounded dielectric slab The normal incident wave is polarized along the y direction Since the x oriented wire is connected with the y r Metal Wire oriented wire electric current will be induced VE VAN Dielectric Slab Ground Plane along the x direction Thus an x polarized reflected field will be generated Two reflection MA AL coefficients will be obtained as shown in 5 Fig 24 Connected metal wire E o E E sa 5 yo inc xy inc Ey Ey Since there is a metal ground plane on the back of the dielectric slab the total reflection energy should equal to the incident energy Therefore the following equation should be satisfied La 6 32 User Manual of Spectral FDTD Code V 1 0 Y Kim and F Yang 10 2 Simulation Results The FDTD simulated results are shown in Fig 25 where the co cross and total reflection coefficients are plotted As expected the total reflection is always 1 as expected from 6 Around 16 and 29 GHz the co polarized field is zero and the cross polarized field reaches the maximum 1 2 1 0 8 5 WZ Roof O 06 Co Pol te ee dd a g Cross Pol Total Ref Maa 04 L e 0 2 do a aan ech es agp a a a SOE E RR a DRDS A MT o RP 0 0 5 10 15 20 25 30 Freq GHz Fig 25 Reflection coefficient2. shows the reflection coefficient and the time domain waveform 1 kx S Frequency Spectral Real E 0 0 5 1 1 5 2 0 500 _ 1000 1500 Freq GHz 10 Time step Reflection coefficient Time domain waveform Fig 5 Reflection coefficient and source incidence Setting the number of different k values to 1 makes a simulation more efficient if users are interested in a specific k value For example if only a normal incidence case is in interest one can set the number of k to 1 and its value to O From the time domain waveform it is clear that the field damps to zero at 1500 time steps This figure helps users determine the number of time steps needed for an accurate simulation 14 User Manual of Spectral FDTD Code V 1 0 Y Kim and F Yang 6 Example l Dielectric Slab In this chapter plane wave incidence on a dielectric slab is discussed The simulation structure an input file grid inp and ways to set up the input parameters will be shown below 6 1 Simulation Model 0 7 Plane Wave Source at z 0 6 0 6 Sampling Reflected Field at z 0 5 0 5 Remarks 04 e Reference Frequency 9 6 0 3 GHz 0 34 Dielectric Slab Wave Length c f 0 03125 m 0 24 m e Reference Cell size 01 des Z dx dy dz 0 01 i af e Dielectric constant 2 56 0 ay 1h X e Thickness 0 01 0 012 x 30 9 375 mm Fig 6 Simulation mo
3. DR o gt O O User Manual of Spectral FDTD Code V 1 0 Y Kim and F Yang EE N rce Plane re E La Plane q Metal Patch Dielectric Slab vila d o M E Em Sround Plane l NM AN Fig 22 Simulation structure on GUI 200 gt Mushroom EBG a TOO trea ae ree ep ee Q ab WY EEE ESEESE E a end did ca e 0 A C Eae e a e o ated te ei RE oe a A Sb a a ev a tue capt ctu dass a SR o a a ORE a na el O 100 be is i haath Be eM ip awe Pete SA al heal Shane ae Mrs ip els Ae See Lt a5 ty th pa a Be PENG a Cap o Sette SEA D 200 10 20 30 0 10 20 30 Frequency GHz Frequency GHz a b Fig 23 a Magnitude and b phase of the reflection coefficient 31 User Manual of Spectral FDTD Code V 1 0 Y Kim and F Yang 10 Example V Cross Polarization In previous examples all structures are symmetric with respect to the incident plane wave so that the reflected wave has the same polarization as the incident wave However a cross polarization may occur for general structures This chapter analyzes a structure that both co and cross polarized fields are observed 10 1 Simulation Model e Substrate thickness 0 04 A2cuz e Substrate permittivity 2 2 e Unit cell length 0 14 A 26Hz Normal incident case TE e Wire length When connected 0 24 A gt cHz VA WHR urce Plane A Observation Plane
4. When the simulation is over output files will be generated and stored in the same folder 3 3 Grid inp The second way is to generate the grid inp manually with any text editors Users can find example files in following chapters Once it is generated users should save it and then type main on the MATLAB command window to start the FDTD simulation gt main The descriptions of grid inp will be discussed in the following chapters with detailed examples User Manual of Spectral FDTD Code V 1 0 Y Kim and F Yang 4 Input File Descriptions grid inp 4 1 Reference Frequency The first step in setting up an input file is to determine an FDTD computational domain The free space wavelength at a reference frequency is used as reference length to describe simulation structure Most physical dimensions such as cell size computational domain size location of plane wave source and sampling field and dielectric slab structure are represented in term of wavelength WSC y 1 C is the free space wave speed and feis the reference frequency For example if the reference frequency is 9 6 GHz the wavelength o is 31 25 mm 4 2 Cell Size The second step is to choose a reference cell size dx dy and dz Usually the cell size is around 0 011 to achieve an accurate result When a high frequency wave propagates through a high permittivity material the cell size needs to be reduced An example will be shown in Cha
5. excitation signal is weak in this ANDAVA id D A Dielectric Slab PN frequency region Accurate results can be V obtained by reducing the BW of the Gaussian AX exaction of the plane wave as discussed in Section 4 5 Fig 14 Simulation structure on GUI 24 Frequency GHz N A O o User Manual of Spectral FDTD Code V 1 0 Y Kim and F Yang x 10 k surface wave region O 0 100 200 300 400 T Kx 1 m Fig 15 The reflection coefficient of the dipole FSS 0 9 0 8 0 7 0 6 0 5 0 4 0 3 0 2 0 1 25 User Manual of Spectral FDTD Code V 1 0 Y Kim and F Yang 8 Example Ill Loop FSS Metal wires are popular structures in EM designs such as vias or feeding probe To illustrate how to implement wires the metal dipole in the previous FSS structure is replaced by a metal wire loop In this example 4 metal wires are mounted on top of a dielectric slab and they form the same boundary as the metal patch in the example Il Users can expect a similar result 8 1 Simulation Model LAS 4 Wires e x direction length 3 mm e y direction length 12 mm Wire4 Wire2 e Dielectric Slab e x dimension 15 mm e y dimension 15 mm Y e Thickness 6 mm Wire1 lt Dielectric Slab Top View Fig 16 Metal wire structure on a dielectric slab Users can place metal wires in the computational domain by simply setting up x y and Z location of the wire St
6. incident case vias Side view Ground Plane Fig 21 Geometry of a mushroom like EBG structure 4 9 2 grid inp Frequency used to describe the structure 1 2e 010 Cell Size 6 Total dimensions along the x y z direction including catter region 14 0 14 0 7 29 User Manual of Spectral FDTD Code V 1 0 Y Kim and F Yang 6 Location of plane wave source 6 Plane wave parameter E to y direction TE 0 TM 90 frequency of interest O O 3e 010 6 Number of Kx amp Ky Lines Frequency and Mode of Scan O O 1 Basic simulation time steps Location of sampling field for parameter extraction SPlate Of vB SPlate UL Ou SWire Owe Oi SDone This structure includes all three objects discussed before dielectric slab metal patch and metal via The input file can be also found in the example folder 9 3 Simulation Result The simulated result is plotted in Fig 23 Note that the reflection coefficient is always 1 which means all incident wave energy is reflected The phase of the reflected field changes from 180 to 180 At the resonant frequency 17 1 GHz the reflection phase is O which is the PMC condition It is important to point out that the phase is normalized to the phase of a PEC ground plane that locates on top of the dielectric slab as discussed in 4 Therefore the reflection phase for a PEC ground plane need to be simulated as a reference 30 Reflection Coefficient O O O O
7. 10 13 15 21 User Manual of Spectral FDTD Code V 1 0 Y Kim and F Yang 7 2 Grid inp 7 3 Simulation Result CHAPTER 8 Example Ill Loop FSS 26 8 1 Simulation Model 8 2 grid inp 8 3 Simulation Result CHAPTER9 Example IV Mushroom Like EBG Structure 29 9 1 Simulation Model 9 2 grid inp 9 3 Simulation Result CHAPTER 10 Example V Cross Polarization 32 10 1 Simulation Model 10 2 Simulation Result CHAPTER 11 Summary 33 1 Introduction Goal of FDTD PBC code User Manual of Spectral FDTD Code V 1 0 Y Kim and F Yang The FDTD PBC algorithm is developed to analyze plane wave scattering from general periodic structures Both the magnitude and phase of the reflection coefficient are calculated and recorded FDTD computational domain In order to use FDTD method a 3 D computational domain is created first The material of each cell within the computational domain needs to be specified accordingly In general the material can be free space by default or metal plates wires perfect electrical conductor or dielectrics whose permittivity and permeability are defined by PBC Periodic structure Fig 1 FDTD computational domain FDTD PBC Code Author users As shown Fig 1 the object structure is periodic along the x and y directions Thus the computational domain is truncated using the periodic boundary conditions PBC on four sides Assume plane waves propagate in the
8. Generate grid inp through a graphic interface Next Call main program e Main program main m Task Control the program flow determine wave excitation and calculate reflection coefficient Call subroutines below e Initialization subroutine FDTD init m Task Read FDTD parameters Define fundamental constants FFT number Read reference frequency reference cell size Determine time step sample rate frequency Read total computational size Read plane wave info Location polarization frequency range Read simulation control Single kx or scan kx Read the number of time step Read location of receiving time step Sor Or at Oy OM ae a Ie JR Define PML region coefficients Use grid inp called by main m e Scatter subroutine scatter PBC m Task Calculate the EM fields and control time step loop Called by main m Use following subroutines e E field calculation fdtd_maine m fdtd_pmle m fdtd plwe m e H field calculation fdtd_mainh m fdtd pmlh m fdtd plwh m e Parameter extraction fdtd param m e Post process subroutine fdtd_post m User Manual of Spectral FDTD Code V 1 0 Y Kim and F Yang Task Save data to output files and plot figures Called by main m e Output file Generated by fdtd_post m Frequency and kx data freq_fig dat kx_fig dat Reflection coefficient magnitude and phase Co polarization Rm_kfc dat Rp kfc dat Cross polarization Rm kfx dat R
9. User Manual of Spectral FDTD Code V 1 0 Y Kim and F Yang User Manual Periodic Structure Analysis Using Spectral Finite Difference Time Domain Code V 1 0 FDTD PBC v1 0 File FOTO Setup Add Objects View Objects Analysis Help EVPRE SEE ERA DRE i O Center for Applied Eleciromanetic Systems Research Department of Electrical Engineering The University of Mississippi Yanghyo Kim and Fan Yang The University of Mississippi September 2008 CHAPTER 1 CHAPTER 2 2 1 2 2 CHAPTER 3 3 1 3 2 3 3 CHAPTER 4 4 1 4 2 4 3 4 4 4 5 4 6 4 7 4 8 4 9 4 10 User Manual of Spectral FDTD Code V 1 0 Y Kim and F Yang Table of Contents Introduction Overview of FDTD PBC Code FDTD PBC Flowchart FDTD PBC Program and Subroutines Start of FDTD PBC Code Software Installation Graphic User Interface GUI Grid inp Input File Descriptions grid inp Reference Frequency Cell Size Total Simulation Dimensions Location of Plane Wave Source Plane Wave Parameters Polarization amp Frequency Number of k and Frequency Time Step Location of Sampling Field Objects of Interests End of Input File CHAPTER5 Output and k 5 1 5 2 CHAPTER 6 6 1 6 2 6 3 CHAPTER 7 7 1 Number of k gt 1 Number of ky 1 Example I Dielectric Slab Simulation Model grid inp Simulation Result and Manners of Setting up Input Parameters Example Il Frequency Selective Surface Simulation model
10. amii Reflection phase characterizations of the EBG ground plane for low profile wire antenna applications IEEE Trans Antennas Propag vol 51 no 10 pp 2691 2703 Oct 2003 34
11. del A dielectric slab can be regarded as a periodic structure with arbitrary periodicity For computational efficiency only one cell is selected along the x and y directions Simulation results based on the different number of time steps permittivity of dielectric slab reference cell size and thickness of dielectric slab are discussed Users can add any number of dielectric materials in the domain by simply setting up the structures on the GUI or grid inp file 15 User Manual of Spectral FDTD Code V 1 0 Y Kim and F Yang 6 2 grid inp 66 Frequency used to describe the structure 9 6e9 CS Total dimensions along the x y z direction including scatter Bad 0 01 Ore PO oe 6 Location of plane wave source 60 O 65S Plane wave parameter E to y direction TE 0 TM 90 Frequency of interest O 0e9 20e9 66 Number of Kx amp Ky Lines Frequency and Mode of Scan 1 O O 1 CS Basic simulation time steps 65 Location of sampling field for parameter extraction O O Dol JOO Db Udo Z 06 SEndD SDone 16 User Manual of Spectral FDTD Code V 1 0 Y Kim and F Yang Users can also determine the input parameters and dielectric slab parameters on GUI FDTD Setup Eak Grid Parameters Reference Frequency sHz Reference Cell Size Total Dimension Total y Dimension Total z Dimension Source amp Observation Source Plane Location Source Polarization source Bandwidth GH
12. for co and cross polarized fields 11 Summary This user manual introduces spectral FDTD software developed by the authors to analyze scattering properties of general periodic structures The program flow chat input output files and several examples are illustrated to explain how to use this electromagnetic software This FDTD software is developed for free usage It is users own responsibility to use the data generated by this software If users have problems and find any mistakes in the software they are welcomed to contact Prof Fan Yang at fyang olemiss edu Your suggestions and comments are greatly appreciated 33 User Manual of Spectral FDTD Code V 1 0 Y Kim and F Yang References 1 A Aminian F Yang and Y Rahmat Samii Bandwidth determination for soft and hard ground planes by spectral FDTD a unified approach in visible and surface wave regions EEE Trans Antennas Propag vol 53 no 1 pp 18 28 Jan 2005 2 A Aminian and Y Rahmat Samii Spectral FDTD a novel technique for the analysis of oblique incident plane wave on periodic structures IEEE Trans Antennas Propag vol 54 no 6 pp 1818 1825 June 2006 3 F Yang J Chen R Qiang and A Elsherbeni FDTD analysis of periodic structures at arbitrary incidence angles a simple and efficient implementation of the periodic boundary conditions 2006 IEEE AP S Digest vol 3 pp 2715 2718 July 2006 4 F Yang and Y Rahmat S
13. h will be explained shortly 6 3 3 Cell Size and High Permittivity At High Frequency 36 dx 0 01 Time Step 15000 dx 0 0051 Time Step 35000 ky 1 0 1 FDTD FDTD ee 4 Analytic E nal 3 Analytic 0 8 iJ q 0 8 E i y i if E a 20 6 yH y tt S 0 6 Th E RE E DER 2 0 4 Y qed ye 4 S04 a EET TY dy qe eT Ty Tay yy 0 2 Wee cr 0 2 th 0 3 i 0 i L 0 0 5 1 1 5 2 2 5 0 0 5 1 1 5 2 2 5 Frequency Hz x 10 Frequency Hz x 10 dx 0 012 Time Step 15000 dx 0 0051 Time Step 35000 Fig 10 Reflection coefficient comparison with different cell size This result shows that the FDTD PBC code needs a smaller reference cell size to fix the discrepancy problem in the high frequency range It is mainly because the number of 19 User Manual of Spectral FDTD Code V 1 0 Y Kim and F Yang cells per guided wavelength is decreased for the high permittivity material at high frequency Therefore if the cell size is small enough in this case the code can take enough samples for an accurate result When the cell size is reduced the time step interval dt is reduced as well according to 4 In order to obtain the response for the same Gaussian incident pulse the number of time steps also needs to be increased When dx 0 005 with time step 35000 the result has a good agreement wit
14. h the analytic method 6 3 4 Thickness of Dielectric Slab 2 56 Thickness 0 2 A 0 35 A dx 0 01 A Time Step 1500 k 1 0 0 5 0 5 FDTD FDTD Analytic 0 4 bi hana E 0 4 2 P o O 0 37 P O 0 3 O O c p c 2 0 2 d 0 2 O O e Ue he ee eer ere Sere Genter ere ere Rd 0 1 A S o 0 0 5 1 1 5 2 2 5 0 0 5 1 1 5 2 2 5 Frequency Hz x 10 Frequency Hz x10 Comparison with 0 2 Comparison with 0 352 Fig 11 Reflection coefficient comparison for different thickness The FDTD results show good agreement with the analytic method as far as the program takes enough number of time steps for the simulation Notice that the thickness of the dielectric slab does not affect the maximum magnitude of the reflection coefficient Instead it only affects the period of oscillation along the frequency axis 20 User Manual of Spectral FDTD Code V 1 0 Y Kim and F Yang 7 Example Il Frequency Selective Surface The FDTD PBC is also used to characterize the reflection transmission coefficients of a frequency selective surface FSS consisting of dipole elements 7 1 Simulation Model Periodic Substrate f f x dimension 15 mm e Periodic Dipole Length 12 mm f f Width 3 mm y dimension 15 mm E a a a a a a E Thickness 6 mm Cross view Fig 12 Frequency selective surface FSS on a dielectric slab For computati
15. l Fig 13 Periodic patch array setup on GUI 22 7 2 User Manual of Spectral FDTD Code V 1 0 Y Kim and F Yang Grid inp A complete input file is shown below 0 Frequency used to describe the structure 3e 009 Cell Size 66 Total dimensions along the x y z direction including scatter region Chao Ceda 0 7 Location of plane wave source Plane wave parameter E to y direction TE 0 TM 90 frequency f interest O 2e 010 6 Number of Kx amp Ky Lines Frequency and Mode of Scan 01 2e 010 O 1 Basic simulation time steps SEndD SPlate 0 06 Ou SDone Wavelength A c f 3 x 10 3 x 10 0 1 m Reference cell size 0 01 A 0 001 m Total x dimension 0 15 15 mm Total y dimension 0 15 15 mm Total z dimension 0 70 70 mm 23 User Manual of Spectral FDTD Code V 1 0 Y Kim and F Yang e Usually the distance in between the top of the structure and the source location is 0 25A 0 5A e Users can set up the parameters on the GUI 7 3 Simulation Result After setting up all parameters a graphic figure appears on the main GUI window The a VU simulated reflection coefficient is shown in Fig durce Plane 15 The reflection and transmission regions A Observation Plane can be clearly identified One observation on the result is that there exist some oscillations near the light line 0 90 k k This is because the
16. onal efficiency only one cell of periodic structure is analyzed inside of the red dashed line in Fig 12 The location of the periodic dipole is determined by x1 y1 z1 and x2 y2 z2 1 x location The total x dimension of the periodic cell is 15 mm which is 0 15 at 3 GHz The dipole width is 3 mm which is 0 03 A and it is placed in the middle of the dielectric slab along the x axis Therefore x1 is 0 06 and x2 is 0 09 in the domain 21 User Manual of Spectral FDTD Code V 1 0 Y Kim and F Yang Plate 0 06 0 01 0 16 0 09 0 13 0 16 2 y location The total y dimension of the periodic cell is 15 mm which is 0 15 The dipole length is 12 mm which is 0 12 Since the reference cell size is 0 01 A it cannot be placed exactly in the middle of the dielectric slab along the y axis Instead y1 is 0 01 and y2 is 0 13 A in the computation domain The periodic condition is still satisfied with this condition Plate 0 06 0 01 0 16 0 09 0 13 0 16 3 z location The patch is mounted on top of the dielectric slab Thus z location is the same as the location of the top surface of the dielectric slab which is 0 16 Therefore both z1 and z2 are 0 16 in the domain Plate 0 06 0 01 0 16 0 09 0 13 0 16 Above parameters also can be selected on the GUI interface as shown in Fig 13 DER Patch Name Dipole FSS x1 Location 4 Location y1 Location ve Location 71 Location 71 Location Cance
17. p kfx dat Total Rm kf dat Rp kf dat Remark Depending on simulation geometry a reflected field polarization can be different from the source polarization Therefore a cross polarization effect has to be considered This will be further explained in Chapter 10 User Manual of Spectral FDTD Code V 1 0 Y Kim and F Yang 3 Start of FDTD PBC Code 3 1 Software Installation In order to use the FDTD PBC program users need to copy all necessary files to a working folder By opening MATLAB Version 7 0 or higher and selecting the proper directory users are ready to start the FDTD PBC program 3 2 Graphic User Interface GUI There are two ways to run a simulation The first way is to use the GUI Users can type start on the MATLAB command window gt start FDTD PBC v1 0 HIEI Fie FOTO Setup Add Objects View Objects Analysis Help Ske GA SESE kl Center for Applied Electromanetic System Research Department of Electrical Engineering The University of Mississippi Fig 3 Graphic User Interface GUID of the FDTD PBC code The FDTD PBC GUI will pop up Users can easily set up the input parameters with an aid of visual structure Some examples will be shown in the following chapters to illustrate input parameters When users click on Analysis on the menu the program User Manual of Spectral FDTD Code V 1 0 Y Kim and F Yang will save current input parameters into grid inp file and begin simulating
18. parameter extraction can be set up next Normally it is placed in between object structure and plane wave source location along the z direction For example if the source location is at z 0 6 A the reflected fields can be sampled at z 0 5 4 9 Objects of Interest The next step is to specify the geometry of the structure In the current FDTD PBC code three types of objects are supported in the input file The first one is a dielectric slab The coordinates of two corner points of the box need to be specified as well as its dielectric constant The second type of geometries is a PEC plate The plate can be placed in parallel to the xy Or xz or yz plane The x y z coordinates of two corner points need to be specified in the input file The third type of geometries is a PEC wire which is assumed to be infinitely thin The wire should be oriented along x y or z direction The x y Z coordinates of two end points need to be specified in the input file 4 10 End of Input File The input file ends with the following line Done 12 User Manual of Spectral FDTD Code V 1 0 Y Kim and F Yang 5 Output and k There are two different types of output formats the number of k is 1 and the number of kx is more than 1 In this section the manners of choosing the number of kx will be discussed with examples 5 1 Number of k gt 1 If the number of k is more than 1 the reflection coefficient in the frequency k
19. plane will be plotted at the end of a simulation The number of different kx values and maximum kx value are specified in the input file Note that the maximum k value is provided in terms of an associated frequency as shown below ke 2m f CIC 5 For example Fig 4 shows the reflection coefficient of a dielectric slab illuminated by a TE incident wave f is set to 20 GHz and the maximum kx is 418 88 rad m according to 5 101 different k values are sampled from O to the maximum k value The data of the horizontal axis kx axis vertical axis frequency axis and reflection coefficients are saved into different output files for future usages 20 Frequency GHz o o On Surface Wave Region O 100 200 300 400 r Kx 1 m Fig 4 Reflection coefficient in the frequency k plane 13 User Manual of Spectral FDTD Code V 1 0 Y Kim and F Yang 5 2 Number of k 1 If the number of k is 1 two plots will show up after simulation One is sample field data in the time domain which can be used to check the convergence of the FDTD simulation The other plot is the magnitude of reflection coefficient versus frequency It is identical to the reflection coefficient on a vertical line with the corresponding k value in the previous 2 D color figure In the previous example if the number of kx is 1 and the 1 is 4 8 GHz the FDTD code will calculate the reflection coefficient for kx 100 6 rad m according to 5 Figure 5
20. pter 6 4 3 Total Simulation Dimensions If the reference cell size is specified users can determine total simulation dimensions along the x y z directions to include the scattering object For example the cell size is 0 012 m If the total dimension along x y z directions are 0 01 0 01 and 0 7 respectively the total dimension to be simulated is 0 1 x 0 14 x 0 7 3 125 mm x 3 125 mm x 21 875 mm size 4 4 Location of Plane Wave Source Once the total dimension is decided the location of the plane wave source needs to be defined For instance if the total z dimension is 0 71 the source excitation can start at z 0 64 and the wave will propagate along z direction If there is a reflected wave field which goes over the source location it will be absorbed by the PML on the top 10 User Manual of Spectral FDTD Code V 1 0 Y Kim and F Yang 4 5 Plane Wave Parameters Polarization amp Frequency Users can choose either O or 90 for the plane wave polarization 0 is the transverse electric field TE mode If a wave incidents on the xz plane it contains Ey Hx Hz components 90 is the transverse magnetic field TM mode If a wave incidents on the xz plane it has Hy Ex Ez components The frequency range of interest is determined by kx value as shown below Frow Ky Cl2a k Clla ae Tin T BW In grid inp the upper frequency equals to the summation of the lower frequency and
21. result is plotted in Fig 19 amp 20 which is close to the dipole FSS case The reflection coefficient at a specific angle is extracted from Fig 19 Zi User Manual of Spectral FDTD Code V 1 0 Y Kim and F Yang x 10 h do N A O Frequency GHZ o ho A O Surface wave region D 100 200 300 Kx 1 m Fig 19 The reflection coefficient of the loop FSS e Patch 15 Wire 15 Patch 30 Wire 30 Patch 45 Wire 45 Reflection Coefficient 6 8 10 12 14 16 Frequency GHz Fig 20 Comparison of reflection coefficient of periodic dipole FSS and metal wire loop FSS for several incident angles 28 User Manual of Spectral FDTD Code V 1 0 Y Kim and F Yang 9 Example IV Mushroom Like EBG Structure There has been an increasing interest in electromagnetic band gap EBG structures When a plane wave normally illuminates upon an EBG structure the phase of the reflected field changes continuously from 180 to 180 as sweep frequency varies 4 This property can be utilized as a Perfect Magnetic Conductor PMC when a reflection phase is O In this chapter a mushroom like EBG structure is analyzed 9 1 Simulation Model e Substrate thickness h 0 04 Mzz e Substrate permittivity 2 2 e Unit cell length 0 14 Ajacuz e Patch width w 0 12 A2cHz e Side gap width g 0 2 A2cHz Top view patches Substrate E o h e Normal
22. ructure components are same as the periodic dipole case which consists of 6 coordinates If a wire is placed along x axis y1 and y2 locations are same and if a wire is placed along y axis x1 and x2 locations are same Since this wire is mounted on the surface Z1 and Z2 coordinates are the same as the location of the upper plate of the dielectric slab 1 Wire 1 e Length 3 mm e x oriented same coordinates for y1 and y2 and z1 and z2 Wire 0 06 0 01 0 16 0 09 0 01 0 16 x1 y1 21 x2 y2 22 26 2 Wire 2 e Length 12 mm User Manual of Spectral FDTD Code V 1 0 Y Kim and F Yang e y oriented same components for x1 and x2 and z1 and z2 Wire 0 09 0 01 0 16 0 09 0 13 0 16 Wire 3 and 4 can be defined with the same method Users can also set up the metal wire structure on the GUI as shown in Fig 17 etal re Mame x1 Location y1 Location 71 Location y2 Location yA Location z Location Cancel Fig 17 Metal wire setup on GUI YA nar Ji g S durce Plane Vv servation Plane A VAV y Dielectric Slab AAA A V Fig 18 Simulation structure on GUI 8 2 grid inp A complete input file can be found in the example folder Basically all the input parameters are same as the dipole case except the 4 metal wires 8 3 Simulation Result After setting up all parameters a graphic structure is generated as shown in Fig 18 The simulated
23. tep and High Permittivity 36 Time Steps 2000 15000 kx 1 0 When there is a high permittivity material in the domain the result reveals that the FDTD PBC code requires a greater number of time steps as shown in Fig 9 This is because if the permittivity is increased the wave speed in the dielectric slab gets slower so that it takes more time for the wave to return to the sampling plane When the number of time steps is increased to 15 000 the result has a good agreement with the analytic method Therefore users need large number of time steps in order to get an accurate result 18 User Manual of Spectral FDTD Code V 1 0 Y Kim and F Yang mm WH es TA JA A ha HR FDTD FDTD 1 7 j i i os TRIER Analytic E 0 8 E Analyte S Ty Py E yy We T i 9 S 0 6 Pu S 0 6 yE O NM O oe 4 O i j 5 e 2 0 4 1 Ht e 0 4 Ta D 11 o A Il r 0 2 cc 0 2 g 3 0 0 0 0 5 1 1 5 2 2 0 0 1 1 5 2 2 5 Frequency Hz x 10 Frequency Hz x 10 Comparison at Time Step 2000 Comparison at Time Step 15000 Fig 9 Reflection coefficient comparison for higher permittivity slab On the second plot Time Step 15000 there is a little discrepancy for the high frequency range from 15GHz to 20GHz This is related to the reference cell size whic
24. the 2 frequency bandwidth BW Depending on the problems users need to specify the bandwidth in the input file A modulated Gaussian waveform is used as the excitation signal 3 4 6 Number of kx and Frequency Kx is the x component of a wave number k If a wave incidents on the xz plane k k sn0 27 f C sn0 3 In general kx is the function of two variables one is the incident angle and the other is the frequency In the FDTD PBC code k is set as a fixed value 1 3 For example if kx is Zero the output is the reflection coefficient vs frequency of interest at the normal incidence 0 0 In the input file users can specify the number of different k values and the maximum k value If more than one k is selected the output is the frequency spectral of the reflection coefficient The output file and k will be further explained in the Chapter 5 with examples 4 7 Time Step For the computational stability the reference time step is internally defined as below dt dx 2 C 4 The number of total FDTD time steps is problem dependent Normally less time steps are required for low permittivity materials Such as 2 56 whereas a large number of 11 User Manual of Spectral FDTD Code V 1 0 Y Kim and F Yang time steps are required for high permittivity materials 16 25 49 etc This will be shown in Chapter 6 with examples 4 8 Location of Sampling Field The location of the sampling field for
25. xz plane with an incident angle 0 The perfectly matched layers PML are placed on the top and bottom of the structure to absorb the propagating plane waves Dr Fan Yang The University of Mississippi Graphic User Interface Designer Yanghyo Kim The University of Mississippi User Manual of Spectral FDTD Code V 1 0 Y Kim and F Yang 2 Overview of FDTD PBC Code 2 1 FDTD PBC Code Flowchart Users Main program Initializations Choose excitation waveform Specify objects ak grid inp Update scatter fields Output data y Calculate reflection coefficient Reflection coefficient Post process data save plot Fig 2 Flowchart of the FDTD PBC code Figure 2 shows the flowchart of the FDTD PBC algorithm Once users decide simulation structure and its parameters an input file grid inp can be created from either a Graphic User Interface GUI or a text editor The FDTD PBC program reads data from the input file and starts to calculate the electromagnetic fields and scattering parameters The simulation stops when it reaches the maximum number of k lines Nsweep and then the program generates output files and related figures 2 2 _FDTD PBC Program and Subroutines e Input file grid inp Object geometries materials and FDTD parameters Manually input or GUI input User Manual of Spectral FDTD Code V 1 0 Y Kim and F Yang e Graphic user interface GUI start m Task
26. z Number of Time Steps Observation Plane Location simulation Type Number of kx amp ky Mode of Scan Maximum kx f kx c 2pi GHz Maximum ky f ky c 4 2pi GHz o a FDTD input parameters HEr Dielectric Slab Mame Dielectric Slab Permittiity 2 56 x1 Location x2 Location y1 Location wa y2 Location 7 Location z2 Location Cancel b Dielectric geometry Fig 7 Input parameters on GUI 17 User Manual of Spectral FDTD Code V 1 0 Y Kim and F Yang 6 3 Simulation Results and Manners of Setting up Input Parameters 6 3 1 Time Step Selection 4 Time steps 500 700 900 1200 1500 k 1 0 3 x 10 E 0 5 Min 2 2 2 RO bea Se eee E nte oa s9 900 0 4 3 1200 O Oyen oe o 1500 O 1 5 7 2 0 3 E Analytic O o 8B 0 2 e e eee eee E E 0 1 0 5 eee ed ie Re At Ra ae eee 0 999 1 1 001 1 002 Frequency Hz x 10 Fig 8 Reflection coefficient comparison with different time steps This result shows that the FDTD PBC code needs a proper number of time steps for an accurate result When the number of time steps is small 500 700 900 there are not enough samples taken from the reflected fields Thus the reflection coefficient is not accurate In contrast if the number of time steps is large enough 1200 1500 the result has a good agreement with a result of the analytic method 6 3 2 Time S
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