031307-8-T USERS MANUAL FOR FEMA-PRISM (VERSION 2) Tayfun Ozdemir John L. Volakis Mission Research Corp. 3975 Research Blvd. Dayton, OH 45340 Rome Laboratory/ERPT U.S. Air Force Griffiss AFB, NY 13441 Wright Patterson AFB U.S. Air Force WPAFB, OH July 1997 31307-8-T = RL-2444

Changes from the previous version: 1. Mesher and the analysis code has been seperated. Mesher is called "mesh.f" and the code is called "FEMA-PRISM.f". 2. Boundary integral option has been added to the analysis code 3. Log-periodic geometry has been added to the list of the geometries that the mesher can tessellate. 4. Non-planar sunstrate option has been added where the layers are decribed by families of linear segments 5. Compressed-row-storage has been implemented in the BI version for memory savings 6. Dimension allocation problem has been reduced to minimum (i.e., specifying surface triangles, edges and nodes before running the mesher. Rest is taken care of by the code itself) 7. Improved MatLab interface For the rest, the previous manual holds true. Running FEMA-PRISM: Mesher: 1. Adjust the dimension parameters "NdmTri", "NdmSEd", and "NdmSNo" in the file called "fema.dml". 2. Compile the mesher "Mesh.f" 3. Create the input file "Meshin". 4. Run the mesher 5. use the MatLab interface to view the mesh, identify feed locations,..etc. Code: 1. Create the input file "MainIn" for the code. 2. Compile "dm.f" 3. Run "dm.f" (reads in the mesh data already created and creates a decent fema.dml" file). 4. Compile "FEMA-PRISM.f' 5. Run the code for memory allocation (see the description of "Mainin") 6. Compile "FEMA-PRISM.f again 7. Run the code for analysis. Currently only Bl option is working.

MainIn * I - = Boundary Integral termination. 2 = Artificial Absorber termination * I = Adaptive frequency sweep, 2 = Uniform frequency sweep ----------------------------------------------- -----.,.. R ', present if the previous line has R -- Desired amount of increment in the input impedance (in Ohms) ' th t " " ' --- — the entry "1 * I --- 1 = Printed, 0 = Slot, -- 1 = Compute memory allocation, 0 = Analysis * I I I I ----- # of substrate layers O — I = all substrate layers are identical and planar, 0 = non-uniform but planar, 2 = Non-uniform and non-planar ---- # of superstrate layers ( enter zero for no superstrate) - 1 = all superstrate layers have the same thickness and material parameters, 0 = otherwise ---------------------------------------------------------------- R C C Ordered from the bottom of the cavity up, each row corresponds to a substrate layer. Only one row::: is needed if all layers are identical ( row has the info for a single layer ). for planar '0* R C C Thickness of the layer substrate - Relative permittivity of the layer ---- - Relative permeability of the layer ------------------------------------------------------------------- I CC - Number of linear segments -— Relative permittivity of the layer -- Relative permeability of the layer * R R R R......R R Ordered from bottom up. " " (forst entry for the bottom for non-planar z- r coordinates of the segments (number of pairs round plane. No entry for substrate. Works is one more than the frist entry on the previous line) the aperture, which is always with BI option only. * i c c planar) * R R R.......R R * I CC R R R R......R R ------------------------------------------------------------- ------------------------------------------------------------------------ ' R C C * R C C Same as above but for the superstrate. Ordered from the antenna surface up (first row corresponds to the '. *.. layer just above the antenna surface). '. R C -C ------ -^ ---. --- —---------—. --- —------------—. --- —-----—. ----. --- —-—. # of probe feeds present only if there is superstrate * I I IC * I I C c and works with the AA option only. Each row corresponds to a probe feed * I I C -' Surface node number #1 ----- Surface node number #2 } Probe current flows from node #1 to node #2. --- Layer # (layer within which the normally oriented probe is located, or the layer at top of which the laterally oriented probe is located). Entry can be positive or negative and increase away from the surface of the antenna with zero corresponding to the layer immediately below the antenna. - Complex amplitude of the probe current * R R R I R I I I - Starting frequency in GHz — 0 Final frequency in GHz Increment frequency in GHz -— Frequency run to save (1 = save the first freq. run, 2 = next frequency, etc.) --- Tolerance ( - 0.01 ) -- 1 = monitor convergence (dump residual error at each iter.), 0 = otherwise - I = compute element matrices assuming distorted prism (must for doubly-cureved or non-planar substrates), 0 = read in element matrices, 2 = compute assuming right prism (excellent for BI case) -- Maximum number of iterations * I - 1 = Read in user specified termination parameters (given in the following row), 0 = code will figure out the optimum parameters (this is the safe course if one is not familiar with the artificial absorber termination). * R I 1 C - Thickness of one layer (all layers have the same thickness) -- Total number of layers from the top of the outer-most superstrate layer to the termination boundary JSiIbgerP oabSPbrJayer -- - i Relative permittivity of the absorbing layers. ) Unity for BI

Mesh.f Three types of configurations: 1) Log-periodic 2) Circular 3) Rectangular The antenna could be printed or slot Reads in input file "MeshIn" which contains geometry info and creates the following files: SurfMesh - For FEMA-PRISM MeshDs Attr Angint AntEdg -, For mesh display on MatLab CavEdg SrfEdg Setup.m Before running "Mesh.f", one must have two files in the same directory: Plot.aux fema.dml Contains the statement "axis('equal') in its first line. Contains the parameter statement for memory allocation. An example is given belov PARAMETER(NdmPri= 12321,NdmTri= 3081,NdmSEd= 4713,NdmSNo= 1634, &NdmVEd= 30093,NdmVNo= 8166,NdmNZE= 19629,NdmLay= 5, &NdmRow= 243569,NdmNZS= 249) This statement is also used by the FEMA-PRISM code, and for the mesher, only three parameter are needed to be specified: NdmTri: Maximum number of triangles expected in the final meshNdmSEd: Maximum number of edges NdmSNo: Maximum number of nodes The file Mesh.f must be compiled after the dimension allocations are specified.

Meshn - 1 Line#1: I I I - 1 = Boundary Integral (BI), 0 = Artificial Absorber (AA) R: Real I = Log-periodic, 2 = Circular, 3 = Rectangular t, 1 =Printed, 0= Slot I: Integer % --- —---- 1 Lines #2-4 depend on the entries on Line #1 (see the following pages). Antenna Ground plane (PEC) A Cavity-backed: Microstrip: *- Cavity Substrate Ground plane (PEC) Modeling of the above two configurations with Bi and AA terminations: (Computation space is circled with dashed lines) Termination <echnique hique Boundary Integral (BI) Artificial Absorber (AA) Configuration Absrober Cavity-backed Absrober Microstrip Does not apply

MeshIn - 2 BI termination / Log-periodic - 1 (Only "cavity-backed" configuration is available) Line #1: 1 1 1 or 1 1 0 Line #2: R R I I R R R R R. a (deg.) - P(deg.) - Na (# of arms) - Ns (# of sections). Ro, R1 - K R: Real I: Integer - AR (suggested radial discretization length for the mesh) - ARc (distance from the antenna boundary to the cavity wall) Line #3: R Definition of the parameters Arm #1. /. Section #1,, Section #2,,.. - - - " " Section #3 Arm #2 R1 R2 R2 R3 <-R1 R2 rl r2 R3 R4 R3 _ r3 Note: K - XT for equal metal and air teeth width AR < Ro / 3 for decent mesh quality around the center of the antenna

MeshIn - 3 BI termination / Log-periodic - 2 Example run - I Line #1: Line #2: Line #3: 1 45.72 1 1 35 2 2.66 1..6.775.22 After running the mesher, one can view the mesh, number the nodes and assess the mesh quality using MatLab as shown below: MATLAB INTERFACE 1. Display the mesh (c) Copyrigq Commands to get started: in Commands for more informati >> Setup >> Mesh ~ O "AI I-~-L~~~-. —1 -..) - - I~- II_ ---- - - ~ -i~~_-l _ -L~ —.ll- - ~~LY I ZL-U --- - -I — - -L - ~-IUC-Y - ---- 2. Number the nodes and zoom in Commands to get started: in Commands for more informati >> Setup >> Mesh >> GloNod > zoom >> I U~ mm- -

Meshln - 4 Bl termination / Log-periodic - 3 Example run -2 3. Distribution of internal angles for the mesh just created This is very useful for assessing the quality of the mesh. The ideal distribution is a delta function located at 60 degrees and represents a ferfect surface mesh. The more concentrated the distribution is around 60 degrees the better. One can conclude that the mesh created is a decent one. In fact, same behavior should be expected each time one uses the mesher to tessellate a log-periodic geometry. | (c) Copyright 1984-94 The MathWo I All Rights Reserved uVersion 4.2c I |Nov 28 1994 Commands to get started: intro, demo, help help Commands for more information: help, whatsnew, i I ~>> AngDst >> n

MeshIn - 5 Bl termination / Circular - 1 Line#1: 1 2 1 or 1 20 (Only "cavity-backed" configuration is available) Line #2: R I Line #3: I D AR (radial thickness of the rings) 0 Na (# of antenna rings) P Nc (# of rings between the antenna and the cavity wall) Definition of the parameters Cavity wall Warning: Nc > 1 For the above example: Na = 5, Nc = 2

MeshIn - 6 Bl termination / Circular - 2 Example run - 1 Line #1: Line #2: Line #3: 1 2 0 (slot antenna) 15 2 After running the mesher, one can view the mesh, number the nodes and assess the mesh quality using MatLab as shown below: MATLAB INTERFACE 1. Display the mesh I Commands to get started: i Commands for more informat I 'A I L >> Setup >> Mesh >> n '. - I 2. Number the nodes and zoom in Commands for more in ion: help, whatsnew, subscribe >> Setup >> Mesh >> GloNod >) ZOI ormat info,.:.................

MeshIn- 7 BI termination / Circular - 3 Example run - 2 3. Distribution of internal angles for the mesh just created rersion 4.2c Nov 28 1994 Dst Commands to get started: intro, demo, help help Commands for more information: help, whatsnew, in fo, subscr ibe >> AngDst >> n

MeshIn - 8 BI termination / Rectangular - 1 Line#1: 1 31 or 130 Line#2: R R I I, Ax ~ Ay - NxA - NyA (sampling cell size in x-direction) (sampling cell size in y-direction) (number of antenna cells in x-direction) (number of antenna cells in y-direction) Line #3: I I NxC (# of cells between the antenna and the cavity wall in x-direction). NyC (# of cells between the antenna and the cavity wall in y-direction) Definition of the parameters _____I I i- I I I - - i - - I I I i f 1 - I ~ - I. ' II Antenna 7 Cavity wall Ay - Ax For the above example: NxA = 12, NyA = 2, NxC = 3, NyC= 4 Warning: NxC, NyC >2

MeshIn- 9 Bl termination / Rectangular - 2 Example run - 1 Line #1: 1 3 1 (printed) Line #2: 1 1 12 2 Line #3: 3 4 After running the mesher, one can view the mesh, number the nodes and assess the mesh quality using MatLab as shown below: MATLAB INTERFACE 1. Display the mesh I. I I" I I 1 I I I s I o, sunscr ne >> etup??? Undefined function or variable etup. >> Setup >> Mesh >> 0:L 'Prl 2. Number the nodes and zoom in i.. By Commands for more intorna tion: help, whatsnew, inf o, subscribe Setup Mesh GloNod zoom D. a damI-iL-" -- - --- ------ --- ----

MeshIn- 10 BI termination / Rectangular - 3 Example run - 2 3. Distribution of internal angles for the mesh just created Version 4.2c Nov 28 1994 AngDst Commands to get started: intro, demo, help help Commands for more information: help, whatsnew, inj fo, subscribe >> AngDst s-1 nr I — Lu

MeshIn- 11 AA termination / Log-periodic Line #1: 0 1 1 or 0 1 0 (printed or slot) Line #2: R R I I R R R R R, a (deg.) - P (deg.) Na (# of arms) W Ns (# of sections) Ro Rl R (suggested radial discretization length for the mesh) AR (suggested radial discretization length for the mesh) Line #3: I 0- 1 = Cavity-backed, 0 = Microstrip Line #4: R R R ARc (distance from the antenna boundary to the cavity wall) ARair (thickness of the air gap) ARabs (thickness of the absorber) cavity-backed Line #4: R R >- ARair (thickness of the air gap) P ARabs (thickness of the absorber) microstrip Definition of the parameters Definitions of Line #2 parameters are the same as before cavity-backed microstrip

MeshIn - 12 AA termination / Log-periodic / Cavity-backed Line #1: 0 1 0 (slot antenna) Line #2: 45 35 2 2 0.66 1. 0.6 0.775 0.22 Line #3: 1 Line #4: 0.72 0.66 0.44 I Commands to ge Commands for m AA termination / Log-periodic / Microstrip Line #1: 0 1 0 (slot antenna) Line #2: 45 35 2 2 0.66 Line #3: 0 Line #4: 0.66 0.44 1. 0.6 0.775 0.22

MeshIn- 13 AA termination / Circular Line #1: 0 2 1 Line #2: R I Line #3: I or 0 2 0 (printed or slot) AR (radial thickness of the rings) ~ Na (# of antenna rings) - 1 = Cavity-backed, 0 = Microstrip ' Line#4: I I I Nc (# of rings between the antenna and the cavity wall) Nair (# of air gap rings) cavty-backe: Nabs (# of absorber rings),, Line #4: I I -Nair (# of air gap rings) Nabs (# of absorber rings) m,, Definition of the Parameters Line #2 parameters have the same definitions as before. cavity-backed I-do microstrip - antenna cavity wall antenna For the above example: Na = 5, Nc = 2, Nair = 3, Nabs = 2 For the above example: Na = 5, Nair = 5, Nabs = 2 Waming: Nair > 1

MeshIn- 14 AA termination / Circular / Cavity-backed Line #1: 0 2 1 (printed) Line #2: 1 5 Line #3: 1 Line #4: 2 3 2 AA termination / Circular / Microstrip Line #1: 0 2 1 (printed) Line #2: 1 5 Line #3: 0 Line #4: 5 2

MeshIn- 15 AA termination / Rectangular Line #1: 0 3 1 or 030 (printed or slot) Line #2: R R I I O Ax (sampling cell size in x-direction). Ay (sampling cell size in y-direction) - NxA (number of antenna cells in x-direction) - NyA (number of antenna cells in y-direction) I -- n. Ti_ 1 - r-nuiltu-karlvAA l- mifrroctrin Line5: A Do- aIv=iLY-ua~uU, v - niaubp ^ cavity-backed 'Line#4: I I I I I I NxC (# of cells between the antenna and the cavity wall in x-direction) - NyC (# of cells between the antenna and the cavity wall in y-direction) b NxAir (# of air gap cells in x-direction), NyAir (# of air gap cells in y-direction) NxAbs (# of absorber cells in x-direction) N NyAbs (# of absorber cells in y-direction) 'Line#4: I I I I NxAir (# of air gap cells in x-direction) ' NyAir (# of air gap cells in y-direction) - NxAbs (# of absorber cells in x-direction) ', NyAbs (# of absorber cells in y-direction) microstrip --- —------------------ ---------- ----------- microstrip I I I I I I I I Definition of te parameters cavity-backed mircrostrip Antenna Cavity wall Absorber region I Il Antenna Ill-f '-uv5I,, I i I I I 1! I i i I I I i "l io =............:'!!!!f! IlrLJ WlM 1- Absorber region. — I —~ I L Air gap region - -. -. Air gap region For the above example: NxA = 24, NyA =4, NxC = 2, NyC = 3, NxAir = 2, NyAir= 3, NxAbs = 2, NyAbs = 2 Warning: NxAir, NyAir > 0 For the above example: NxA = 12, NyA = 2, NxAir = 2, NyAir= 3, NxAbs = 1, NyAbs = 1 Warning: NxAir, NyAir > 1

MeshIn- 16 AA termination / Rectangular / Cavity-backed Line #1: Line #2: Line #3: Line #4: 0 1 1 2 3 0 (slot) 1 24 4 3 2 3 2 2 Setup Mesh Commands to get Commands for mo AA termination / Rectangular / microstrip Line #1: Line #2: Line #3: Line #4: 0 3 0 (slot) 1 1 12 2 0 23 11