Modeling Printed Antennas Using The Matlab Antenna Toolbox Wajih Iqbal Clemson University Advisor: Dr. Martin Outline Background Integral equations and method of moments overview Formulating the antenna model LP patch antenna Future work Background Graduate students usually use Ansoft HFSS for antenna modeling Too complicated and expensive for undergrads A much easier and user-friendly code has been developed by Makarov (Worcester Polytechnic Institute) called the Matlab Antenna Toolbox (MAT) Background (contd) The code is based on method of moments and is limited to about 7000 unknowns The code is reasonably precise for simple printed antennas I have modeled and studied 15 different antenna structures Integral Equations and Method of Moments Overview Statement of an Electromagnetic Boundary Condition Consider an incident wave (with no z variation i.e. 2D problem) 5 E Exsxi+ = 0 on stripP e r f e c t l y c o n d u c t i n gt h i n s t r i p- w|ixwyEi9 0 - |i|iFormulation of an Integral Equation E xkddxk Jx H kx x dxxswwbg bg c hbg= +FHGIKJ' ' 'zq422202E Exsxi+ = 0 on stripE E exi i ijk xi=0 sincos||e j( ),s ix xE E x w w = e The Electric Field Integral Equation q4202kk Jx H kx x dxww' ' 'RSTzbg c hbg+'' ' 'UVW= e zddxddxJx H kx x dx E x x w wwwxibg c h bg b gbg02,The current on the strip is the unknown to be determined. The unknown quantity is under the integral sign. J w Jw = =b g bg0Solution of Integral Equations (MoM) Step 1: Approximate unknown (surface current) by means of a finite sum of N known functions each with an unknown coefficient. ( )1( )Nn nnI=~Jr f rThree Major Steps +'' ' 'UVW= e zddxddxJx H kx x dx E x x w wwwxibg c h bg b gbg02,Solution of Integral Equations (MoM) Step 2: Substitute the approximation (Step 1) into the IE and establish a well-conditioned system of linear equations by enforcing the resulting equations over N subintervals which are within the interval where a solution is desired ( )1( )Nn nnI=~Jr f rq4202kk Jx H kx x dxww' ' 'RSTzbg c hbg(substitute and apply testing function) 1 11 2 12 3 13 4 14 11 21 2 22 3 23 4 24 21 31 2 32 3 33 4 34 31 41 2 42 3 43 4 44 4for subinterval 1for subinterval 2for subinterval 3for subinterval 4iiiiJ Z JZ JZ JZ EJ Z JZ JZ JZ EJ Z JZ JZ JZ EJ Z JZ JZ JZ E+ + + =+ + + =+ + + =+ + + =JZ E m Nn mn minN= ==, , , , 121Solution of Integral Equations (MoM) Step 3: Solve the N by N linear system of equations from step 2 and thereby obtain values for the coefficients. 11 12 13 14 1121 22 23 24 2231 32 33 44 3341 42 43 44 44iiiiZ Z Z Z JEZ Z Z Z JEZ Z Z Z JEZ Z Z Z JE ( (( ( (( ( (( =( (( ( (( ( Z J Emn n mi=111 12 13 14 1121 22 23 24 2231 32 33 44 3341 42 43 44 44iiiiZ Z Z Z JEZ Z Z Z JEZ Z Z Z JEZ Z Z Z JE ( (( ( (( ( (( = ( (( ( (( ( | | | |1in mn mJ Z E (= Once we have found J(r) we can find all the radiation properties of the antenna Why Printed Antennas? Printed antennas are low-profile planar structures that utilize printed circuit board (PCB) technology They are compact, low cost, easy to manufacture and suitable for integration with electronic systems Multi-band operation can also be achieved by integrating several coupled printed antenna elements of different lengths and geometries on the same PCB Dimension can be smaller with higher dielectric GPS, Radar, Satellite communication, Military, cell phones, and wireless laptops Execution Flow Chart Create 2D geometry Create 3D geometryand feed PatchGround Plane Feeding Probe MoM Calculations q4202kk Jx H kx x dxww' ' 'RSTzbg c hbg+'' ' 'UVW= e zddxddxJx H kx x dx E x x w wwwxibg c h bg b gbg02,JZ E m Nn mn minN= ==, , , , 121( )1( )Nn nnI=~Jr f rZ J Emn n mi= Input impedance/ Return loss Near field and farfield properties -0.02-0.0100.010.02-0.03-0.02-0.0100.010.020.0300.511.5x 10-3xyzPatchGround Plane Feeding Probe Formulating the Antenna Model Design: Dielectric View with Dielectric View without Dielectric Linearly polarized patchantennaPatch is 30x40mmGround plane is 50x60mm Substrate has r = 2.55 Side View Patch Ground Plane Feeding Probe 2-D Mesh Projection Feed point Patch Ground plane Volume Mesh Generation Layer(s) properties Substrate structure Ground plane Vertical metal faces Feeding points Patch 3D model ready! Properties of the Patch Antenna 4800 unknowns took 1.5 hours for 50 frequency points (65sec for each point) Input Impedance Solid line Matlab Dotted line Ansoft HFSS Resonance Properties of the Patch Antenna Return Loss 2.93 GHz2.99 GHz2.96 GHz2.99 2.932%2.96Bandwidth= =Far Field Properties Directivity (xz-plane)Co-polar dominates At 2.96GHz Front to back ratio is about 10dB Far Field Properties Total Directivity (dB)3D Directivity The maximum directivity is approximately 7.4 dB at zenith Near Field Properties z-Directed Electric Fieldx-Directed Electric Field xy y-Directed Electric Field Near Field Properties Surface Current Distribution (x-directed)Surface Current Distribution (y-directed)Surface Current Distribution (z-directed) Future Work Simulate more multiband antennas accordingly with future wireless communication needs Incorporate the genetic algorithm with the code for antenna optimization After convergence studies construct and test a multiband antenna in the spherical near field chamber Acknowledgements Dr. Anthony Martin Dr. Daniel Noneaker Dr. Xiao-Bang Xu Michael Frye Questions ? ? ? ? ? ? ? ?