Tutorial: Circular Waveguide

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  • Download the latest matlab file using Github: Circ_Waveguide.m
  • Simulation Time: ~ 7 min for a 2m long waveguide

We will cover in this tutorial:

  • setting up a cylindrical mesh
  • setup a mode profile excitation
  • create voltage and current probes using the mode profile
  • calculate the waveguide impedance and S-Parameter


First Steps

Matlab Simulation Script

  • Start the script within an empty environment:
close all
  • Setup the simulation parameters
unit = 1e-3; %drawing unit in mm
% waveguide dimensions
length = 2000;
rad = 350;     %waveguide radius in mm
% frequency range of interest
f_start =  300e6;
f_stop  =  500e6;
mesh_res = [10 2*pi/49.999 10]; %targeted mesh resolution
  • Set cylindrical FDTD parameters and the Gaussian excitation pulse
FDTD = InitFDTD('EndCriteria',1e-4,'CoordSystem',1);
FDTD = SetGaussExcite(FDTD,0.5*(f_start+f_stop),0.5*(f_stop-f_start));
% boundary conditions
BC = [0 0 0 0 3 3]; %pml in pos. and neg. z-direction
FDTD = SetBoundaryCond(FDTD,BC);
  • Define the cylindrical homogeneous mesh
CSX = InitCSX('CoordSystem',1); % init a cylindrical mesh
mesh.r = SmoothMeshLines([0 rad], mesh_res(1)); %mesh in radial direction
mesh.a = SmoothMeshLines([0 2*pi], mesh_res(2)); % mesh in azimuthal dir.
mesh.z = SmoothMeshLines([0 length], mesh_res(3));
CSX = DefineRectGrid(CSX, unit,mesh);
  • Apply waveguide ports
start=[mesh.r(1)   mesh.a(1)   mesh.z(8)];
stop =[mesh.r(end) mesh.a(end) mesh.z(15)];
[CSX, port{1}] = AddCircWaveGuidePort( CSX, 0, 1, start, stop, rad*unit, 'TE11', 0, 1);
start=[mesh.r(1)   mesh.a(1)   mesh.z(end-13)];
stop =[mesh.r(end) mesh.a(end) mesh.z(end-14)];
[CSX, port{2}] = AddCircWaveGuidePort( CSX, 0, 2, start, stop, rad*unit, 'TE11');
  • Define a dump box using the HDF5 file format
CSX = AddDump(CSX,'Et','FileType',1,'SubSampling','4,4,4');
start = [mesh.r(1)   mesh.a(1)   mesh.z(1)];
stop  = [mesh.r(end) mesh.a(end) mesh.z(end)];
CSX = AddBox(CSX,'Et',0 , start,stop);
  • Save & Run the simulation
Sim_Path = 'tmp';
Sim_CSX = 'circ_wg.xml';
[status, message, messageid] = rmdir(Sim_Path,'s');
[status, message, messageid] = mkdir(Sim_Path);
WriteOpenEMS([Sim_Path '/' Sim_CSX],FDTD,CSX);
RunOpenEMS(Sim_Path, Sim_CSX)


  • Calculate s-parameters and waveguide impedance
freq = linspace(f_start,f_stop,201);
port = calcPort( port, Sim_Path, freq);
s11 = port{1}.uf.ref./ port{1}.uf.inc;
s21 = port{2}.uf.ref./ port{1}.uf.inc;
ZL = port{1}.uf.tot./port{1}.if.tot;
  • Plot S-Parameters
xlim([freq(1) freq(end)]*1e-6);
grid on;
hold on;
l = legend('S_{11}','S_{21}','Location','Best');
ylabel('S-Parameter (dB)','FontSize',12);
xlabel('frequency (MHz) \rightarrow','FontSize',12);
  • Compare analytic and numerical wave-impedance
hold on;
grid on;
ylabel('ZL (\Omega)','FontSize',12);
xlabel('frequency (MHz) \rightarrow','FontSize',12);
xlim([freq(1) freq(end)]*1e-6);
l = legend('\Re(Z_L)','\Im(Z_L)','Z_L analytic','Location','Best');


Waveguide line impedance
Waveguide scattering parameters


  • Try different/multiple modes for excitation/detection
  • Add an unsymmetrical dielectric material load to see a mode-conversion (multiple mode detection necessary)
  • Try adding a periodic dielectric material to see a frequency selective reflection (Bragg reflections)

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