Optimal microstrip lumped port size/placement and Thirds Rule question.

[georgy-moshkin]

FDTD Mesh page of OpenEMS wiki mentions Thirds Rule: "...to put a mesh line 1/3 inside and 2/3 outside the metal." From my understanding, the thirds rule is especially important for sparse FDTD grid (low resolution grid). Image above shows four arrangements:
1 - "standard" placement. This is what we usually see in commercial simulators. Note that port width is not aligned with vertical mesh lines. I don't know if this a problem, but port will not work if it is not aligned with horizontal mesh line.
2 - Horizontal mesh line and lumped port are placed 1/3 * max_res from microstrip edge. Lumped port thickness is 2 * 3 * max_res.
3 - The same as (2), but port width is decreased to be aligned with "1/3" rule mesh lines
4 - The same as (1), but horizontal mesh line and port are placed 1/3 * max_res away from microstrip edge
I know that using 1/3 rule doesn't make much sense on a port (vertical direction), it's just to make grid and placement more uniform.
My question is about port width. Should it be aligned with mesh lines or with metal width? I use OpenEMS for my educational project and want to use best approach in my examples. Most likely case 1 is the best option if mesh is dense enough. Are there any know-hows on port placement, especially for sparse mesh?

Case 1:

start = [-feed.width/2 feed.pos 0];
stop  = [feed.width/2 feed.pos substrate.thickness];

mesh.x = [mesh.x -feed.width/2-max_res/2*0.66 -feed.width/2+max_res/2*0.33 feed.width/2+max_res/2*0.66 feed.width/2-max_res/2*0.33]
mesh.y = [mesh.y feed.pos];

Case 2:

start = [-feed.width/2 feed.pos+2*max_res/2*0.33 0];
stop  = [feed.width/2 feed.pos substrate.thickness]

mesh.x = [mesh.x -feed.width/2-max_res/2*0.66 -feed.width/2+max_res/2*0.33 feed.width/2+max_res/2*0.66 feed.width/2-max_res/2*0.33]
mesh.y = [mesh.y feed.pos+max_res/2*0.33];

Case 3:

start = [-feed.width/2+max_res/2*0.33 feed.pos+2*max_res/2*0.33 0];
stop  = [feed.width/2-max_res/2*0.33 feed.pos substrate.thickness]

mesh.x = [mesh.x -feed.width/2-max_res/2*0.66 -feed.width/2+max_res/2*0.33 feed.width/2+max_res/2*0.66 feed.width/2-max_res/2*0.33]
mesh.y = [mesh.y feed.pos+max_res/2*0.33];

Case 4:

start = [-feed.width/2 feed.pos+max_res/2*0.33 0];
stop  = [feed.width/2 feed.pos+max_res/2*0.33 substrate.thickness];

mesh.x = [mesh.x -feed.width/2-max_res/2*0.66 -feed.width/2+max_res/2*0.33 feed.width/2+max_res/2*0.66 feed.width/2-max_res/2*0.33]
mesh.y = [mesh.y feed.pos+max_res/2*0.33];

[georgy-moshkin]

Answering my own question. I did a lot of tests using 50 Ohm line and came up to a conclusion that first case placement is enough. I found out that unwanted variation in impedance was caused by the automatically generated mesh and not by the port itself. I excluded port from DetectEdges() function:
mesh = DetectEdges(CSX, mesh,'ExcludeProperty',{'patch','network','port_excite_1','port_resist_1'});
and created mesh lines manually. I've noticed that 4 cells + 1/3 rule at the edges may not be enough: 50 Ohm impedance sometimes goes up to 60 Ohm, which causes a accumulating mismatch on power dividers connected in series. After adding more cells manually I get correct results. To sum up, I used the wrong approach: tried different port geometry while the problem was caused by meshing.

[Miceuz]

@georgy-moshkin I am going thru similar steep self-teaching curve.

Can you please elaborate a bit more on 4+1/3 rule - do you mean 2 cells inside of microstrip and 2 on the sides where 1/3 of them is taken by microstrip, just like in your picture?

Then you state that this is not enough to achieve accuracy. Can you elaborate and maybe post a screenshot - what is enough for accuracy in your case? Do you split internal 2 cells into more, say 4 and leave 2 coarse cells on the outside or do you split to finer mesh but still make sure that external cells still comply with 1/3 rule?

Basically my question is where do we need finer mesh - inside of microstrip only or both inside and on the boundary of microstrip?

[georgy-moshkin]

We need finer mesh on the edges (left, right) and possibly at the ports too. Or simply use finer mesh everywhere.
Here is what I did:

  % "1/3" rule for patches and inset cutouts

  for sx = 0:patch.NX-1
    offs.X=sx*patch.step-(patch.NX-1)*patch.step/2;
    x=-patch.width/2+offs.X;

    mesh.x = [mesh.x  x-max_res*0.66  x+max_res*0.33];
    mesh.x = [mesh.x -x+max_res*0.66 -x-max_res*0.33];

    x=feed.width/2+inset.width+offs.X;
    mesh.x = [mesh.x  x-max_res*0.66  x+max_res*0.33];
    mesh.x = [mesh.x -x+max_res*0.66 -x-max_res*0.33];
  endfor

  for sy = 0:patch.NY-1
    offs.Y=sy*patch.step-(patch.NY-1)*patch.step/2;
    y=-patch.length/2+offs.Y;
    mesh.y = [mesh.y  y-max_res*0.66  y+max_res*0.33];
    mesh.y = [mesh.y -y+max_res*0.66 -y-max_res*0.33];

    if (mod(sy, 2) != 0)
      y=-patch.length/2+inset.length+offs.Y;
      mesh.y = [mesh.y  y-max_res*0.66  y+max_res*0.33];
    else
      y=-(-patch.length/2+inset.length)+offs.Y;
      mesh.y = [mesh.y  y+max_res*0.66  y-max_res*0.33];
    endif

  endfor


  % Extra cells for main feeding network
  res=max_res/4;

  % "1/3" rule for 50 ohm feeding lines
  mesh.y = [mesh.y -mainFeed.width/2+res*0.33+move90 mainFeed.width/2-res*0.33+move90];
  mesh.y = [mesh.y -mainFeed.width/2-res*0.66+move90 mainFeed.width/2+res*0.66+move90];
  mesh.x = [mesh.x -mainFeed.width/2+res*0.33 mainFeed.width/2-res*0.33];
  mesh.x = [mesh.x -mainFeed.width/2-res*0.66 mainFeed.width/2+res*0.66];

  % "1/3" rule for quarterwave transformer
  mesh.x = [mesh.x -trans.W/2+res*0.33 trans.W/2-res*0.33];
  mesh.x = [mesh.x -trans.W/2-res*0.66 trans.W/2+res*0.66];
  mesh.y = [mesh.y mainFeed.width/2+trans.L-res*0.33+move90];
  mesh.y = [mesh.y mainFeed.width/2+trans.L+res*0.66+move90];

  % mesh lines for 100 Ohm sections
  mesh.x = [mesh.x linspace(-patch.step/2-feed.width/2,-patch.step/2+feed.width/2,4+1)];
  mesh.x = [mesh.x linspace(patch.step/2-feed.width/2,patch.step/2+feed.width/2,4+1)];

  % mesh lines for feeding port
  mesh.y = [mesh.y mainFeed.posY];
  mesh.y = [mesh.y mainFeed.posY+res];
  mesh.y = [mesh.y mainFeed.posY-res];


  mesh = SmoothMesh(mesh, max_res*2, 1.25, 'algorithm',3); % lgorithm=3 works nice

  CSX = DefineRectGrid(CSX, unit, mesh);

The most important part is that feeding network uses finer mesh than the patches (everything below "res=max_res/4" line).
Plus, I've added two more meshing lines near the feeding port. And then, final SmoothMesh(mesh, max_res*2,...
To sum up,

1. patches with resolution max_res
2. feeding network with resolution max_res/4
3. smooth mesh with resolution max_res/2 (this is for decrease computation time only, max_res/4 will be better).

For example, https://wiki.openems.de/index.php/FDTD_Mesh.html shows
a great image, but resolution is too low. Works for education, but before manufacturing this either correct result by some correction coefficient or something like that to shift S11/S22 measurements. A simple solution is to use higher resolution mesh for everything, but then need to wait much longer. So, we can force a finer mesh by placing manual max_res/4 lines on the edges of the line, and then let SmoothMesh() smooth it to a lower resolution mesh in empty space.

[KajWiik]

This thread saves a lot of time for me, many thanks!

[georgy-moshkin]

Here is a more intuitive explanation based on computer graphics example. Following image demonstrates 3D scene direct and indirect light calculation (radiosity approximation algorithm https://www.researchgate.net/publication/239562773).

Low-polygonal model on the right was used to calculate the light intensities, e.g., at the edges of each triangle. Then this low-resolution light distribution can be cleverly averaged to get the light distribution for the image on the left. Note that if we use less triangles for the low-resolution model, then it will be impossible to retrieve details such as shadow under the sphere. For example, if the floor consists only of two large triangles (4 vertices = 4 intensity values). The similar effect happens with FDTD: we can't get realistic electromagnetic light distribution if the polygonal mesh is too rough.

[KajWiik]

@georgy-moshkin I am still struggling with LumpedPorts, they have very slow convergence related to MSLPorts. What are your boundary sizes and conditions, it looks like that the ground plane is larger (longer) than the microstrip? Could you share your code?