rabiazainab
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If your ground plane acts as a ground plane, influence of ground plane size variations should be well below the influence of patch size variations.
When your ground plane is not much larger then the patch size, there is dependency between antenna parameters and ground plane size, so it is normal that you experience this. If you want less dependency, you may increase the ground plane size.
Just to make sure: what happens when you reduce the meshing size to (for example) 70% (so reduce it with 30%)?
Using (grounded) CPW: is this a requirement as microstrip works very well also?
When the characteristic impedance of the CPW equals the reference impedance for your smith chart (the source in the simulator), the length does change S11, but not |S11| (it only rotates around the origin of the Smith Chart).
If Zcpw is not equal to Zsource, then |S11}, VSWR, return loss, etc will change. Very likely your simulator has an add-on utility to design the CPW. When the ground plane is close to the CPW, Z0 reduces significantly.
Do you have ground under your CPW? If so, when you change the length of the CPW, you also should change the length of a finite groundplane. Changing the size of a relatively small ground plane, will change the antenna's input S11.
There can be some change in |S11| even when Zcpw = Zsource. This happens when a common mode current exists on the CPW. In other words the CPW becomes part of the radiating structure of the antenna.
Can you post your structure (inclusive (finite) ground plane if present)?
Regarding how to make them equal, try a search on CPW impedance. You can check the CWP impedance by simulating a CPW section terminated on both sides with a port. Do a frequency sweep where the line length varies at least with 0.25 lambda. S11 (or S22) should be close to the origin for the full sweep range. If not, Zcpw <> Zsource, or there is something not well in de port definition. When looking to S12 or S21 you can also calculate the loss of your CPW structure.
1. Uncheck the renorm all modes box on your port and look at setup->matrix and see that port impedance is 77 ohms not the 50 you are targeting. For 50 ohms from TXline program linewidth of feedline should be 0.29mm keeping all other parameters same.
2. Remove the PerfE boundaries from copper objects.
3. Thickness of metal will have an effect, more capacitance to ground conductors.
4. Why do you have a finite conductivity boundary on the bottom of the airbox way below the substrate ground? Probably delete this unless your board is floating over a metal object in which case you would use an infinite ground plane I'd think.
5. In general, assign boundaries to faces/planes not 3D objects
6. You may find it helpful to use variables to set linewidth, gap, patch_width, patch_length, then changes are quicker.
7. Consider making the top ground plane smaller than your bottom ground plane and see effects on gain and resonant frequency.
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