Master Slave Boundary in HFSS
I know they are used to model the periodic structures and are used to plot dispersion curves.
My question is how can we relate Master and Slave boundary conditions with PEC and PMC boundaries.
I need help
I explain my question further
If we have waveguide we define PEC at both ends as boundaries we get one set of resonance frequencies changing it to PMC boundary generate another set and if we have PEC at one end and PMC at the other we have resonance frequency which lies between two extremes defines by PEC and PMC on both ends.
Now if we replace both ends with master and slave at 90 phase advance we can generate same set of resonance frequencies as PEC at one end and PMC on the other. so I conclude that Master slave boundary condition with 90 phase advance is same as PEC at one end and PMC on other.
How can I map the other two case which are PEC on both ends and PMC on both ends
The PEC and PMC cases represent two extremes with similar behavior in that they don't allow power to pass through them. These points also exist on a 1D dispersion diagram at the 0 and 180 degree points, where the dispersion is flat for non-TEM, continuous-structure modes (indicating zero group velocity and hence, no power flow). Usually, you'll find that one corresponds to a PEC condition and the other to a PMC condition.
I'm not sure about the 90-degree point, that sounds a bit sketchy. If you plot the Poynting vector, I would expect it to be non-zero through at least one of the sides.
That was very elaborate answer I was also expecting this while I was searching for trapped modes in the structure. So I replaced Master and Slave with PEC on both ends and then PMC but I have following observations
1. Few resonance frequencies vanish completely
2. Some new resonance frequencies appear
So what I am getting in this case does not correspond to the modes with extreme cases of master and slave with 0 and 180 phase advance.
This I have found by simulation as 90 phase advance in master and slave boundary corresponds exactly to dispersion curve with PEC and PMC which was expected for me
That's interesting, thinking about it further I guess it's possible since if the faces are parallel they enforce orthogonal field conditions -- I've just never come across it.
It must have no power flow through the master/slave boundary conditions, though, is that correct?
Let me explain a bit about what I want to do?
I found a mode at 9.33417 GHz which had same frequency throughout the dispersion curve.
Since it was not dependent on boundary conditions of Master and Slave case so it was a good candidate for trapped mode.
To dig out further I need to find the two frequencies of mode fe with PEC as boundary conditions and fm with PMC as boundary conditions so that i may calculate K
K = 2|fe-fm|/fe+fm
But to this point I am not able to co relate my dispersion frequencies with master and slave boundary condition to PEC and PMC as whole the world changes.
So I am stuck
I don't know much about that equation, but I doubt it depends on the reference plane used for the start/end of each period.
Since your fields are maximum on the current boundaries, you want to shift this reference plane (the start/end position of each period) by half the period, such that the fields are maximum near the middle of the unit cell instead of the outer edges.
In this case, I would think that using PMCs/PECs shouldn't change much, and I would expect those two frequencies to be the same.
What you mean by reference plans?
And what attacking strategy I can use with HFSS to solve this issue means so that I can prove my point that extreme point of Master and slave dispersion curves correspond to PEC and PMC boundary conditions
The reference plane is simply the plane in each cell where you have applied your master/slave boundary.
Since a 1D periodic structure such as this exhibits translational symmetry, the dispersive properties of the unit cell won't change if you were to recreate your unit cell with the narrowest channel points on the outside edges of the unit cell with the widest cavity point in the middle (shift by half a period along the z-axis, according to your figure above).
However, this will change the effects that PEC/PMC boundaries have on the various modes.