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# complex fields problem in a circular wave guide

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#### oldsamples

##### Newbie level 3
First of all hello to all of you and I wish you a happy new year!

I am quite, quite new in this forum and also in the topic.
I need to design a cylindrical cavity in HFSS. In order to start understanding HFSS I decided to create some referential structures and compare the results for a case where I can analytically obtain results the same simple structures using MATLAB. To be more specific I made a circular waveguide in Matlab and now I want to compare it with the very same but in HFSS.
Here is my initial data:

freq ~1.93e+09
cutoff freq = 1.755e+09
the calculated value for the guide wavelength in Matlab and HFSS matches ~ 0.15511m
the mode I use is TE, n=1, m=1.
I have 0.5 meters in axial direction for both the simulation and the program in Matlab
I don't have losses - the surface is PEC

Once I obtained the propagation constant I calculated the complex fields in MATLAB and wanted to see if they will be the same in HFSS.

In MATLAB what I plot is a 2d plane of the fields where the coordinates are in the range
rho [0 to radius], z [0 to 0.5m], phi is equal to pi/2, All fields are relative to amplitude 1.
Since this is in cylindrical geometry the equivalent plane in HFSS is the yz plane.
So the components to compare between Matlab and HFSS respectively are:

Eφ is -Ex
Eρ is Ey
Hz = Hz
etc.

So I want to compare the real and imaginary parts for all the components of the E and H.
I created them with the help of the calculator and I plotted them. The wavelengths are the same with those that I obtained with Matlab, but the phases of the signal differ.

for example the expression that I use in Matlab in order to obtain the Hz field in the TE 11 is:

Hz = besselj(n,rho*K_cut)*(A*sin(n*phi) + B*cos(n*phi))*exp(-γ*z)*exp(alpha*z)
for z 0 to 0.5 m I get the axial field Hz starting from amplitude 0.5 (1 is maximal amplitude)

However in HFSS I get the same plot relative to 1 watt but Hz starting from 0 at points y=radius, z=0.
The signal has pi/2 difference right from the start and I cannot understand why, since my formula is not showing that. It is not my integration line because this will lead only to change of the sign coming from: (A*sin(n*phi) + B*cos(n*phi))
Also in HFSS I have 0 as the initial phase of the source signal. The end of this structure is another wave port in order to be a perfectly matched end.
I have similar problems with the axial and radial distribution for the other field components. What is that I am doing wrong?
I will appreciate for the help and I really apologize for my lame English.