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# How to simulate GVD using HFSS

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#### x529

##### Junior Member level 3
How to simulate GVD using HFSS？

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Are you obtaining the data from a dispersion simulation, or a driven simulation? The dispersion will directly give you Beta as a function of frequency, but if your structure isn't continuous or periodic this wouldn't be the most appropriate.

You can extract Beta from the scattering parameters of a driven simulation through assuming homogenization (i,e, convert the scattering parameters to something like ABCD parameters, and Beta will be imag{acos(A)/l}, where l is the length of your homogenized line).

You can take the derivative in either of these cases by using the "deriv" function in the output variables (HFSS->Results->Output Variables)

### x529

Points: 2
Are you obtaining the data from a dispersion simulation, or a driven simulation? The dispersion will directly give you Beta as a function of frequency, but if your structure isn't continuous or periodic this wouldn't be the most appropriate.

You can extract Beta from the scattering parameters of a driven simulation through assuming homogenization (i,e, convert the scattering parameters to something like ABCD parameters, and Beta will be imag{acos(A)/l}, where l is the length of your homogenized line).

You can take the derivative in either of these cases by using the "deriv" function in the output variables (HFSS->Results->Output Variables)
Thanks for your apply. I tried to use group delay results to calculate GVD in HFSS.
The group delay dispersion (also sometimes called second-order dispersion) of an optical element is a quantitative measure for chromatic dispersion. It is defined as the derivative of the group delay, or the second derivative of the change in spectral phase, with respect to the angular optical frequency:
(https://www.rp-photonics.com/group_delay_dispersion.html)

For two-port networks/devices, HFSS has group delay result, group delay(2,1).
GVD=GDD/distance,
(1) To get group delay in HFSS. Group delay is a function of frequency f.

Using Matlab/Python for data processing
(2) GDD is defined as the derivative of the group delay.
To get GDD: Solve for the partial derivative of group delay. w=2*pi*f, then GDD is the partial derivative of group delay with respect to frequency.

(3) To get GDD: Divide by length.

Solving GVD Using Partial Derivatives of Group Delay；
I think this approach is correct in physically, but I'm not sure this is the right approach;

I wasn't aware that HFSS had a built-in group delay function, shows what I know! Thanks for pointing that out.

Your statements looks fine, expect I think item (3) should read: to get GVD: divide GDD by length. This is because GDD measures the second derivative of phase, whereas phase is Beta x Length, and GVD measures the second derivative of Beta.

x529

### x529

Points: 2
I wasn't aware that HFSS had a built-in group delay function, shows what I know! Thanks for pointing that out.

Your statements looks fine, expect I think item (3) should read: to get GVD: divide GDD by length. This is because GDD measures the second derivative of phase, whereas phase is Beta x Length, and GVD measures the second derivative of Beta.
Thanks for your apply. I think you are right. I'm glad I learned something new

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