Technical Notes > The HFSS Solution Process > Solution Types > Eigenmode Solutions               

Calculating the Resonant Frequency

Eigenmodes are the resonances of the structure. The eigenmode solver finds the resonant frequencies of the structure and the fields at those resonant frequencies. For a Driven Solution, HFSS solves the following matrix equation (for a lossless case):

(1)

where

• S and T are matrices that depend on the geometry, the materials, and the mesh.

• x is the electric field solution.

• k_o is the free-space wave number.

• b is the value of the source defined for the problem.

However, in order to find the resonances of the structure, the eigenmode solver sets b to zero, and solves the equation

(2)

for sets of (ko,x), one ko for every x. The variable x is still the electric field solution, and ko is the free space wave number corresponding to that mode. The resonant frequency of the eigenmode can be found using:

,

(3)

where

• c is the speed of light.