Calculating the Values of E and H Fields on the Surface

How do you calculate the values of E and H fields on the surface of an object solved as an IE hybrid region (or in HFSS IE design)?

If an object is solved using the IE solver, the E and H fields are not available through the standard field reporter. The IE solver is used either in HFSS IE Design or inside Finite Element Method (FEM) Design if the object is assigned as an IE hybrid region. The standard fields reported in these cases are electric and magnetic surface current densities and charges: J, Jm,Q,,and Qm. It is possible to use Maxwell’s equations to reconstruct values of electric and magnetic fields on the surfaces if necessary. For example, for a metal object solved with the IE solver, the magnetic current and charge density are equal to zero: Jm=0, Qm=0.

We assume that E and H fields inside the conductor are 0, from Maxwell’s equations: n dot D = Q, where D=ε*E.

For a metal object in a vacuum: E_normal to surface = Q/ε _o, where the boundary condition is n cross H = J.

For a lossy metal object in vacuum: H_tangential to surface = J, and the E_tangential can be calculated using the surface impedance definition:

E_tangential to surface = Zs*(n cross H_tangential to surface), where Zs is a surface impedance: Zs=(1+j)/(conductivity*skin_depth)

Note that for a good conductor, the surface impedance is very small compared to free space (for copper at 1 GHz: (8e-3)*(1+j) Ohm, so the value of E_tangential is expected to be very small compared to E_normal).

Solution Document