I am interested in calculating the input impedance \$Z_{in}=R_{in}+jX_{in}\$ of a dipole antenna numerically. However, I am unsure how I would compute the imaginary part of the impedance (\$X_{in}\$).

In order to compute \$R_{in}\$ of a dipole of length \$l\$ which is fed with a current of frequency \$\omega\$ and is oriented along the z-Axis, I would follow the following steps (conceptually):

  1. Assume a standard sinusoidal current distribution on the antenna \$\underline{I}(z)\$.
  2. Compute the vector potential \$\underline{\vec{A}}(\vec{r})\$ from this current distribution.
  3. Compute the magnetic field \$\underline{\vec{H}}(\vec{r})\$ and the electric field \$\underline{\vec{E}}(\vec{r})\$ from the vector potential.
  4. Compute the far-field energy-flux (Poynting-Vector) of the field \$\underline{\underline{\vec{S_{ff}}}}(\vec{r})=\frac{1}{2}\underline{\vec{E}}(\vec{r})\times\underline{\vec{H}}^{*}\$
  5. Compute the overall power which is radiated by the dipole : \$P_{\mathrm{rad}}=\iint_{B_{R}}\underline{\underline{\vec{S_{ff}}}}(\vec{r})\cdot d\vec{A}\$

So in this case, since I know the input current which is fed into the antenna \$\underline{I}(z=0):=\underline{I}_{0}\$ and since I can calculate the radiated power \$P_{\mathrm{rad}}(\underline{I}_{0})\sim I_{0}^2\$ I would be able to calculate \$R_{in}\$ from \$P_{\mathrm{rad}}=R_{in} I_{0}^2\$.

Is there a way to calculate the reactance of the dipole antenna \$X_{in}\$ from the fields \$\underline{\vec{E}}(\vec{r})\$ and \$\underline{\vec{H}}(\vec{r})\$?

The result that I am looking for looks like this:

enter image description here


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