# Half wave dipole with parasitic element, (Gain calculation)

good morning all,

I have difficulties to find the correct formula that allows me to calculate the gain of half wave dipole in parallel with another parasitic half wave dipole.

I'm trying to calculate the gain(theta,phi) of this array for different distances bentween the two dipoles.

I found the equation $$|E_T|$$ down below and i want to know how can i calculat the gain frome this equation ?

I'm admitting the reciprocity of the antennas so:

$$Z_{21}=Z_{12}$$ and $$Z_{11}=Z_{22}$$.

$$\gamma_{12}=\frac{Z_{22}-Z_{0}}{Z_{22}+Z_{0}}$$ and $$\gamma_{12}=\frac{Z_{12}-Z_{0}}{Z_{12}+Z_{0}}$$

$$Z_{11}=73.12 +42.54i$$

$$\beta=\frac{2\pi}{\lambda}$$

$$E_{T}=\frac{KI_{1}}{r} \sqrt{1+\frac{|Z_{12}|^2}{|Z_{22}|}-2\frac{|Z_{12}|}{|Z_{22}|}\cos(\gamma_{12}-\gamma_{22}-\beta d \cos{\phi\sin{\theta})}}$$

I plotted the value of $$Z_{21}$$ with respect of d (separation distance between the dipoles

Best regards

• Does the graph illustrate the difference between the calculated results of the equations and NEC2 simulations? Oct 8 '20 at 12:17
• Hey Tarik, I tried to write the equation in MathJax. How did I do? I couldn't read a few of the subscripts. If I made any mistakes please let me know in the comments and I'll fix them, or edit the question if you want to fix them yourself. Oct 13 '20 at 19:48
• Hello @rclocher3, thanks a lot, i just rewrite the question and gave some data :) Oct 21 '20 at 14:38
• the equation is frome : LES ANTENNES Théorie, conception et applications, Odile Picon, P266, book in french Oct 21 '20 at 14:45

The demo version of EZNEC software (free) would be able to do that, with a fairly short learning curve: https://www.eznec.com/demoinfo.htm

• Thanks a lot sir. I already did it with EZNEC and 4NEC2, but i'm looking for the right mathematical formula. Oct 8 '20 at 8:03