# Dipole array antenna radiation pattern

I have the radiation pattern for a dipole antenna with working frequency of 11 GHz, it looks like figure 1. I wanted to create an array antenna consisting of 2 elements with that same individual radiation pattern and a spacing of 0.75*wavelength, it should look something like figure 2.

My doubt is, how do I create the antenna pattern for the array, with the single element radiation pattern? In other words, how do I create figure 2 using figure 1?

Figure 1

Figure 2

• What makes you think that there's a simple transformation that you can apply to Figure 1 to get Figure 2? The software that created these figures went to a lot of work to integrate the field contributions of the two conductors. – Dave Tweed Jul 6 '20 at 23:13
• @DaveTweed Why do you assume that I think there is a simple transformation? The figure 1 to figure 2 think was just a way of talking. – DaDSPGuy Jul 6 '20 at 23:19
• In your own words, "...how do I create figure 2 using figure 1?" How else was I supposed to interpret that? – Dave Tweed Jul 6 '20 at 23:27
• @DaveTweed You totally missed my first question: “how do I create the antenna patter for the array with the single element radiation pattern?”. Anyways, you’ve been very helpful – DaDSPGuy Jul 6 '20 at 23:30
• If I understand the question correctly, you're trying to create a standard linear antenna array consisting of two elements. The total radiation pattern of such an array is approximated by the product of the element factor (your first figure, the pattern of a single element), and the array factor (the pattern resulting from the constructive/destructive summation of the two patterns, assuming omnidirectional antennas). There's complete derivations in many antenna books, for example Stutzman and Thiele's Antenna Theory and Design. – LetterSized Jul 7 '20 at 0:02

Part of the answer is in the comments of the question. In order to compute the directivity of an array antenna first you need to compute the electrical field produced by one of the antenna elements. Once you have computed it, you will need to compute the array factor, which is given by

$$AF(\theta, \phi) = \sum_{m = 0}^{N - 1} I_m e^{j(k \hat{r} \cdot \mathbf{r_m})}$$

with $$\mathbf{r_m}$$ being the position vector the element m of the antenna, $$I_m$$ the complex amplitude of the excitation of the element m, and $$\hat{r} = \sin{\theta} \; cos{\phi} \; \hat{x} + \sin{\theta} \; \sin{\phi} \hat{y} + \cos{\theta} \; \hat{z}$$

The total array pattern is given by the multiplication of the array factor and the element radiation pattern, the previously computed electrical field of the antenna element. Finally, the directivity is given by

$$D = \frac{U(\theta, \phi)}{\frac{1}{4\pi} \int_0^{2\pi} \int_0^{\pi} \frac{U(\theta, \phi)}{\max{\{U(\theta, \phi)\}}} \sin{\theta} d\theta d\phi}$$

where $$U(\theta, \phi)$$ is the radiation pattern. The radiation pattern is given by

$$U(\theta, \phi) = |B(\theta, \phi)|^2$$

with $$B(\theta, \phi)$$ being the normalized total array pattern.

Please note that the spherical coordinates are given by figure 1.

Figure 1