I was wondering if there was a mathematical way to combine two different types of antenna elements. Let's say that I have an antenna of $$\lambda/2$$ and I want to combine it with an antenna of $$\lambda/4$$. Since the beam pattern, as far as I know, is computed as:

$$BP = R_1(\theta, \phi) \cdot w_1 e^{-jkr_1} + R_2(\theta, \phi) \cdot w_2 e^{-jkr_2} + \ldots + R_n(\theta, \phi) \cdot w_n e^{-jkr_n}$$

with, R being the radiation pattern of one of the elements of the array antenna,

Should I just compute the radiation pattern of the element of lambda/4 and lambda/2, and add them as shown in the equation above?

  • \$\begingroup\$ How do you plan to combine them? Like, technically, how does that look like? \$\endgroup\$ Commented Oct 29, 2020 at 11:30
  • \$\begingroup\$ My idea is to place them as in a Yagi antenna, but instead of connecting the feed to one of the dipoles, connect the other elements, the so-called reflectors and directors, to other feeds to see how the directivity and beam pattern are affected. \$\endgroup\$
    – DaDSPGuy
    Commented Oct 29, 2020 at 11:52
  • \$\begingroup\$ well, as you see from the fact that yagi antennas work: They will mutually couple. Instead of two independent systems, you're having one with a hard-to-predict (but for proper simulation) coupling and thus impedance. Sadly, not that easy (it would be that easy if you arranged them orthogonally) \$\endgroup\$ Commented Oct 29, 2020 at 12:02
  • \$\begingroup\$ How far apart are the elements spaced? How long is the coax (if there is some) between them? What frequencies? How far above the ground is it? Those factors will also significantly affect the pattern. \$\endgroup\$
    – Duston
    Commented Oct 29, 2020 at 13:33
  • \$\begingroup\$ @MarcusMüller I was planning to computationally simulate it, not doing it by hand. So, could I use that formula for the simulation? \$\endgroup\$
    – DaDSPGuy
    Commented Oct 29, 2020 at 14:53

2 Answers 2


Technically, yes, the radiation pattern is the sum of the individual element radiation patterns, adjusted for geometric differences in distance to the receiving point. But you're mixing together several fundamental antenna concepts:

  1. The size of individual antenna elements (you've suggested πœ†/2 and πœ†/4 as examples).

  2. The arrangement of several antenna elements to create an array (orientation of, and spacing between, the elements).

  3. The radiation pattern of the resulting array.

And you've not considered the important factor of how the individual elements are excited (i.e. fed with RF energy). When you have more than one antenna element, there is coupling between them (mutual impedance) that affects the currents flowing in them and the impedance they present to the feeding system.

Typically, a πœ†/2 length antenna is a dipole, fed at the center (but there are variations to end-feed it). And typically, a πœ†/4 length antenna is a monopole, fed at the end and working against a ground plane. It would be unusual to design an array using these different elements together.

Here are some practical examples you will see:

  1. Simple πœ†/2 dipole antenna: old-fashioned TV "rabbit ears"
  2. Simple πœ†/4 monopole against ground: AM radio station with one tower
  3. Phased array of πœ†/4 monopoles against ground: AM radio station with multiple towers (to produce specific nulls to protect other stations from interference)
  4. Array of πœ†/2 dipoles, with one or two elements fed, and other elements passively excited: Yagi-style outdoor TV antenna

When you combine antennas of different wavelengths (even if they are resonant) on the same circuit. The transmission and reception become highly directional.

Also, constructive and destructive nodes exist.

If the application is fixed point to fixed point. With a little patience and a lot of precision you can get an awesome high gain signal.

If it's omnidirectional application, I wouldn't even bother.

  • 1
    \$\begingroup\$ Sorry, the combination of antennas of different wavelengths is not what makes an antenna "highly directional". The elements usually are all the same wavelength, and it takes a lot of them to create a highly directional beam. \$\endgroup\$ Commented Oct 29, 2020 at 20:22
  • \$\begingroup\$ My mistake, I was assuming fractal antennas for around the Wifi spectrum. \$\endgroup\$ Commented Oct 30, 2020 at 22:31

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