# E and H pattern of 2 element antenna array.

• yungman
In summary, the conversation discusses a question about creating an H pattern using pattern multiplication and how it differs from the expected E pattern. The equations and concepts are explained and the individual asks for clarification on certain aspects. They also mention that the array pattern is not dependent on the E or H pattern.

#### yungman

This is not a homework, too old for that! I just have a question that I create myself. All the books only show the pattern that is more obvious...they show either the E or the H pattern. I took an exercise that asked for the H pattern, in turn, using the pattern multiplication to try to find the E pattern and ran into road block. Here is the exercise:

Given two Hertzian dipoles oriented in z-direction. Both line up on x-axis and $\;d=\frac {\lambda} 2 \;$ apart. Both are driven by the same amplitude and phase $\alpha =0$. Find the E and H pattern.

From pattern multiplication:

$$|E(\theta, \phi)| = \frac {E_m}{R_0}\;| F(\theta, \phi)|\;\left|\cos\left(\frac {\beta d \cos\phi \sin\theta -\alpha} {2} \right)\right|$$

Where $\;| F(\theta, \phi)|= |\sin\theta| \;$ is the element factor for the Hertzian dipole of each element and $\;\left|\cos\left(\frac {\beta d \cos\phi \sin\theta -\alpha} 2 \right)\right|$ is the array factor.

The pattern function is:

$$| F(\theta, \phi)|\;\left|\cos\left(\frac {\beta d \cos\phi \sin\theta -\alpha} {2} \right)\right|$$

I have no problem getting the H pattern by just putting $\;\theta=\frac {\pi}{2}$. I get the two almost ball shape one on +ve y-axis and one on -ve y axis. There are no E field on x direction as expected.

But when I try to look at the E pattern at $\;\phi=0$, I don't get what I expected. From the H pattern above, I expect I'll get no E field at $\;\phi=0 \;\hbox { and } \phi=\pi$ for all angle of $\;\theta$. But according to the pattern function:

$$| F(\theta, \phi)|\;\left|\cos\left(\frac {\beta d \cos\phi \sin\theta -\alpha} {2} \right)\right| = |\sin\theta| \left|\cos\left(\frac {\pi}{2}( \sin\theta ) \right)\right|$$

You can see it is zero when $\theta= 0 \;\hbox { or }\;\theta=\frac{\pi}{2}$, but it is not zero in between. Can anyone help explaining this?

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Anyone?

I know the equations are correct as it is given in the book and was used to solve the H pattern. Far as my understanding, array pattern is not E or H pattern dependent, in fact it is not antenna elements dependent. It only depend on the $\theta, \phi, \alpha, d$.

## 1. What is the purpose of using a 2 element antenna array?

The purpose of using a 2 element antenna array is to improve the directivity and gain of the antenna. By combining the signals from two antennas, the radiation pattern becomes more directional and the gain increases.

## 2. What is the difference between the E and H pattern of a 2 element antenna array?

The E pattern refers to the electric field pattern of an antenna, while the H pattern refers to the magnetic field pattern. In a 2 element array, the E and H patterns are similar but have slightly different shapes due to the placement of the antennas.

## 3. How do the spacing and orientation of the antennas affect the E and H patterns of a 2 element array?

The spacing between the two antennas and their orientation with respect to each other can significantly impact the E and H patterns of a 2 element array. The distance between the two antennas should be carefully chosen to achieve the desired radiation pattern.

## 4. Can the E and H patterns of a 2 element array be controlled?

Yes, the E and H patterns of a 2 element array can be controlled by adjusting the spacing, orientation, and phase of the antennas. This allows for customization of the radiation pattern to best suit the specific application of the antenna.

## 5. What are some advantages of using a 2 element antenna array compared to a single antenna?

Some advantages of using a 2 element antenna array include improved directivity and gain, as well as the ability to control the radiation pattern. This can be beneficial for long-range communication, reducing interference, and improving signal strength in a specific direction.