# Maximum Theoretical Angular Accuracy of Planer arrays

• senmeis
In summary, the paper discusses the maximum theoretical angular accuracy of planar and linear arrays of sensors. Equations 19 and 20 provide accuracies for the x and y axes. The angle between the incoming ray and the normal direction to the array does play a role, with the best accuracy achieved when the ray is along the normal direction. As the angle of incidence moves off of broadside, the angular resolution and SNR decrease due to the shrinking of the array's normal direction. Additionally, the accuracy and resolution vary with different directions of incidence.

#### senmeis

Hello,in this link http://dtic.mil/dtic/tr/fulltext/u2/a028054.pdf a paper „Maximum Theoretical Angular Accuracy of Planer and Linear Arrays of Sensors“ can be found.The accuracies are given in equations 19 (respect to the x axis) and 20 (respect to the y axis).My question is: Shall the angle between the incoming ray and the normal direction to the planar array also play a role? I mean, the 90 degrees angle (along the normal direction) shall have the greatest accuracy. In example of line array on page 15 this angle (15 degrees there) is considered. Do I understand it correctly?Senmeis

I haven't read your link, but I can make some general comments about angular resolution. As the angle of incidence moves off of broadside, the apparent extent of the array normal to the incoming wave shrinks by cos(θ), due to simple geometry. This has two effects. First, the angular resolution suffers since it varies inversely proportional to the aperture length. Second, the SNR drops for the same reason. In fact, the electrical gain of the array drops more quickly than cos(θ) because the antenna elements become mismatched (no longer 50 ohms, e.g.) due to varying phase shifts in the mutual antenna coupling terms as the angle increases. It is common to approximate the rolloff in antenna gain (hence SNR) as cos(θ)^1.5, though this is just an approximation. Both of these effects will reduce the resolution and accuracy.

Thank you. Can I understand what you are saying as following in simple words?1. For a planar array the best accuracy and resolution can only be achieved if the incidence ray is on the normal direction.

2. The accuracy and resolution are different with different directions of incidence (different elevation and azimuth angle).Senmeis

I'll need to look at that paper...

## 1. What is the maximum theoretical angular accuracy of planar arrays?

The maximum theoretical angular accuracy of planar arrays refers to the maximum possible precision in determining the direction of incoming signals using a planar array antenna. It is determined by the spacing and number of elements in the array, as well as the frequency of the signals being received.

## 2. How is the maximum theoretical angular accuracy of planar arrays calculated?

The maximum theoretical angular accuracy of planar arrays can be calculated using the formula: θ_max = λ / (2 * N * d), where θ_max is the maximum theoretical angular accuracy, λ is the wavelength of the signal, N is the number of elements in the array, and d is the spacing between elements.

## 3. Can the maximum theoretical angular accuracy of planar arrays be improved?

Yes, the maximum theoretical angular accuracy of planar arrays can be improved by increasing the number of elements in the array, decreasing the spacing between elements, and using higher frequency signals. However, practical limitations such as size and cost may prevent achieving the maximum theoretical accuracy.

## 4. What factors can affect the maximum theoretical angular accuracy of planar arrays?

The maximum theoretical angular accuracy of planar arrays can be affected by various factors such as environmental conditions (e.g. weather, interference), imperfections in the array's construction, and limitations in signal processing algorithms.

## 5. How is the maximum theoretical angular accuracy of planar arrays used in practical applications?

The maximum theoretical angular accuracy of planar arrays is used as a benchmark for evaluating the performance of planar array antennas in real-world applications. It serves as a guide for engineers and scientists in designing and optimizing array antennas for specific purposes, such as radar systems, communication systems, and wireless networks.