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Binomial Array

Definition: A binomial array is a type of linear array antenna where the current amplitudes of the elements are proportional to the coefficients of a binomial expansion. This configuration is designed to produce a radiation pattern with no side lobes, which enhances the directivity and reduces unwanted radiation.

Detailed Description:

  1. Configuration:
  • Linear Array: The binomial array consists of a series of antenna elements arranged in a straight line.
  • Current Amplitudes: The current amplitudes applied to each element follow a binomial distribution. For instance, in a 3-element binomial array, the current amplitudes might be proportional to 1, 2, and 1, respectively, following the binomial coefficients of (a+b)^2.
  1. Binomial Expansion:
  • Mathematical Basis: The binomial coefficients come from the binomial theorem, which expresses the coefficients in the expansion of (a+b)^n.
  • Example: For a 4-element array, the coefficients are 1, 3, 3, and 1, corresponding to the binomial expansion of (a+b)^3.
  1. Radiation Pattern:
  • No Side Lobes: One of the main advantages of a binomial array is its ability to produce a radiation pattern with minimal or no side lobes. This is achieved by carefully controlling the amplitude distribution of the currents.
  • Main Lobe: The main lobe of the radiation pattern is sharp and well-defined, providing better directionality and focus.
  1. Applications:
  • Communication Systems: Binomial arrays are used in communication systems where reduced side lobes are desirable to minimize interference and improve signal clarity.
  • Radar Systems: They are also used in radar systems where a clean, well-defined main lobe is crucial for accurate target detection.
  1. Design Considerations:
  • Element Spacing: The spacing between antenna elements in a binomial array is typically uniform.
  • Current Distribution: The design requires precise control of the current amplitudes to match the binomial coefficients.

Summary:

A binomial array is a linear antenna array where the current amplitudes of the elements follow binomial coefficients from a binomial expansion. This arrangement results in a radiation pattern with no side lobes, improving directivity and minimizing unwanted radiation. Binomial arrays are used in communication and radar systems for their clean and focused radiation patterns.

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