Binomial Array Calculator
Calculate the binomial excitation coefficients for a uniform linear antenna array using Pascal's Triangle. Binomial arrays eliminate sidelobes at the expense of wider beamwidth and lower directivity.
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Inputs
Live
Math
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Related
Enter parameters and click Calculate to view results
Formula & Theory
Coefficient(k) = C(N−1,k) = (N−1)! / (k!(N−1−k)!)This formula is used to calculate antenna parameters for binomial array calculator.
Overview
The Binomial Array Calculator computes amplitude excitation coefficients for non-uniform linear antenna arrays using Pascal's Triangle ($C(N-1, k)$). Binomial array synthesis yields a maximally flat radiation pattern that completely eliminates side lobes for element spacing $d \le \lambda/2$, making it an ideal theoretical model for zero-sidelobe antenna design.
Input Guide
Enter Number of Elements exactly in the units shown by this binomial array. Check the operating band, unit prefix, and decimal position before calculating; these are the inputs used by the formula.
- Number of Elements.
Output Guide
The results describe the calculated binomial array values for the inputs you entered. Check each value against the available space, selected components, feed system, and operating conditions before making a final design decision.
How This Calculator Works
The Binomial Array uses Coefficient(k) = C(N−1,k) = (N−1)! / (k!(N−1−k)!). Supply Number of Elements in the displayed units, then use the calculated values as the first engineering target for this antenna arrays design or analysis.
Design Notes
Binomial arrays distribute amplitude power following binomial expansion coefficients. While they guarantee total side lobe suppression, they suffer from two major practical drawbacks: a significantly wider main lobe half-power beamwidth (HPBW) and lower directivity compared to uniform arrays. Additionally, as the element count ($N$) grows, the excitation ratio between inner and outer elements increases exponentially ($2^{N-1}$ dynamic range), making precise power division in feed networks difficult to implement.
Build and Tuning Notes
When building physical binomial arrays, use precision power dividers or attenuator networks to maintain exact current ratios across array elements. Keep inter-element spacing strictly at $d = \lambda/2$ to prevent grating lobes. For real-world applications requiring a controllable balance between side lobe level and main beam width, consider Dolph-Chebyshev or Taylor distribution arrays as practical alternatives.
Frequently Asked Questions
What is a Binomial Antenna Array?
A binomial antenna array is a non-uniform linear array where element current amplitudes follow binomial coefficients from Pascal's Triangle. Its defining feature is the total elimination of minor side lobes.
Why does a Binomial Array have no sidelobes?
The mathematical formulation of binomial excitation creates a maximally flat spatial radiation pattern. For element spacing $d \le \lambda/2$, all spatial roots overlap, eliminating pattern nulls and minor lobes.
What are the disadvantages of a Binomial Array?
The main drawbacks are a broad main beam (low directivity) and an extreme dynamic range of excitation currents across elements, which makes feed network construction challenging for large arrays.
How does a Binomial Array compare to a Dolph-Chebyshev Array?
Binomial arrays eliminate side lobes entirely at the cost of a wide main beam. Dolph-Chebyshev arrays allow designers to specify a target side lobe level (e.g., -30 dB) to achieve the narrowest possible main beamwidth for that constraint.
Alex Warren
B.Sc. in Electrical & Electronic Engineering (EEE)
Alex specialises in antenna design and wave propagation. His expertise helps ensure these calculators present practical RF concepts, useful design estimates, and clear engineering guidance for students, HAM operators, and wireless professionals.