Broadside vs. end-fire linear arrays – Beamwidth and directive gain Let L be the overall element-center length of a uniform linear array and λ be the wavelength. Consider the statements: The major-lobe width between first nulls (BWFN) of a broadside array and an end-fire array are different. The directive gains of a broadside array and an end-fire array are different (for the same L). The directive gain of a broadside array is 4 (independent of L). Which statements are correct?

Introduction:
Array radiation characteristics depend on the progressive phase and element spacing. Broadside arrays concentrate energy normal to the array axis; end-fire arrays point energy along the axis. This changes beamwidth and directivity relationships even when the physical aperture length L is fixed, which is vital when trading gain against beam steering or end-fire sensing requirements.

Given Data / Assumptions:

• Uniform linear array with fixed overall length L.
• Free space, identical isotropic or identical element patterns.
• Broadside: progressive phase 0; End-fire: progressive phase chosen for end-fire maximum (e.g., Hansen-Woodyard adjustment).

Concept / Approach:

Broadside and end-fire arrays exhibit different array factors, yielding different first-null positions and thus different beamwidth between first nulls (BWFN). Their directivities are also generally different for the same L because end-fire requires destructive interference off-axis and constructive interference on-axis; classic approximations show broadside tends to have a narrower main lobe for a given L, while end-fire often exhibits a wider main lobe and somewhat lower directivity than broadside for the same aperture extent.

Step-by-Step Solution:

Verification / Alternative check:

Textbook plots and closed-form approximations confirm distinct beamwidths for broadside vs. end-fire arrays of equal length and differing directivities as L/λ varies. Numerical array-factor simulations produce the same qualitative differences.

Why Other Options Are Wrong:

Any choice including statement 3 is incorrect because directivity is not a fixed constant of 4 for all broadside arrays. Choosing only statement 1 ignores the known difference in D for the two types of arrays under equal L.

Common Pitfalls:

Assuming directivity is independent of aperture; conflating BWFN with half-power beamwidth (HPBW); forgetting that element pattern and mutual coupling can modify results, though the fundamental trend holds across practical designs.

Final Answer:

1 and 2 only.