End-Fire Array Calculator
Calculate ordinary and Hansen–Woodyard end-fire array parameters including progressive phase, array length, directivity estimate, and gain.
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Inputs
Live
Math
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Related
Enter parameters and click Calculate to view results
Formula & Theory
β=-360(d/λ), βHW=-360(d/λ)-180/NThis formula is used to calculate antenna parameters for end-fire array calculator.
Overview
The End-Fire Array Calculator helps RF engineers, antenna designers, researchers, and students design ordinary and Hansen–Woodyard end-fire antenna arrays. It calculates progressive phase shift, Hansen–Woodyard phase correction, array length, electrical length, estimated directivity, array gain, and element spacing assessment. End-fire arrays concentrate radiation along the axis of the antenna array, making them suitable for directional communication, radar systems, satellite links, microwave engineering, phased arrays, and beamforming applications.
Input Guide
Enter Number of Elements, Element Spacing, Element Gain, Array Efficiency exactly in the units shown by this end-fire array. Check the operating band, unit prefix, and decimal position before calculating; these are the inputs used by the formula.
- Number of Elements.
- Element Spacing — use λ.
- Element Gain — use dBi.
- Array Efficiency — use %.
Output Guide
The results describe the calculated end-fire 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 End-Fire Array uses β=-360(d/λ), βHW=-360(d/λ)-180/N. Supply Number of Elements, Element Spacing (λ), Element Gain (dBi), Array Efficiency (%) in the displayed units, then use the calculated values as the first engineering target for this antenna arrays design or analysis.
Design Notes
An end-fire antenna array radiates its strongest beam along the axis of the array instead of perpendicular to it, as in a broadside array. Proper element spacing and progressive phase excitation are essential for achieving maximum directivity and efficient radiation. The Hansen–Woodyard end-fire method introduces a small additional phase shift beyond the ordinary end-fire condition, producing higher directivity and a narrower main beam. Practical performance depends on antenna element patterns, mutual coupling, feed network accuracy, manufacturing tolerances, ground reflections, and overall array efficiency. Excessive element spacing may introduce grating lobes, while very small spacing increases mutual coupling between elements.
Build and Tuning Notes
Use the calculated phase shift and array dimensions as the starting point for electromagnetic simulation using software such as CST Studio Suite, HFSS, or FEKO. During antenna construction, maintain accurate element spacing, equal feedline lengths, and precise phase control throughout the array. Measure the radiation pattern inside an anechoic chamber or open-area test range, then optimise the amplitude and phase distribution to compensate for practical mutual coupling and manufacturing tolerances. Verify the final antenna gain and beam direction before deployment in communication or radar systems.
Frequently Asked Questions
What is an end-fire antenna array?
An end-fire antenna array is a directional antenna array that radiates its maximum energy along the axis of the array. It is commonly used when a highly directional beam is required in the forward direction.
What is the Hansen–Woodyard end-fire array?
The Hansen–Woodyard end-fire array is an improved end-fire design that applies an additional progressive phase shift beyond the ordinary end-fire condition. This technique increases directivity and produces a narrower main beam.
How is progressive phase shift calculated?
For an ordinary end-fire array, the progressive phase shift is approximately β = −360° × (d/λ). The Hansen–Woodyard design adds an additional phase correction of approximately 180° divided by the number of array elements.
Why is element spacing important in an end-fire array?
Element spacing affects directivity, beamwidth, mutual coupling, and the formation of grating lobes. Proper spacing helps maximise forward radiation while maintaining efficient antenna performance.
Where are end-fire arrays commonly used?
End-fire arrays are widely used in radar systems, microwave communication, phased array antennas, satellite communication, radio astronomy, defence systems, wireless communication, and directional RF applications.
Why can measured antenna performance differ from calculated results?
Actual performance may differ because of mutual coupling, antenna element characteristics, feed network losses, phase errors, manufacturing tolerances, environmental reflections, and installation conditions. Electromagnetic simulation and practical measurements are recommended to validate the final design.
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.