Calculator Inputs
Use the form below to estimate steering phase, beam pattern, beamwidth, coherent gain, and grating lobe risk for a linear array.
Example Data Table
These sample cases show how different spacing, tapering, and steering choices affect beamwidth and grating lobe risk.
| Frequency (GHz) | Elements | Spacing | Steering | Taper | Estimated HPBW | Grating Risk |
|---|---|---|---|---|---|---|
| 3.50 | 8 | 0.50 λ | 20° | Uniform | 16.3° | Low |
| 5.80 | 12 | 0.45 λ | 10° | Hamming | 10.2° | Low |
| 10.00 | 16 | 0.50 λ | 35° | Hann | 7.1° | Low |
| 28.00 | 32 | 0.60 λ | 45° | Uniform | 3.0° | High |
Formula Used
This page models a steered linear phased array with optional amplitude taper and optional phase quantization. The key equations are:
λ = c / (f √εr)
k = 2π / λ
d = spacing × λ when spacing is entered in wavelengths.
Δφ = -k d sin(θs) for the ideal adjacent-element steering phase.
AF(θ) = |Σ an e^{j[m k d sin(θ) + φm]}|
The normalized array factor is converted to decibels with
20 log10(|AF| / |AF|max).
Beamwidth values are estimated numerically from the sampled pattern.
Coherent gain uses
(Σan)² / Σ(an²).
The grating lobe check uses the approximate scan-safe spacing limit
d/λ ≤ 1 / (1 + |sin(θs)|).
These are engineering estimates for a one-dimensional array factor. They do not include mutual coupling, element radiation patterns, feed losses, thermal drift, or manufacturing tolerances.
How to Use This Calculator
- Enter the operating frequency in MHz.
- Set the total number of elements in the linear array.
- Choose spacing in wavelengths or meters, then enter the spacing value.
- Enter the target steering angle for the main beam.
- Pick an amplitude taper to compare sidelobe behavior.
- Set phase shifter bits to zero for ideal continuous phase, or choose a finite value to estimate quantization effects.
- Adjust the scan window to control the angle range shown in the graph.
- Press the calculate button to display the result above the form.
- Review beamwidth, gain, grating warning, and the plotted pattern.
- Use the export buttons to download summary data as CSV or PDF.
Frequently Asked Questions
1. What does the steering angle control?
It sets the intended direction of the main beam. The calculator applies a progressive phase shift so the strongest array response points near that chosen angle.
2. Why is element spacing important?
Spacing changes the aperture size and the risk of grating lobes. Larger spacing can narrow the beam, but it can also create unwanted extra lobes when scanning.
3. What does amplitude taper do?
Tapering reduces sidelobes by lowering edge amplitudes. The tradeoff is lower coherent gain and often a wider main beam than a uniform distribution.
4. What is phase quantization?
Real phase shifters often move in discrete steps. Finite bit depth means the commanded phase is rounded, which can shift the beam slightly and degrade the pattern.
5. What does HPBW mean?
Half-power beamwidth is the angular width between the two points where the main beam drops by 3 dB from its peak. It is a common measure of angular resolution.
6. Is the gain value a full antenna gain model?
No. It is an ideal coherent array estimate based on array weights. It does not include element pattern, efficiency losses, packaging, or mutual coupling.
7. Why can the peak angle differ slightly from the steering angle?
Sampling resolution, taper choice, phase quantization, and extreme scan angles can move the numerical peak slightly away from the requested steering direction.
8. Can this calculator model planar arrays?
This version models a linear array factor. For planar or conformal arrays, you would need separate steering terms for both axes and a more detailed geometry model.