Ideal coherent gain
G = N² and GdB = 20 log10(N)
RIS Configuration and Link Budget
Use the basic sections first, then open advanced sections for measured or research-grade inputs.
Performance Charts
Explore gain scaling, received power with distance, and phase-resolution efficiency.
Gain versus Element Count
Received Power versus Distance
Phase Quantization Efficiency
Current Geometry Summary
Tx–RIS distance: 20.000 m
RIS–Rx distance: 30.000 m
Direct distance: 40.000 m
Incident angle: 25.00°
Reflection angle: 30.00°
Surface: 0.171 m × 0.171 m
RIS–Rx distance: 30.000 m
Direct distance: 40.000 m
Incident angle: 25.00°
Reflection angle: 30.00°
Surface: 0.171 m × 0.171 m
Element Phase Matrix Generator
Generate a compact far-field steering, near-field focusing, or random-error matrix.
Saved Scenarios and Session History
Store configurations in the browser and review recent calculations in this PHP session.
Browser Scenarios
Session History
| Time | Elements | GHz | Gain | Rx power | SNR |
|---|
Formula Reference
Ideal gain, practical gain, aperture gain, noise, path loss, and field boundaries remain separate.
Practical coherent gain
Gpractical = N² × ηtotal
Aperture gain
G = ηap × 4πA / λ²
Free-space path loss
FSPL = 20 log10(4πd / λ)
Thermal noise
N = kTB
SNR
SNRdB = Pr,dBm − Ntotal,dBm
Far-field boundary
Rff = 2D² / λ
Reactive boundary
Rreactive ≈ 0.62√(D³ / λ)
Quantization efficiency
ηq = [sin(π/L)/(π/L)]²
Phase-error efficiency
ηφ = exp(−σφ²)
Power density
S ≈ EIRP/(4πd²)
Beamwidth estimate
HPBW ≈ 0.886λ/D
The N² expression is a coherent scaling benchmark. It does not imply unlimited passive power creation. Physical aperture, geometry, losses, element patterns, and energy conservation must remain consistent.
How to Use This Calculator
Follow a transparent sequence and document every assumption.
- Choose the RIS architecture and calculation mode.
- Enter frequency, bandwidth, rows, columns, spacing, and dimensions.
- Select phase resolution and practical hardware efficiencies.
- Describe Tx–RIS–Rx distances, coordinates, heights, angles, and visibility.
- Enter transmitter power, antenna gains, receiver sensitivity, and noise figure.
- Choose a propagation model and add environmental margins.
- For active RIS hardware, add gain, noise, saturation, DC power, and stability.
- Compare ideal coherent gain, practical gain, and aperture gain separately.
- Check received power, SNR, link margin, and field-region warnings.
- Save, export, print, and verify the design with higher-fidelity methods.
A high surface gain does not automatically produce a strong received signal. Both propagation segments may contribute substantial attenuation. Large scan angles, obstruction, phase error, coupling, and limited aperture can reduce the practical result.
Near-field systems require spherical phase compensation across the surface. This calculator provides boundary warnings but does not replace full element-level field integration, ray tracing, channel sounding, or full-wave simulation.
RIS Engineering Glossary
Definitions for the main concepts used by the calculator.
RIS surface
A programmable electromagnetic surface containing many controllable unit cells.
Unit cell
The repeated element that controls reflection, transmission, phase, amplitude, or polarization.
Coherent gain
A benchmark obtained when contributions arrive with aligned phase.
Aperture gain
A physical-area estimate based on wavelength and aperture efficiency.
Reflection efficiency
The useful reflected or transmitted power fraction.
Phase quantization
The restriction of control to a finite number of phase states.
Mutual coupling
Electromagnetic interaction between nearby elements.
Near field
A region where spherical wavefronts and focusing distances matter.
Far field
A region where angular steering and plane-wave approximations are more applicable.
Cascaded path loss
The combined attenuation of Tx–RIS and RIS–Rx propagation segments.
Active RIS
A surface using gain elements that add power, noise, saturation, and stability limits.
Link margin
Received power above the sensitivity or noise-plus-SNR requirement.
Grating lobe
An unwanted strong beam caused by excessive spacing or large steering angles.
Calibration error
Residual phase or amplitude error after hardware calibration.
Power density
Incident RF power per unit area at the RIS.
Noise figure
SNR degradation introduced by receiver or active surface electronics.
Shadow fading
Slow variation caused by buildings, terrain, furniture, or other large objects.
Beamwidth
Approximate angular width of the main reflected or transmitted lobe.
Assumptions and Limitations
Use these notes when reporting or reviewing the results.
- Element amplitudes are represented by aggregate efficiency factors.
- Ideal coherent scaling assumes correct phase at the observation point.
- Mutual coupling is represented by a single correction value.
- Wideband beam squint and group-delay dispersion are not fully simulated.
- Direct and RIS paths use a simplified two-path phase combination.
- Near-field warnings do not perform full spherical-wave field integration.
- Active RIS noise uses an aggregate noise figure.
- Active stability and saturation require circuit-level verification.
- Indoor and urban presets are editable estimates, not certified standards.
- Final deployments should be verified through simulation, prototypes, and measurements.