Measurement Techniques

Cylindrical Near-Field (Detail)

Q: What sample spacing is required for a cylindrical near-field scan?

Two independent rules apply. The vertical (z) sample spacing must satisfy delta-z less than or equal to lambda/2 to avoid aliasing the linear spectral components, identical to the planar case. The angular (phi) spacing is governed by the highest cylindrical mode order n_max, where n_max is approximately k times the measurement radius rho_0 plus a margin of about 10. The angular step must satisfy delta-phi less than or equal to 180 degrees divided by n_max. For a 1 m radius cylinder at 10 GHz, k times rho_0 is about 210, so n_max is near 220 and delta-phi is about 0.8 degrees, requiring roughly 440 azimuth samples per ring. Because the angular requirement is fixed by the cylinder radius rather than the antenna size, keeping the radius as small as the antenna and probe clearance allow directly reduces the number of points.

Q: Why choose cylindrical scanning over planar or spherical for a fan-beam antenna?

Cylindrical scanning gives full 360 degree azimuth coverage with no truncation in that plane, which is exactly what a fan-beam, sectoral, or base-station panel antenna needs. The only truncation is in the vertical extent of the cylinder, and that error is bounded because the antenna radiates little energy at high elevation angles. A planar scan can only recover a forward cone (typically plus or minus 60 to 70 degrees) and therefore cannot capture the wide azimuth pattern of a fan-beam. A spherical scan captures the complete sphere but needs an azimuth-over-elevation positioner and far more sample points. Cylindrical scanning sits between the two: it captures the full azimuth a fan-beam cares about while using a simpler linear-plus-rotation positioner and fewer points than spherical.

Q: How does probe correction work in a cylindrical near-field system?

The measured signal is the convolution of the antenna fields with the probe response, so the raw cylindrical mode coefficients are distorted by the probe pattern. Probe correction divides the measured mode coefficients by the probe transmission coefficients in the cylindrical wave basis before the far-field transformation. The probe must be characterized over the angular range it views the antenna, and for accurate correction it should be a first-order probe such as an open-ended waveguide or a small horn whose azimuthal mode content is limited to mu equal to plus or minus 1. Skipping probe correction introduces errors of 0.5 to 2 dB in the main beam and several dB in the sidelobes when the probe is directive or the measurement radius is small.

/sih-LIN-drih-kuhl NEER-feeld/

Sampling the radiated near-field on a cylindrical surface that surrounds the antenna under test, this technique recovers the complete azimuth radiation pattern by expanding the measured amplitude and phase into cylindrical wave modes and propagating them to the far field. The probe travels along a vertical line while the antenna rotates in azimuth, tracing rings of data on a cylinder of radius ρ₀. Because azimuth coverage is a full 360° with no truncation, cylindrical scanning is the preferred method for fan-beam, sectoral, and base-station panel antennas, where the only bounded error comes from the finite vertical height of the scan cylinder.

Category: Measurement Techniques

Vertical spacing: Δz ≤ λ/2

Azimuth coverage: Full 360°

How the Cylindrical Scan Recovers the Far Field

A cylindrical near-field range measures the tangential electric field on a cylinder of radius ρ₀ that encloses the antenna. The mechanical implementation pairs a vertical linear scanner carrying the probe with an azimuth rotary stage carrying the antenna under test, so a single ring of samples is acquired at each height z and the probe steps up the cylinder ring by ring. This azimuth-over-linear geometry is mechanically simpler than the azimuth-over-elevation positioner a spherical range requires, which is one reason cylindrical scanning became the workhorse for large fan-beam and sectoral antennas.

The transformation theory treats the field outside the cylinder as a sum of outward-traveling cylindrical waves. Each mode is indexed by an integer azimuthal order n and a continuous vertical wavenumber k_z, and its radial behavior is described by a Hankel function of the second kind, H_n⁽²⁾(k_ρρ). A two-dimensional transform of the measured ring data, a discrete Fourier transform in φ and a continuous Fourier transform in z, yields the mode coefficients. Dividing each coefficient by the corresponding Hankel function removes the radial dependence, and a final far-field evaluation gives the pattern as a function of azimuth φ and elevation. The result is exact in azimuth and limited only by the vertical extent of the cylinder.

Two sampling constraints control accuracy. Vertical samples must be spaced no more than half a wavelength apart, exactly as in a planar scan, because the z-axis spectrum is a linear plane-wave spectrum. The azimuth sampling is set instead by the highest significant mode order n_max, which scales with the electrical radius kρ₀ of the measurement cylinder. Keeping ρ₀ small, just large enough for probe clearance and reactive-field decay, minimizes n_max and therefore the total point count.

Cylindrical Mode Expansion and Sampling

Cylindrical wave expansion of the field:
E(ρ,φ,z) = ∑_n ∫ a_n(k_z) H_n⁽²⁾(k_ρρ) e^jnφ e^jk_zz dk_z, k_ρ = √(k² − k_z²)

Highest mode order:
n_max ≈ k × ρ₀ + 10, k = 2π/λ

Sample-spacing rules:
Δz ≤ λ/2 (vertical), Δφ ≤ 180° / n_max (azimuth)

Where a_n(k_z) are the cylindrical mode coefficients, H_n⁽²⁾ is the Hankel function of the second kind, ρ₀ is the cylinder radius, and λ is the wavelength. Example: ρ₀ = 1 m at 10 GHz gives kρ₀ ≈ 210, n_max ≈ 220, so Δφ ≈ 0.8° (about 440 azimuth samples per ring).

Cylindrical vs. Planar vs. Spherical Scanning

Attribute	Cylindrical	Planar	Spherical
Angular coverage	Full 360° azimuth; vertical truncated	Forward cone, ±60° to ±70°	Complete sphere
Positioner	Linear z + azimuth rotation	Two linear axes (X, Y)	Azimuth over elevation
Wave basis	Cylindrical (Hankel) modes	Plane waves (2-D FFT)	Spherical harmonics
Best antenna type	Fan-beam, sectoral, base-station panels	High-gain, low-sidelobe pencil beams	Low-directivity, wide-coverage
Sample count	Moderate	Lowest	Highest
Main error source	Vertical (z) truncation	Edge truncation of plane	Positioner alignment

Common Questions

Frequently Asked Questions

What sample spacing is required for a cylindrical near-field scan?

Two rules apply. Vertical spacing must satisfy Δz ≤ λ/2 to avoid aliasing the linear spectrum, as in a planar scan. Azimuth spacing is set by the highest mode order n_max ≈ kρ₀ + 10, giving Δφ ≤ 180°/n_max. A 1 m radius cylinder at 10 GHz has kρ₀ ≈ 210, so Δφ ≈ 0.8° (about 440 azimuth points per ring). Keeping ρ₀ small directly reduces the point count.

Why choose cylindrical scanning over planar or spherical for a fan-beam antenna?

Cylindrical scanning gives full 360° azimuth coverage with no truncation in that plane, exactly what a fan-beam, sectoral, or base-station panel antenna needs. The only truncation is vertical, and that error is bounded because the antenna radiates little at high elevation. A planar scan recovers only a forward cone (±60° to ±70°), and a spherical scan captures the whole sphere but needs an azimuth-over-elevation positioner and far more points.

How does probe correction work in a cylindrical near-field system?

The measured data is the antenna field convolved with the probe response, so the raw mode coefficients are distorted. Probe correction divides the measured cylindrical mode coefficients by the probe transmission coefficients before the far-field transform. The probe should be a first-order type (open-ended waveguide or small horn) limited to azimuthal modes μ = ±1. Skipping correction adds 0.5 to 2 dB of main-beam error and several dB in the sidelobes.

Related Terms

← Cylindrical Near-Field Cylindrical Wave →