Antenna Technology

Cylindrical DRA

Q: How do you calculate the resonant frequency of a cylindrical DRA in the HEM11 delta mode?

The HEM11 delta broadside mode is the most common cylindrical DRA mode because it radiates like a horizontal magnetic dipole. A widely used closed-form approximation gives the normalized frequency factor k0a = (6.324 / sqrt(epsilon_r + 2)) times (0.27 + 0.36(a/2h) + 0.02(a/2h)^2), where a is the cylinder radius, h is the height, and epsilon_r is the relative permittivity. The actual resonant frequency follows from f0 = (k0a times c) / (2 pi a). For example, a cylinder with epsilon_r = 10, a = 5 mm, and h = 5 mm gives k0a = 0.83 and resonates near 7.9 GHz. Increasing the aspect ratio a/h lowers the radiation Q and widens the impedance bandwidth at the cost of a larger footprint.

Q: How is a cylindrical dielectric resonator antenna fed?

Cylindrical DRAs are excited by several feed structures, each coupling to a different mode. A coaxial probe inserted next to or into the puck excites the TM01 delta monopole-like mode or the HEM11 delta mode depending on position. A slot or aperture in the ground plane fed by a microstrip line couples magnetically to the HEM11 delta mode and provides good isolation between feed and radiator. A microstrip line running under the edge of the puck offers a simple planar feed. Conformal strips on the cylinder wall give designers control over input impedance and polarization. Choosing the feed sets which mode dominates and therefore the radiation pattern and polarization.

Q: What sets the bandwidth of a cylindrical DRA?

Impedance bandwidth is inversely proportional to the radiation Q factor: BW = (S - 1) / (Q times sqrt(S)), where S is the maximum tolerable VSWR. The radiation Q rises sharply with permittivity, roughly as epsilon_r to the 1.2 to 1.5 power, so a high-epsilon_r ceramic (epsilon_r = 38) gives a narrow 2 to 5 percent bandwidth while a low-epsilon_r material (epsilon_r = 10) can reach 8 to 12 percent. Aspect ratio matters too: a flat, wide puck (large a/h) radiates more readily and lowers Q. Designers widen bandwidth further by stacking dielectric layers, adding parasitic pucks, or using a hybrid probe-plus-slot feed to merge two adjacent resonances.

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Among the canonical shapes of the dielectric resonator antenna, the cylindrical form is the most widely used because its two geometric degrees of freedom, radius and height, decouple the resonant frequency from the radiation Q factor. A ceramic puck of relative permittivity typically between 10 and 40 is mounted on a ground plane and excited in a mode such as HEM_11δ (a broadside horizontal magnetic dipole), TM_01δ (monopole-like vertical pattern), or TE_01δ. Because there is no metal radiator, conductor loss vanishes and radiation efficiency commonly exceeds 95% well into the millimeter-wave bands, making the cylindrical DRA attractive for 24 to 80 GHz arrays where patch antenna metal loss becomes prohibitive.

Category: Antenna Technology

Dominant Mode: HEM_11δ

Typical ε_r: 10 to 40

Geometry, Modes, and Why the Cylinder Wins

A cylindrical dielectric resonator antenna is fully described by three parameters: the radius a, the height h, and the relative permittivity ε_r of the ceramic. Unlike a hemispherical DRA, which fixes the aspect ratio by its shape, or a rectangular DRA, which offers three independent dimensions but a more complex mode spectrum, the cylinder gives the designer exactly one shape ratio, a/h, to tune. That single knob controls the radiation Q factor, and therefore the bandwidth, independently of the operating frequency that the radius primarily sets. This clean separation is the practical reason the cylindrical geometry dominates published DRA designs.

The puck supports a family of resonant modes. The HEM_11δ mode behaves like a short horizontal magnetic dipole and radiates broadside, normal to the ground plane, with a pattern resembling a patch antenna but without the surface-wave and conductor losses. The TM_01δ mode radiates like a vertical electric monopole, producing an omnidirectional azimuth pattern useful for base-station and vehicular antennas. The TE_01δ mode, the lowest mode of an isolated puck, is rarely used for radiation on a ground plane because its fields are largely confined. Mode selection is governed almost entirely by the feed type and its placement.

Aspect Ratio and Bandwidth Trade-off

Pushing the aspect ratio a/h higher flattens the puck, lowers the radiation Q, and widens the impedance bandwidth, but it also enlarges the footprint and can bring higher-order modes closer to the operating band. Lowering ε_r has the same bandwidth-widening effect because the fields radiate more readily out of a less dense dielectric. A designer targeting 10% bandwidth at 28 GHz might choose ε_r ≈ 10 with a/h ≈ 1.0, whereas a narrowband filter-coupled radiator might use ε_r = 38 to shrink the puck.

Feed Selection and Polarization

Sequentially rotated probe or slot feeds around the cylinder excite two orthogonal HEM_11δ modes in phase quadrature, producing circular polarization without a separate polarizer. This makes the cylindrical DRA a compact circularly polarized element for satellite and GNSS receivers, where the same low-loss behavior that helps at millimeter-wave also preserves axial ratio across a wide scan angle.

Governing Equations

HEM_11δ Resonant Frequency:
k₀a ≈ (6.324 / √(ε_r + 2)) × [0.27 + 0.36(a/2h) + 0.02(a/2h)²]
f₀ = (k₀a × c) / (2πa)

Radiation Q (approximate scaling):
Q_rad ≈ A × ε_r^1.2 × [1 + B × (a/h)]

Impedance Bandwidth:
BW = (S − 1) / (Q_rad × √S)

Where a = cylinder radius, h = height, ε_r = relative permittivity, c = speed of light, k₀ = free-space wavenumber, S = maximum VSWR, and A, B = geometry-fit constants. Example: ε_r = 10, a = h = 5 mm (a/2h = 0.5) → k₀a ≈ 0.83, f₀ ≈ 7.9 GHz.

Cylindrical DRA Mode Comparison

Mode	Radiation Behavior	Pattern	Typical Feed	Common Use
HEM_11δ	Horizontal magnetic dipole	Broadside	Slot/aperture or probe	Arrays, mmWave elements
TM_01δ	Vertical electric monopole	Omnidirectional (azimuth)	Center coaxial probe	Base station, vehicular
TE_01δ	Magnetic dipole (confined)	Weak radiator on ground	Coupling loop	Filter resonators
Higher HEM	Multi-lobe	Split main beam	Offset probe	Avoided in band

Common Questions

Frequently Asked Questions

How do you calculate the resonant frequency of a cylindrical DRA in the HEM_11δ mode?

Use the normalized factor k₀a ≈ (6.324 / √(ε_r + 2)) × [0.27 + 0.36(a/2h) + 0.02(a/2h)²], then f₀ = (k₀a × c) / (2πa). For ε_r = 10 with a = h = 5 mm (a/2h = 0.5) this gives k₀a ≈ 0.83 and roughly 7.9 GHz. Raising the aspect ratio a/h lowers radiation Q and widens bandwidth at the cost of a larger footprint.

How is a cylindrical dielectric resonator antenna fed?

Common feeds are a coaxial probe (excites TM_01δ at center or HEM_11δ off-center), a ground-plane slot fed by microstrip (couples magnetically to HEM_11δ with good feed isolation), an edge-coupled microstrip line, and conformal strips on the puck wall. The feed and its position determine which mode dominates, and therefore the pattern and polarization.

What sets the bandwidth of a cylindrical DRA?

Bandwidth follows BW = (S − 1) / (Q_rad × √S). Radiation Q rises with permittivity roughly as ε_r^1.2, so ε_r = 38 yields a narrow 2 to 5%, while ε_r = 10 reaches 8 to 12%. A flat, wide puck (large a/h) lowers Q further. Stacked layers, parasitic pucks, or a hybrid probe-plus-slot feed merge resonances for even wider bands.

Related Terms

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