Waveguide Engineering

Curved Bend

Q: What bend radius gives the lowest return loss in a curved waveguide bend?

Reflection from a curved bend falls as the mean radius increases, because a larger radius reduces the abrupt impedance change at the entry and exit of the arc. As a practical rule, a constant-radius bend with a mean radius of at least 1.5 to 2 guide wavelengths typically achieves better than 30 dB return loss across a standard waveguide band. For WR-90 X-band hardware near 10 GHz, the guide wavelength is roughly 39 mm, so a mean radius of about 60 to 80 mm is a good starting point. Tighter radii increase reflection and risk exciting higher-order modes, while very large radii waste space. Electromagnetic simulation or measured S-parameters should confirm the final geometry, since fabrication tolerances and surface finish also influence the result.

Q: In an E-plane curved bend, do the broad or narrow walls follow the arc?

In an E-plane bend the propagation axis sweeps in the direction of the narrow b dimension, so the two broad a dimension walls follow the arc while the narrow walls stay flat; the bend lies in the plane of the electric field. An H-plane bend is the opposite: the axis sweeps in the direction of the broad a dimension, so the two narrow walls follow the arc and the broad walls stay flat. Because the electric field is concentrated across the narrow dimension, an E-plane bend is usually the more reflection-sensitive of the two for a given mean radius. H-plane bends are often easier to fabricate by milling or electroforming. Designers choose the plane based on the routing geometry of the assembly and the required budget for return loss and insertion loss.

Q: How does a curved bend compare to a mitered or stepped bend?

A curved bend uses a continuous smooth arc, which spreads the discontinuity over the length of the arc and typically yields the broadest bandwidth and lowest mode conversion. A mitered bend uses one or two flat angled cuts and relies on the reflection from those cuts to cancel at the design frequency, giving a compact part but a narrower optimized band. A stepped or compound bend approximates the turn with several short straight segments. Curved bends are preferred when broadband low reflection matters and space allows, while mitered bends are chosen for compact right-angle turns in tight assemblies where a slightly narrower band is acceptable.

/kurvd bend/

Smoothly arced sections of rectangular waveguide redirect the propagation path through a constant radius rather than an abrupt corner. By spreading the geometric discontinuity over the full length of the arc, a curved bend holds reflection low and suppresses unwanted mode conversion from the dominant TE₁₀ mode into higher-order modes. The bend may turn in the E-plane (the broad a walls sweep the arc) or the H-plane (the narrow b walls sweep the arc), and a mean radius of roughly 1.5 to 2 guide wavelengths typically keeps return loss better than 30 dB across a full band. Curved bends are a staple of compact millimeter-wave routing where space, low insertion loss, and broadband match all matter.

Category: Waveguide Engineering

Typical Radius: 1.5 to 2 λ_g

Return Loss: > 30 dB

How a Constant-Radius Arc Redirects Waveguide Energy

At any bend the guide forces the propagating fields to follow a curved path, which perturbs the otherwise uniform TE₁₀ field distribution. An abrupt right-angle corner presents a sharp impedance step that reflects energy and couples power into higher-order modes such as TE₂₀ and TE₃₀. A curved bend avoids that step by introducing the change of direction gradually: the wall follows a circular arc of mean radius R subtending an angle φ, so the effective discontinuity is distributed instead of localized. The longer the arc relative to the guide wavelength, the more adiabatic the transition and the lower the reflected and converted power.

The choice of bending plane sets which pair of walls follows the arc. An E-plane bend curves in the plane of the electric field, so the propagation axis sweeps in the direction of the narrow b dimension and the two broad a-dimension walls follow the arc while the narrow walls stay flat. An H-plane bend curves in the plane of the magnetic field, so the axis sweeps in the direction of the broad a dimension and the two narrow b-dimension walls follow the arc while the broad walls stay flat. Because the E-field is concentrated across the narrow dimension, an E-plane bend is generally the more reflection-sensitive of the two for a given mean radius, so designers either open up its radius or compensate the corner. Both are routinely cut by precision milling or paired with a waveguide twist for tight tolerance at high frequency.

In practice a curved bend is one option in a family that also includes mitered and stepped bends. The smooth arc trades a larger footprint for the broadest bandwidth and the cleanest mode purity, which is why it is favored in instrumentation feeds, antenna manifolds, and low-loss interconnects where the match must hold across an entire waveguide band rather than a single design frequency.

Bend Radius and Reflection

Guide wavelength (TE₁₀):
λ_g = λ₀ / √(1 − (λ₀ / 2a)²)

Arc length of the bend:
L_arc = R × φ (φ in radians)

Reflection guideline:
R ≳ 1.5 to 2 × λ_g → |S₁₁| < −30 dB

Where λ₀ = free-space wavelength, a = broad inner dimension, R = mean bend radius, φ = bend angle. Example: WR-90 at 10 GHz gives λ_g ≈ 39 mm, so a 90° bend with R ≈ 70 mm has an arc length of about 110 mm and typically achieves better than 30 dB return loss.

Curved Bend vs Other Waveguide Turns

Bend Type	Geometry	Bandwidth	Mode Conversion	Footprint	Best Use
Curved (constant radius)	Smooth circular arc	Full band	Very low	Large	Broadband low-loss feeds
Mitered (single cut)	One angled flat	Narrow	Moderate	Compact	Tight right-angle turns
Mitered (double cut)	Two angled flats	Moderate	Low to moderate	Compact	Optimized 90° corner
Stepped / compound	Short straight segments	Moderate	Moderate	Medium	Machined chassis routing
Twist + bend	Arc plus rotation	Band dependent	Higher	Large	Polarization + path change

Common Questions

Frequently Asked Questions

What bend radius gives the lowest return loss in a curved waveguide bend?

Reflection drops as mean radius increases, because a larger radius softens the impedance step at the entry and exit of the arc. A practical target is a mean radius of at least 1.5 to 2 guide wavelengths for better than 30 dB return loss across a band. For WR-90 near 10 GHz, λ_g ≈ 39 mm, so R ≈ 60 to 80 mm is a good start. Tighter radii raise reflection and risk higher-order modes; simulation or measured S-parameters should confirm the final geometry.

In an E-plane curved bend, do the broad or narrow walls follow the arc?

In an E-plane bend the axis sweeps in the direction of the narrow b dimension, so the two broad a-dimension walls follow the arc while the narrow walls stay flat; the bend lies in the plane of the electric field. An H-plane bend is the opposite: the axis sweeps in the direction of the broad a dimension, so the two narrow walls follow the arc and the broad walls stay flat. Because the E-field is concentrated across the narrow dimension, an E-plane bend is usually the more reflection-sensitive of the two for a given mean radius. The plane is chosen to fit the routing geometry and the return-loss budget.

How does a curved bend compare to a mitered or stepped bend?

A curved bend uses a continuous arc that spreads the discontinuity over its length, giving the broadest bandwidth and lowest mode conversion. A mitered bend uses one or two angled cuts whose reflections cancel at the design frequency, yielding a compact part with a narrower band. A stepped bend approximates the turn with short straight segments. Curved bends win when broadband match matters and space allows; mitered bends win for compact right-angle turns.

Related Terms

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