Why Does Flexible Waveguide Have Higher Loss?

Conventional flexible metal waveguide generally loses more power than comparable rigid waveguide because its corrugated or jointed wall changes the RF surface-current distribution, while material, surface finish and installation geometry add further losses. Bending, twisting and imperfect connections can also reflect power. The measured insertion loss therefore includes more than metal heating, and there is no universal flexible-to-rigid loss multiplier.

A useful historical comparison comes from NASA’s 1970 antenna design study: flexible WR-90 was assigned 0.08 dB/ft, versus 0.04 dB/ft for rigid aluminium and 0.033 dB/ft for rigid oxygen-free copper. The rigid figures are specified at 12.2 GHz; the flexible figure has no stated frequency. These are design-study values, not a controlled measurement of otherwise identical guides. [1]

Where the extra loss comes from

Wall geometry changes the current distribution

RF current flows near the conducting surface. In the dominant TE₁₀ mode, a rectangular guide’s broad walls carry both transverse and longitudinal surface-current components. Conductor dissipation depends on the surface resistance and the integral of squared current over the wall. A corrugated wall changes that geometry and current distribution; a seam can add contact resistance where current crosses it. This is more precise than imagining all the current travelling straight down the guide or climbing every fold in the same direction. The smooth-wall derivation provides the baseline, not a numerical corrugation penalty. [2]

Construction matters: a continuous conducting wall and a mechanically contacting seam need not have the same loss. Compare the core material, plating and seam construction of the actual flexible assembly, rather than treating every flexible product as electrically identical.

Surface resistance and finish matter

For a good conductor, surface resistance increases approximately as √(f/σ), where f is frequency and σ is conductivity. Using pure copper at 5.8 × 10⁷ S/m, the calculated skin depth is about 0.66 µm at 10 GHz and 0.21 µm at 100 GHz. Finish and plating quality therefore matter on a very small scale; those skin depths alone do not establish a roughness-loss multiplier. [3]

A NASA-sponsored North Carolina State University study investigated conductor-surface treatment and roughness effects on millimetre-wave attenuation. It supports treating surface condition as a loss variable, but does not establish that every flexible guide has the same roughness or a fixed percentage penalty. [4]

Bends and interfaces can reflect power

A tight bend, distorted cross-section or misaligned flange can change the field distribution and worsen the impedance match. Higher-order fields near a discontinuity are not automatically power lost forever: below their cutoff they are evanescent, and their effect is included in the overall reflection and transmission. The operating frequency and geometry determine which modes can propagate. [2]

Match the flange interfaces and any transitions as well as the guide size. For illustration, VSWR 1.2:1 corresponds to |Γ| = 0.0909, or 0.826% reflected power. The associated mismatch loss is approximately 0.036 dB, calculated as −10 log₁₀(1 − |Γ|²). That reflected power is not heat deposited in the flexible wall, and multiple interfaces cannot generally be assessed by simply adding their isolated mismatch losses.

How much higher is the loss?

The NASA study provides a traceable starting point. Converting its figures with 1 ft = 0.3048 m gives the following values. [1]

The arithmetic ratios are 2.0 against aluminium and about 2.4 against copper. They describe these reported values only. Differences in frequency conditions, material, finish and interfaces prevent using them as an isolated measure of corrugation loss.

Dolph’s seamless flexible catalogue lists 0.40 dB/m for WR-90 over 8.2–12.5 GHz. Its rigid tube table lists 0.126–0.182 dB/m for WR-90 aluminium. Dividing 0.40 by 0.182 gives about 2.2, but these are catalogue entries with different assembly boundaries, not matched measurements at one frequency. Use the ordered assembly’s insertion-loss specification to set the budget.

A second catalogue cross-check is useful when units differ. The WR650 model DH-14WWEL300PMC lists 0.035 dB for a 300 mm section over 1.12–1.7 GHz. Dividing by 0.300 m gives 0.117 dB/m, close to the family entry of 0.12 dB/m over 1.13–1.73 GHz. The bands are different, and normalising one assembled section does not prove that its complete loss scales linearly at every other length.

What the smooth-wall formula can tell you

For an air-filled, smooth rectangular guide carrying TE₁₀, the conductor attenuation is:

α_c = R_s[1 + (2b/a)(f_c/f)²] / [bη₀√(1 − (f_c/f)²)] Np/m.

Here a and b are the internal broad and narrow dimensions, f_c = c/(2a), R_s = √(πfµ₀/σ), and η₀ is the intrinsic impedance of air, approximately 376.73 Ω. It is not the frequency-dependent TE-mode wave impedance. Multiply Np/m by 8.686 to obtain dB/m. The cutoff-dependent square-root term is essential. [2]

With WR-90 dimensions a = 22.86 mm and b = 10.16 mm at 12.2 GHz, this calculation gives approximately 0.0975 dB/m for copper at σ = 5.8 × 10⁷ S/m, or 0.146 dB/m for brass at an assumed σ = 2.6 × 10⁷ S/m. These are ideal smooth-wall calculations, not product measurements. The conductivity values follow the university examples. [3] [2]

This model helps separate conductivity and cross-section effects. It cannot tell you what fraction of a flexible assembly’s loss comes from corrugations without matching its material, frequency, finish and interfaces.

A worked loss budget for a 3 m run

Consider a hypothetical WR-90 run with 3 kW incident average power. For a preliminary band-level estimate, assume 0.40 dB/m for the flexible length and 0.126–0.182 dB/m for rigid aluminium, using the catalogue entries above. These are not verified attenuation values at a particular frequency, and the example is not approval to operate a particular assembly at 3 kW.

For distributed attenuation, L = αℓ in dB and P_out = P_in × 10^−L/10. Applying those equations gives:

The flexible estimate costs an additional 0.654–0.822 dB, or roughly 370–474 W less delivered power at the same input. If all the attenuation were dissipative and reflection negligible, the missing power would become heat. With measured insertion loss, some power may instead be reflected. For a passive two-port with a matched output and power-normalised S-parameters, absorbed power is P_in(1 − |S₁₁|² − |S₂₁|²), provided radiation and other propagating output modes are negligible.

Do not multiply the first metre’s heat by three. Under the purely dissipative 0.40 dB/m assumption, successive metres dissipate about 264 W, 241 W and 219 W because less power reaches each section. Their total is about 724 W.

If the installation needs only 300 mm of flexible length, its distributed-loss allowance at 0.40 dB/m is 0.12 dB, corresponding to about 82 W not transmitted at 3 kW. Confirm the actual short assembly’s complete insertion loss: fixed end effects need not scale with length. Include additional adapters or transitions once, using the same reference planes throughout the budget.

What documented engineering experience shows

NASA’s limited-motion joint study used a total of 12 inches of flexible WR-90 per channel and estimated approximately 0.10 dB total joint loss, including the rigid portions. Its mechanical analysis used 6-inch sections for ±10° motion and computed a bend radius at least 15 times the manufacturer’s minimum. This was a design-specific fatigue analysis, not a universal bend-radius rule. The useful lesson is to specify the motion and repeated-flexing requirement before choosing the shortest workable section. [1]

TRW’s 1980 Ku-band multiple-beam antenna report provides a measured system example. Its 25-element feed included 25 flexible waveguide sections, with measured total feed-circuit loss of 0.56 dB at 11.7 GHz and 0.47 dB at 12.2 GHz, and in-band VSWR below 1.2:1. These are losses of the whole feed network, not of the flexible sections alone. [5]

The report describes phase adjustment by reforming flexguide and trimming flanges. It attributes excess breadboard feed loss to the long waveguide run and flexible sections used for phase equalisation, then proposes eliminating the flexible sections and shortening the run in flight hardware. That is a documented design proposal, not evidence that rigid guide accommodated ongoing mechanical movement or that a completed flight assembly achieved a particular loss. [5]

How to reduce and verify the loss

• Keep flexibility local. Use rigid guide for fixed runs and compare rigid miter bends for fixed turns. Reserve flexible length for alignment, vibration isolation or specified motion.
• Specify the installed shape. Provide flange orientations, bend radius in each plane, twist angle, support positions and motion limits. Bending capability does not establish torsion capability; check the separate twistable assembly specifications.
• Check power and temperature together. State average and peak power, duty cycle, pressure, ambient temperature and cooling. Product-family figures are not guarantees for every length, jacket or bend configuration.
• Request installed-condition measurements. Ask for insertion loss and return loss across the operating band, with calibration reference planes at the assembly ends. Compare the straight and installed configurations, and include relevant motion positions when the guide moves.
• Keep the comparison controlled. Use the same frequency, flange interfaces, length basis and measurement setup. Record calibration method and uncertainty; a small loss difference is meaningful only relative to measurement uncertainty.

NIST Technical Note 2109 documents traceable waveguide calibration models and uncertainty propagation for WR15 measurements at 50–75 GHz. It supports the measurement principle, not a certification or test result for flexible WR-90. Choose a calibration and verification kit matched to the actual band and interfaces. [6]

The practical answer is to minimise the length that must flex and budget the specified loss of the complete installed assembly. Geometry, conductivity, surface condition and matching all matter. A historical 2× comparison can illustrate the trade-off, but it cannot replace an assembly-specific loss and power specification.

References

1. NASA CR-72628, Antenna Pattern Shaping, Sensing, and Steering Study, 1970. Sections 2.2.3, 2.2.7 and 4.1.1.2.
2. University of Houston, D. R. Jackson, Notes 8: Rectangular and Circular Waveguide. TE₁₀ wall currents and conductor attenuation, slides 27–32.
3. University of Houston, D. R. Jackson, Notes 7: Attenuation. Surface resistance, skin depth and conductor loss.
4. North Carolina State University, Study of Rectangular-Guide-Like Structures for Millimeter Wave Transmission, NASA-sponsored progress report, 1970.
5. C. C. Chen and C. F. Franklin, TRW for NASA, Ku-Band Multiple Beam Antenna, December 1980. Feed development and conclusions.
6. NIST Technical Note 2109, Physical Models and Dimensional Traceability of WR15 Rectangular Waveguide Standards, 2020.