3×5:8λ PMR antenna :Clean, Matched, 3D Printable

Here’s a estimate of RF losses in PVC tube.

Assumptions: D = 20 mm, wall = 1 mm → r2 = 10 mm, r1 = 9 mm; centered radiator a ≈ 1 mm; f = 446 MHz so λ ≈ 0.672 m and R ≈ λ/(2*pi) ≈ 107 mm; epsilon_r ≈ 3.2; tan(delta) ≈ 0.01–0.02.

Fraction of energy in the PVC wall

Formula (thin-wire in a coax-like shell): Wd/Wtot = (epsilon_r * ln(r2/r1)) / (epsilon_r*ln(r2/r1) + ln(r1/a) + ln(R/r2))

Numbers (mm): ln(r2/r1) = ln(10/9) = 0.10536 epsilon_rln(r2/r1) = 3.20.10536 = 0.337 ln(r1/a) = ln(9/1) = 2.197 ln(R/r2) = ln(107/10) = 2.370

So: Wd/Wtot = 0.337 / (0.337 + 2.197 + 2.370) = 0.337 / 4.905 = 0.069 ≈ 6.9>#/p###

Dielectric loss (referred to radiated power)

Formula: Pdiel/Prad ≈ Qrad * tan(delta) * (Wd/Wtot)

Typical dry case: Qrad = 10 (thin wire), tan(delta) = 0.01 → Pdiel/Prad = 100.010.069 = 0.0069 (0.69%) → ≈ 0.03 dB

Pessimistic dry case: Qrad = 20, tan(delta) = 0.02 → Pdiel/Prad = 200.020.069 = 0.0276 (2.76%) → ≈ 0.12 dB

Conclusion (D = 20 mm, wall 1 mm, dry, retuned): additional RF loss ≈ 0.03–0.12 dB, typically ~0.05–0.08 dB. The dominant effect remains detuning but as I explained I correct during tuning (and it's true the effect of PVC is important).