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Helical resonator filter calculator

When you need this

A helical resonator is a quarter-wave line coiled into a helix and put inside a shield. At VHF and UHF it gives a Q in the hundreds or thousands where an LC circuit gives tens.

A two-section helical resonator filter: two helices in a common shield
Drawing from the design method
trimmer capacitorintapiouttapuHSdbKhdetail of the windingτd₀NZ₀Qu
A section through the front wall, in the true proportions of the model. There is one liberty: the tap point is raised a little above the floor — in reality it sits almost hard against the «cold» end of the helix
Operating frequency f₀ (MHz)
−3 dB bandwidth ΔF (MHz)
Permissible passband loss α (dB)
Input impedance Ri (Ω)
Output impedance Ru (Ω)
Helix diameter d (cm) — leave empty for the optimum
Resonator
Unloaded Q, Qu
Loaded filter Q, Ql
Resonator characteristic impedance Z₀
Calculated passband loss α₀
Helix
Helix diameter d
Helix length b
Number of turns N
Winding pitch τ
Wire diameter d₀
Input tap (turns from the cold end)
Output tap (turns from the cold end)
Shield and partition
Shield width S
Shield height H
Window above the partition h
Partition height K

📐 Formulas​

The design runs from the requirements to the hardware: the passband and the permissible loss give the Q you need, the Q gives the diameter of the helix, and the diameter gives every remaining dimension.

Qu = (f₀/ΔF) · 1.414 / (10^(α/20) − 1)      required Q
d  = Qu / (35.9·√f₀)                         helix diameter, cm

b  = 1.5·d                                   length of the helix
S  = d / 0.66                                width of the shield
H  = 1.6·S                                   height of the shield
N  = 2674 / (f₀·d)                           number of turns
τ  = b / N                                   winding pitch
d₀ = τ / 2                                   wire diameter
Z₀ = 136190 / (f₀·d)                         characteristic impedance of the resonator

f₀ is in megahertz, the lengths are in centimetres.

Tap points. The loaded Q of a two-section filter is Ql = 0.707·f₀/ΔF:

X = π/4 · (1/Ql − 1/Qu)
tap(R) = arcsin( √(0.5·X·R/Z₀) ) · N · 2/π

The wall between the sections:

h = d · (10·α/f₀)^(1/1.91)
K = 1.5·d + 0.3·d/0.66 − h

The reverse pass (with the diameter entered by hand):

Qu = 35.9·d·√f₀
α  = 20·log₁₀( 1 + 1.414·(f₀/ΔF)/Qu )

Notation:​

  • f₀ — working frequency [MHz]
  • ΔF — passband at the −3 dB level [MHz]
  • α — permissible in-band loss [dB]
  • Qu — unloaded Q of the resonator
  • d — helix diameter [cm]
  • Z₀ — characteristic impedance of the resonator [Ω]
Limits of the calculator:
  • The proportions (b = 1.5d, S = d/0.66, H = 1.6S) are empirical: depart from them badly and the calculation no longer holds
  • If the passband you ask for is narrower than the achievable Q allows, the calculator says so: Ql cannot exceed Qu
  • The calculated Q is an optimistic upper bound: the real one depends on the surface finish of the conductor and on the contact between the helix and the shield

🎯 Where it is used​

  • VHF band-pass filters in receivers and transmitters.
  • Preselectors where an LC circuit does not give the selectivity needed.
  • Protecting a receiver front end from strong out-of-band signals.
Practical notes:
  1. The ±0.1 cm buttons fit the diameter to the enclosure you have: the calculator runs backwards and shows what the Q and the real loss then become. The price of a smaller box is visible at once.
  2. Silver-plating the inside of the shield and the helix itself raises the Q noticeably — at VHF that is not cosmetic.
  3. The taps are counted from the «cold», earthed end of the helix. Mixing up the ends is the commonest mistake when tuning.

© 2026 UR3PKI · CyberDev.Space · Content licensed under CC BY-NC-SA 4.0.

How to cite this calculator
UR3PKI. «Helical resonator filter calculator». CyberDev.Space. https://cyberdev.space/en/radio/calculators/coils/helical_resonator (licence CC BY-NC-SA 4.0).

The licence lets you use this material freely, including in teaching materials, but only with attribution to the author and a link to the source.

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