Split ring: estimate resonance
A split ring is a conductor ring with a gap. Without a component in the gap it resonates, to a first approximation, like a bent half-wave dipole; with a capacitor in the gap, like an LC circuit. The tool provides starting values for measurement, also for several rings.
Free, no account needed
Abbreviations and symbols on this page (6)
- Split ring (SRR)
- Conductor ring with a gap (split ring resonator). To a first approximation it resonates like a bent half-wave dipole; a capacitor in the gap turns it into an LC circuit.
- L
- Inductance of a coil, unit henry (H). Indicates how strongly the coil opposes a change in current.
- C
- Capacitance of a capacitor, unit farad (F). Indicates how much charge it stores per volt.
- pF, nF, µF
- Pico-, nano-, microfarad: 1 nF = 1000 pF, 1 µF = 1000 nF.
- k (shortening)
- Factor by which a wire antenna is shorter than the free-space half wave; about 0.95 for thin wires (rule of thumb 468 ÷ f in feet). Height and surroundings shift it.
- λ/4
- Quarter of the wavelength λ = c ÷ f (c = speed of light). A secondary coil resonates much like a quarter-wave radiator.
| Ø | Wire length | L | Resonance (half wave) |
|---|---|---|---|
| 100 mm | 31.22 cm | 250.8 nH | 456.2 MHz |
Capacitance of the empty gap only about 13.91 fF: without a capacitor the wire length determines the resonance.
Formula
Without capacitor: f ≈ k × c ÷ (2 × wire length), wire length = π D − gap, k ≈ 0.95. With capacitor C in the gap: f = 1 ÷ (2π √(L (C + C_gap))), L = µ0 R (ln(8 R ÷ a) − 2) (high frequency, a = wire radius), C_gap ≈ ε0 π a² ÷ gap.
Example
Ring Ø 100 mm of 2 mm wire with a 2 mm gap: wire length 31.2 cm, resonance as a bent half-wave dipole about 456 MHz. With 100 pF in the gap (L ≈ 251 nH) about 32 MHz.
Notes
- Both models are rough approximations; deviations of 10–30 % are normal. Always measure the resonance, e.g. with a dip meter or a network analyzer and a coupling loop.
- A thin gap without a component has only a tiny capacitance (femtofarads); the wire length then determines the resonance.
- Several concentric rings influence each other; the values apply to each ring on its own.
- Only electrical quantities are calculated, no effects on living beings.