ITML Calculator

Inductively Tunable Magnetic Loop

DJ5SE | Coax Loop Antenna Calculator

Calculate Coax Loop Antenna:

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find_itml

Frequency → Geometry

Finds optimal loop geometries for a target frequency.

"What loop size for 10 MHz?"

→

sweep_itml

Geometry → Frequency Range

Calculates the tuning range for a given loop geometry.

"What range does my 50 cm loop cover?"

Concept

ITML antennas use coaxial cable simultaneously as:

Inductance - Shield as RF conductor (loop)
Capacitance - Inner conductor + shield as coaxial capacitor
Tuning element - Variable turn spacing changes mutual inductance M

How It Works

The ITML is a series-resonant magnetic loop antenna entirely made of coaxial cable. Like any LC circuit, it resonates when inductive and capacitive reactance are equal: X_L = X_C, giving a resonant frequency of f = 1 / (2π · √(L · C)). At resonance, RF current circulates in the loop at very high amplitude, producing a strong magnetic near-field and, consequently, radiation.

What makes the ITML unusual is that the same coaxial cable simultaneously provides both reactive components:

Inductance — the outer shield forms the loop conductor. Two turns are wound into a circular loop. Total inductance L_total = 2·L₁ + 2·M_eff combines the self-inductance of each turn (L₁, via the Neumann formula) with the mutual inductance M_eff between them — which depends on their axial spacing d(φ).
Capacitance — with one end short-circuited (inner conductor to outer shield), the cable acts as a distributed coaxial capacitor: C = C_pF/m · N · π · D. No separate vacuum or butterfly capacitor is required.

Differences from a classic single-turn magnetic loop

Two turns instead of one — doubles inductance, enabling resonance at a practical diameter for the 80m, 40 m, 30 m, and 20 m bands.
Fixed capacitance — the coax itself provides C, eliminating the most expensive and mechanically fragile component of a classic mag loop.
Tuning via turn spacing — increasing the axial gap d_oben at the top of the loop reduces M_eff, lowers L_total, and shifts resonance upward. A few centimetres of movement sweeps several hundred kHz.
Smaller diameter — the two-turn geometry and higher coax capacitance allow resonance at roughly half the diameter of a comparable single-turn loop.

Geometry dimensioning

Dimensioning is an iterative process: for a given cable type and target frequency, the calculator sweeps loop diameters D, checks whether f_target falls within the achievable tuning range, and uses a Brent root-finding algorithm to solve for the exact turn spacing d_oben that yields resonance at f_target. Results are ranked by practical Q factor Q_prakt = Q_theo / k_prakt, where k_prakt is a cable-specific empirical derating factor accounting for connector resistance, skin-effect corrections, and construction quality.