Binocular transformer calculator

When you need this

When you have to wind a broadband impedance transformer (a 1:1, 4:1 or 9:1 balun), a feed choke or an isolating winding: on a two-hole binocular core both windings are threaded through the holes, so it gives isolation and transformation in one body.

A — length, B — width, C — height, H — hole diameter; one turn is the wire passed through both holes

Core
Lowest operating frequency f (MHz)
Low-impedance side Z1 (Ω)
Impedance ratio Z2:Z1
Power (W)
Reactance margin k

Result
Minimum inductance L_min
Primary turns N1 (Z1 side)
Secondary turns N2 (Z2 side)
Secondary impedance Z2
Actual inductance L at N1
Required reactance k·Z1
Actual primary XL at N1
Primary voltage (RMS)
Secondary voltage (RMS)
Mode from the datasheet

📐 Formulas

A turn on a binocular core is counted differently from a turn on a toroid: one turn is the wire passed through both holes and closed around the end of the core. That is the winding the manufacturer measures AL for, so the formulas below hold only for it.

The inductance of a winding on a ferrite core is set by the inductance factor AL, which says how many nH one turn gives:

L [µH] = AL·N² / 1000
N = √(L·1000 / AL)

Here AL is the inductance factor [nH/turn²] (the catalogue figure for the core) and N is the number of turns.

The minimum primary inductance follows from the condition that its reactance at the lower band edge must exceed the load by a factor of k:

L_min = k·Z1 / (2π·f)
XL = 2π·f·L

The impedance ratio is the square of the turns ratio, so the winding on the high-impedance side has more turns:

Z2 / Z1 = (N2 / N1)²
N2 = N1·√(Z2 / Z1)

Notation:

L — inductance [µH]
AL — inductance factor [nH/turn²]
N — number of turns
k — reactance margin (3, 5 or 10)
Z1, Z2 — impedances of the low and high sides [Ω]
f — lowest working frequency [MHz]
XL — reactance [Ω]

Limits of the calculator:

AL has a tolerance of ±10–20% — the real figure for a particular core can differ; better to measure it than to trust the datasheet
The upper band edge is empirical: the winding adds its own capacitance, and above resonance the transformer stops behaving as one — the more turns, the lower that edge
Not for power chokes in switching supplies: there it is core saturation that decides, not AL, and the core is chosen by its L·I² energy
AL holds only for a winding through both holes: wind around a single hole and the catalogue figure no longer applies, so the inductance has to be measured

🎯 Where it is used

A 4:1 balun, 50 → 200 Ω with a lower edge of 3.5 MHz: enter Z1 = 50 Ω and the ratio 4:1, and the calculator gives the primary and secondary turns.
A feed choke for 160 m (1.8 MHz) in a receiver: a single winding through both holes, with a high reactance at the working frequency.
Isolating the antenna from the feeder — a 1:1 balun at the feedpoint of a balanced antenna, where the impedances already match but the current on the coax braid has to be cut off.

Practical notes:

Count the turns properly: the wire goes into one hole and back through the other. One and a half passes is not «one and a half turns» but a spoiled calculation: what goes into the formula is the number of complete passes through both holes.
Keep the leads short — every extra centimetre adds leakage inductance and lowers the upper band edge.
Do not use wire thicker than the hole in the core: it must pass through freely, otherwise the winding distorts or damages the ferrite.

How to cite this calculator

UR3PKI. «Binocular transformer calculator». CyberDev.Space. https://cyberdev.space/en/radio/calculators/coils/ferrite_cores/binocular (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.

📐 Formulas​

Notation:​

🎯 Where it is used​

📐 Formulas

Notation:

🎯 Where it is used