Broadband RF Transformers: Ratio, Ferrite, Loss and Power

“68:1,” “70:1,” turn count and a self-resonant-frequency label do not define a transformer. Start with the topology and port definitions, the measured complex source and load, the intended modes, a frequency-by-frequency loss budget and the worst electrical and thermal service conditions.

First Specify the Job, Ports and Modes

“Broadband RF transformer” covers several networks with different physics:

A two-port “unun,” a three-port balun and an installed antenna feed system are not interchangeable measurement objects. State which conductors form each port, where voltage is measured, how power returns, whether the enclosure or coax shield is a conductor in the model, and which common-mode current is allowed.

An Impedance Ratio Is Not a Complete Winding Recipe

For an ideal two-winding transformer with turns ratio a = N2/N1:

The relation transforms reactance as well as resistance. A 3,400 + j1,000 Ω antenna does not become a pure 50 Ω load through a nominal 68:1 impedance transformer; ideally it becomes 50 + j14.7 Ω before transformer parasitics and the return path are added.

What “68:1” and “70:1” mean in the ideal arithmetic

From a 50 Ω reference, the nominal real loads would be 3,400 Ω and 3,500 Ω. Their ideal turns ratios are √68 ≈ 8.246 and √70 ≈ 8.367—a difference of only about 1.46%. Integer turns, taps and transmission-line sections do not automatically realize either decimal value. A manufacturer may use the label for a target transformed impedance or a measured/compensated design, so the topology and test definition must accompany the number.

End-fed half-wave feed impedance is not fixed. It changes with wire length and diameter, frequency, height, slope, nearby conductors, ground, feedline route, counterpoise or return conductor and loss. The impedance can also move sharply between harmonically related bands. Measure the installed complex impedance at the transformer output plane, with the intended return path present, before selecting a ratio.

The Low-Frequency Limit Is a Complex Shunt Problem

At low frequency, finite magnetizing impedance draws current that does not reach the load. It is not enough to say “make X_L high.” The branch includes stored and dissipative terms that change with frequency, excitation and temperature:

Fair-Rite’s current page for its 61-material 61 mm toroid, for example, lists A_L = 170 nH ±25% and says that value is tested at 10 kHz. Its complex-permeability and power-loss data are separate. The example is not a recommendation for this transformer. It shows why a small-signal A_L value cannot be treated as the HF, high-voltage magnetizing inductance or as a complete core-loss model.

Rules such as “make magnetizing reactance four or ten times 50 Ω” are starting heuristics with a declared insertion-loss target and load. They are not universal pass criteria. Calculate the complete network with the actual complex load and confirm accepted current, transformed impedance, loss and temperature at the low-band corner.

The High-Frequency Limit Is Usually Multi-Resonant

Leakage inductance, winding capacitance, lead inductance, the transmission-line propagation delay, compensation and the load form a distributed network. That network can have several poles and zeros. “The SRF” measured with one open, short or resistive termination may not be the resonance that controls performance with the antenna attached.

More turns often increase magnetizing inductance. They may also increase winding length and inter-turn electric-field coupling, but capacitance and leakage are not guaranteed to move monotonically: sectioning, winding distribution, conductor spacing, interleaving, the core window and the topology decide. The useful engineering rule is:

Wire diameter and insulation affect AC resistance, skin and proximity effect, conductor temperature, spacing, characteristic impedance, capacitance, voltage withstand and mechanical fit. Lead routing and connector/enclosure fields may be as important as the turns on the core. A build drawing needs conductor type, finished diameter, insulation system, pitch, crossover positions, start/finish routing, tap positions and permitted movement—not just “N turns.”

Ferrite “Mix” Is a Family Name, Not a Power Model

Ferrite behaviour is described by frequency-, field- and temperature-dependent data. In a common phasor convention, complex permeability is written μ* = μ′ − jμ″: μ′ represents the field-storage contribution and μ″ the loss contribution. Both change across HF, and high excitation requires amplitude permeability and core-loss data rather than only small-signal initial permeability.

Fair-Rite currently describes its 67 material as a NiZn ferrite intended for broadband transformers and antennas up to 50 MHz. For one 61 mm toroid, it publishes A_L = 55 nH with +35/−25% tolerance, measured at 10 kHz, plus core dimensions and material curves. That is useful part-specific input—not evidence that any winding on that core is efficient or safe to 50 MHz.

TDK’s ferrite definitions state the essential power boundary: core loss depends on material, core shape, frequency, flux density and temperature, while total component loss also includes winding loss, insulation, skin effect and proximity effect. IEC 62044-2 covers low-excitation core-property measurement; IEC 62044-3:2023 covers power loss and amplitude permeability at high excitation. Do not combine values taken under incompatible tests.

Mechanical stress belongs in the magnetic specification

Fair-Rite warns that strong magnetic fields or excessive mechanical stress can irreversibly change permeability or losses. Adhesive, tape or clamping is therefore not universally good or bad: the material compatibility, cure shrinkage, clamp force, thermal expansion, heat path and winding retention must be qualified. A cracked core or moving winding can change both magnetic and parasitic behaviour.

Changing One Turn Is Not a Neutral Production Trim

Adding or removing a turn per unit when A_L varies can be a documented design variant, but it is not automatically the correct production response:

• magnetizing inductance changes approximately with N² under the applicable small-signal conditions;
• an ordinary transformer’s turns ratio and transformed impedance change;
• a tap or transmission-line section may change its voltage/current relationship;
• winding length, spacing, crossover and lead position change parasitics;
• flux per turn and insulation stress change at the same applied voltage.

Design for specified component tolerances, choose or bin parts using a documented property when justified, control the winding process, and validate statistical or worst-case units. If turn count is an allowed adjustment, define the permitted variants and require every electrical, thermal and mode-balance limit to pass—not only input SWR.

Define Bandwidth by Several Limits

A broadband passband should state the source/load conditions, reference planes and limits for the properties that matter:

• input return loss or VSWR;
• transducer loss and dissipative loss;
• output impedance or transformation error;
• amplitude and phase balance for a balanced output;
• common-mode rejection or common-mode impedance when required;
• maximum core, conductor, insulation and enclosure temperature;
• peak voltage, RMS current, waveform, accepted power and mismatch envelope;
• repeatability across unit, lot, temperature and ageing.

One transformer can meet the SWR limit and fail the temperature or current-balance limit. Another can show a smooth 50 Ω sweep while dissipating unacceptable power. “Works from 80 to 10 metres” is not a specification until those limits and test loads are supplied.

Power Handling Has Magnetic, Copper and Dielectric Limits

Faraday’s law is the clean starting point for the flux-coupled portion:

In a transmission-line transformer, the voltage that drives net core flux depends on topology, balance and common-mode excitation; it is not automatically the full port voltage. Derive the winding voltage from the actual circuit. At HF, heating can become unacceptable well below a catalogue saturation-flux value because core-loss density is nonlinear in frequency, flux and temperature.

High ratio creates a real insulation problem

The following ideal arithmetic assumes a pure 50 Ω input transformed to a pure 3,400 Ω load with no loss. It is not a rating:

Those voltages demand specified conductor insulation, spacing, creepage, terminals, enclosure clearance, contamination and humidity conditions. A Fair-Rite statement that a particular thermo-set core coating withstands 1,000 V RMS uniformly across the core’s C dimension is only that coating test. It is not a winding-to-winding, winding-to-core, terminal or assembled-transformer voltage rating.

Thermal rating requires a complete loss budget

Core curves apply only at their stated material, shape, frequency, flux waveform and temperature. Copper loss uses AC—not merely DC—resistance and includes proximity effects. Dielectric and contact losses may localize near the high-voltage end or a tap. Temperature depends on duration, transmit fraction, ambient, enclosure, airflow, mounting and nearby heat sources.

Mode names are not thermal specifications. State carrier or PEP, modulation, transmit fraction, tune interval and test duration. Test the highest expected mismatch and complex load, not only a matched dummy load. Stop on temperature, resistance, impedance, odour, discharge or mechanical-change limits defined before the test.

Measure the Device You Intend to Use

Mini-Circuits defines transformer insertion loss relative to an ideal transformer of the same ratio in a properly terminated system and shows that non-50 Ω outputs need transformation or matching in the test. That is the central discipline: a 50 Ω VNA does not make a high-impedance output into a 50 Ω device.

Small-signal two-port or multiport characterization

1. Define ports and modes. For a balanced output, use a three-port or mixed-mode representation where practical; do not hide imbalance by combining conductors incorrectly.
2. Move the calibration plane. Calibrate at the fixture connection or characterize and de-embed adapters, launches and high-impedance fixtures. IEEE 370-2020 and Keysight’s handbook describe fixture and reference-plane discipline.
3. Use appropriate terminations. Measure with the design load and a matrix of representative complex loads. Renormalization alone does not remove fixture parasitics or create a physical high-impedance standard.
4. Report the full response. Include complex S- or Z-parameters, return loss, transfer, balance and uncertainty—not a screenshot of SWR.
5. Repeat connections and units. Cable movement, connector repeatability, fixture geometry, instrument noise and unit variation belong in the uncertainty budget.

At 28 MHz, only 1 pF has a reactance magnitude of about 5.68 kΩ—already comparable with a 3.4 kΩ target load. An open fixture, probe pad, enclosure wall or winding crossover can therefore change a high-ratio result materially. Open/short/load compensation or a characterized fixture must reproduce the DUT connection geometry.

S₂₁ is not automatically efficiency

For a matched two-port at small signal, power-wave transmission is useful. With unequal reference impedances, mismatch, a balanced port, reactive termination or a lossy matching fixture, raw |S₂₁|² is not the complete load efficiency. State source and load impedances, remove fixture/matching losses with uncertainty, calculate accepted input power, and measure delivered load power.

A back-to-back pair can compare a combined matched path, but dividing dB by two assumes suitably identical devices and non-interacting fixtures under that condition. It cannot prove loss into a different complex antenna load. Direct multiport characterization and a separate large-signal power balance are stronger evidence.

Large-signal and thermal validation

1. Measure the actual source and load networks across the required bands.
2. Set calibrated input and output power planes; include coupler directivity, mismatch and meter uncertainty.
3. Apply the declared waveform, duty and mismatch in safe steps with interlocking and shielded high-voltage construction.
4. Measure delivered power, reflected power, harmonic content and temperature until the specified thermal condition is reached.
5. Use sensors that do not disturb the RF field; correct thermal imaging for emissivity and viewing geometry.
6. Repeat at ambient extremes and after mechanical/thermal ageing; inspect ferrite, insulation, solder joints and winding position.

A Repeatable Production Control Plan

Bottom Line

Broadband RF transformers are not copy-and-paste components. Core tolerance, conductor, winding geometry and assembly all affect the result. A defensible engineering process begins with topology, ports, modes and the complex source/load, then ends with calibrated large-signal and thermal qualification.

Do not use nominal turns, A_L, “SRF,” a dummy-load SWR trace or a ferrite frequency label as a proxy for efficiency or power. Specify transformation error, loss, balance, common mode, voltage, current and temperature over frequency and load. Then control the drawing, fixtures and lots tightly enough that every released unit meets those limits.

Questions, antenna-factor records or height trials to share? Contact RF.Guru.