From a Back-to-Back Trace to a Real EFHW Transformer Test

The familiar experiment is attractive: transform 50 Ω upward through one EFHW transformer, reverse the ratio through a second transformer and measure between two 50 Ω instruments. If the pair loses 0.4 dB, it is tempting to write 0.2 dB on each unit. That split is an estimate with conditions, not a universal measurement law.

What the Pair Actually Measures

A full two-port VNA measurement returns S11, S21, S12 and S22 for the complete cascade between its calibrated planes. That includes both transformers, connectors, low-side wiring, the high-impedance junction, compensation components, enclosure coupling and any unintended exterior-current or radiation path.

The pair is useful for finding:

• small-signal passband and resonances;
• input and output mismatch;
• forward/reverse transmission and reciprocity;
• repeatability between builds and orientations; and
• sensitivity to junction length, spacing, shielding and compensation.

It does not contain an installed EFHW radiator, its ground environment or its coax return path. It therefore cannot measure antenna radiation efficiency, realized gain or pattern.

Why Pair Loss Is Not Automatically Twice Unit Loss

If two electrically identical, reciprocal units are cascaded with a well-defined internal connection and negligible fixture effects, half the pair loss in decibels can be a useful estimate. Real high-ratio transformers challenge each assumption.

The high-impedance ports are sensitive to lead inductance, a few picofarads of capacitance, enclosure position and nearby conductors. Their complex port impedances may not be conjugately matched at the junction. Waves can reflect repeatedly between the two units, and the phase of that interaction can raise or lower S21.

Make the Bench Result Reproducible

Before comparing traces, record:

• transformer topology, winding arrangement and component values;
• port definitions, reference impedance and calibration planes;
• high-impedance-junction length, spacing, support and shield geometry;
• cable and adapter characterization or de-embedding method;
• sweep power, IF bandwidth, averaging and frequency points;
• orientation of cores, enclosures and coax; and
• temperature, unit identity and connector repeatability.

Repeat the measurement with the two units exchanged and each physically reversed where the topology allows it. A result that moves with orientation or spacing is evidence that the fixture is part of the measurement.

Use All Four S-Parameters

S21 magnitude alone hides input mismatch, output mismatch and phase. Measure S11, S21, S12 and S22 as complex quantities. If the units and junction can be represented by characterized two-port networks, cascade or de-embed them with scattering-transfer methods rather than multiplying magnitudes alone.

Calibration removes systematic error only to its stated planes. Port extension corrects electrical delay; it does not generally remove connector, launch, lead and high-impedance-junction behaviour.

Add a Representative Load Matrix

An EFHW feedpoint is a complex, installation-dependent load. A nominal 49:1 calculation maps one 2450 Ω resistance to 50 Ω in an ideal transformer, but the antenna rarely presents that fixed value across all used bands.

After the pair test, evaluate a single transformer with characterized loads spanning the resistance and reactance expected at its antenna port. For each load, record input impedance, accepted power, delivered power, fixture loss and uncertainty. Do not expose an ordinary resistor or VNA fixture to voltage beyond its rating.

Small-Signal Loss Is Not Rated-Power Loss

A VNA normally operates at milliwatt levels. At transmitter power, ferrite behaviour, conductor resistance, dielectric loss and temperature may change. Reactive loads can create high winding current or terminal voltage even when average delivered power seems modest.

A rated-power test needs calibrated incident, reflected and delivered-power planes, a characterized load, remote temperature sensing, a declared waveform and duty cycle, safe clearances and an uncertainty budget. Do not infer continuous-duty capability from a brief speech-peak test.

Turn the Test Into a Power Ledger

Report the quantities separately:

• incident and reflected power at the transformer input;
• power accepted by the transformer;
• power delivered to the characterized load;
• fixture and connector loss;
• transformer temperature rise and stabilization time; and
• measurement uncertainty.

If a result is only the pair’s S21, publish it as the pair’s S21. That is not a weak conclusion. It is an honest and repeatable starting point for the next experiment.

Engineering References

• Keysight: S-Parameter Techniques for Network Design
• Keysight: De-Embedding and Embedding S-Parameter Networks
• NIST: De-Embedding and Unterminating Microwave Fixtures
• Fair-Rite: Use of Ferrites in Broadband Transformers

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