VNA-Only Calibration of Waveguide Thermistor Mounts with Self-Consistent Determination of the Thermistor-Port Impedance

Preprint, November 2026. Under submitted to Metrologia journal. Extends the three reflection-coefficient method of P. Greco, “VNA-only calibration of coaxial thermistor mounts via a physically constrained thermistor model”, IEEE Access, 2026, doi:10.1109/ACCESS.2026.3740995. A method is presented for determining the calibration factor and the effective efficiency of waveguide thermistor mounts from vector-network-analyzer reflection data alone, without a microcalorimeter, extending the three reflection-coefficient method of the coaxial case. In waveguide the thermistor is coupled to the line through a matching structure and the reference impedance of the thermistor port, Z0, is not known a priori; it is inferred through a power-consistency relation between pairs of states, under the convention that it is real. The method reproduces the factory certificates (U = 2 %) of four K486A mounts within 1.0 % rms and the PTB-traceable values (U = 0.85–0.98 %) of a fifth within 0.34 % rms; its expanded measurement uncertainty is 0.5–1.16 % (k = 2) for the best specimen and below 2 % for the five. A mount with its waveguide-to-coaxial adapter is calibrated directly, without characterizing the adapter, from the model factor of the mount and the geometric factor measured through the adapter. The scattering matrix implied by the solution is not passive; a minimum-norm correction of the thermistor impedances along the two directions invisible to the calibration factor – the ratios of the efficiencies of the three states – brings it to the floor of passivity, where the efficiency depends on the load only through its mismatch factor, leaves the result unchanged, and gives the sensitivity of the efficiency to the bias resistance in closed form: below 4×10⁻⁵ Ω⁻¹ in band mean, proportional to the mismatch of the operating state and to the loss of the mount. Keywords (campo aparte, separados por coma): effective efficiency, calibration factor, waveguide thermistor mount, bolometric power sensor, vector network analyzer, characteristic impedance, self-consistent calibration, WR-42, microcalorimeter