 Heterodyne RF-to-DC gain transfer check

A heterodyne RF-to-DC gain transfer check tests whether the calibration converting a beat-frequency measurement into current amplitude is compatible with the calibration of the separate arm currents. The gain-matching condition for heterodyne normalization involves amplitude gains, so an RF power gain cannot be substituted without conversion.

For corrected peak beat current $B$ and arm currents $I_1,I_2$, the normalized overlap is $\gamma =B/(2\sqrt{I_1{I}_2})$. Suppose an electrical model gives sinusoidal peak current $B$ through a known resistive load $Z$. Its average beat power isSource/load division and impedance corrections must already be included when relating that load current to the detector-current convention. A factor converting power is therefore square-rooted when converting amplitude.

Let measured RF power carry multiplicative factor $g_P$, while the arm currents carry factors $g_1,g_2$. Under this model,Cancellation requires $g_P=g_1{g}_2$. With one common DC current factor $g_{\mathrm{DC}}$, the condition is $g_P=g_{\mathrm{DC}}^2$, not $g_P=g_{\mathrm{DC}}$.

An original example takes $g_{\mathrm{DC}}=1.10$. An RF power factor 1.21 produces amplitude factor 1.10 and cancels in the normalized overlap. Applying RF power factor 1.10 instead leaves multiplier $1/\sqrt{1.10}\approx 0.95346$, despite using the same numerical gain label in both paths. The example isolates heterodyne amplitude-versus-power gain conversion, rather than a change of optical overlap.

NIST's receiver experiment measured microwave power and separately corrected sensor calibration, electrical loss and impedance matching. Its two-laser optical source used polarization and spatial matching to establish calculable modulation.^[ref] Those separate operations make the RF-to-DC comparison a physical calibration problem.

Record peak versus RMS conventions, frequency response, load model and arm-current calibration. Test a known or independently characterized modulation while varying power within the linear range. Changed polarization, aperture clipping or optical alignment can alter the true overlap and imitate a gain-transfer defect, so one unexplained normalized ratio does not uniquely diagnose the electrical path.