= Current-plane convention in heterodyne calibration
A \b[current-plane convention in heterodyne calibration] specifies which electrical current an inferred beat amplitude denotes: the detector's generated small-signal current, the current entering a cable, or the current dissipating power in a particular load. Those amplitudes need not be equal. A power-to-current conversion is meaningful only with its circuit and reference plane.
An original <photodiode> model uses generated peak-current phasor $I_d$, detector shunt admittance $Y_d$ and load impedance $Z_L$. Kirchhoff's current balance gives
$$
I_L=\frac{I_d}{1+Y_dZ_L},\qquad
P_L=\frac12|I_L|^2\operatorname{Re}Z_L.
$$
The factor one half assumes peak phasors; with RMS phasors it disappears. The current in the load determines delivered <electric power>. The generated current is recovered only after correcting the current division and any intervening network.
For a resistive Norton model with source resistance and load resistance both $R$, $Y_d=1/R$, so $I_L=I_d/2$ and $P_L=|I_d|^2R/8$. If the source shunt admittance is negligible, $I_L\approx I_d$ instead. Calling both circuits “a detector feeding a 50-ohm instrument” does not establish the same current conversion.
<Capacitive current division in heterodyne receivers> adds frequency dependence. With $Y_d=i\omega C_d$ and resistive load $R$,
$$
\left|\frac{I_L}{I_d}\right|=\frac1{\sqrt{1+(\omega C_dR)^2}}.
$$
For stipulated $C_d=1$ pF and $R=50\,\Omega$, this magnitude is approximately 0.9540 at 1 GHz and 0.3033 at 10 GHz. The same generated amplitude then gives a smaller measured load current at the higher frequency. These are equivalent-circuit calculations, not measured specifications of a particular <photodiode>.
NIST's primary optical-receiver experiment distinguishes microwave power delivered to a reference load from the power indicated by a sensor. It corrects sensor calibration, interconnecting-network loss and impedance mismatch using measured scattering and reflection parameters.<Frequency response metrology for high-speed optical receivers by Paul D. Hale and others>[PDF pp. 1–2, Eqs. 1–4 and Fig. 1]{ref} That apparatus makes the reference plane an experimental calibration choice rather than a label applied after analysis.
Document the detector model, load, frequency, cable and connector corrections, and peak-versus-<root mean square> convention before normalizing by separate arm currents. If the arm currents describe generated DC photocurrent while the beat numerator describes uncorrected load current, the resulting overlap includes electrical current division. <Heterodyne amplitude-versus-power gain conversion> and <impedance matching> address different parts of that chain and both may be needed.
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