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During a mixer noise figure test (NF) why are the NF and gain not equivalent to zero after a user calibration?

The input and output frequencies of the mixer are different. Due to this fact the NF and gain will not be zero after a user calibration. The noise figure of the DUT is calculated by following equation.

F1 = Fsys - (F2 - 1) / G1

F1 : Noise Figure of the DUT
F2 : Noise Figure of the NF analyzer
Fsys : Combined Noise Figure of DUT and the NF analyzer
G1 : Gain of the DUT

The purpose of the calibration is to measure the NF of the analyzer, F2 and allow this to be removed from the subsequent DUT measurement.
Because the input frequency of the NF analyzer is the IF frequency of the mixer, the ENR value at the IF frequency is used during the calibration. However, after the calibration the NF analyzer switches the ENR value from the IF frequency to the RF frequency.
The difference of the ENR value at the IF frequency and RF frequency is displayed after the calibration, as well as the sum of the inherent measurement uncertainty.
The measurement uncertainty may be significant. This is due to the fact that immediately after calibration, prior to insertion of the MIXER/DUT, the device gain and noise figure are both zero, resulting in possibly high uncertainty.

Note, if the ENR values at the IF frequency and RF frequency are same the NF and Gain may be displayed as zero.

For additional details on NF analysis of frequency translating devices review Application Note 1487

For additional details on NF uncertainty analysis after calibration review Application Note 1484

Keysight Technologies also provides a web based NF uncertainty calculator that is available at NFA Uncertainty Calculator.