In order to check the noise level of the RFAM detector, the power and cross spectra for the same signal source
were simultaneously measured with the two RFAM detectors.

As a signal source, 37MHz OCXO using a wenzel oscillator was used. The output from the signal source
was equaly splitted by a power splitter and fed to the RFAM detector CHB(Mon1) and CHA(Mon2).

The error signal for CHB (Mon1) were monitored by an oscilloscope to find an appropriate bias value.
The bias for CHA are adjusted automatically by the slow bias servo.

The spectra were measured with two different power settings:

Low Power setting: The signal source with 6+5dB attenuation was used. This yielded 10.3dBm at the each unit input.
The calibration of the low power setting is dBc = 20*log10(Vrms/108). (See previous elog entry)

High Power setting: The signal source was used without any attenuation. This yielded 22.4dBm at the each unit input.
The calibration for the high power setting was measured upon the measurement.
SR785 was set to have 1kHz sinusoidal output with the amplitude of 10mVpk and the offset of 4.1V.
This modulation signal was fed to DS345 at 30.2MHz with 24.00dBm
The network analyzer measured the carrier and sideband power levels
30.2MHz 21.865dBm
USB    -37.047dBm
LSB    -37.080dBm  ==> -58.9285 dBc (= 0.0011313)

The RF signal was fed to the input and the signal amplitude at Mon1 and Mon2 were measured
MON1 => 505   mVrms => 446.392 Vrms/ratio
MON2 => 505.7 mVrms => 447.011 Vrms/ratio
dBc = 20*log10(Vrms/446.5).

Using the cross specrum (or coherence)of the two signals, we can infer the noise level of the detector.

Suppose there are two time-series x(t) and y(t) that contain the same signal s(t) and independent but same size of noise n(t) and m(t)

x(t) = n(t) + s(t)
y(t) = m(t) + s(t)

Since n, m, s are not correlated, PSDs of x and y are

Pxx = Pnn + Pss
Pyy = Pmm+Pss = Pnn+Pss

The coherence between x(t) and y(t) is defined by

Cxy = |Pxy|^2/Pxx/Pyy = |Pxy|^2/Pxx^2

In fact |Pxy| = Pss. Therefore

sqrt(Cxy) = Pss/Pxx

What we want to know is Pnn

Pnn = Pxx - Pss = Pxx[1 - sqrt(Cxy)]
=> Snn = sqrt(Pnn) = Sxx * sqrt[1 - sqrt(Cxy)]

This is slightly different from the case where you don't have the noise in one of the time series (e.g. feedforward cancellation or bruco)

Measurement results

Power spectra:
Mon1 and Mon2 for both input power levels exhibited the same PSD between 10Hz to 1kHz. This basically supports that the calibration for the 22dBm input (at least relative to the calibration for 10dBm input) was corrected. Abobe 1kHz and below 10Hz, some reduction of the noise by the increase of the input power was observed. From the coherence analysis, the floor level for the 10dBm input was -178, -175, -155dBc/Hz at 1kHz, 100Hz, and 10Hz, respectively. For the 22dBm input, they are improved down to -188, -182, and -167dBc/Hz at 1kHz, 100Hz, and 10Hz, respectively.