The VCO/PLL chip that generates the LO signal on the IF board has frequency or phase noise. This note show that this is small compared to TLS frequency noise.

Why

We want the readout system noise to be limited by the devices and the HEMT, not the readout. Therefore, we must be sure the LO generator does not add noise.

How

Email from Jonas on the topic indicates that VCO/PLL frequency noise is strongly attenuated at audio frequencies.

From: Jonas Zmuidzinas <jonas@caltech.edu>

Date: July 15, 2010 12:12:08 PM PDT

To: rduan@caltech.edu

Cc: "Rick Raffanti" <rikraf@earthlink.net>, "Tom Downes" <tpdownes@caltech.edu>, "Sunil Golwala" <golwala@caltech.edu>, "Ben Mazin" <bmazin@physics.ucsb.edu>

Subject: Re: MKID IF Board consideration

Hi Ran et al,

This is a quick note regarding the phase noise performance that we need for synthesizers & clocks.

Let's first consider the synth for the microwave up/down conversion. The output frequency going to the cryostat is fout = fLO + fDAC, where fDAC is the frequency produced by the two DACs,-fsample/2 < fDAC < +fsample/2. Meanwhile, a resonator has some resonance frequency fr. The resonator transmission S21 depends on the frequency difference, fout - fr. Noise in either fout or fr will contribute noise to this difference, therefore, you want to operate in the regime that synthesizer frequency noise is well below resonator frequency noise (from surface TLS layer). Ideally, the synthesizer frequency noise should be well below the HEMT noise floor as well.

Phase noise and frequency noise are connected, since frequency is the time derivative of the phase. Therefore, the synthesizer frequency noise PSD Sf(\nu) is related to the phase noise PSD S\phi(\nu) via

Sf(\nu) = (2 \pi \nu)2 S\phi(\nu)

where \nu is the noise frequency. We normally plot resonator noise in terms of the fractional frequency noise, Sfr / fr2. The synthesizer fractional frequency noise is

Sf(\nu) / fLO2 = (2 \pi \nu / fLO)2 S\phi(\nu)

You can use this equation to convert phase noise to fractional frequency noise, and then compare to resonator noise (e.g. use Jiansong's and Omid's papers). The values for Sf / f2 are in the < 10-20 /Hz range for TLS noise. HEMT noise is considerably lower, and depends on the resonator Q. You should try to work out for yourself what that is, using the expression for S21 for the resonator transmission.

We generally care about noise frequencies in the 0.1 - 1 kHz range. That means that the factor (\nu / fLO)2 will be quite small, and so as along as the synth phase noise isn't terrible you should be OK.

The same sort of considerations can be applied to the DAC/ADC clocks.

The basic lesson here is that *frequency* noise is what's important for us, rather than phase noise.

Cheers, Jonas