Frequency standard noise

4.1 Frequency standard noise

In two-way Doppler coherence is maintained by the frequency standard to which the up- and downlinks are referenced. Thus noise introduced by the frequency standard is of particular importance. Figure 6

shows fractional frequency stability as a function of integration time for several frequency standard technologies. In Cassini-era observations noise in the frequency and timing system (FTS) contributed less than 10^–15 at 1000 s and, although fundamental, is not the leading noise source at the current level of sensitivity. (FTS stability required for future Doppler experiments is discussed in Section 7.)

Figure 6:

Allan deviation (square root of Allan variance [23

]) as a function of integration time for several frequency and timing technologies. The technology used in precision Doppler observations for GW searches with Cassini has $σy$ (1000 s) less than 10^–15. (Figure courtesy of Lute Maleki; see also references [10

, 11

, 22

].)

FTS noise enters the two-way Doppler time series via the transfer function [49 , 43 , 118 ] $yFTS (t) ∗ [δ(t) − δ(t − T2)]$ . The transfer functions of this and other principal noises are illustrated schematically in Figure 7 . (An example of the FTS transfer function using real data is shown in Figure 8 . Although the stability of the ground frequency standard is excellent, for a few days at the start of the first Cassini Gravitational Wave Experiment there was an intermittent problem with an FTS distribution amplifier at the Goldstone complex. The effect was to introduce isolated, fairly large, and very short glitches into the frequency reference for both the transmitter and the receiver. This produced characteristic anticorrelated glitches, separated by a two-way light time, in both the X- and Ka-band two-way Doppler time series; see Figure 8 )

Figure 7:

Schematic transfer functions of noises to the two-way Doppler link, adapted from [43

, 118

]. For each type of disturbance a separate diagram (space vertically, time horizontally) is shown. Radio waves propagate continuously up to and down from the spacecraft; some of these are represented as the dashed lines to illustrate the indicated Doppler frequency perturbations. For example, a momentary glitch in the FTS affects the frequency reference for both the receiver and the transmitter. This shows up as an immediate effect in the received Doppler (difference between the transmitted and received frequency). Because the glitch also affects the transmitted frequency, it shows up again – but with the opposite sense – in the Doppler after a two-way light time. These various noise responses contrast with the three-pulse GW response, shown in Figure 1

; these differences are exploited in the signal processing.

Figure 8:

Time series of Cassini two-way Ka-band frequency residuals from a DSS 25 track on 2001 DOY 350. The data are sampled at 0.2 s after being detected with a time constant $≃$ 1 s. At this time resolution, the visual appearance of the time series is dominated by high-frequency noise. Superimposed on this noise are two systematic glitches which were traced to an intermittently-faulty distribution amplifier in the signal chain providing frequency references to the transmitter and receiver. The distribution amplifier fault acts like an FTS glitch and, in the two-way Doppler, appears twice in the time series anticorrelated at the two-way light time (Figure 7

). The glitches in the figure are paired with the indicated two-way light time separation T₂ $≃$ 5737.7 s. The lower panels show blowups of the pair; the glitch waveforms are unresolved (shapes set by the impulse response of the software phase detector) but clearly show the characteristic FTS anticorrelation.