J. Delporte

1 × 10 −16 frequency transfer by GPS PPP with integer ambiguity resolution

For many years, the time community has been using the precise point positioning (PPP) technique which uses GPS phase and code observations to compute time and frequency links. However, progress in atomic clocks implies that the performance of PPP frequency comparisons is a limiting factor in comparing the best frequency standards. We show that a PPP technique where the integer nature of phase ambiguities is preserved consitutes significant improvement of the classical use of floating ambiguities. We demonstrate that this integer-PPP technique allows frequency comparisons with 1 × 10−16 accuracy in a few days and can be readily operated with existing products.

Modeling of quartz crystal oscillators by using nonlinear dipolar method

A quartz crystal oscillator can be thought of as a resonator connected across an amplifier considered as a nonlinear dipole the impedance of which depends on the amplitude of the current that flows through it. The nonlinear amplifier resistance and reactance are obtained by using a time domain electrical simulator like SPICE (Simulation Program with Integrated Circuit Emphasis): the resonator is replaced with a sinusoidal current source of the same frequency and a set of transient analyses is performed by giving the current source a larger amplitude. A Fourier analysis of the steady-state voltage across the dipolar amplifier is performed to calculate both real and imaginary parts of the dipolar impedance as a function of the current amplitude. From these curves, it is then possible to accurately calculate the oscillation amplitude and frequency without having to perform unacceptably long transient analyses needed by a direct oscillator closed loop simulation. This method implemented in the Analyse Dipolaire des Oscillateurs a Quartz or Quartz Crystal Oscillators Dipolar Analysis (ADOQ) program calculates the oscillation start-up condition, the oscillation steady-state features (oscillation amplitude and frequency), and the oscillator sensitivity to various parameters. The oscillation nonlinear differential equation is solved by using the slowly varying function method so that the program quickly and accurately calculates the current amplitude and frequency transients. Measurements performed on an actual amplifier show a very good agreement with the results obtained by the simulation program.

Limitations to the short term frequency stability in a compact cold atom clock

The HORACE device is a compact cold atom clock where about 10/sup 8/ cesium atoms are laser cooled at a few /spl mu/K, then interrogated and detected directly in a 20 cm/sup 3/ spherical microwave cavity. The optimization of the short term stability with the cooling and interrogation durations is presented, leading to an estimation of the Allan deviation of /spl sigma//sub y/(/spl tau/) -1 10/sup -13/ /spl tau/ /sup - 1/2 /on earth and /spl sigma//sub y/(/spl tau/) = 7 10/sup -14/ /spl tau//sup -frac12;/ in space. The quantum projection noise, the Dick effect and the detection laser noises are taken into account. The calculations are based on a preliminary model for the recapture of cold atoms, in reasonable agreement with measurements.

ADOQ: a quartz crystal oscillator simulation software

This paper presents the actual state of a computer program especially designed to simulate the behavior of quartz crystal oscillators. The program is based on the fact that the current through the quartz crystal is almost perfectly sinusoidal. Consequently the oscillator can be modeled by a resonator across a nonlinear impedance that depends only on the current magnitude through it. The resonator being replaced by a current source, the nonlinear impedance of the amplifier is computed from a series of transient analyses performed at the resonator frequency. When the steady state is reached, the resonator impedance is exactly equal and of opposite sign to the amplifier impedance. This identity allows one to compute the oscillation amplitude and the frequency shift with respect to the resonator frequency. This computation does not require to perform unacceptable long transient analyses in case of high-Q oscillator. Our program is intended to help the designer in checking or improving oscillator circuit design. From the Spice netlist, it enables the user to compute the steady state features of the oscillator, namely frequency and amplitude. Then, the user can study the effect of temperature change on any components or the influence of quartz characteristic. It is also possible to perform accurate oscillator sensitivity calculation to various parameters (component value, supply voltage, ...) as well as worst case analysis.

Fidelity - Progress Report on Delivering the Prototype Galileo Time Service Provider

The Fidelity consortium is currently implementing and will operate the Galileo Time Service Prototype Facility (GTSPF) in order to deliver Coordinated Universal Time (UTC) services to the Galileo satellite system during its in-orbit validation phase (due to begin in 2008). A key element of this plan is to integrate the Galileo timing activities into the wider time and frequency community, including the Bureau International des Poids et Mesures (BIPM). The main function of the GTSPF is to provide parameters for steering Galileo System Time (GST), as realized at the Galileo Precise Timing Facility (PTF), to UTC (modulo 1 s). This will be achieved in a three step process. First, the GST (as realized in the Galileo PTF from an ensemble of atomic clocks (active H-masers, high performance Caesium standards) with dedicated measurement equipment and clock ensemble algorithm) is compared against the participating UTC(k) time scales by Two-Way Satellite Time and Frequency Transfer (TWSTFT) and GPS P3 techniques. These raw data are sent to the GTSPF for processing. The Fidelity consortium is responsible for the calibration of the time transfer equipment. Second, the GTSPF generates a prediction of the difference UTC -GST (modulo 1 s) by means of an intermediate composite clock obtained from an ensemble of atomic standards maintained in the PTFs and in the participating European National Metrology Institutes (NMIs), and using the data of UTC -UTC(k) as computed by the BIPM. The benefits of the composite clock include enhanced stability and integrated integrity monitoring. Third, the GTSPF sends daily steering parameters to the PTF to be used to align the physical realization of GST against UTC (modulo 1 s) as required by the Galileo system specifications. The specification and design phase of the implementation of the GTSPF was concluded in August 2006 with the successful completion of the Critical Design Review (CDR). This included the functional and physical design of the GTSPF and the verification of the uncertainty budget by means of extensive simulations. The design and functions of the GTSPF currently being implemented are detailed in this paper. The algorithm to be used for the prediction of UTC - GST is described. The time transfer link calibration activities under the responsibility of Fidelity are detailed. The PTF interactions with the GTSPF are described. A possible relationship between the GTSPF and EGNOS, the first step of European navigation satellite systems, is proposed. Finally, this paper gives a summary of the current status of the GTSPF implementation and the planned future activities of the Fidelity consortium.

Stability of the compact cold atom clock HORACE

HORACE is a compact cold cesium atom clock which is being developed in LNE-SYRTE for space applications and onboard systems. The operation of this clock is different from fountains since the laser cooling, the microwave interrogation and the detection are sequentially performed inside the spherical microwave cavity. We recently achieved short term stability of 5.5 10-13 tau-0.5 reaching the 10-14 level at 3000 sec. We report in this paper recent developments and improvements, particularly on the cooling sequence. We also study the main limitations.

Performance assessment of the time difference between EGNOS-network-time and UTC

The European SBAS (Satellite Based Augmentation System) EGNOS (European Geostationary Navigation Overlay Service) provides in its navigation message the time difference between EGNOS Network Time (ENT) and UTC. For that purpose, an EGNOS ground station was installed in the Observatoire de Paris (OP) and is connected to UTC(OP). Applying EGNOS corrections on GPS measurements provides a precise time and navigation solution referenced to ENT. Therefore the assessment of the time difference between ENT and UTC is a key issue for time users. A new EGNOS system release has been tested since the beginning of 2008, it includes some improvements in the timing functions. This paper deals with the evaluation of the performances obtained by these functions.

Reaching a few 10 −13 τ −1/2 stability level with the compact cold atom clock HORACE

HORACE is a compact cold cesium atom clock which is being developed in LNE-SYRTE for space applications and onboard systems. The operation of this clock is different from fountains since the laser cooling, the microwave interrogation and the detection are sequentially performed inside the spherical microwave cavity. The entire simplified operation sequence is described. A short term relative frequency stability of 2.2 10-13 tau-1/2 is achieved. Preliminary results on mid term show that a level of 4 10-15 is reached after 5 103s of integration. Limitations are investigated.

Straightforward estimations of GNSS on-board clocks

In this paper, we present two techniques to estimate GNSS on-board clocks. These techniques only require a single GNSS receiver and allow to evaluate the stability on a given pass of the time difference between the GNSS on-board clock and the clock that drives the GNSS receiver. These methods have been validated using IGS clock products for GPS on-board clocks. We also show that they can be used to characterize ground clocks provided a better space clock is available.

Design of an ultra-compact reference ULE cavity

This article presents the design and the conception of an ultra-compact Fabry-Perot cavity which will be used to develop an ultra-stable laser. The proposed cavity is composed of a 25 mm long ULE spacer with fused silica mirrors. It leads to an expected fractional frequency stability of 1.5 x 10-15 limited by the thermal noise. The chosen geometry leads to an acceleration relative sensitivity below 10-12 /(m/s2) for all directions.