Frequency Servo Research Articles

A frequency servo SoC with output power stabilization loop technology for miniaturized atomic clocks

A frequency servo system-on-chip (FS-SoC) featuring output power stabilization technology is introduced in this study for high-precision and miniaturized cesium (Cs) atomic clocks. The proposed power stabilization loop (PSL) technique, incorporating an off-chip power detector (PD), ensures that the output power of the FS-SoC remains stable, mitigating the impact of power fluctuations on the atomic clock's stability. Additionally, a one-pulse-per-second (1PPS) is employed to synchronize the clock with GPS. Fabricated using 65 nm CMOS technology, the measured phase noise of the FS-SoC stands at −69.5 dBc/Hz@100 Hz offset and −83.9 dBc/Hz@1 kHz offset, accompanied by a power dissipation of 19.7 mW. The Cs atomic clock employing the proposed FS-SoC and PSL obtains an Allan deviation of 1.7 × 10−11 with 1-s averaging time.

Dual closed-loop control method for resonant integrated optic gyroscopes with combination differential modulation

In order to optimize the detection accuracy and output stability of Resonant Integrated Optic Gyroscopes (RIOG), a dual closed-loop control method for combined differential modulation (DCM Control) has been proposed. Two optical signals are differentially modulated in sync, and their differential-mode output results are compensated in real-time. Considering the distinct characteristics of the two frequency servo loops, they are respectively utilized to tune the laser frequency to track the resonant frequency's wide fluctuations and continuously changing resonant frequency due to random rotation. Through this novel structure, we have enhanced reciprocity while reducing optical components, suppressing RIM noise and laser frequency noise in the gyroscope system, and effectively reducing control errors. We analyze the principles affecting angular velocity detection accuracy and the system's output model. Experimental results indicate that this method can effectively achieve high reciprocity and high-precision frequency control, offering a larger dynamic detection range and better linearity. The long-term bias instability (BI) based on Allan deviation is measured at 0.95°/h, and the angle random walk (ARW) is 0.119°/√h, providing a simple and efficient approach for RIOG closed-loop signal processing.

Optimal design of high frequency and high precision fast tool servo system

Optimal design of high frequency and high precision fast tool servo system

Improving thermal stability of a resonant fiber optical gyroscope using triple closed loops.

A closed-loop resonant fiber optic gyroscope (RFOG) configuration with three resonance frequency servo loops is proposed. By using one laser-servo loop and two symmetrical phase modulator (PM) servo loops, the effect of the reset due to the limited tracking range of the laser-servo loop is solved. Further long-term stability for 48 h and thermal stability at moderate rate measurements show that the output of the triple closed-loop RFOG is insensitive to environmental temperature variations. When the temperature increased from 17.5°C to 40.7°C in 1800 s and the maximum temperature rate was about 0.025°C/s during heating, the laser-servo loop was reset a total of 413 times. However, the output of the triple closed-loop RFOG is not affected by those frequent resets in the laser-servo loop because the two PM-servo loops are free of glitch pulses under this new scheme. Compared to the traditional double closed-loop RFOG, the thermal bias stability of the triple closed-loop RFOG is improved by a factor of 15 times from 29.8°/h to 1.88°/h.

Resonator fiber-optic gyro with intensity error suppression using a bias-sampling compensation technique.

Resonator fiber-optic gyros (RFOGs) are one of the most promising candidates for next-generation inertial rotation sensors. The frequency servo loop is used to lock the laser frequency to the resonance frequency of fiber ring resonator via adjusting the laser diode current, which increases accompanying intensity variation and induces RFOG drift. RFOG output compensation using a bias-sampling technique is proposed to suppress intensity error. The linear relationship between the RFOG output and bias is verified by theory and experimental results, and the bias-sampling compensation technique by monitoring the bias signal is analyzed in detail. With the compensation technique, intensity error is significantly suppressed, and the RFOG bias stability is effectively improved from 127.2 to 7.4 deg/h, which demonstrates tactical-grade performance.

Laser frequency noise measurement in a resonant fiber optic gyro

A resonant fiber optic gyro (RFOG) is a high-accuracy inertial rotation sensor based on the Sagnac effect. Knowledge of the laser frequency noise, especially the study of its transfer characteristics is critical to optimize the resonant frequency servo loop parameters in the RFOG. In this paper, a Mach–Zehnder interferometer (MZI) is used to measure the changes of the power spectral density (PSD) of the laser frequency noise. Three different observation points are set to investigate the transfer characteristics of the laser beam along the transmission loop of the RFOG. Through real-time observation and analysis of the PSDs of the laser frequency noise, we found that the effects of the laser frequency noise on the RFOG can be clearly determined, and the resonant frequency servo loop parameters can be optimized according to the required gyro bandwidth. We also demonstrate the significance of reducing the residual error at the lock-in frequency while ensuring a sufficient gyro bandwidth.

Enhanced IMC synthesis for tracking control of magnetic levitation system

This paper presents an enhanced internal model control (EIMC) scheme for a time-delayed second order unstable process, which is subjected to exogenous disturbance and model variations. Even though the conventional internal model control (IMC) can provide an asymptotic tracking response with desired stability margins, the major limitation of conventional IMC is that it cannot be applied for an unstable system because a small exogenous disturbance can trigger the control signal to grow unbounded. Hence, modifying the conventional IMC structure to guarantee the internal stability, we present an EIMC scheme which can offer better trade-off between setpoint tracking and disturbance rejection characteristics. To improve the load disturbance rejection characteristics and attenuate the effect of sensor noise, we solve the selection of controller gains as an H∞ optimization problem. One of the key aspects of the EIMC scheme is that the robustness of the closed loop system can be tuned via a single tuning parameter. The performance of the EIMC scheme is experimentally assessed on a magnetic levitation plant for reference tracking application. Experimental results substantiate that the EIMC scheme can effectively counteract the inherent time delay in the model and offer precise tracking, even in the presence of exogenous disturbance. Moreover, by comparing the trajectory tracking performance of EIMC with that of the proportional integral velocity (PIV) controller through cumulative power spectral density (CPSD) of the tracking error, we show that the EIMC can offer better low frequency servo response with minimal vibrations.

Absolute frequency measurement of the 88Sr+ clock transition using a GPS link to the SI second

We report the results of a recent measurement of the absolute frequency of the – transition of the ion. The optical frequency was measured against the international atomic time realization of the SI second on the geoid as obtained by frequency transfer using a global positioning system link and the precise point positioning technique. The measurement campaign yielded more than 100 h of frequency data. It was performed with improvements to the stability and accuracy of the single-ion clock compared to the last measurement made in 2012. The single ion clock uncertainty is evaluated at when contributions from acousto-optic modulator frequency chirps and servo errors are taken into account. The stability of the ion clock is at 1 s averaging, a factor of three better than in the previous measurement. The results from the two measurement campaigns are in good agreement. The uncertainty of the measurement, primarily from the link to the SI second, is 0.75 Hz (). The frequency measured for the S–D clock transition of is Hz.

Parameter optimization analysis to minimize the polarization error in a localized thermal tunable fiber ring resonator gyro.

The accuracy of the resonant frequency servo loop is a major concern for the high-performance operation of a resonant fiber optic gyro. For instance, a bias error as large as tens or even hundreds of degrees/hour has been observed at the demodulated output of the resonant frequency servo loop. The traditional frequency servo mechanism is not an efficient tool to address this problem. In our previous work, we proposed a novel method to minimize the laser frequency noise to the level of the shot noise by refractive index modulation by a thermally tunable resonator. In this paper, we performed the parameter optimization for the resonator coil, multifunction integrated-optics chip, and couplers by the transition matrix using the Jones matrix methodology to minimize the polarization error. With the optimized parameter values, we achieved the bias value of the resonator fiber optic gyro to 1.924°/h.

Frequency noise processes in a strontium ion optical clock

A recent comparison of the frequencies of a pair of optical clocks based on the 674 nm 2S1/2–2D5/2 optical clock transition in 88Sr+ has highlighted the need to understand factors affecting frequency instability. We have developed statistical models to show that our clock is capable of reaching the quantum projection noise limit; for our clock using 100 ms probe pulses, this is ∼3 × 10−15/√τ. However, this optical clock uses atomic transitions with a linear Zeeman shift, which can lead to a degradation in stability in the presence of magnetic field noise. We show that this generally leads to an increase in white frequency noise, even in cases dominated by magnetic field flicker or random walk noise. By taking into account both the quantum projection and magnetic field noise we are able to explain our observed frequency instabilities. This analysis will relate to any optical clock with a linear Zeeman shift where cancellation of this shift is achieved by interrogating pairs of components. Furthermore, implementing automatic control of lasers and minimization of micromotion requires pausing of the frequency servo occasionally; this leads to only a small degradation of frequency stability.

Design of Energy-Saving Piezoelectric Actuator Drive for High Frequency Servo Valve

The paper presents a circuit topology favorable to drive piezoelectric actuators for high frequency servo valve. It begins with a short overview of different energy-saving PZA drive types and their tradeoff between efficiency and circuit complexity. Then the mechanical structure and equivalent model of the piezoelectric servo valve are described. And the circuit topology including an energy-saving oscillator, an efficient DC bias power and a repetitive controller especially for tracking reciprocating motion, is proposed. The efficiency-improved PZA drive is then derived from the above design. Finally, the drive together with the servo valve is tested in the simulation experiments.

Eliminating bias drift error in lock-in frequency for a resonant fiber optic gyro.

The accuracy of the resonant frequency servo loop is a major concern for high-performance operation of a resonant fiber optic gyro. This is usually resolved by adopting the central frequency of the laser source to track the resonance of the optical fiber ring resonator in one direction. However, the drift of the resonant frequency arising from resonator temperature fluctuation must be eliminated to maintain this accuracy. The traditional proportional integral (PI) frequency servo loop cannot address this issue very well. For instance, a bias error as large as tens or even hundreds of degrees/hour has been observed at the demodulated output of a resonant frequency servo loop. In this paper, we propose a method to eliminate this bias error by adding a double integral term in the traditional PI-based resonant frequency servo loop. We demonstrate that the double integral term can precisely track the linear resonant frequency drift, evidenced by our experimentally achieved close-to-zero bias error of -0.0009 deg/h at the demodulated output of the resonant frequency servo loop.

Reduction of reset pulse in resonant frequency servo loop for resonant fiber-optic gyro by an auto-controlled reset technique

Resonant fiber-optic gyro (RFOG) based on the Sagnac effect has the potential to achieve the inertial navigation system requirement with a short sensing coil. A high-accuracy resonant frequency servo loop is indispensable for a high-performance RFOG. A digital proportional-integral (PI) controller is always adopted in the resonant frequency servo loop. The resonant frequency of the optical fiber ring resonator drifts with environmental temperature changes. When the resonant frequency drift is beyond the tracking range of the resonant frequency servo loop, the digital PI controller overflows and outputs a reset signal. A large reset pulse, which is equivalent to a rotation rate error of 26°/h, has been observed at the output of the RFOG, while a long time is required for returning to the lock-in state simultaneously. To reduce the effect of the overflow resetting in the digital PI controller, an auto-controlled reset technique is proposed and experimentally demonstrated. As a result, the time for returning to the lock-in state is reduced to 5ms from 8s. With the integration time of 1s, the equivalent accuracy of the resonant frequency servo loop is improved to 0.18°/h.

Analysis and design of an improved servo system for rubidium atomic frequency standard

In this paper, we analyze and design a new type of servo system with noninteger voltage controlled crystal oscillator (VCXO) for rubidium atomic frequency standard (RAFS), which does not require fractional frequency synthesizer. By the establishment of the loop equations with noises and drifts, we prove that all the components of the loop can affect its performance index, and in which, RAFS long-term frequency stability is mainly determined by frequency multiplier, quantum system, and servo amplifier; the short-term one is mostly decided by VCXO. Owing to the elimination of the frequency synthesizer and its additive mixing unit, we can reduce phase noise and stray of the servo system, and it is favorable for miniaturizing the RAFS system. In addition, we adopt some targeted optimization measures to improve the frequency stability index. The good short-term frequency stability index is also validated by the test results.

Full investigation of the resonant frequency servo loop for resonator fiber-optic gyro

Resonator fiber-optic gyro (RFOG) is a high-accuracy inertial rotation sensor based on the Sagnac effect. A high-accuracy resonant frequency servo loop is indispensable for a high-performance RFOG. It is composed of a frequency discriminator, a loop filter, and a laser actuator. Influences of the loop parameters are fully developed. Optimized loop parameters are obtained by considering the noise reduction and wide dynamic performance of the RFOG. As a result, with the integration time of 10 s, the accuracy of the resonant frequency loop is increased to 0.02 Hz (1σ). It is equivalent to a rotation rate of 0.067°/h, which is close to the shot noise limit for the RFOG, while a minimum rotation of ±0.05°/s has been carried out simultaneously. These are the best results reported to date, to the best of our knowledge, for an RFOG using the miniature semiconductor laser that benefits from the optimization of the resonant frequency servo-loop parameters.

Digital Filter Design for CPT Atomic Clocks and FPGA Realization

We present our study result of applying digital filters in the Coherent Population Trapping (CPT) atomic clock. We design and realize the filter in a Field Programmable Gates Array (FPGA). The filter is constructed of a cascaded integrator-comb (CIC) decimation filter, a CIC compensation filter, and a finite-impulse response (FIR) filter in series. The CIC decimation filter operates for descending the sampling frequency and anti-aliasing, the CIC compensation filter refines the magnitude frequency response of the CIC decimation filter, and the FIR filter removes noises and extracts the wanted signal. By replacing the original analog filters with the digital filters in both laser frequency and microwave frequency servo loops, the experimental results show that the frequency stability of the CPT atomic clock is improved by 1×10τ (τ=1-100 s), the power dissipation is reduced by 23.6%, and the size of circuit board is also reduced.

Erratum to: Optimization of the resonant frequency servo loop technique in the resonator micro optic gyro

Erratum to: Optimization of the resonant frequency servo loop technique in the resonator micro optic gyro

Resonator micro optic gyro with double phase modulation technique using an FPGA-based digital processor

Experiments on resonator micro-optic gyro (RMOG) with a digital proportional integral (PI) feedback scheme are performed. In this experimental setup, the key rotation sensing element is a polarization maintaining silica waveguide ring resonator (WRR) with a ring length of 7.9 cm and a diameter of 2.5 cm. A good linearity of 0.0015% over a wide range of ± 2 × 10 4 °/s can be achieved for the RMOG theoretically. The optimal digital PI feedback scheme is adopted in the frequency servo loop to reduce the reciprocal frequency fluctuations due to the WRR resonance frequency and laser frequency drifts. Residual equivalent input fluctuation can be reduced as low as 0.03 °/s/√Hz based on the optimal digital PI feedback scheme, which is close to the shot noise limited spectral density 0.02 °/s/√Hz of the RMOG with the input optical power of 0.2 mW. Relationship between RMOG output signal and angular rate is obtained from ± 0.1 °/s to ± 5 °/s. The standard deviation of the residuals between RMOG output results and linear fit curve is 0.066 °/s. For an integration of the processing circuit, all the processing circuit is implemented by a field programmable gate array (FPGA) instead of instruments. The output of this digitalized RMOG is obtained over a range of ± 550 °/s. The linearity of this digitalized RMOG is 0.0169%.

Optimization of the resonant frequency servo loop technique in the resonator micro optic gyro

Proportional integrator (PI) is always adopted in the resonant frequency servo loop in a resonator micro optic gyro (RMOG). The oscillation phenomenon is observed when adjusting the loop gain surpassing a threshold. This phenomenon limits system performance on step response speed and residual error. Based on the experiment system, a simulation model was set up. Further analysis shows that the threshold gain is related to the system loop filter setting and the loop delay. The traditional PI frequency servo loop technique in the RMOG system cannot keep up with the environment’s disturbance quickly enough, which leads to a large residual error. A compensating method is proposed to optimize the tracking performance, solve the oscillation problem, and speed up the system response. Simulation and experiment results show that the compensated system is superior in performance. It has less residual error in the stable state and is 10 times quicker than the uncompensated system on the step response.

Measuring the photodetector frequency response for ultrasonic applications by a heterodyne system with difference- frequency servo control

A technique for the calibration of photodiodes in ultrasonic measurement systems using standard and cost-effective optical and electronic components is presented. A heterodyne system was realized using two commercially available distributed feedback lasers, and the required frequency stability and resolution were ensured by a difference-frequency servo control scheme. The frequency-sensitive element generating the error signal for the servo loop comprised a delay-line discriminator constructed from electronic elements. Measurements were carried out at up to 450 MHz, and the uncertainties of about 5% (k = 2) can be further reduced by improved radio frequency power measurement without losing the feature of using only simple elements. The technique initially dedicated to the determination of the frequency response of photodetectors applied in ultrasonic applications can be transferred to other application fields of optical measurements.