Showing papers on "Phase noise published in 2017"

1.5 μm Lasers with Sub-10 mHz Linewidth

Abstract: We report on two ultrastable lasers each stabilized to independent silicon Fabry-Perot cavities operated at 124 K. The fractional frequency instability of each laser is completely determined by the fundamental thermal Brownian noise of the mirror coatings with a flicker noise floor of 4×10^{-17} for integration times between 0.8 s and a few tens of seconds. We rigorously treat the notorious divergences encountered with the associated flicker frequency noise and derive methods to relate this noise to observable and practically relevant linewidths and coherence times. The individual laser linewidth obtained from the phase noise spectrum or the direct beat note between the two lasers can be as small as 5 mHz at 194 THz. From the measured phase evolution between the two laser fields we derive usable phase coherence times for different applications of 11 to 55 s.

Photonic microwave signals with zeptosecond-level absolute timing noise

Abstract: Ultralow-noise microwave signals are generated at 12 GHz by a low-noise fibre-based frequency comb and cutting-edge photodetection techniques. The microwave signals have a fractional frequency stability below 6.5 × 10–16 at 1 s and a timing noise floor below 41 zs Hz–1/2. Photonic synthesis of radiofrequency (RF) waveforms revived the quest for unrivalled microwave purity because of its ability to convey the benefits of optics to the microwave world1,2,3,4,5,6,7,8,9,10,11. In this work, we perform a high-fidelity transfer of frequency stability between an optical reference and a microwave signal via a low-noise fibre-based frequency comb and cutting-edge photodetection techniques. We demonstrate the generation of the purest microwave signal with a fractional frequency stability below 6.5 × 10−16 at 1 s and a timing noise floor below 41 zs Hz−1/2 (phase noise below −173 dBc Hz−1 for a 12 GHz carrier). This outperforms existing sources and promises a new era for state-of-the-art microwave generation. The characterization is achieved through a heterodyne cross-correlation scheme with the lowermost detection noise. This unprecedented level of purity can impact domains such as radar systems12, telecommunications13 and time–frequency metrology2,14. The measurement methods developed here can benefit the characterization of a broad range of signals.

Phase-detection distributed fiber-optic vibration sensor without fading-noise based on time-gated digital OFDR

Abstract: For a distributed fiber-optic vibration sensor (DFVS), the vibration signal extracted from the phase of backscattering has a linear response to the applied vibration, and is more attractive than that from the intensity term. However, the large phase noise at a random weak-fading-point seriously limits the sensor's credibility. In this paper, a novel phase-detection DFVS is developed, which effectively eliminates the weak-fading-point. The relationship between phase noise and the intensity of backscattering is analyzed, and the inner-pulse frequency-division method and rotated-vector-sum method are introduced to effectively suppress phase noise. In experiments, two simultaneous vibrations along the 35-kilometer-long fiber are clearly detected by phase detection with the signal-to-noise ratio (SNR) over 26 dB. The spatial resolution approaches 5 m and the vibration response bandwidth is 1.25 kHz.

Electronic synthesis of light

Abstract: We report on bidirectional frequency conversion between the microwave and optical domains using electro-optics. Advances in communications, time keeping, and quantum sensing have all come to depend upon the coherent interoperation of light wave and microwave signals. To connect these domains, which are separated by a factor of 10,000 in frequency, requires specialized technology that has until now only been achieved by ultrafast mode-locked lasers. In contrast, electro-optic modulation (EOM) combs arise deterministically by imposing microwave-rate oscillations on a continuous-wave laser. Here we demonstrate electro-optic generation of a 160 THz bandwidth supercontinuum and realize f-2f self-referencing. Coherence of the supercontinuum is achieved through optical filtering of electronic noise on the seed EOM comb. The mode frequencies of the supercontinuum are derived from the electronic oscillator and they achieve <5×10−14 fractional accuracy and stability, which opens a novel regime for tunable combs with wide mode spacing apart from the requirements of mode locking.

Impact of General Channel Aging Conditions on the Downlink Performance of Massive MIMO

Abstract: Recent works have identified massive multiple-input multiple-output (MIMO) as a key technology for achieving substantial gains in spectral and energy efficiency. Additionally, the turn to low-cost transceivers, being prone to hardware impairments, is the most effective and attractive way for cost-efficient applications concerning massive MIMO systems. In this context, the impact of channel aging, which severely affects performance, is investigated herein by considering a generalized model. Specifically, we show that both Doppler shift due to the users' relative movement, as well as phase noise due to noisy local oscillators, contribute to channel aging. To this end, we first propose a joint model, encompassing both effects, to investigate the performance of a massive MIMO system based on the inevitable time-varying nature of realistic mobile communications. Then, we derive the deterministic equivalents for the signal-to-noise-and-interference ratios (SINRs) with maximum ratio transmission (MRT) and regularized zero-forcing (RZF) precoding. Our analysis not only demonstrates a performance comparison between MRT and RZF under these conditions but, most importantly, also reveals interesting properties regarding the effects of user mobility and phase noise. In particular, the large antenna limit behavior profoundly depends on both effects, but the burden due to user mobility is much more detrimental than phase noise even for moderate user velocities ( $\approx$ 30 km/h), whereas the negative impact of phase noise is noteworthy at lower mobility conditions. Moreover, massive MIMO systems are favorable even in general channel aging conditions. Nevertheless, we demonstrate that the transmit power of each user to maintain a certain quality of service can be scaled down, at most, by $\text{1}\sqrt{M}$ ( $M$ is the number of base station antennas), which indicates that the joint effects of phase noise and user mobility do not degrade the power scaling law but only the achievable sum-rate.

Implicit Common-Mode Resonance in LC Oscillators

Abstract: The performance of a differential LC oscillator can be enhanced by resonating the common mode of the circuit at twice the oscillation frequency. When this technique is correctly employed, Q-degradation due to the triode operation of the differential pair is eliminated and flicker noise is nulled. Until recently, one or more tail inductors have been used to achieve this common-mode resonance. In this paper, we demonstrate that additional inductors are not strictly necessary by showing that common-mode resonance can be obtained using a single tank. We present an NMOS architecture that uses a single differential inductor and a CMOS design that uses a single transformer. Prototypes are presented that achieve figure-of-merits of 192 and 195 dBc/Hz, respectively.

Optoelectronic Oscillators for High Speed and High Resolution Optical Sensing

Abstract: An optoelectronic oscillator (OEO) can be employed to perform high speed and ultra-high resolution optical sensing. The fundamental concept is to convert a measurand-dependent wavelength change in the optical domain to a frequency change of an OEO-generated microwave signal in the microwave domain. Since the frequency of a microwave signal can be measured by a digital signal processor at a high speed and high resolution, an OEO-based optical sensor is able to provide optical interrogation at a high speed and ultra-high resolution. In this paper, OEO-based optical sensors proposed for strain, temperature, or transverse load sensing are discussed. The key to implement an OEO-based optical sensor is to implement a microwave photonic filter with a passband having a center frequency that is a function of the optical wavelength change. In this paper, techniques to implement microwave photonic filter for OEO-based optical sensing are discussed.

Analysis and Design of Secure Massive MIMO Systems in the Presence of Hardware Impairments

Abstract: To keep the hardware costs of future communications systems manageable, the use of low-cost hardware components is desirable. This is particularly true for the emerging massive multiple-input multiple-output (MIMO) systems which equip base stations (BSs) with a large number of antenna elements. However, low-cost transceiver designs will further accentuate the hardware impairments, which are present in any practical communication system. In this paper, we investigate the impact of hardware impairments on the secrecy performance of downlink massive MIMO systems in the presence of a passive multiple-antenna eavesdropper. Thereby, for the BS and the legitimate users, the joint effects of multiplicative phase noise, additive distortion noise, and amplified receiver noise are taken into account, whereas the eavesdropper is assumed to employ ideal hardware. We derive a lower bound for the ergodic secrecy rate of a given user when matched filter data precoding and artificial noise (AN) transmission are employed at the BS. Based on the derived analytical expression, we investigate the impact of the various system parameters on the secrecy rate and optimize both the pilot sets used for uplink training and the AN precoding. Our analytical and simulation results reveal that: 1) the additive distortion noise at the BS may be beneficial for the secrecy performance, especially if the power assigned for AN emission is not sufficient; 2) all other hardware impairments have a negative impact on the secrecy performance; 3) despite their susceptibility to pilot interference in the presence of phase noise, so-called spatially orthogonal pilot sequences are preferable unless the phase noise is very strong; and 4) the proposed generalized null-space AN precoding method can efficiently mitigate the negative effects of phase noise.

Self-coherent phase reference sharing for continuous-variable quantum key distribution

Abstract: We develop a comprehensive framework to model and optimize the performance of continuous-variable quantum key distribution (CV-QKD) with a local local oscillator (LLO), when phase reference sharing and QKD are jointly implemented. We first analyze the limitations of the only existing approach, called LLO-sequential, and show that it requires high modulation dynamics and can only tolerate small phase noise. Our main contribution is to introduce two designs to perform LLO CV-QKD, respectively called LLO-delayline and LLO-displacement, and to study their performance. Both designs rely on a self-coherent approach, in which phase reference information and quantum information are coherently obtained from a single optical wavefront. We show that these designs can lift some limitations of the existing LLO-sequential approach. The LLO-delayline design can in particular tolerate much stronger phase noise and thus appears to be an appealing alternative to LLO-sequential in terms of network integrability. We also investigate, with the LLO-displacement design, how phase reference information and quantum information can be multiplexed within a single optical pulse. By studying the trade-off between phase reference recovery and phase noise induced by displacement, we, however, demonstrate that this design can only tolerate low phase noise. On the other hand, the LLO-displacement design has the advantage of minimal hardware requirements and provides a simple approach to multiplex classical and quantum communications, opening a practical path towards the development of ubiquitous coherent classical-quantum communications systems compatible with next-generation network requirements.

Insights Into Phase-Noise Scaling in Switch-Coupled Multi-Core LC VCOs for E-Band Adaptive Modulation Links

Abstract: High-capacity wireless links at millimeter-Waves are candidate for backhaul infrastructure to small-cell mobile networks. However, the use of high-order modulation schemes sets challenging phase-noise specifications for integrated frequency synthesizers. Moreover, the use of adaptive modulation suggests local oscillators exploiting noise scaling, up to several decibel depending on channel conditions. In this paper, multi-core switch-coupled LC voltage-controlled oscillators are proposed to achieve ultra-low phase noise and scalable noise performance according to system requirements in a power-efficient way. A theoretical model investigating the effect of LC core component mismatches shows very good agreement with experiments. Design insights are provided, key in order to take effective advantage from the proposed low-noise technique. A quad-core ~20 GHz oscillator prototype, followed by a frequency quadrupler, has been realized in 55-nm BiCMOS technology. Measured performances are ~70-to-81 GHz frequency range with −106.5-dBc/Hz minimum phase noise at 1-MHz offset from an 80-GHz carrier with 50-mW power consumption and 1.2-V supply. To authors’ knowledge, this is the lowest phase noise measured in the E-Band using integrated technologies and CMOS-compatible supplies. When noise requirements are relaxed, auxiliary cores are turned off rising phase noise by 6 dB but with power consumption reduced down to 18 mW only.

A 28-GHz Quadrature Fractional-N Frequency Synthesizer for 5G Transceivers With Less Than 100-fs Jitter Based on Cascaded PLL Architecture

Abstract: This paper introduces a quadrature fractional-N cascaded frequency synthesizer and its phase noise analysis, optimization, and design for future 5G wireless transceivers. The performance improvement of the cascaded phase-locked loop (PLL) over single-stage PLL in terms of jitter and power consumption is theoretically presented and verified with measured results. The cascaded PLL is implemented using a first-stage fractional-N charge-pump PLL followed by a second-stage quadrature dividerless subsampling PLL. The fractional division in the first-stage PLL is implemented using a high-resolution phase mixer for lower quantization noise. Two prototypes of the single-stage PLL and the cascaded PLL were implemented in the 65-nm bulk CMOS process. The 26–32 GHz quadrature cascaded PLL consumes a total of 26.9 mW from 1-V supply and achieves less than 100-fs integrated jitter with −116.2 and −112.6-dBc/Hz phase noise at 1-MHz offset for the integer-N and the fractional-N modes, respectively. The fractional-N single-stage and cascaded PLLs achieve figure-of-merits of −230.58 and −248.75 dB, respectively.

High-order dispersion in Kerr comb oscillators

Abstract: We numerically investigate the effect of high-order dispersion on Kerr frequency comb generation in optical microresonators characterized with anomalous group velocity dispersion (GVD) using realistic slot-waveguide-based silicon nitride microring and spheroidal crystalline magnesium fluoride resonators. Our numerical simulations indicate that all orders of GVD should be taken into account to obtain the correct envelope shape of the generated Kerr frequency comb. High-order GVD affects the 3 dB comb bandwidth, nonlinear conversion efficiency, and frequency recoil of the comb spectrum (i.e., spectral shift effect), as well as pulse peak power and the power dependence of the pulse timing. Additionally, high-order dispersion terms affect the spectral position of a dispersive wave generated in a microresonator. Our results emphasize the influence of the pump power on the dispersive wave radiation frequency as well as the repetition rate of the generated frequency comb. The latter has significant practical ramifications, for instance, for the use of resonator-based frequency combs in optical clocks. We also observe competition in the generation of two different pulses corresponding to nearly the same spectral envelope. These mode-locked combs appear in the presence of a strong negative fourth-order GVD; one of them takes a hyperbolic-secant soliton shape, while the other resembles a Gaussian pulse superimposed on a modulated pedestal. The appearance and stability of the latter pulse depend on the numerical integration technique utilized.

A 76- to 81-GHz Multi-Channel Radar Transceiver

Abstract: This paper presents a packaged 76- to 81-GHz transceiver chip implemented in SiGe BiCMOS for both long-range and short-range automotive radars. The chip contains a two-channel transmitter (TX), a six-channel receiver (RX), a local-oscillator (LO) chain, and built-in self-test (BIST) circuitry. Each transmit channel includes multiple variable-gain amplifiers and a two-stage power amplifier. Measured on-die output power per channel is +18 dBm at 25 °C, decreasing to +16 dBm at 125 °C. Each receive channel includes a current-mode mixer, followed by intermediate-frequency buffers. At 25 °C, measured on-die noise figure is 10–11 dB, conversion gain is 14–15 dB, and input 1-dB compression point exceeds +1 dBm. An integrated LO chain drives the transmit and receive chains and includes an 18.5- to 20.6-GHz voltage-controlled oscillator connected to cascaded frequency doublers and a divide-by-four prescaler. At 25 °C, measured phase noise is −100 dBc/Hz at 1-MHz offset from a 77-GHz carrier. Integrated BIST circuits enable the measurement of signal power, RX gain, channel-to-channel phase, and internal temperature. The chip is flip-chip packaged into a ball-grid array and extracted interconnect loss for the package is 1.5 to 2 dB. Total power consumption for the chip is 1.8 W from 3.3 V for a single-TX, six-RX mode.

Impacts of Phase Noise on Digital Self-Interference Cancellation in Full-Duplex Communications

Abstract: In full-duplex (FD) radios, phase noise leads to random phase mismatch between the self-interference (SI) and the reconstructed cancellation signal, resulting in possible performance degradation during SI cancellation. To explicitly analyze its impacts on the digital SI cancellation, an orthogonal frequency division multiplexing (OFDM)-modulated FD radio is considered with phase noises at both the transmitter and receiver. The closed-form expressions for both the digital cancellation capability and its limit for the large interference-to-noise ratio (INR) case are derived in terms of the power of the common phase error, INR, desired signal-to-noise ratio (SNR), channel estimation error and transmission delay. Based on the obtained digital cancellation capability, the achievable rate region of a two-way FD OFDM system with phase noise is characterized. Then, with a limited SI cancellation capability, the maximum outer bound of the rate region is proved to exist for sufficiently large transmission power. Furthermore, a minimum transmission power is obtained to achieve $\beta$ -portion of the cancellation capability limit and to ensure that the outer bound of the rate region is close to its maximum.

4-W, 100-kHz, few-cycle mid-infrared source with sub-100-mrad carrier-envelope phase noise.

Abstract: We demonstrate an optical parametric chirped-pulse amplifier delivering 4-cycles (38-fs) pulses centered around 3.1 µm at 100-kHz repetition rate with an average power of 4 W and an undersampled single-shot carrier-envelope phase noise of 81 mrad recorded over 25 min. The amplifier is pumped by a ~1.1 ps, Yb-YAG, thin-disk regenerative amplifier and seeded with a supercontinuum generated in bulk YAG from the same pump pulses. Carrier-envelope phase stability is passively achieved through difference-frequency generation between pump and seed pulses. An additional active stabilization at 10 kHz combining 2f-to-f interferometry and a LiNbO3 acousto-optic programmable dispersive filter achieves a record low phase noise.

Subcarrier PSK Performance in Terrestrial FSO Links Impaired by Gamma-Gamma Fading, Pointing Errors, and Phase Noise

Abstract: For terrestrial free-space optical (FSO) communication systems, subcarrier intensity modulation represents an attractive alternative to on-off keying or pulse-position modulation, which is mainly because of the larger spectral efficiency. However, some degradation of the error performance must be taken into account due to nonperfect synchronization of carrier frequency and phase. In a recently published paper, the average bit error probability has been analyzed for $M$ -ary phase-shift keying in the presence of phase noise for a terrestrial FSO link impaired by lognormal fading. In the this paper, we are extending this study to a gamma-gamma model, which is usually applied in case of moderate-to-strong scintillation effects. On top of that, pointing errors, caused by a misalignment between transmitter and receiver of the FSO link, are considered as well. Since a closed-form solution is not available under general conditions and because numerical methods are time-consuming, suffering in part also from serious convergence and stability problems, we provide approximate closed-form expressions, which are accurate enough over a wide signal-to-noise ratio range.

Distributed Fiber-Optic Vibration Sensing Based on Phase Extraction From Optical Reflectometry

Abstract: Distributed fiber-optic vibration sensing based on phase extraction from optical reflectometry is discussed in this paper. The principles on the phase extraction from coherent phase-sensitive optical time-domain reflectometry and time-gated digital optical frequency-domain reflectometry are introduced, and the experimental results of distributed vibration measurements based on the two techniques are demonstrated. To have a better understanding on the performance of the techniques, the phase extraction noise in the phase extraction process is analyzed. To solve the problem of existing measurement dead zones, the influence of Rayleigh fading phenomenon is investigated, and a solution of using statistical analysis to overcome this drawback is introduced and experimentally verified. With these improvements, long-range nondead-zone distributed vibration sensing techniques with linear response to external vibration signals based on phase extraction from optical reflectometry are realized.

SIR Analysis of OFDM and GFDM Waveforms With Timing Offset, CFO, and Phase Noise

Abstract: In this paper, we analyze the impacts of timing offset (TO), carrier frequency offset (CFO), and phase noise in orthogonal frequency division multiplexing (OFDM) and generalized frequency division multiplexing (GFDM) waveforms. As TO can be classified into four cases depending on the direction of offset, we provide the analysis of signal-to-interference ratio (SIR) for each of the cases when phase noise and synchronization errors of the desired user occur in frequency selective channel. We also propose the receiver filter for GFDM systems that is optimized to maximize SIR with CFO in additive white Gaussian noise channel. Simulation results show that GFDM is more sensitive to CFO than OFDM. We also confirm that GFDM systems using proposed receiver filter are robust against CFO compared with conventional systems.

Wideband tunable optoelectronic oscillator based on the deamplification of stimulated Brillouin scattering.

Abstract: A wideband tunable optoelectronic oscillator (OEO) based on the deamplification of stimulated Brillouin scattering (SBS) is proposed and experimentally demonstrated. A tunable single passband microwave photonic filter (MPF) utilizing phase modulation and SBS deamplification is used to realize the tunability of the OEO. Theoretical analysis of the MPF and phase noise performance of the OEO are presented. The frequency response of the MPF is determined by the + 1st sideband attenuation due to SBS deamplification and phase shift difference between the two sidebands due to chromatic dispersion and SBS. The close-in (< 1 MHz) phase noise of the proposed OEO is shown to be dominated by the laser frequency noise via phase shift of SBS. The conversion of the laser frequency noise to the close-in phase noise of the proposed OEO is effectively reduced compared with the OEO based on amplification by SBS. Tunable 7 to 40 GHz signals are experimentally obtained. The single-sideband (SSB) phase noise at 10 kHz offset is −128 dBc/Hz for 10.30 GHz signal. Compared with the OEO based on SBS amplification, the proposed OEO can achieve a phase noise performance improvement beyond 20 dB at 10 kHz offset. The maximum frequency and power drifts at 10.69 GHz are within 1 ppm and 1.4 dB during 1000 seconds, respectively. To achieve better close-in phase noise performance, lower frequency noise laser and higher pump power are preferred. The experimental results agree well with the theoretical models.

A 3.5–6.8-GHz Wide-Bandwidth DTC-Assisted Fractional-N All-Digital PLL With a MASH $\Delta \Sigma $ -TDC for Low In-Band Phase Noise

Abstract: This paper proposes a digital-to-time converter (DTC)-assisted fractional-N wide-bandwidth all-digital phase-locked loop (ADPLL) with a fine-resolution time-to-digital converter (TDC). The TDC employs a two-channel time-interleaved time-domain register with an implicit adder/subtractor realizing an error-feedback topology. Such an error-feedback unit of a first-order $\Delta \Sigma $ -TDC can be cascaded as a multi-stage noise shaping configuration to achieve higher-order noise-shaping and, thereby, low in-band phase noise (PN) of the ADPLL. A digitally controlled oscillator with a transformer and a pair of cross-coupled NMOS amplifiers exploits magnetic and capacitive coupling to achieve nearly an octave frequency coverage, i.e., 1.73–3.38 GHz (after a $\div $ 2 division). Fabricated in 40-nm CMOS, the ADPLL achieves better than −110-dBc/Hz in-band PN and occupies an active area of 0.5 mm2. With a 50-MHz reference clock, a 2-GHz output RF clock, and a loop bandwidth of 800 kHz, this prototype achieves 420-fs $_{{\mathrm{rms}}}$ jitter, integrated from 1-kHz to 30-MHz offset, while drawing 10.7 mW.

A 14-nm 0.14-ps rms Fractional-N Digital PLL With a 0.2-ps Resolution ADC-Assisted Coarse/Fine-Conversion Chopping TDC and TDC Nonlinearity Calibration

Abstract: A digital fractional-N phase-locked loop (PLL) is presented. It achieves 137- and 142-fs rms jitter integrating from 10 kHz to 10 MHz and from 1 kHz to 10 MHz, respectively. With a frequency multiplication ratio of 207.0019231 [digitally controlled oscillator (DCO) frequency is 50 kHz away from an integer multiple of the 26-MHz reference clock], a −78.6-dBc fractional spur is achieved for an output clock that runs at half of the DCO frequency. Time-to-digital converter (TDC) chopping technique, TDC fine conversion through successive approximation register analog-to-digital converters (SARADCs), and TDC nonlinearity calibration improve integrated phase noise and fractional spurs. This design meets the performance requirement of the 256-QAM $4 \times 4$ MIMO LTE standard in 5-GHz ISM band and also the 5G cellular 64-QAM standard in 28-GHz band. This work, implemented in a 14-nm fin-shaped field effect transistor (FinFET) CMOS process, is integrated to a cellular RF integrated circuit supporting advanced carrier aggregation operation. This PLL draws 13.4 mW and occupies 0.257 mm2.

High-Power and High-Efficiency Millimeter-Wave Harmonic Oscillator Design, Exploiting Harmonic Positive Feedback in CMOS

Abstract: Based on time-variant behavior of metal-oxide–semiconductor field-effect transistors in large-signal operations, harmonic translations and their mutual effects are analyzed. Large amplitudes at terminal voltages of these transistors push them into different regions of operation. In this paper, harmonic translations are derived as a result of such changes in operation region of transistors. Operation in triode region for a portion of oscillation cycle results in iterative harmonic translations between fundamental frequency and second harmonic. They boost each other constructively for significantly stronger oscillation, more second harmonic output power, and enhanced dc-to-RF efficiency. Based on this analysis, a 215-GHz signal source, implemented in a TSMC 65-nm CMOS LP is presented. The proposed oscillator achieves a maximum output power of 5.6 dBm and a dc-to-RF efficiency of 4.6%. The measured phase noise is −94.6 dBc/Hz at 1-MHz offset. The proposed oscillator occupies only 0.08 mm2 of chip area.

An Ultra-Low Power 1.7-2.7 GHz Fractional-N Sub-Sampling Digital Frequency Synthesizer and Modulator for IoT Applications in 40 nm CMOS

Abstract: This paper introduces an ultra-low power 1.7-2.7-GHz fractional-N sub-sampling digital PLL (SS-DPLL) for Internet-of-Things (IoT) applications targeting compliance with Bluetooth Low Energy (BLE) and IEEE802.15.4 standards. A snapshot time-to-digital converter (TDC) acts as a digital sub-sampler featuring an increased out-of-range gain and without any assistance from the traditional counting of DCO edges, thus further reducing power consumption. With a proposed DCO-divider phase rotation in the feedback path, the impact of the digital-to-time converter’s (DTC’s) non-linearity on the PLL is reduced and improves fractional spurs by at least 8 dB across BLE channels. Moreover, a “variable-preconditioned LMS” calibration algorithm is introduced to dynamically correct the DTC gain error with fractional frequency control word (FCW) down to 1/16384. Fabricated in 40 nm CMOS, the SS-DPLL achieves phase noise performance of −109 dBc/Hz at 1 MHz offset, while consuming a record-low power of 1.19 mW.

A Model for Designing Ultralow Noise Single- and Dual-Loop 10-GHz Optoelectronic Oscillators

Abstract: A complete model describing both single- and dual-loop optoelectronic oscillators (OEO) is introduced. It is compared to several experimental configurations, with excellent agreement in all cases. The physical insight into noise coupling mechanisms brought by the model further allows us for the design of ultralow noise OEO. Phase noise performances at 10 GHz with a single 1 km delay line and with a dual 1 km/100 m delay lines are reported. An optimized dual loop configuration exhibits low phase noise floor at high offset frequency (–160 dBc/Hz at 100 kHz) and low spur levels (–145 dBc/Hz), here again in close agreement with our model.

Compact, thermal-noise-limited reference cavity for ultra-low-noise microwave generation.

Abstract: We demonstrate an easy-to-manufacture 25-mm-long ultra-stable optical reference cavity for transportable photonic microwave generation systems. Employing a rigid holding geometry that is first-order insensitive to the squeezing force and a cavity geometry that improves the thermal noise limit at room temperature, we observe a laser phase noise that is nearly thermal noise limited for three frequency decades (1 Hz to 1 kHz offset) and supports 10 GHz generation with phase noise near −100 dBc/Hz at 1 Hz offset and 600 Hz. The fractional frequency stability reaches 2×10−15 at 0.1 s of averaging.

Injection locking of an electro-optomechanical device

Abstract: Advances in optomechanics have enabled significant achievements in precision sensing and control of matter, including detection of gravitational waves and cooling of mechanical systems to their quantum ground states. Recently, the inherent nonlinearity in the optomechanical interaction has been harnessed to explore synchronization effects, including the spontaneous locking of an oscillator to a reference injection signal delivered via the optical field. Here, we present, to the best of our knowledge, the first demonstration of a radiation-pressure-driven optomechanical system locking to an inertial drive, with actuation provided by an integrated electrical interface. We use the injection signal to suppress the drift in the optomechanical oscillation frequency, strongly reducing phase noise by over 55 dBc/Hz at 2 Hz offset. We further employ the injection tone to tune the oscillation frequency by more than 2 million times its narrowed linewidth. In addition, we uncover previously unreported synchronization dynamics, enabled by the independence of the inertial drive from the optical drive field. Finally, we show that our approach may enable control of the optomechanical gain competition between different mechanical modes of a single resonator. The electrical interface allows enhanced scalability for future applications involving arrays of injection-locked precision sensors.

Linear CMOS $LC$ -VCO Based on Triple-Coupled Inductors and Its Application to 40-GHz Phase-Locked Loop

Abstract: A linear CMOS $LC$ voltage-controlled oscillator (VCO) utilizing triple-coupled inductors and a 40-GHz integer-N phase-locked loop (PLL) are fabricated in a standard 90-nm CMOS process. The VCO utilizes triple-coupled inductors to couple varactor pairs, which compensate each other to linearize the VCO gain. The triple-coupled $LC$ tank is theoretically analyzed using equivalent circuit models. With the triple-coupled inductors, there is no need for tuning-voltage shifting circuits or dc-block capacitors, suitable for high-performance millimeter-wave (mm-wave) VCO design. A 40-GHz PLL has also been design and built around this linear $LC$ -VCO to demonstrate a stable PLL with small loop bandwidth variations. The measured tuning bandwidth, phase noise, and figure of merit (FOM $_{T}$ ) of the linear VCO is 15.8%, −100.7 dBc/Hz at 1-MHz offset, and −181.8 dBc/Hz, respectively. Utilizing the linear VCO, the experimental PLL is stably locked from 38.61 to 44.55 GHz. The PLL without output buffer consumes 76 mW from 1.5/1.0 V supplies. The measured in-band and out-band phase noise of the 40-GHz PLL are −81 dBc/Hz at 100-kHz offset, and −114.5 dBc/Hz at 10-MHz offset, respectively. Thanks to the proposed linearization method, the VCO gain shows very small variations, compared with reported works. The implemented PLL demonstrates good stabilities with small loop bandwidth variations across the operation frequency range.

120 Gb/s Multi-Channel THz Wireless Transmission and THz Receiver Performance Analysis

Abstract: A photonic multi-channel terahertz (THz) wireless transmission system in the 350-475 GHz band is experimentally demonstrated. The employment of six THz carriers modulated with 10 Gbaud Nyquist quadrature phase-shift keying baseband signal per carrier results in an overall capacity of up to 120 Gb/s. The THz carriers with high-frequency stability and low phase noise are generated based on photonic photomixing of 25-GHz spaced six optical tones and a single optical local oscillator derived from a same optical frequency comb in an ultrabroadband uni-travelling carrier photodiode. The bit-error-rate performance below the hard decision forward error correction threshold of 3.8×10 -3 for all the channels is successfully achieved after wireless delivery. Furthermore, we also investigate the influence of the harmonic spurs in a THz receiver on the performance of transmission system, and the experimental results suggest more than 30 dB spur suppression ratio in downconverted intermediate frequency signals for obtaining less than 1 dB interference.

Switched Substrate-Shield-Based Low-Loss CMOS Inductors for Wide Tuning Range VCOs

Abstract: A switched substrate-shield inductor (SSI) topology in bulk CMOS is proposed which minimizes parasitic capacitance and substrate losses, while tuned magnetically induced currents facilitate inductor tunability. The high frequency behavior of the induced current is analyzed, resulting in intuitive insights and design guidelines for a high-performance SSI. An SSI prototype in 65-nm bulk CMOS achieves 34% inductance tunability with a quality factor of >10.3. A voltage-controlled oscillator (VCO) using SSI achieves 40.3% tuning range, from 21 to 31.6 GHz, and a phase noise of −119.1 ± 3.7 dBc/Hz at 10-MHz offset frequencies. The VCO core consumes 4.3 ± 0.2 mW from a 1-V supply.