Quadrature Signals Research Articles

A Luenberger observer-based phase locked loop for single-phase systems under harmonic disturbances

Harmonics in single-phase systems challenge the performance of quadrature signal generator-based phase-locked loops (QSG-PLLs). This paper proposes a Luenberger observer-based PLL (LO-PLL) to address the issue. The proposed method enhances the harmonic suppression capability when estimating the fundamental grid voltage, thus leading to improved system harmonic rejection robustness. In detail, the improvement is enabled by the integrated grid voltage, which is mathematically established in this paper. Subsequently, the observer is adopted to generate the fundamental grid voltage and its quadrature signal. The resultant two signals for synchronization are highly robust against arbitrary-order harmonic disturbances, especially for interharmonics and noises. More importantly, as the poles of the observer can be designed flexibly, fast dynamics and strong harmonic robustness can be ensure for the entire PLL system. Experiments verify the performance of the proposed LO-PLL in terms of high harmonic immunity and fast dynamics.

Adjustment of Phase Shift of Measurement Signals in an Optical Encoder from the Parameters of an Analyzing Scale

Optical sensors of linear displacements with diffraction gratings serving as the measurement scales are investigated. A method of stabilization of the phase difference of quadrature measurement signals, consisting in the use of an analyzing scale with a special structure, is proposed. A design of an optical encoder based on the method is proposed. Mathematical simulation of the phase shift of the measurement signals as a function of the parameters of the diffraction grating is performed, and the results of the simulation are presented. The RCWA method is used to simulate the passage of radiation through the optical system. The optimal parameters of the structure of the analyzing scale are calculated. Experimental investigations of a mock-up of the encoder are performed and results of measurements of the phase difference of the measurement signals are presented.

Analysis and Design of Wideband I/Q CMOS 100–200 Gb/s Modulators

This paper presents the analysis and design of wideband I/Q CMOS modulators and transmitters. Non-idealities and performance limitations of Cartesian transmitter and modulator systems are discussed, and circuit design techniques and analyses are shown. A DC-60 GHz I/Q modulator/transmitter chip in 45-nm SOI CMOS is presented as a critical building block for next-generation multi-standard and high-capacity wireless backhaul links. The modulator consists of a wideband quadrature signal generator, wideband buffers, and two current-combined DC-100 GHz low-noise double-balanced mixers driven in quadrature. The 1.4 mm2 modulator chip achieves 60 dB of dynamic range in a 1-GHz bandwidth, with an OP1dB of ~ −10 dBm, thus enabling spectrally efficient high-order modulation schemes such as 256-QAM. The I/Q modulator achieves 200 Gb/s in 16-QAM (50 Gbaud/s) while consuming 200 mW, resulting in record 1-pJ/bit modulation efficiency. In addition to backhaul links, the modulator is an attractive and cost-effective alternative to short-range optical links for data center interconnects (DCI) and for chip-to-chip communications.

24-GHz Injection-Locked Frequency Tripler With Third-Harmonic Quadrature Phase Generator

This paper presents a quadrature injection-locked frequency tripler (ILFT) adopting third-harmonic phase shifters for quadrature signal injection at the third-harmonic band. Two capacitively degenerated differential transconductor pairs inject quadrature currents to the main I/Q LC tanks. The degeneration networks are optimally designed to create quadrature injection signals at the third harmonic of injection signal. The presented third-harmonically quadrature phasing technique increases an injection-locking range effectively with the minimizing injection signal loss compared with prior conventional injection techniques employing phase shifters at the fundamental frequency. The proposed ILFT is implemented in 130-nm CMOS technology. The measured injection-locking range is 3.3% (~800 MHz) at the 23.6-GHz center frequency with 0-dBm input injection power. The locking range of the proposed ILFT is twice wider than that of prior state-of-the-art ILFTs adopting single differential signal injections or polyphase filter-based quadrature signal injections. The proposed ILFT consumes 10.4 mW, and the chip size is 0.5 × 0.25 mm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> without pads.

Parametric Amplification and Noise Squeezing in Room Temperature Atomic Vapors.

We report on the use of parametric excitation to coherently manipulate the collective spin state of an atomic vapor at room temperature. Signatures of the parametric excitation are detected in the ground-state spin evolution. These include the excitation spectrum of the atomic coherences, which contains resonances at frequencies characteristic of the parametric process. The amplitudes of the signal quadratures show amplification and attenuation, and their noise distribution is characterized by a strong asymmetry, similar to those observed in mechanical oscillators. The parametric excitation is produced by periodic modulation of the pumping beam, exploiting a Bell-Bloom-like technique widely used in atomic magnetometry. Notably, we find that the noise squeezing obtained by this technique enhances the signal-to-noise ratio of the measurements up to a factor of 10, and improves the performance of a Bell-Bloom magnetometer by a factor of 3.

Improving the Accuracy of an Absolute Magnetic Encoder by Using Harmonic Rejection and a Dual-Phase-Locked Loop

This paper proposes a method to improve the accuracy of an absolute magnetic encoder by using harmonic rejection (HR) and a dual-phase-locked loop (DPLL). The encoder consists of two permanent magnets: an edge-located multipolar magnet (MPM) and a center-located bipolar magnet, in which the signal-processing accuracy of the MPM is crucial for achieving high accuracy of the entire encoder. However, the MPM signals are disturbed by nonidealities such as dc offsets, amplitude mismatch, low- and high-order harmonics, and random noises. In this paper, the HR approach investigates the characteristics of nonidealities of the phase detector and rejects them by using gradient descent. In addition, the DPLL remains robust by maintaining a zero steady-state error during a phase jump, a constant frequency, and a ramp frequency. The proposed method is simulated with MATLAB software and implemented in ARM STM32F407ZG. The obtained results demonstrate efficient performance. This method can be applied to any use of quadrature sinusoidal signals, such as in power grids and in permanent-magnet synchronous motor phase detection.

A Low Phase Noise, High Phase Accuracy Quadrature LC-VCO With Dual-Tail Current Biasing to Insert Reconfigurable Phase Delay

This brief presents a novel low phase noise and low phase error quadrature LC-tank voltage controlled oscillator (LC-VCO), which utilizes the dual-tail current biasing technique to insert a phase shift in the coupling path. The dual-tail current bias each oscillation branch, and are gated by quadrature signals. One tail current, named coupling-tail current, is gated by the quadrature phase signal to force the voltage controlled oscillator to keep quadrature state. The other tail current, named self-tail current, is gated by the anti-phase signal to introduce a phase shift in total bias current. The phase shift is reconfigurable by adjusting the DC biasing voltage of tail current transistors to resist the performance deterioration caused by process variations. Compared with the conventional quadrature LC-VCO, the proposed quadrature LC-VCO enhances the phase accuracy and optimize the phase noise simultaneously. Additionally, it has the distinct advantage of reconfigurability. The core was fabricated in 180 nm 1P6M CMOS process, and occupied a die area of 0.96 mm2 totally. The measurement results show it achieves a phase noise of −129.3 dBc/Hz @1 MHz offset and a phase error of 0.09° while $k=0.4$ , $V_{\mathrm {b0}}= 0.8$ V, and $V_{\mathrm {b1}}= 0.6$ V @2.5 GHz. The total power consumption is 20.6 mW with a supply voltage of 1.8 V.

A Full 360° Measurement Range Liquid Capacitive Inclinometer With a Triple- Eccentric-Ring Sensing Element and Differential Detection Scheme

This paper proposes a low-cost and full 360° measurement range inclinometer based on fluidic motion. The inclinometer is fabricated using printed circuit board manufacturing techniques. The principle is via measuring two channels of capacitance changes between three plates, which are partially filled with nonconductive liquid to obtain two amplitude modulation quadrature signals as the resolver. In this inclinometer, the electrode subdivision is changed from the traditional radial direction to a circumferential direction by a triple-eccentric-ring sensing element to achieve full-range measurement capability from 0° to 360°. In addition, the application of a differential detection scheme leads to the dc capacitance C 0 being eliminated in the measurement, resulting a high voltage-to-capacitance ratio in a low voltage source requirement. Both analytical calculation and finite-element analysis verified the feasibility of the principle. Furthermore, nonlinear error simulation is conducted and the main effected reason is figured out. Finally, a prototype is fabricated and assembled. Experimental results show that sensor can measure the tilt angle in a range of 360°, with an accuracy of 0.1° and a resolution better than 0.01°.

A Harmonic Error Cancellation Method for Accurate Clock-Based Electrochemical Impedance Spectroscopy.

Electrochemical impedance spectroscopy (EIS) is a widely used method to characterize the biological materials. In traditional methods for EIS, a sinusoidal current is used to excite the material under test and the measured voltage across that material is demodulated by a linear multiplication with quadrature sinusoidal signals. From the resulting demodulated output, the impedance (magnitude and phase) can be calculated. Although this sine-wave-based impedance measurement method can produce accurate impedance measurements, it requires bulky components and suffers from poor power efficiency due to sinusoidal waveform generation and linear multiplication. Alternatively, a method using square-wave signal, which is simply a clock, for both excitation and demodulation can be much more area and power efficient, but inherently suffers from substantial errors in the result due to significant harmonics in square waves. In this paper, we propose a technique to cancel out the errors caused by such harmonics of the square-wave-based excitation and demodulation. The proposed technique, based on the fact that the magnitude ratio of all the harmonics of a square wave are known, cancels out harmonic errors by subtracting or adding the square-wave-based measured results at higher harmonic frequencies as a simple post-processing calculation. Simulations on specific and also generic impedance models demonstrate the applicability of this technique to various impedance models. Experimental results using a discrete circuit model show that this technique can provide a precise measurement of the impedance with 1% magnitude error and 0.5° phase error considering just five terms. In addition, measurements with a biological tissue show an average magnitude and phase error of 0.7% and [Formula: see text], respectively, using the proposed error cancellation. Because this method replaces sinusoidal signal generation and linear multiplication with clock generation and simple switching, it has great potential to be integrated in a wearable and implantable health monitoring device at low area and power consumption.

Passive stabilization scheme for polarization mode interferometers using a polarization beam splitter

A passive stabilization scheme for polarization mode interferometers (PMIs) using a polarization beam splitter (PBS) is proposed and experimentally demonstrated. Polarization eigenmodes in a highly birefringent fiber are modulated by external signals. Quadrature signals utilized in demodulation algorithm are acquired from the square roots of the photo-voltages, which are detected from the transmission lights of the PBS. Experimental results show that the scheme has a large dynamic range (100.8 dB), good linearity (99.937%) and is capable of high sensitivity (10−7 rad detectability above 150 Hz). Furthermore, it is immune to intensity noise of lasers so that the system instability and complexity are obviously reduced.

Noncontact photoacoustic imaging based on optical quadrature detection with a multiport interferometer.

A noncontact photoacoustic imaging method based on optical quadrature detection is proposed. The photo-induced acoustic signal is detected by an optical method without contacting the specimen. By utilizing the intrinsic phase difference of a multiport optical interferometer, the quadrature signal of a conventional interferometric signal could be obtained. With this quadratic signal pair, we could reconstruct the photoacoustic signal without suffering from the initial phase drift that usually occurs in a conventional interferometric system. The performance of the proposed system is verified by imaging human hairs embedded in a polydimethylsiloxane resin block. The system's lateral and axial resolutions are measured to be 84 and 86μm at a 1.5mm depth of a PDMS resin block, respectively. The experimental result is good enough to distinguish the hairs staggered in depth.

Dual-Band Millimeter-Wave Quadrature LO Generation With a Common-Centroid Floorplan

This brief presents a dual-band millimeter-wave (mm-Wave) quadrature signal generation network comprising an RC-CR polyphase filter (PPF) and two quarter-wave coupled-line couplers. A common-centroid layout is proposed to improve the phase and amplitude matching of quadrature signals. The effects of interconnects and parasitic capacitances on PPFs are investigated, and design guidelines are provided to achieve low insertion loss and broad bandwidth. A proof-of-concept image-reject mixer is implemented in a 0.13 $ \mu \text{m}$ SiGe BiCMOS technology, which achieves a mean image-rejection ratio of 34 dB over a wide frequency range of 36 – 100 GHz. To the best of authors’ knowledge, this design achieves the widest bandwidth of any mm-Wave mixer having a mean image rejection ratio above 30 dB, and accomplishes this without calibration or tuning.

Characteristics of magnetic sensor with assembly errors in a rotary recording system

A magnetic position sensing system consists of a magnetic rotary ring with polarities magnetized on its radial surface and a position sensor made of magnetoresistance. Two quadrature sinusoidal output signals from sensor are processed into position information for motion control application. Magnetoresistance varies with the angle between magnetization (M) of external field and flow current (I) inside the sensor patterns. Therefore, the assembly error either in sensor or rotary ring would cause distorted signal. The assembly error between sensor and the medium such as offset, pitch, roll, yaw error and eccentricity between scale and stage of motion centre of read head would be discussed in this paper. Experimental and analytical parameter studies were conducted in this paper to discuss the accuracy error and variation of output quadrature signal caused by assembly error. Through the parameter studies, the data under various conditions can then be used to serve as a baseline.

Bell–Bloom Magnetometer Linearization by Intensity Modulation Cancellation

This paper describes a technique for enhancing the linearity of a Bell–Bloom optical magnetometer. Both the $M_{x}$ and Bell–Bloom magnetometers are examined, and the characteristics of their photodetector signals are compared. It is noted that the phase signal has better linearity than the quadrature amplitude signal for a $M_{x}$ magnetometer, while phase and quadrature amplitude give similar performance in Bell–Bloom. A cancellation technique is proposed whereby the laser intensity modulation of Bell–Bloom is mitigated to improve the linearity. A cesium microfabricated atomic magnetometer in a frequency-locked-loop configuration is demonstrated, and the improved slew rate and frequency-domain linearity are shown. This linearity enhancement should prove useful for operating atomic magnetometers in interference-rich environments outside of magnetic shields.

Signal Error Detection and Correction of Quadrature Detectors of Laser Interferometers

Errors of laser interferometers using quadrature detectors depend not only on the interferometers themselves, but also on the electronic systems for processing quadrature signals. There are three sources of errors of quadrature detector signals that affect the displacement measurement error: the inequality of the amplitudes of quadrature signals, the phase shift of these signals (not equal to 90°), and the zero offset in each signal. A simple method for identifying and correcting these errors based on experimental data on signals obtained using analog-to-digital converters is considered. The proposed method is applicable to any interferometer with sinusoidal quadrature outputs.

Calibration of DC offsets in quadrature mixing structure based on Hilbert transform

DC offsets in a quadrature mixing structure will affect the system performance. This paper proposes a Hilbert transform-based algorithm to blindly calibrate the DC offsets by filtering the inphase and quadrature signals with the same Hilbert filters. Compared with the traditional averaging-based method, this method consumes less time and resources. Moreover, the proposed method need not interrupt analog-to-digital converter's conversion, featuring the characteristics of high efficiency and good real-time performance. The Matlab simulation results verify the correctness of the proposed algorithm, and finally, an experimental platform is designed in detail to verify the practicability of this blind calibration algorithm.

A CMOS Highly Linear Doherty Power Amplifier With Multigated Transistors

This paper presents a highly linear and power back-off efficiency-enhanced Doherty power amplifier (PA) fully integrated into CMOS. The proposed Doherty PA employs a transformer-based quadrature signal generator, multigated transistors (MGTRs) in the main PA, Class-C mode auxiliary PA, and synthesized transformer-based Doherty parallel output network with the second-harmonic control circuits. An on-chip 8-port transformer-based quadrature signal generator is designed within a single transformer footprint ( $340\,\,\mu \text{m}\,\,\times 340\,\,\mu \text{m}$ ) and provides 0°/−90° differential signals to the main/auxiliary PAs. The MGTR in the main PA is implemented using four transistors with different sizes and biases to generate and extend a near-zero $\text {g}_{\text {m3}}$ operation region. Moreover, an on-chip transformer-based Doherty parallel output network with the second-harmonic control circuits shows higher passive efficiency compared with a conventional Doherty parallel output network and provides low second-harmonic loads to the main/auxiliary PAs. Both the proposed MGTR in the main PA and the second-harmonic control circuits in the main/auxiliary PAs suppress the third-order intermodulation distortion of the Doherty PA. This results in a substantial linearity improvement of the Doherty PA, which can support high-order modulation signals and reduce or even eliminate the need for digital predistortion (DPD). As a proof-of-concept design, a 5.8 GHz Doherty PA is implemented in a standard 55 nm bulk CMOS process. The proposed Doherty PA exhibits 27.2 dBm saturated output power with 24.5% power-added efficiency (PAE) at 5.8 GHz. The measured error vector magnitude with 40/80 MHz of 64-QAM/256-QAM is 2.5%/1.8% with 20.7/17 dBm average output power, 9.5%/5.3% average PAE, and −33.2/−36.3 dBc adjacent channel leakage ratio without any DPD.

Filter-free image-reject microwave photonic downconverter based on cascaded modulators.

As essential equipment of the receiver, a novel filter-free image-reject mixer based on a Mach-Zehnder modulator (MZM) and a polarization-division multiplexing Mach-Zehnder modulator (PDM-MZM) is proposed and experimentally demonstrated in this paper. The received radio frequency signal is applied to the MZM, and quadrature local oscillator signals are sent to the PDM-MZM, which includes two submodulators in parallel. After a polarization controller and a polarization beam splitter, quadrature intermediate frequency (IF) signals are obtained by two photodetectors. Image rejection is implemented by combining quadrature IF signals via an electrical 90° hybrid coupler. The scheme uses no filter, so the working frequency can be widely tuned and effective spectrum utilization is achieved. Experimental results verify that image rejection ratios can reach 50dB. Moreover, the variation of the conversion gain is lower than 2dB.

Data-Driven Deep Learning for Automatic Modulation Recognition in Cognitive Radios

Automatic modulation recognition (AMR) is an essential and challenging topic in the development of the cognitive radio (CR), and it is a cornerstone of CR adaptive modulation and demodulation capabilities to sense and learn environments and make corresponding adjustments. AMR is essentially a classification problem, and deep learning achieves outstanding performances in various classification tasks. So, this paper proposes a deep learning-based method, combined with two convolutional neural networks (CNNs) trained on different datasets, to achieve higher accuracy AMR. A CNN is trained on samples composed of in-phase and quadrature component signals, otherwise known as in-phase and quadrature samples, to distinguish modulation modes, that are relatively easy to identify. We adopt dropout instead of pooling operation to achieve higher recognition accuracy. A CNN based on constellation diagrams is also designed to recognize modulation modes that are difficult to distinguish in the former CNN, such as 16 quadratic-amplitude modulation (QAM) and 64 QAM, demonstrating the ability to classify QAM signals even in scenarios with a low signal-to-noise ratio.

An Efficient ISAR Imaging Method for Non-Uniformly Rotating Targets Based on Multiple Geometry-Aided Parameters Estimation

The inverse synthetic aperture radar (ISAR) imaging for non-uniformly rotating target plays an important role in many applications. However, it always faces a serious challenge, i.e., the time-varying Doppler frequency induced by the target complex motions will degrade the quality of ISAR image seriously. Several algorithms based on motion parameter estimation have been proposed in recent years. However, most of them always suffer from the heavy computational burden and considerable propagation errors, which deteriorate the performances of algorithms and limit their practical applications. To tackle this problem, an efficient ISAR imaging algorithm is proposed for non-uniformly rotating targets based on geometry-aided parameters estimation in this paper. After the motion compensation, the ISAR echoes are modeled as the quadratic frequency modulated signal first, then is transformed into time-chirp distribution (TCD) plane and the least square Radon transform (RT) based on TCD (LSRT) to estimate the derivative of chirp rate efficiently is proposed. To improve the estimation performance and robustness, the pre-processing and the weighted least square RT TCD methods are both developed. Similarly, the weighted LSRT based on time-frequency distribution is also proposed to estimate the chirp rate. The proposed multiple geometry-aided method can eliminate the effect of propagation error and reduce the computational complexity simultaneously. The simulated data and real-measured data results are both presented to validate the proposed method.