Loop Output Research Articles

Sensing offset analysis and compensation of a capacitive displacement transducer for space inertial sensors

Abstract Capacitive displacement transducers play a crucial role in inertial sensors especially for space gravitational wave detection missions. One of the major requirements for the displacement transducer is to have a lower sensing offset. The sensing offset will adversely affect the accuracy of the absolute position measurement of the test mass, providing erroneous data to the drag-free controller and leading to spacecraft mispositioning. Additionally, the offset could introduce multiplicative noise to the sensing output and the closed loop output of the inertial sensor. The asymmetry of the sensing bridge within the front-end electronics has been identified as the primary source of these offsets. This paper analyzes the requirements of the main parameters in the sensing bridge. A method is proposed to reduce the sensing offset by utilizing differentiated resonant capacitors while maintaining the ability to tune the resonant frequency and ensure a sufficiently low sensing noise level. Experimental results show that this approach can effectively reduce the residual sensing offset to (−15.7 ± 5.0) ppm, which satisfies the stringent requirement for space inertial sensors in the TianQin mission.

Spatial Equilibria: The Case of Two Regions

In this paper we characterize the set of equilibria in a generalized version of the canonical two-region economic geography model that nests the class of models in Allen and Arkolakis (2014) as well as Krugman (1991) and features an input–output loop. We provide sufficient conditions for uniqueness of equilibria that — in contrast to the well-know result in Allen and Arkolakis (2014) — allow for positive agglomeration externalities, which concentrate economic activity, even in the absence of congestion effects, which disperse it, and highlight the key role played by three additional parameters: the trade elasticity, which regulates the strength of the dispersion force associated with the decline in the terms of trade caused by migration into a region; trade costs, which weaken this dispersion force by limiting trade across regions; and the importance of the agricultural sector, which pushes against agglomeration forces in manufacturing.

An online comprehensive health monitoring system for automotive auxiliary converter

Abstract As an essential part of the electronic system in electric vehicles (EVs), the automotive auxiliary converter (AAC) connects the batteries and burdens the auxiliary power supply. This paper mainly proposes an online comprehensive health monitoring system for AAC. Firstly, based on the control diagram of the LLC resonant converter, three critical components are emerging, including capacitor, optocoupler, and semiconductor. These components can partly reflect the operation condition of the output loop, feedback loop, and control link, respectively. Then the characteristics parameters of these three components, equivalent series resistance (ESR) of the capacitor, current transfer ratio (CTR) of the optocoupler, and on-resistance of the semiconductor jointly construct the three-dimensional health monitoring vector. Finally, the online monitoring accuracy is verified and the proposed system can thus effectively promote the operation and maintenance of AAC. Furthermore, the online health monitoring system enables a flexible expansion, which can be further customized into different kinds of power converters, showing high applicability and practicality.

A comprehensive optimization method for dual redundancy aviation electric propulsion control system

Abstract This paper comprehensively optimizes and improves the traditional vector control method to improve the control performance of dual-redundancy electric aircraft and ensure the stability of its system operation in complex meteorological environments. First, the PI controller of the speed loop is replaced with the designed fuzzy PI controller, and its quantization factor and scale factor parameters are adjusted using a beetle antennae search algorithm (BAS) to enhance the system’s ability to respond quickly and resist interference. Secondly, a sliding mode load observer was designed to feed forward the observed values to the speed loop output, solving the torque and current ripple problems caused by the direct input of the redundant electric propulsion system when the aircraft switches from a single-redundant cruise state to a dual-redundant high-speed state. Finally, the design method was simulated and validated using MATLAB/SIMULINK, verifying the feasibility of the design.

Mapping the Dynamic Complexity of Social Isolation Among Older Adults in Singapore

This study aims to develop a causal map of social isolation among older people that incorporates feedback to inform system-wide interventions. For this study, conducted between September 2019 and November 2019, 19 Senior Activity Centres (SACs) were first contacted, of which 10 responded and 5 agreed to participate. Based on an in-depth qualitative interview with 21 older people (50 years and older) who frequently attended Senior Activity Centres (SACs) in Singapore, a series of causal maps were generated and synthesized to describe the complex dynamic mechanisms of social isolation. Using thematic analysis based on grounded theory, 13 feedback loops (outputs of a system routed back as inputs as part of a chain of cause-and-effect) were elicited and categorized into 4 domains: (a) health and wellbeing, (b) income and unemployment, (c) relationships with family and friends, and (d) behavior and personality. These domains were found to be the most salient factors influencing social isolation. A qualitative mapping approach based on System Dynamics Methodology can provide a comprehensive understanding of the system-level factors of social isolation among older people.

Beam steering using delays generated from an optical OAM mode shifting recirculating loop

This paper investigates the performance of generated delays from an orbital angular momentum mode shifting recirculating delay loop (OAM-SL) in simulation using Kirchhoff-Fresnel diffraction (KFD) and the delays applicability for RF signal beam steering applications. OAM-SL is a novel structure that has been recently reported to produce multiple delayed signal replicas on independent OAM carriers using a single compact system. The objective of this research is to explore the impact of several limiting factors on the quality of OAM-SL delays for beam steering applications, such as where there is (i) displacement of the OAM mode shifter, (ii) displacement of the center of the OAM mode demultiplexer at the loop output, and (iii) the limited resolution. The methodology includes: (i) simulating the beam propagation using KFD, (ii) producing the output as a coherent summation of the recirculating beams, and (iii) characterizing the SCR by dividing the power of the recirculating beam (ρ) on its OAM mode by the power accumulated from the other recirculating beams. Our findings show that delays generated from a system with lin=−30, lshift=+1, and a resolution of 1024 pixels can steer a 100 MHz signal at a steering angle of 11.5° in a four antenna system with 0.1° error if loop alignment is perfect. Also, for steering the 100 MHz signal in an eight antenna system, we analyze the system assuming the system loss can be compensated, and a similar result of 0.1° error is obtained. Additionally, we report the beam steering performance at 23.6° and 36.8°.

Modified reverse puncture technique for esophagojejunostomy during totally laparoscopic total gastrectomy for gastric cancer

Objective: To evaluate the value of implementing a modified reverse puncture procedure for esophagojejunostomy during totally laparoscopic total gastrectomy. Methods: This was a descriptive case series. Relevant clinical data, including the operative procedure, recovery, and pathological findings of 35 patients with gastric cancer who had undergone esophagojejunostomy with a modified reverse puncture technique during totally laparoscopic total gastrectomy in the Department of Gastrointestinal Surgery, Fujian Provincial Hospital, from June 2022 to January 2023, were prospectively collected and retrospectively analyzed. The age of all patients in the group was (64.9±8.0) years old, with 22 males (62.9%) and a body mass index of (23.2±2.4) kg/m2. The tumors were located in the upper and middle parts of the stomach in 24 cases (68.6%) and in the junction of the esophagus and stomach in 11 cases (31.4%). Important technical aspects of the modified reverse puncture procedure are as follows. (1) Site of the esophageal incision: a transverse incision is made across the right lateral wall of the esophagus at the expected site of esophageal disjunction. (2) Technique for inserting an anvil: after threading a silk thread through the tip of anvil, the end of the thread is knotted and fixed as the traction thread, after which an anvil is inserted into the esophagus through the esophageal incision, leaving the end of the traction line exposed. Next, a 60-mm linear cutter is placed through the right midclavicular trocar to straighten the opened esophagus vertically, after which the rod of the anvil is pulled out of a small incision that has been made in the esophagus by pulling the traction thread, thus completing anvil placement. (3) Jejunal binding: the jejunum on the central bar of the stapler is fastened with silk thread to the stump of the jejunum, and then tied to the output loop of the jejunum with a gauze strip. Results: All 35 surgeries were successful, with no mortality or conversion to laparotomy. The operation time, anvil insertion time, and digestive tract reconstruction time were (232.7±34.4), (8.5±1.4), and (40.5±4.8) minutes, respectively. The intraoperative blood loss was 100 (20-250) mL and the incision was (5.3±0.9) cm long. The upper surgical margin was negative in all patients and the mean distance between the upper and tumor margins was (3.5±1.2) cm. The mean number of lymph nodes dissected per patient was 33.9±7.1. The times to initial ambulation, initial passage of flatus , postoperative fluid intake, and length of postoperative hospital stay were (3.2±1.1), (3.7±1.5), (4.6±2.3), and (9.8±3.2) days, respectively. Postoperative complications occurred in five patients: one case of anastomotic leak, two of anastomotic stenosis, one of pulmonary infection, and one of incomplete intestinal obstruction, all of which were successfully managed conservatively. Conclusion: Esophagojejunostomy using a modified reverse puncture technique during totally laparoscopic total gastrectomy is safe and feasible for gastric cancer, requiring only a small incision and achieving higher upper esophageal resection margins and good postoperative recovery, and therefore warrants further implementation.

Fast Computation of Neck-Like Features.

Locating neck-like features, or locally narrow parts, of a surface is crucial in various applications such as segmentation, shape analysis, path planning, and robotics. Topological methods are often utilized to find the set of shortest loops around handles and tunnels. However, there are abundant neck-like features on genus-0 shapes without any handles. While 3D geometry-aware topological approaches exist to find neck loops, their construction can be cumbersome and may even lead to geometrically wide loops. Thus we propose a "topology-aware geometric approach" to compute the tightest loops around neck features on surfaces, including genus-0 surfaces. Our algorithm starts with a volumetric representation of an input surface and then calculates the distance function of mesh points to the boundary surface as a Morse function. All neck features induce critical points of this Morse function where the Hessian matrix has precisely one positive eigenvalue, i.e., type-2 saddles. As we focus on geometric neck features, we bypass a topological construction such as the Morse-Smale complex or a lower-star filtration. Instead, we directly create a cutting plane through each neck feature. Each resulting loop can then be tightened to form a closed geodesic representation of the neck feature. Moreover, we offer criteria to measure the significance of a neck feature through the evolution of critical points when smoothing the distance function. Furthermore, we speed up the detection process through mesh simplification without compromising the quality of the output loops.

The orchestration of green supply chain management practices to enable performance measurement and evaluation

This study aims at investigating the relationship between the implementation of green supply chain management (GSCM) practices and the implementation of environmental performance measurement and evaluation (EPME) practices. The theoretical model was empirically validated using structural equation modelling in a survey of 199 Brazilian managers working in sustainability areas. We introduce a novel framework that bridges systems theory with the practice-based perspective of firms. The framework advances the current understanding of factors influencing EPME adoption, structuring GSCM practices as system components: inputs, processes, outputs, and feedback loops. More specifically, we identify the direct effects of different GSCM practices in the implementation of EPME but also indirect effects cascading through input, process, output, and feedback loop practices. Our research addresses industry needs for guidance on how to implement GSCM practices and facilitate EPME. Managers need to orchestrate the adoption of GSCM practices in each of these system components by monitoring of inter-organisational and intra-organisational activities of their supply chains. Both EPME and feedback loop practices (e.g. customer collaboration) are key to achieving benefits concerning the environmental impact of supply chain operations.

Effects of ionosphere dispersion on wideband GNSS signals

Wideband GNSS signals suffer signal distortions such as waveform deformations and correlation peak reduction when traverse the ionosphere. Basing on the standard model of the ionosphere, we first demonstrate a modified ionosphere model to capture the ionosphere dispersion effects on wideband signals. We decompose the first-order ionosphere model into Taylor series. By using the first three terms of Taylor series, it is possible to account for all frequency components of wideband signals rather than treating them as single tone. We then make an analysis of the ionosphere dispersion effects on wideband GNSS signal tracking. It is revealed that the ionosphere dispersion degrades correlation peak results and shifts carrier-phase in the phase locked loop (PLL) output but dose not cause an additional delay for code measurements. Furthermore, we carry out a simulation for evaluating the ionosphere dispersion effects on tracking of various new generation wideband GNSS signals such as Galileo E5 AltBOC(15, 10) signals and BDS B3 BOC(15, 2.5) signals during ionosphere quietness and activities. The results show that the wider the bandwidth and the greater the total electron content (TEC) values, the more dramatic the ionosphere effects are. The Galileo E5 AltBOC(15, 10) signals are most affected among various wideband GNSS signals. For AltBOC(15, 10) signal tracking the correlation power loss is around 0.1 dB and the carrier-phase change is about 20° caused by the dispersion in quiet ionosphere case, and increases up to 0.35 dB and 33° during ionosphere activities, respectively.

Direct data driven safety control for aircraft flight system-Part 1: the theory case

Purpose This new paper aims to combine the recent new contributions about direct data driven control and other safety property to form an innovative direct data driven safety control for aircraft flight system. More specifically, within the framework of direct data driven strategy, the collected data are dealt with to get the identified plant and designed controller. After reviewing some priori information about aircraft flight system, a closed loop system with the unknown plant and controller simultaneously is considered. Data driven estimation is proposed to identify the plant and controller only through the ratios of two correlation functions, computed from the collected data. To achieve the dual missions about perfect tracking and safety property, a new notion about safety controller is introduced. To design this safety controller, direct data driven safety controller is proposed to solve one constrain optimization problem. Then the authors apply the Karush–Kuhn–Tucker (KKT) optimality conditions to derive the explicit safety controller. Design methodology approach First, consider one closed loop system corresponding to aircraft flight system with the unknown plant and feed forward controller, data driven estimation is used to identify the plant and feed forward controller. This identification process means nonparametric estimation. Second, to achieve the perfect tracking one given transfer function and guarantee the closed loop output response within one limited range simultaneously, safety property is introduced. Then direct data driven safety control is proposed to design the safety controller, while satisfying the dual goals. Third, as the data driven estimation and direct data driven safety control are all formulated as one constrain optimization problem, the KKT optimality conditions are applied to obtain the explicit safety controller. Findings Some aircraft system identification and aircraft flight controller design can be reformulated as their corresponding constrain optimization problems. Then through solving these constrain optimization problems, the optimal estimation and controller are yielded, while satisfying our own priori goals. First, data driven estimation is proposed to get the rough estimation about the plant and controller. Second, data driven safety control is proposed to get one safety controller before our mentioned safety concept. Originality/value To the best of the authors’ knowledge, some existing theories about nonparametric estimation and tube model predictive control are very mature, but few contributions are applied in practice, such as aircraft system identification and aircraft flight controller design. This new paper shows the new theories about data driven estimation and data driven safety control on aircraft, being corresponded to the classical nonparametric estimation and tube model predictive control. Specifically, data driven estimation gives the rough estimations for the aircraft and its feed forward controller. Furthermore, after introducing the safety concept, data driven safety control is introduced to achieve the desired dual missions with the combination of KKT optimality conditions.

A data-driven LQG method for linear time-varying systems to monitor the controller performance in the batch process

PurposeThe flexibility of batch process enables its wide application in fine-chemical, pharmaceutical and semi-conductor industries, whilst its complexity necessitates control performance monitoring to ensure high operation efficiency. This paper proposes a data-driven approach to carry out controller performance monitoring within batch based on linear quadratic Gaussian (LQG) method.Design/methodology/approachA linear time-varying LQG method is proposed to obtain the joint covariance benchmark for the stochastic part of batch process input/output. From historical golden operation batch, linear time-varying (LTV) system and noise models are identified based on generalized observer Markov parameters realization.FindingsOpen/closed loop input and output data are applied to identify the process model as well as the disturbance model, both in Markov parameter form. Then the optimal covariance of joint input and output can be obtained by the LQG method. The Hotelling's Tˆ2 control chart can be established to monitor the controller.Originality/value(1) An observer Markov parameter approach to identify the time-varying process and noise models from both open and closed loop data, (2) a linear time-varying LQG optimal control law to obtain the optimal benchmark covariance of joint input and output and (3) a joint input and output multivariate control chart based on Hotelling's T2 statistic for controller performance monitoring.

Long-term postoperative outcomes of Roux-en-Y cholangiojejunostomy in patients with benign biliary stricture

BackgroundAlthough there are common postoperative complications, Roux-en-Y cholangiojejunostomy is still broadly used as a standard surgical procedure for patients with biliary stricture. This study aimed to explore long-term risk factors of cholangiojejunostomy in patients with biliary stricture who underwent revisional cholangiojejunostomy.MethodsClinical data of 61 patients with biliary stricture undergoing revisional cholangiojejunostomy were retrospectively analyzed. These patients were classified into two groups (patients with traumatic biliary stricture and non-traumatic biliary stricture). Postoperative complications and survival time were successfully followed up.ResultsAmong the patients, 34 underwent revisional cholangiojejunostomy due to traumatic biliary stricture, and 27 underwent revisional cholangiojejunostomy due to non-traumatic biliary surgery. Although there was no statistical difference in most clinical data between two groups, biliary dilation or not during the first surgery, cholelithiasis or not during the first surgery, long-term complications after first surgery, cholelithiasis or not during the second surgery, identifying abnormalities during the second surgery and long-term complications after second surgery were significantly different. All patients were successfully followed up and average follow-up time for patients with traumatic and non-traumatic biliary stricture was (88.44 ± 35.67) months and (69.48 ± 36.61) months respectively. Survival analysis indicated that there was no statistical difference in overall survival between two groups. Additionally, cox proportional hazard analysis demonstrated that first preoperative bilirubin level, short-term complication after first surgery and identifying abnormalities during the second surgery were independent risk factors that may have significant effects on patients' overall survival and long-term prognosis after cholangiojejunostomy. Among the intraoperative abnormal findings, residual lesions after the first operation had significant effects on the patients overall survival in the earlier stage. Relatively, anastomotic stoma stricture and biliary output loop problems had obvious effects on patients' overall survival at later stages.ConclusionFirst preoperative bilirubin level, short-term complication after first surgery and abnormal findings during the second surgery were independent risk factors of revisional cholangiojejunostomy, which may affect patients' long-term survival. Therefore, surgeons should minimize incidence of postoperative complications through fully evaluating optimal operative time and standardizing surgical procedures.

Low power class-AB VCII with extended dynamic range

In this paper we present a novel CMOS second generation voltage conveyor (VCII) topology featuring a wide voltage swing both at the X terminal and at the Z terminal. The VCII consists of a regulated common gate configuration at the Y current input terminal and a class-AB complementary-MOS closed loop output voltage follower that ensures the voltage buffering action between the voltage input X and the voltage output Z terminals. Spice simulation results using AMS 0.35 μm with a ±0.9 V supply voltage are provided to demonstrate the validity of the proposed topology. With a total power consumption of 28 µW, the VCII achieves a voltage swing at the X terminal of ±0.8 V, whereas a ±0.72 V is achieved on the Z terminal. Simulation results for DC and AC voltage and current gains are given, as well as harmonic distortions and noise figures. A final comparison table is also presented, where the proposed VCII is compared with other solutions presented in the literature.

High-Voltage Repetitive Nanosecond Pulse Generator Utilizing Power Synthesis of Modified Avalanche Transistorized Marx Circuits

In order to further improve the output voltage amplitude and repetitive operation reliability of nanosecond pulse generator (PG) based on avalanche transistor (AT), the method of power synthesis of modularized Marx circuits with transmission line transformer (TLT) is employed in this article. The modified positive <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$4\times11$ </tex-math></inline-formula> -stage Marx circuit introducing base-triggering method is designed and implemented to improve the operation reliability. The triggering synchronization and the consistence of output characteristics of multiple Marx modules with an identical trigger pulse are validated. The feasibility of combining pulses generated from four Marx modules with an optimized four-stage TLT is demonstrated. The influences of the type and quantity of magnetic core and the superimposed stage number of TLT on the output performance of the generator are investigated. The operation characteristics of the generator including output parameters, trigger time-delay, and loop efficiency in the whole working range are evaluated. The experimental results show that the working range of the overall device has been widened significantly with the injection of additional initial carrier. Accordingly, the generator prototype is capable of achieving the output performance with an adjustable voltage amplitude in the range of 7.8–26.7 kV on a matched 300- <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\Omega $ </tex-math></inline-formula> resistive load and 12.2–38.9 kV on the high-resistance load, respectively, a 10%–90% rise time of 3.6 ns, and a full-width at half-maximum (FWHM) of 12.2 ns. A long-term test with the maximum repetition rate of 3 kHz is conducted to realize high-voltage output and high-frequency operation simultaneously.

Dynamic optimal operational control for complex systems with nonlinear external loop disturbances

&lt;abstract&gt;&lt;p&gt;This paper studies a two-layer control strategy for optimal operational control which is prevalent in industrial production. The upper layer determines and adjusts the target set values, while the lower layer makes the loop output track the target value. In the two-layer structure optimal setting control system, the widely used PID controller is used in the bottom layer. Firstly, the parameters of the PID controller are obtained by solving linear matrix inequalities (LMI). Secondly, for industrial processes with nonlinear harmonic disturbances, a disturbance observer is designed to estimate these disturbances. Thirdly, the effects of disturbances or noises are minimized by dynamically adjusting the setting points. This method does not change the structure or parameters of the bottom controller, and thus meets the actual industrial requirements to a certain extent. Finally, in the numerical simulation section, the value of the performance index before set-points adjustment is compared with that after set-points adjustment.&lt;/p&gt;&lt;/abstract&gt;

Mathematical modelling of atrial and ventricular pressure–volume dynamics and their change with heart rate

This paper presents mathematical models that can simulate the cardiovascular system of a healthy sheep under normal resting conditions in which the heart rate changes significantly. The models include several new modelling features that are introduced progressively. The contraction of the cardiac chambers is modelled using a time-dependent muscle force with constant elasticity instead of time dependent elasticity. A new hypothesis about the mechanical contraction of the atria generates realistic pressure volume (PV) loops. The inter-ventricular interaction is modelled as well. Additionally, hysteresis is incorporated in the aortic valve to produce an end-systolic reverse (negative) flow. Most of the model parameter values are based on previous literature data while time periods of delay, atrial and ventricular contraction are derived using experimental data from 14 sheep. We provide new relationships between contraction time and delay as a function of heart period. The effects of different aspects of our modelling on the mean cardiac output, stroke volume, ejection time, ejection fraction and PV loops are studied. Model outputs are compared with published experimental results where possible, and are within a wide range of physiological observations.

Design and evaluation of a Quadratic Buck Converter

This paper presents design and evaluation of a Quadratic Buck Converter (QBC). A step-by-step procedure to select the converter’s component values and semiconductor device ratings is demonstrated. A prototype QBC with a simple closed loop output voltage control is constructed and experimentally evaluated. It is shown that the converter performs well within the design specification, has good output voltage regulation and fast transient response, and achieves the highest efficiency of 82%.

Experimental characterization and modular modeling of hystereses for smart material actuators

In this article, we present a novel modular modeling approach to describe the hystereses for piezoelectric, magnetostrictive and shape memory alloy (SMA) actuators. For the above actuators, the output vs. input loops exhibit varying hystereses under the input signals of the different frequencies and amplitudes. To this end, the experimental characterization is conducted and hysteresis modeling approach is studied. Two characteristic indexes, i.e. loop relative width, loop asymmetry coefficients, are quantitatively analyzed according to the open-loop experiments for the three actuators. Based on the hysteresis phenomenon analyses, different submodels are selected to describe those phenomena. The Prandtl-Ishlinskii submodel is applied for symmetry rate-independent hysteresis identification; the arctangent-polynomial modified Prandtl-Ishlinskii submodel is proposed for asymmetry rate-independent hysteresis identification; infinite impulse response submodel is used for rate-dependent hysteresis identification. Those submodels are selected to construct a cascaded overall model to describe the hysteresis of piezoelectric, magnetostrictive, and SMA actuators. The hysteresis experimental identification results show that, with the proposed phenomenon-based hysteresis modular modeling approach, better performance can be obtained in terms of modeling accuracy and computation time than some other approaches.

All-Optical In-Phase/Quadrature Microwave Mixer for Antenna Remoting Applications

A new microwave photonic signal processing structure for realising in-phase/quadrature (I/Q) mixing is presented. It is based on a dual-drive Mach Zehnder modulator (DDMZM) and an optical phase modulator inside a Sagnac loop interferometer. Two output IF signals with a quadrature phase difference are obtained by using two photodetectors to detect the upper and lower sidebands of the optical signal at the Sagnac loop output. A quadrature phase difference in the two IF signals is realised by biasing the DDMZM at the quadrature point. This has the advantage of very little quadrature phase errors as a standard modulator bias controller can accurately lock the DDMZM bias point. The optical phase modulator driven by an RF signal can be placed in a remote location for antenna remoting. Theoretical analysis and simulation show using the proposed I/Q mixer for image rejection can overcome the modulation index dependent image rejection ratio problem in the reported I/Q mixers based on a cascaded modulator structure. The Sagnac loop based I/Q mixer is experimentally verified with results show only ±1° quadrature phase error and more than 50 dB image rejection ratio over the operating frequency range of 6 to 20 GHz.