Showing papers on "Electrical impedance published in 2021"

An Impedance Model-Based Multiparameter Identification Method of PMSM for Both Offline and Online Conditions

Abstract: Existing online motor parameter identification methods mostly depend on the fundamental frequency voltage equations, which lead to the unsatisfactory identification effect at low current and low speed operation. This article proposes a parameter identification method based on the high frequency (HF) equivalent impedance model of permanent magnet synchronous motor with HF signal injection at both the dq -axes. This method identifies the resistance and the dq -axis inductances offline and online, along with the flux linkage online. In order to improve the identification accuracy, the parameter sensitivity analysis-based algorithm is proposed to detect the resistance and the flux linkage. Meanwhile, the inverter nonlinearities and the HF influence on parameter identification are compensated effectively. In order not to affect the normal operation of the motor drive, the selection of the amplitude, and the frequency of the injected signal is investigated. The proposed method is validated on a 2.2-kW motor and confirmed by finite element analysis. The experimental results show the good identification effect in different operation conditions.

Metamaterial mechanical antenna for very low frequency wireless communication

Abstract: Very low frequency wireless communication (3–30 kHz) often is restricted by the antenna size and complex impedance matching network in practical applications. Mechanical antenna has recently stimulated much practical research interest due to the potential capacity for breaking the size limitation. However, mechanical antenna is barely investigated from the perspective of material science. Here, we demonstrate a compact piezoelectric metamaterial mechanical antenna with high radiation efficiency, multi-frequency bands, and small size. Three operating frequencies at 22 kHz, 24 kHz, and 26 kHz are independently adjusted by the structure parameters and material of a piezoelectric radiating unit cell, and the modulation range is beyond 15 kHz. The basic parameters studies reveal the detailed modulation mechanism and provide a theory base for the metamaterial antenna design. Except for the smaller than 1/1000 wavelength size, the radiated magnetic field intensity is also averagely increased by 3 × 104 fT. All the simulated results demonstrate the great potential of the proposed piezoelectric metamaterial antenna in the applications of portable, small, high-performance wireless communication devices. A compact piezoelectric metamaterial–based mechanical antenna is reported. Simulations of unit cell antenna and analyzes of characteristics reveal the influence of material parameters and structure parameters on the electromagnetic performance of the proposed antenna. The utilization of metamaterial structure brings multi-band properties for the mechanical antenna, and each resonant peak can be independently modulated.

Impedance Circuit Model of Grid-Forming Inverter: Visualizing Control Algorithms as Circuit Elements

Abstract: The impedance model is widely used for analyzing power converters. However, the output impedance is an external representation of a converter system, i.e., it compresses the entire dynamics into a single transfer function with internal details of the interaction between states hidden. As a result, there are no programmatic routines to link each control parameter to the system dynamic modes and to show the interactions among them, which makes the designers rely on their experience and heuristic to interpret the impedance model and its implications. To overcome these obstacles, this article proposes a new modeling tool named as impedance circuit model , visualizing the closed-loop power converter as an impedance circuit with discrete circuit elements rather than an all-in-one impedance transfer function. It can reveal the virtual impedance essence of all control parameters at different impedance locations and/or within different frequency bandwidths, and show their interactions and coupling effects. A grid-forming voltage source inverter is investigated as an example, with considering its voltage controller, current controller, control delay, voltage/current $dq$ -frame cross-decoupling terms, output-voltage/current feedforward control, droop controllers, and three typical virtual impedances. The proposed modeling tool is validated by frequency-domain spectrum measurement and time-domain step response in simulations and experiments.

Grid Impedance Estimation Through Grid-Forming Power Converters

Abstract: In more-electronics power systems, grid-forming power converters, which operate as ac voltage sources, regulate the grid frequency and voltages in replacement of synchronous generators. Notably, grid impedances greatly influence the small signal and voltage stability of grid-forming converters. As such, prior knowledge of grid impedances can be very helpful for controller design. However, grid impedance estimation schemes are normally designed for current-controlled grid-following converters. Moreover, they are either very complicated or only yield grid inductances in a generally intrusive way. To fill this research gap, an impedance estimation method well suited to grid-forming converters is proposed. The method consists of four operating modes, which work well in voltage and power control cases. In the voltage control case, the voltage amplitude perturbation or phase angle information is exploited. Subsequently, the grid inductance and resistance are derived from power measurement. Alternatively, the active or reactive power information serves to estimate the grid impedance in the power control case. The proposed method features an easy implementation without any harmonic distortion, safety concern, or dependence on control parameters. Moreover, the method operates nonintrusively in most scenarios. Furthermore, a novel Kalman filtering scheme is proposed to provide added incentives. Finally, simulation and experimental results validate the effectiveness and simplicity of the proposed method.

Fault Current Control and Protection in a Standalone DC Microgrid Using Adaptive Droop and Current Derivative

Abstract: This article presents a novel fault detection, characterization, and fault current control algorithm for a standalone solar-photovoltaic (PV) based dc microgrids. The protection scheme is based on the current derivative algorithm. The overcurrent and current directional/differential comparison based protection schemes are incorporated for the dc microgrid fault characterization. For a low impedance fault, the fault current is controlled based on the current/voltage thresholds and current direction. Generally, the droop method is used to control the power-sharing between the converters by controlling the reference voltage. In this article, an adaptive droop scheme is also proposed to control the fault current by calculating a virtual resistance $R_{\mathrm{ droop}}$ , and to control the converter output reference voltage. For a high impedance fault, differential comparison method is used to characterize the fault. These algorithms effectively control the converter pulsewidth and reduce the flow of source current from a particular converter, which helps to increase the fault clearing time. Additionally, a trip signal is sent to the corresponding dc circuit breaker (DCCB), to isolate the faulted converter, feeder or a dc bus. The dc microgrid protection design procedure is detailed, and the performance of the proposed method is verified by simulation analysis.

An Active Damping Strategy for Input Impedance of Bidirectional Dual Active Bridge DC–DC Converter: Modeling, Shaping, Design, and Experiment

Abstract: The dual-active-bridge (DAB) converter is applied for power transmission and voltage conversion in dc power grid. To improve the quality of input current, an input LC filter is cascaded to DAB converter. However, due to the interaction between LC filter and DAB converter, substantial oscillation and instability occur, leading to the excessive electromagnetic interference, large voltage ripple, and power loss and even operation failure. To solve this issue, an active damping strategy is proposed in this article to reshape the small-signal input impedance by parallel virtual impedance. The input voltage is regarded as a control objective, as well as the output voltage, therefore, a triple-closed-loop control structure is established. Besides, all dynamics of controllers are considered for the input impedance modeling of DAB converter. Moreover, compared with traditional methods, an active damping method for cascaded DAB converter with LC filter is adopted to design the virtual impedance and controller, suppressing resonance of LC filter and achieve a larger bandwidth. Therefore, a more stable and rapid dynamics cascaded system composed of DAB converter and LC filter are achieved. Finally, a prototype is set up and the effectiveness and superiority of proposed strategy are verified by experiments.

Impedance-Based Analysis and Stability Improvement of DFIG System within PLL Bandwidth

Abstract: This paper analyzes the negative impact of phase-locked loop (PLL) on the stability of the doubly fed induction generators (DFIG) system. The small-signal disturbance of PLL mainly affects the coordinate transformation of rotor current, and introduces a negative resistance within PLL bandwidth. Two impedance reshaping methods are carried out to weaken this negative resistance. A virtual impedance in the conventional current control is added to the first reshaping method. The second reshaping method completely removes the coordinate transformation of rotor current by switching the control target from current to power. The difference between these two reshaping methods are analyzed based on the equivalent single-input single-output (SISO) impedance model. The experimental results validate the effectiveness of these two reshaping methods, and the superiority of the second reshaping method at a lower short circuit ratio (SCR).

A Novel On-Board Electrochemical Impedance Spectroscopy System for Real-Time Battery Impedance Estimation

Abstract: This article proposes a real-time electrochemical impedance spectroscopy (EIS) technique that can provide high accurate estimation of the impedance of each lithium-ion (Li-ion) cell of a battery (BT) stack, even for less than mΩ. Thus, the suggested EIS technique can be used in high demanding applications, such as nearly zero-energy buildings, microgrids, and electric vehicles. This is attained because a smooth cell excitation current is utilized that is provided by the proper control of the gate-source of each cell's parallel-connected MOSFET and thus, effective harmonic analysis can be accomplished. Since the circuit topology of the EIS is implemented without requiring expensive electronic equipment, it is affordable to be applied in the BT system of any application. The proposed EIS system can cooperate with a BT cell equalization (BCE) system that utilizes the same MOSFET control scheme to provide the excitation current. Thus, a combined EIS–BCE system is developed that can be used to improve the performance of a Li-ion BT management system. The accuracy of the EIS technique and its high performance by operating within a combined EIS–BCE system are experimentally validated.

Stability-Guaranteed Variable Impedance Control of Robots Based on Approximate Dynamic Inversion

Abstract: Variable impedance control has been considered as one of the most important compliant control approaches for its abilities in improving compliance, safety, and efficiency in robot–environment interaction. However, existing variable impedance controllers have deficits in stability guarantee. This article proposes a stability-guaranteed variable impedance control approach for robots with modeling uncertainties based on approximate dynamic inversion (ADI). Novel constraints on variable impedance profiles are given to guarantee the exponential stability of the desired variable impedance dynamics. An ADI-based impedance control law is designed to achieve the desired variable impedance dynamics through the convergence of a variable impedance error. Based on the extended Tikhonovs theorem, it is proven that the closed-loop control system has semiglobal practical exponential stability. The proposed impedance controller can be implemented in a PID form and is appealing for its simple structure, easy implementation, and control stability guarantee. The effectiveness of the proposed variable impedance controller is illustrated by an illustrative example taken on a five-bar parallel robot.

An Impedance Debris Sensor Based on a High-Gradient Magnetic Field for High Sensitivity and High Throughput

Abstract: In this article, an impedance debris sensor capable of simultaneously detecting inductance and resistance parameters is presented, which mainly consists of two planar coils in parallel, two excitation silicon steel strips inserted in the inner hole of coils and a built-in silicon steel strip located in the center of channel. The excitation silicon steel strips and the built-in silicon steel strip establish a detection region with a high-gradient magnetic field to improve the sensitivity of the sensor. And the square channel makes full use of the sensitive detection region, thereby further increasing the detection throughput. Experiments have shown that the amplitudes of the inductance and resistance pulses generated by the same particle many times through the detection region are different. The uncertainty of the sensor can be reduced for accurate size information by combining the detection results of the inductance and resistance parameters. By comparing and analyzing the inductance parameter detection result and the resistance parameter detection result, the impedance debris sensor can distinguish and measure 25 μ m iron particle and 85 μ m copper particle. With its high sensitivity, high throughput, and capability of multiparameter detection, this sensor can potentially be used for health monitoring of hydraulic equipment.

Improving Small-Signal Stability of Grid-Connected Inverter under Weak Grid by Decoupling Phase-Lock Loop and Grid Impedance

Abstract: The wide bandwidth of Phase-Locked Loop (PLL) will increase the negative real part of the output impedance of the grid-connected inverter (GCI), thus destroying the stability of the weak grids. This paper proposes a novel method to improve the system stability through decoupling the PLL and grid impedance. Initially, the coupling relationship between PLL and grid impedance is revealed. It can explain why the choice of PLL bandwidth and the grid impedance magnitude is limited. Then, the decoupling method is proposed where the primary control structure of GCI does not need to change and uses the structured voltage, the product of PCC voltage and grid admittance, as the improved input of PLL. The proposed method can achieve the full-frequency passive of the output impedance of GCI even if the PLL has high bandwidth and the impedance measurement error is up to 60%, which means the adverse stability effect of PLL on the system is eliminated. The theoretical analysis is verified by simulations and experiments.

DQ-Frame Impedance Measurement of Three-Phase Converters Using Time-Domain MIMO Parametric Identification

Abstract: The dq- frame impedance model is increasingly employed to analyze the grid-converter interactions in three-phase systems. As the impedance model is derived at a specific operating point, it is required to connect the converter to actual power grids during the impedance measurement. Yet, the nonzero grid impedance causes cross-couplings between perturbation and response signals, which consequently jeopardize the accuracy of impedance measurement. This article analyzes first the coupling effect of the grid impedance on the measured impedance, and then proposes a multiple-input multiple-output parametric impedance identification method for mitigating the effect. Instead of using the fast Fourier transform, the method allows for obtaining the parametric impedance model directly from the time-domain data. Further, with the simultaneous wideband excitations, only a single measurement cycle is needed. The effectiveness of the method is verified in both simulations and experimental tests.

A Novel Helical Superconducting Fault Current Limiter for Electric Propulsion Aircraft

Abstract: It is crucial to achieve a high safety and reliability standard in future electric propulsion aircraft (EPA). Due to low short-circuit impedance and high rate of fault current rise in EPA systems, the superconducting fault current limiter (SFCL) plays a promising role, with advantages of lightweight, high efficiency, and compact size compared with conventional FCL. A novel helical bifilar coil is proposed, which is composed of two windings wound in opposite directions on the same bobbin; these are connected in series to achieve equal current sharing and a noninductive circuit. The 12-mm-wide stainless steel-reinforced superconducting tape from AMSC was used for the windings. To characterize the proposed helical bifilar coil connected in series (BCS), AC loss tests under three frequencies and quench tests under prospective fault current up to 2223 A were carried out. They were compared with the results measured from a conventional helical bifilar coil connected in parallel (BCP) that had an identical specification to the BCS. It was concluded that the AC losses measured in the BCP are dependent on the current and frequency. The fault current was suppressed effectively by the BCS at the first half peak from 2223 to 495 A, corresponding to 22.3% of the prospective fault current. The quench performance of BCP was also tested and discussed.

Analysis of Impedance Tuning Control and Synchronous Switching Technique for a Semibridgeless Active Rectifier in Inductive Power Transfer Systems for Electric Vehicles

Abstract: In inductive power transfer (IPT) systems, load, and magnetic coupling variations cause an impedance mismatch. Impedance mismatch is one of the most serious problems in IPT systems for electric vehicles (EVs) because an EV is not always parked in the same location. Therefore, an impedance tuning control for semibridgeless active rectifiers (SBARs) is proposed in this article to compensate for this mismatch. The proposed impedance tuning control is achieved by adjusting the turn- on point and duty of the SBAR without using any additional component. Moreover, a technique for detecting the voltage-rising edge of the SBAR switch is proposed to extract the switching frequency and to synchronize the SBAR with the primary system. A 3.3-kW prototype of the IPT system with the SBAR is manufactured, and the proposed impedance tuning control is verified through experimental results according to the coupling coefficient. The proposed control can achieve an efficiency improvement of 6.4% under the impedance mismatch.

Artificial Neural Network Based Identification of Multi-Operating-Point Impedance Model

Abstract: The black-box impedance model of voltage source inverters (VSIs) can be measured at their terminals without access to internal control details, which greatly facilitate the analysis of inverter-grid interactions. However, the impedance model of VSI is dependent on its operating point and can have different profiles when the operating point is changed. This letter proposes a method for identifying the impedance model of VSI under a wide range of operating points. The approach is based on the artificial neural network (ANN), where a general framework for applying the ANN to identify the VSI impedance is established. The effectiveness of the ANN-based method is validated with the analytical impedance models.

A Novel System for Measuring Alternating Current Impedance Spectra of Series-Connected Lithium-Ion Batteries With a High-Power Dual Active Bridge Converter and Distributed Sampling Units

Abstract: Alternating current (ac) impedance spectra facilitate lithium-ion battery management Realizing a low-cost and low-complexity onboard impedance measuring system is a vital issue for the management based on the ac impedance In the article, a novel impedance measuring system combined with a high-power dual active bridge (DAB) converter and distributed sampling units is proposed and verified The DAB converter is designed to generate the ac disturbance to ensure a quasi-steady measurement of the battery impedance The distributed signal sampling units simultaneously measure the voltage and current of all the series-connected battery cells in a module to measure their impedance The measured impedance in a frequency range of 01–500 Hz shows the feasibility of the system The root-mean-square errors of the measured impedance phase from 02 to 200 Hz and the magnitude from 01 to 500 Hz are less than 69% and 40%, respectively The errors in some frequency ranges are slightly larger, which are analyzed The novelty is reflected in that the system is easily integrated into a bidirectional onboard charger and compatible with the battery management system, thus reducing costs and complexity It provides a basis for the onboard application of the battery impedance

Highly Sensitive Phase Variation Sensors Based on Step-Impedance Coplanar Waveguide (CPW) Transmission Lines

Abstract: Reflective-mode step-impedance transmission line based sensors for dielectric characterization of solids or liquids have been recently proposed. In this article, in order to further increase the sensitivity, the sensor is implemented in coplanar waveguide (CPW technology), and this constitutes the main novelty of this work. The sensor thus consists of a high-impedance 90° (or low-impedance 180°) open-ended sensing line cascaded to a low-impedance 90° (or high-impedance 90°) line. The output variable is the phase of the reflection coefficient, which depends on the dielectric constant of the material under test (MUT), the input variable. Placing a MUT on top of the sensing line causes a variation in the effective dielectric constant of the line, thereby modifying the phase of such line. This in turn produces a multiplicative effect on the phase of the reflection coefficient, by virtue of the step-impedance discontinuity. The main advantage of the CPW-based sensor, over other similar sensors based on microstrip technology, is the stronger dependence of the phase velocity of the sensing line with the dielectric constant of the MUT, resulting in sensitivities as high as −45.48° in one of the designed sensors. The sensor is useful for dielectric characterization of solids and liquids, and for the measurement of variables related to changes in the dielectric constant of the MUT (defect detection, material composition, etc.).

Participation Analysis in Impedance Models: The Grey-Box Approach for Power System Stability

Abstract: This paper develops a grey-box approach to small-signal stability analysis of complex power systems that facilitates root-cause tracing without requiring disclosure of the full details of the internal control structure of apparatus connected to the system. The grey-box enables participation analysis in impedance models, which is popular in power electronics and increasingly accepted in power systems for stability analysis. The Impedance participation factor is proposed and defined in terms of the residue of the whole-system admittance matrix. It is proved that, the so defined impedance participation factor equals the sensitivity of the whole-system eigenvalue with respect to apparatus impedance. The classic state participation factor is related to the impedance participation factor via a chain-rule. Based on the chain-rule, a three-layer grey-box approach, with three degrees of transparency, is proposed for root-cause tracing to different depths, i.e. apparatus, states, and parameters, according to the available information. The association of impedance participation factor with eigenvalue sensitivity points to the re-tuning that would stabilize the system. The impedance participation factor can be measured in the field or calculated from the black-box impedance spectra with little prior knowledge required.

A New Extremely Low Power Temperature Insensitive Electronically Tunable VCII-Based Grounded Capacitance Multiplier

Abstract: In this brief, a new circuit topology to realize an electronically tunable grounded capacitor multiplier with extremely low power consumption and low supply voltage requirement is investigated. The proposed circuit uses an electronically tunable second generation voltage conveyor (VCII) and a single floating capacitor. Owing to the translinear principle, current gain of VCII is varied through a control current and, as a result, the value of simulated capacitor is also varied. Favorably the obtained gain is temperature insensitive. Both of the required supply voltage and control currents are very low because all transistors are biased in subthreshold region: therefore, electronic tunability is achieved while the power consumption is kept at very low value. In addition, the circuit realization is very simple since only twelve transistors are required. Simulation results, performed at schematic level in 0.18 $\mu \text{m}$ CMOS technology and supply voltage of ±0.3V, are presented. It is shown that a multiplication factor from 1 to 100 is possible while the power consumption varies from 10 nW to 67 nW.

Compact Dual Microwave/Millimeter-Wave Planar Shared-Aperture Antenna for Vehicle-to-Vehicle/5G Communications

Abstract: This paper presents a compact dual-port dual-frequency planar shared-aperture antenna with large frequency ratio. It consists of a microwave magneto-electric (ME) dipole antenna and a millimeter-wave parallel-plate resonator antenna (PPRA). It has two vertical conducting walls that form an upper-band parallel-plate resonator and meanwhile provide a magnetic source to the lower-band ME dipole. The design is a shared-aperture structure and is therefore very compact. For demonstration, a dual-frequency antenna simultaneously covering the 5.9-GHz vehicle-to-vehicle (V2V) band (5.855–5.925 GHz) and the 28-GHz 5G band (27.5–28.35 GHz) was designed, fabricated, and measured. Good agreement between the measured and simulated results was found. The lower and upper bands have the measured 10-dB impedance bandwidths of 41.6% (5.30–8.08 GHz) and 6.66% (27.15–29.02 GHz), and measured peak antenna gains of 5.80 dBi and 8.46 dBi, respectively. The antenna can be used on vehicular platforms for providing V2V communications and 5G millimeter-wave connections simultaneously.

Efficient Dual-Band Rectifier Using Stepped Impedance Stub Matching Network for Wireless Energy Harvesting

Abstract: This letter presents an efficient dual-band rectifier using stepped impedance stub matching circuit. Theoretical analysis of the dual-band impedance matching circuit comprising a stepped impedance stub is carried out, which plays a key role in designing the resultant dual-band rectifier. The proposed dual-band matching circuit can achieve wide frequency ratio which is analyzed and predicted by simulation. For demonstration, a dual-band rectifier working at 0.915 and 2.45 GHz is fabricated with dimensions of 21.47 mm $\times18.93$ mm. The measured results show that with a $1500~\Omega $ load, the maximum efficiencies of the rectifier reach 74% and 73% at 0.915 and 2.45 GHz, respectively. Due to the simple but efficient structure of the dual-band matching network, the dual-band rectifier in this work exhibits merits of compact size and high efficiency.

High-Selectivity Frequency-Selective Rasorber Based on Low-Profile Bandpass Filter

Abstract: A frequency-selective rasorber (FSR) with a high selectivity transmission passband and two absorption bands is proposed in this letter. The design method is introduced based on the equivalent circuit model (ECM). This structure consists of a lossy layer and a lossless layer. The lossy layer is composed of Jerusalem elements with a parallel resonance unit in center, and load with resistors on the metal branch. The lossless layer is integrated by a multilayer frequency selective surface to realize the high selectivity and wide transmission band. The surface current distributions and surface loss density were illustrated to explain the working principle. The simulated results show that the 1 dB transmission window is obtained from 7.9 to 9.0 GHz. The −10 dB absorption bands are over 3.3–7.1 GHz and 9.4–12.0 GHz. A prototype of the proposed FSR was fabricated and measured to verify our design; the measured results show a good agreement with simulated results.

Impedance Variation and Learning Strategies in Human-Robot Interaction.

Abstract: In this survey, various concepts and methodologies developed over the past two decades for varying and learning the impedance or admittance of robotic systems that physically interact with humans are explored. For this purpose, the assumptions and mathematical formulations for the online adjustment of impedance models and controllers for physical human-robot interaction (HRI) are categorized and compared. In this systematic review, studies on: 1) variation and 2) learning of appropriate impedance elements are taken into account. These strategies are classified and described in terms of their objectives, points of view (approaches), and signal requirements (including position, HRI force, and electromyography activity). Different methods involving linear/nonlinear analyses (e.g., optimal control design and nonlinear Lyapunov-based stability guarantee) and the Gaussian approximation algorithms (e.g., Gaussian mixture model-based and dynamic movement primitives-based strategies) are reviewed. Current challenges and research trends in physical HRI are finally discussed.

A Virtual Impedance Based Control Scheme for Modular Electrolytic Capacitor-Less Second Harmonic Current Compensator

Abstract: The second harmonic current compensator (SHCC) can be added into the single-phase converters for compensating the second harmonic current (SHC) and thus removing the undesired electrolytic capacitor. In this paper, a virtual impedance, which is in the form of a capacitor and a resistor connected in parallel, is introduced to be in parallel at the bus-side port of the SHCC for effectively compensating the SHC while guaranteeing the system stability. This virtual parallel impedance is realized by feeding forward the bus-side port voltage of the SHCC, and thus the SHCC can be modular designed. The closed-loop parameter design of the SHCC is also presented. A 3.3-kW prototype of a two-stage single-phase power factor correction converter is built and tested in the laboratory, and the experimental results verify the effectiveness and feasibility of the proposed control method.

Phase-Variation Microwave Sensor for Permittivity Measurements Based on a High-Impedance Half-Wavelength Transmission Line

Abstract: A phase-variation microwave sensor operating in transmission and implemented by means of a high-impedance half-wavelength sensing line is reported in this paper. The sensor is useful for dielectric constant measurements and dielectric characterization of materials. By forcing the electrical length of the sensing line to be a half-wavelength when it is loaded with the so-called reference (REF) material, perfect matching is obtained regardless of the characteristic impedance of the line. This fact can be used to enhance the sensitivity for small perturbations, by merely increasing the characteristic impedance of the sensing line. An exhaustive analysis that supports such conclusion is reported in the paper. Then, two prototype sensors are designed and fabricated for validation purposes. As compared to the ordinary phase-variation permittivity sensor implemented by means of a matched ( $50-\Omega $ ) line with identical length, the sensitivity for small perturbations in the proposed sensor is 2.1 times larger. Further advantages of these sensors are low-cost, small size, implementation in planar technology, and very simple design and fabrication, derived from the fact that the sensing region is a half-wavelength transmission line.