non-Foster Elements Research Articles

A Methodology to Design Broadband Negative Inductors with Tight Tolerance for Microwave Applications

Introduction. Non-Foster elements (NFEs) mimic behavior of hypothetical negative inductors or capacitors in a certain frequency band. NFEs are used to compensate reactance of conventional inductors and capacitors that allows designing broadband microwave devices. To realize NFEs, active circuits referred to as negative impedance converters (NICs) are employed to convert the load impedance into the negative input impedance. The conversion error, caused by non-optimal choice of NIC parameters and non-idealities of NIC components, limits the accuracy and operating bandwidth of NFEs. The necessity to account for many factors, which indirectly and oppositely impact the final result, and unavailability of a universal design methodology complicate the design of NFEs significantly. As a result, broadband NFE characteristics differ from the target ones remarkably that limits practical applications.Aim. Elaboration of a design methodology to compensate the Linvill’s NIC conversion error and realize high-accuracy broadband negative inductors.Materials and methods. Influence of NIC constituent parameters on the negative inductor frequency characteristics is considered. The performed analysis and the identified relationships allowed us to propose a step-by-step methodology to design negative inductors having tight tolerance over a broad frequency band. The use of a transmission line section instead of a lumped inductor in the NIC load when realizing negative inductors of high absolute values is shown to be advantageous as this allows providing better tolerance and wider bandwidth.Results. In order to demonstrate possibilities enabled by the proposed methodology, simulation results are presented for the GHz-range negative inductors with a set of inductance and tolerance values.Conclusion. The results obtained show that the proposed methodology makes it possible to compensate the conversion error without any numerical optimization and therefore to reduce the deviation of the negative inductance from the target value in the given frequency range or to broaden the bandwidth for a given tolerable deviation of the negative inductance.

Reconfigurable Non-Foster Elements and Squint-Free Beamforming Networks Using Active Transversal Filter-Based Negative Group Delay Circuit

A new type of reconfigurable negative group delay (NGD) circuits based on active transversal filter topology is introduced in this work. By incorporating varactors with the NGD circuit at the input and output ports of active transversal filter based on distributed amplifiers (DAs), one can notably enhance the tunability for both amplitude and phase responses, thereby enabling NGD characteristic synthesis with a wider reconfigurable range. In this article, the proposed reconfigurable NGD circuits are applied to create both tunable non-Foster elements and tunable squint-free beamforming networks, which are verified by experiment. Furthermore, a general <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$N$ </tex-math></inline-formula> -stage transfer function for the proposed reconfigurable NGD circuit is derived, in which a two-stage particular case is given as an illustrative proof-of-concept example. Based on the reconfigurable NGD circuits, a prototype of a tunable negative capacitor is fabricated and measured, of which the capacitance can be tuned from −1.0 to −4.0 pF over a bandwidth of 100 MHz at 1 GHz or around 10% relative bandwidth. In addition, such an NGD circuit is utilized to create a low-dispersion superluminal transmission line, which enables a reconfigurable series antenna feedline for squint-free beam steering. Experimental results show that the main beam of the NGD antenna array has a tuning range from −15° to 15° within a squint-free bandwidth of 100 MHz at 2 GHz or within a relative bandwidth of around 5%.

Broadband metasurfaces loaded with non-Foster elements

Metasurfaces have been widely used to design low-profile antennas, thin absorbers, lenses etc. The operational frequency band of a metasurface is rather narrow due to its resonant nature. Loading metasurface unit cells with non-Foster elements allows for remarkable bandwidth extension. In this paper, design of a broadband metasurface to operate as an artificial magnetic conductor is considered. The main issues which influence the bandwidth extension such as implementation of the non-Foster load, minimization of conversion error of a negative impedance converter, and circuit stabilization are addressed.

DESIGNING A REFLECTION-TYPE NGD NETWORK USING OPEN AND SHORT SHUNT STUBS FOR WIDEBAND ELECTRICALLY SMALL ANTENNAS

Wireless communication devices such as mobile phones play a vital role in our daily life. They need to cover an increasingly wide frequency band with low profile antennas. Electrically small antennas (ESAs) comply with these requirements. However, they are subject to gain-bandwidth limits when matched with passive matching networks. Non-Foster reactive elements have been proposed to bypass those restrictions. This paper addresses designing negative group delay NGD-based non-Foster networks to overcome stability problems when using Negative Impedance Converters (NICs) in order to realise on-Foster reactive circuits. The NGD network model was designed using open short stubs to achieve a non-Foster behaviour, and to act as a negative capacitor in the frequency range of interest. This technique of compensating the inherent loss of the proposed NGD network in the reflection mode was to realise a new structure of reactive non-Foster elements. It involves a negative resistance amplifier and a Lange coupler. The proposed technique is applicable to antenna matching where both transmit and received capabilities are required. It was simulated and the experimental results of the new NGD network circuit were introduced.

Negative Group Delay Circuits and Applications: Feedforward Amplifiers, Phased-Array Antennas, Constant Phase Shifters, Non-Foster Elements, Interconnection Equalization, and Power Dividers

With the rapid development of newgeneration communication technology such as multiple-input/multiple-output technology, ultrawideband communication, and 5G technology, communication systems have higher requirements for the quality of signal transmissions. Achieving this quality requires attention not only to signal amplitude characteristics but also to phase characteristics because of the long delays and signal distortion that come with positive group delay (PGD). However, negative group delay (NGD) circuits are an effective way to compensate for PGD and decrease the variability of passband group delay.

Chu limit and non-Foster radiation for sound

We show that the quality factor of a small passive acoustic radiator is fundamentally limited by its volume normalized to the emitted wavelength, imposing important constraints on the bandwidth and efficiency of compact acoustic sources. We overcome this bound, known in electromagnetics as Chu’s limit, by realizing a piezoelectric transducer loaded with a non-Foster circuit, showing that its radiation bandwidth is fundamentally limited only by stability considerations. Based on these principles, we experimentally observe over a threefold bandwidth enhancement compared to its passive counterpart, paving the way towards non-Foster acoustic elements and metamaterials that overcome the bandwidth constraints of passive systems.

A Miniature Actively Matched Antenna for Power-Efficient and Bandwidth-Enhanced Operation at Low VHF

Active matching techniques with non-Foster reactive elements have been introduced to overcome fundamental performance limits on electrically small passive antennas. While several experimental studies have demonstrated successful bandwidth enhancement with active matching applied to small unmatched passive antennas, their radiation performance against similar-sized, efficient, resonant antennas alone (and/or applied to active matching) has not yet been confirmed to assess their effectiveness for practical wireless communications applications. Beginning with a highly miniaturized efficient resonant antenna (λ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> /50 in height), we design an active matching network derived from an antenna impedance model. We conduct an extensive simulation analysis to address challenging issues associated with the design arising from a tradeoff between degree of bandwidth enhancement and stability of the matching network. Based on experimental performance assessment, the effective 3 dB bandwidth of the proposed actively matched antenna is improved by more than three times compared with the passive version and improved in efficiency by more than 10 dB relative to cases that apply active matching techniques to similar-sized, unmatched passive antennas.

Improved Signal-to-Noise Ratio, Bandwidth-Enhanced Electrically Small Antenna Augmented With Internal Non-Foster Elements

Non-Foster technology facilitates the ability to surpass the Chu bandwidth limit associated with electrically small antennas (ESAs). Nonetheless, in addition to challenging stability issues, the enhanced performance can come at the cost of increased noise and resistance losses generated by the active circuit. Consequently, low total efficiency and degraded signal-to-noise ratio (SNR) values can arise. Stability and SNR have dominated most reports to date; little has been discussed with regard to the underlying innovative physics of non-Foster augmented radiators. In this communication, we propose a broad bandwidth non-Foster ESA, emphasizing those aspects. By embedding a non-Foster element into the near-field resonant parasitic element of a metamaterial-inspired antenna, its electrically small size is maintained. On the other hand, a 5-times enhancement of its −10 dB fractional bandwidth (15 times its −3 dB bandwidth) is measured, significantly surpassing its passive Chu limit. Under a good matching, the measurements demonstrate that this non-Foster ESA achieves a 1.05 dBi peak gain and realizes average 5.0 dB SNR and 17 dB gain improvements over its passive counterpart.

Theoretical design and analysis of wideband active hard electromagnetic surfaces using non-Foster circuit loaded anisotropic metasurfaces

The electromagnetic (EM) hard surface which can both support transverse electric and transverse magnetic surface wave modes has the important ability to reduce the EM blockage of metallic obstacles. We propose a method to design an electrically thin hard surface with wide bandwidth by loading with non-Foster elements. The wideband hard surface composed of an anisotropic impedance coating can be considered as a kind of active metasurface. We develop a method to determine the values of the loading non-Foster circuit which can minimize the dispersion of the unit cells. For this method, we derive accurate values for the loading non-Foster elements through theoretical analysis. We also determine the fundamental limitations on the bandwidth due to stability requirements. To verify our theoretical design, we simulate the transmission performance between the two ports on opposite sides of a metallic rhombus-shaped obstacle coated with the non-Foster based metasurface. The simulated results show that the blockage has been largely reduced over a broad bandwidth from 0.2 GHz to 1.5 GHz. Finally, we provide a discussion on how the resistive part of the non-Foster circuit can affect the performance of the wideband hard surface coating.

Robust stability characterizations of active metamaterials with non-Foster loads**Project supported by the National Natural Science Foundation of China (Grant No. 61701349), the Natural Science Foundation of Shandong Province, China (Grant Nos. ZR2017QF012 and ZR2017MF042), and the Program for the Top Young Innovative Talents, China (Grant No. Q1313-03).

Active metamaterials incorporating with non-Foster elements have been considered as one of the means of overcoming inherent limitations of the passive counterparts, thus achieving broadband or gain metamaterials. However, realistic active metamaterials, especially non-Foster loaded medium, would face the challenge of the possibility of instability. Moreover, they normally appear to be time-variant and in unsteady states, which leads to the necessity of a stability method to cope with the stability issue considering the system model uncertainty. In this paper, we propose an immittance-based stability method to design a non-Foster loaded metamaterial ensuring robust stability. First, the principle of this stability method is introduced after comparing different stability criteria. Based on the equivalent system model, the stability characterization is used to give the design specifications to achieve an active metamaterial with robust stability. Finally, it is applied to the practical design of active metamaterial with non-Foster loaded loop arrays. By introducing the disturbance into the non- Foster circuit (NFC), the worst-case model uncertainty is considered during the design, and the reliability of our proposed method is verified. This method can also be applied to other realistic design of active metamaterials.

Active Anomalous Transmission and Its Application in Compensating Waveform Distortions**Supported by the National Natural Science Foundation of China under Grant Nos 61771421, 61771422, 61528014 and 6140139, and the Zhejiang Provincial Natural Science Foundation under Grant No LY16F010009.

In theory, engineered anomalous transmission in passive materials and waveguide devices can be used to compensate for waveform distortions. However, they suffer from inherent dissipation. Recently, active non-Foster elements with imaginary immittance monotonically decreasing with frequency have shown important potentials in broadening bandwidths of electromagnetic devices. So far, they are implemented based on negative impedance convertors (NICs) loaded with Foster devices. This makes them intrinsically one-port elements and thus cannot be used to compensate for distortions of signals. We construct a two-port network with a non-Foster transmission coefficient based on an unconventional use of NICs. Simulation and experiments show that it can compensate for extremely distorted signals. The proposed method can be used to broaden existing applications in different areas such as antennas, circuits and systems, and physical-layer signal processing.

Unconditionally Stable Non-Foster Element Using Active Transversal-Filter-Based Negative Group Delay Circuit

This letter introduces a novel type of non-Foster element using a microwave transversal-filter-based negative group delay (NGD) circuit that can exhibit unconditional stability. The proposed device is realized by a distributed amplifier, in which the NGD response is synthesized by adjusting the ratio of transconductance of transistors in each stage. On top of this, by properly amending the in-band magnitude and phase characteristics, the NGD circuit can realize non-Foster elements within the operating band. Furthermore, thanks to the distributed topology, the proposed network has very good input and output matching characteristics. As proof-of-concept, a prototype of the proposed non-Foster element is built to validate the proposed scheme. The experimental results show that the proposed circuit can realize a unilateral non-Foster element composed of a −1 pF shunt capacitor and a −1.25 nH series inductor.

Stability Analysis of Non-Foster Circuit Using Normalized Determinant Function

Non-Foster elements are highly desired to overcome the bandwidth limit of electrically small antennas, cloaking, and metamaterials. However, they are prone to be unstable and thus it is quite challenging to implement non-Foster circuits in practice. Hence a rigorous and effective method of analyzing the stability should always be the priority when designing a non-Foster network. This paper applies normalized determinant function to analyze the stability of non-Foster circuits. A floating-version negative capacitor based on Linvill’s negative impedance converter is taken as the example. Factors affecting the stability in the practical design are thoroughly investigated, including device parasitics, dc biasing, distributed transmission line in the layout and load impedance. Circuit parameters are substituted with practical values to reduce the complexity of calculation. Finally, experiments are conducted to verify the analysis.

Electrically Small, Broadside Radiating Huygens Source Antenna Augmented With Internal Non-Foster Elements to Increase Its Bandwidth

A broadside radiating, linearly polarized, electrically small Huygens source antenna system that has a large impedance bandwidth is reported. The bandwidth performance is facilitated by embedding non-Foster components into the near-field resonant parasitic elements of this metamaterial-inspired antenna. High-quality and stable radiation performance characteristics are achieved over the entire operational bandwidth. When the ideal non-Foster components are introduced, the simulated impedance bandwidth witnesses approximately a 17-fold enhancement over the passive case. Within this –10-dB bandwidth, its maximum realized gain, radiation efficiency, and front-to-back ratio (FTBR) are, respectively, 4.00 dB, 88%, and 26.95 dB. When the anticipated actual negative impedance convertor circuits are incorporated, the impedance bandwidth still sustains more than a 10-fold enhancement. The peak realized gain, radiation efficiency, and FTBR values are, respectively, 3.74 dB, 80%, and 28.01 dB, which are very comparable to the ideal values.

A Wideband Frequency-Tunable Dipole Antenna Based on Antiresonance Characteristics

We propose a novel frequency-tunable dipole antenna using varactor diodes and shunt inductors, which provides a much wider frequency tuning bandwidth. First, based on the simple series connection of non-Foster elements, we have predicted required reactance ensuring good impedance matching over a wide target frequency tuning band. Next, we have devised parallel connection of the diodes and the inductors to generate antiresonance behavior, which is necessary to produce the required reactance throughout the target frequency band. However, the inductor connected in parallel with the varactor diode always made the diode short-circuited. To solve the problem, we have inserted a narrow longitudinal slit in each dipole arm, which can maintain not only necessary dc isolation but also required RF connection with the help of a dc blocking capacitor bridging the slit. All measured results show good agreement with simulated ones, which proves the validity of our proposal.

Design Method for Actively Matched Antennas With Non-Foster Elements

The design of electrically small antennas (ESAs) loaded with active non-Foster elements is a topic whose interest has grown in the last years. In this communication, a new strategy for the design of actively matched antennas loaded with non-Foster elements is presented. The analysis of different parameters, such as the sensitivity to non-Foster circuit placement, the overall antenna system stability, and current distributions, has to be considered in order to enhance the antenna performance. A design example using an ESA and its realization is presented to validate the proposed strategy.

Non-Foster 회로를 이용한 FM 안테나의 신호 대 잡음비 개선

In this paper, we demonstrate a Non-Foster matching method for an electrically small antenna to improve the signal-to-noise ratio (SNR) of communication link. For the experiment, we used a general FM antenna whose resonance frequency is about 52-57 MHz and a floating type Linvill negative impedance converter(NIC)-based circuit as a Non-Foster matching element. By implementing the Non-Foster circuit to cover FM band, we can achieve a wide bandwidth matching covers 40-200 MHz. Our measurement shows 3-7 dB improvement of SNR for the same bandwidth though there are several spikes which means no improvement of SNR in the band.

An Active Wideband and Wide-Angle Electromagnetic Absorber at Microwave Frequencies

Two-dimensional (2-D) metamaterials (MTMs) can be used to create perfect electromagnetic absorbers. In this letter, a novel active MTM absorber with non-Foster loads is proposed. For obliquely incident plane waves with both transverse-electric (TE) and transverse-magnetic (TM) polarizations, its effective circuit model is analytically demonstrated, accounting the material losses. Based on the circuit model, a stability characterization is introduced to give the design principles for the non-Foster elements to achieve a wideband and wide-angle metamaterial absorber (MA). These active elements are achieved by a two-port non-Foster circuit based on the resonant tunneling diodes. For the purpose of verification, a sample active MA design is presented, exhibiting a high electromagnetic absorption rate for wideband and wide-angle incidence for both TE and TM polarizations at microwave frequencies, as compared to its passive counterpart.

Properties of purely reactive Foster and non‐Foster passive networks

The mathematical concept of strongly real functions of positive and negative types is introduced to network theory for the first time. The driving-point reactance/susceptance of a pure Foster network, made up of only ideal positive inductance and capacitance elements, is a strongly real function of real frequency of positive type. As a corollary, for a pure non-Foster network made up of only ideal negative inductance and capacitance elements, the driving-point reactance/susceptance is a strongly real function of real frequency of negative type. It is shown that a condition for a purely reactive passive network to exhibit a positive or negative reactance/susceptance-frequency gradient is that the driving-point immittance should have alternating poles and zeroes lying on the real frequency axis. Finally, it is shown that either purely Foster or non-Foster networks can be constructed by combining ideal Foster and non-Foster reactive elements.

Arbitrary-Angle Squint-Free Beamforming in Series-Fed Antenna Arrays Using Non-Foster Elements Synthesized by Negative-Group-Delay Networks

Beamforming in series-fed antenna arrays can inherently suffer from beam-squinting. To overcome the beam-squinting problem, low-dispersion, fast-wave transmission lines can be employed. Such transmission lines can be designed by loading a regular transmission line with non-Foster reactive elements (e.g., negative capacitors and inductors). As a result of a recent development, these non-Foster reactive elements can be implemented using loss-compensated negative-group-delay (NGD) networks, providing a solution to the stability issues associated with conventional non-Foster networks. In this work, transmission lines augmented by loss-compensated NGD networks, representing the non-Foster reactive-element loading, are employed for designing wideband fast-wave, low-dispersion transmission lines. This work consolidates this non-Foster reactive element loading method with earlier efforts where NGD networks were used to implement zero-degree phase shifters for beamforming at the broadside direction, and generalizes these methods for arbitrary-angle beamforming from backfire to endfire including the broadside direction. Experimental results are presented for a wideband linear four-element transmitting array feed network for beamforming at 30° with respect to the broadside direction in the frequency range 1-1.5 GHz. By connecting this feed network to four wideband tapered-slot antennas, the beamforming performance is experimentally verified inside an anechoic chamber. Moreover, the antenna array is experimentally tested for transmission of a narrow pulse, where low distortion is observed at the beamforming angle over the entire operating bandwidth. The physical length of the feed network is realistic and is 0.96 wavelengths long at the center of this frequency range. In addition, switched-line phase shifters are employed for squint-free beamforming in three other angles: 60°, 0°, and $-30^{\circ}$.