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The peculiarities of doing a canonical analysis of the first-order formulation of the Einstein–Hilbert action in terms of either the metric tensor g^αβ or the metric density along with the affine connection are discussed. It is shown that the difference between using g^αβ as opposed to h^αβ appears only in two spacetime dimensions. Despite there being a different number of constraints in these two approaches, both formulations result in there being a local Poisson brackets algebra of constraints with field independent structure constants, closed off-shell generators of gauge transformations and off-shell invariance of the action. The formulation in terms of the metric tensor is analyzed in detail and compared with earlier results obtained using the metric density. The gauge transformations, obtained from the full set of first-class constraints, are different from a diffeomorphism transformation in both cases.

To extend the existing knowledge on first-order voltage-mode all-pass filters, this paper presents two novel first-order voltage-mode all-pass sections, each employing single fully differential second-generation current conveyor (FDCCII) being used as the newly obtained fully differential voltage conveyor (FDVC), a resistor and a grounded capacitor. Both the proposed circuits possess high-input and low-output impedance feature, which makes the proposed circuits ideal for voltage-mode systems. Non-ideal study along with simulation results is given for validation.

In this paper, a new first-order current-mode (CM) universal filter employing two dual output second-generation current conveyors (DO-CCIIs), one resistor and a grounded capacitor is proposed. The proposed filter has low input and high output impedances; thus, it can be easily connected with other CM circuits. It can simultaneously realize first-order low-pass (LP) and all-pass (AP) responses and can provide high-pass (HP) response with interconnection of LP and AP responses. It can be tuned electronically by replacing with dual output second-generation current controlled conveyors (DO-CCCIIs) instead of DO-CCIIs and removing the resistor. It has only a resistor but no capacitor connected in series to X terminal of DO-CCII; accordingly, it can be operated at high frequencies. Also, it does not need any critical passive component matching conditions and cancellation constraints. A number of simulation results based on SPICE program are included to exhibit performance, workability and effectiveness of the proposed filter configuration.

Two new simple and effective voltage mode frequency selective structures that pass all signals are proposed and explored in this paper. The proposed structures use a single active element and three passive components in each. Dual-X second generation current conveyor (DXCCII) is employed as an active element along with two resistors and a capacitor as passive elements. The capacitor is grounded which goes well with the IC fabrication requirements. Both the structures offer low active and passive sensitivities. The presented structures also exhibit the feature of high input impedance. A comprehensive study of device non-idealities and parasitic is also included to highlight the non-ideal performance of the presented ideas. In addition, to prevent the use of passive resistors, resistor less realizations of proposed structures are also explored by replacing the passive resistors with MOS-based active resistors. A quadrature oscillator is also presented as one of the possible applications of the proposed frequency selective structures. Simulations results are in match with the theoretically analyzed performance.

This paper deals with the realization of two first-order all-pass filter (APF) structures. First structure provides both inverting and non-inverting voltage-mode APF functions. This structure utilizes one differential difference dual-$X$ second generation current conveyor (DD-DXCCII) without $Z$ terminals, one active resistor and one capacitor only. The use of active resistor makes the proposed structure electronically tunable. Therefore, the attributes such as use of single DD-DXCCII without $Z$ terminals and electronic tunability make the proposed structure simple and attractive. Conversely, second proposed circuit structure of first-order APF enriches the quality of this paper as both inverting and non-inverting APF functions in both voltage and current forms are available simultaneously within the same circuit structure. This circuit is realized with the help of one DD-DXCCII, three active resistors and one capacitor. The second circuit structure also enjoys gain controllability feature along with electronically tunable pole frequency that proves to be very essential in many of the applications. Additionally, the proposed APF structures provide the demanding feature of cascadability along with chip fabrication support. Furthermore, the performance of proposed circuits is less affected by the non-idealities and parasitic of DD-DXCCII. PSPICE simulations are provided to validate the theoretical presumptions.

A current-mode first-order filter configuration simultaneously providing noninverting and inverting low-pass (LP) and high-pass (HP) responses depending on passive element choice is proposed. In addition, all-pass filter (APF) responses can be easily obtained with interconnection of LP and HP output currents. The proposed filter employs only two differential voltage current conveyors, a grounded resistor and a grounded capacitor, so it is suitable for integrated circuit realization. It provides the feature of high output impedance. It does not need any passive element matching constraints. A voltage-mode oscillator based on the inverting APF is presented as a typical application. The performance of the proposed configuration is verified through many SPICE simulation and experimental test results.

An extra-X second-generation current conveyor (EXCCII) based first-order current-mode all-pass frequency selective structure is presented through this paper. A grounded resistor and a grounded capacitor are used as passive components. Single active element based realization directly correlates with the circuit’s simplicity. The grounded nature of passive components is advantageous from IC fabrication aspects. The proposed circuit offers cascadability support through low input impedance and high output impedance. The ability of the presented idea to deliver the desired output without meeting any stringent component matching condition further simplifies the circuit’s operation. Sensitivity performance of the proposed circuit is good. The quality performance at high frequency is another value addition to the circuit’s signal processing attributes. Analyses showing the circuit’s behavior under non-ideal conditions are also described in detail. Validation of theoretical analyses is supported by simulations carried out on PSPICE at 0.25$\mu$m technology.

In this paper, two new first-order voltage-mode all-pass filters (APFs) are proposed. Each of the proposed APFs comprises a single modified DDCC-, and has high input impedance. The first and second APFs can provide first-order noninverting and inverting APF responses, respectively. As passive elements, the first APF comprises two grounded capacitors, and a floating resistor while the second one uses a grounded resistor, a floating resistor and a grounded capacitor. However, both of the APFs suffer from a matching problem. Two quadrature oscillators (QOs) obtained from the APFs are presented. Simulations of the APF and QO circuits are fulfilled via the SPICE program. Besides, diverse experiments for the APFs are made to verify the performances.

A novel first-order universal filter structure supporting current mode operation is proposed in this paper. The filter has a single active building block based realization and utilizes an extra-X second-generation current conveyor as an active building block. Additionally, the proposed circuit employs a grounded resistor and a grounded capacitor as passive components. The circuit has the ability to deliver the all-pass, high-pass, and low-pass functionalities simultaneously without meeting any passive components matching constraint. High output impedance and load insensitive outputs are other remarkable signal processing features offered by the proposed filter structure. Theoretical behavior of the proposed filter is described by presenting ideal, non-ideal, parasitic, and stability analyses. Additionally, the resistorless variant of the proposed filter is also shown to impart the tunability feature. Personal simulation program with integrated circuit emphasis (PSPICE) simulation results are presented to verify the theoretically described performance of the proposed universal filter. Complementary metal oxide semiconductor (CMOS) realization of extra-X second-generation current conveyor is utilized for the purpose of simulations, therefore, the filter is CMOS compatible.

In this paper, a novel complementary metal-oxide semiconductor (CMOS) transistors based first-order voltage-mode all-pass filter is proposed. The filter circuit employs six metal-oxide semiconductor (MOS) transistors and minimal number of passive components, i.e., a resistor and a capacitor. The core of the proposed filter is a CMOS inverting amplifier with unity gain. The proposed circuit exhibits some attractive features such as compact design, high input impedance and ability to provide non-inverting and inverting all-pass responses simultaneously. Additionally, it does not require any kind of passive element matching constraints. Furthermore, by replacing the passive resistor with an active negative channel metal-oxide semiconductor (NMOS) transistor, the proposed filter is enriched with the much-desired feature of tunability. The theoretical behavior is tested and demonstrated by carrying SPICE simulations using TSMC 0.18$\mu$m level-7 CMOS process parameters.

In this paper, a differential-input plus-type differential voltage current conveyor-based first-order universal filter is designed. This voltage-mode filter uses a grounded capacitor. In addition, it can provide all the noninverting and inverting first-order universal filter responses. The circuit provides high common-mode rejection ratio of about 76.5 dB. Nevertheless, it needs a single matching problem and comprises two floating resistors. Quadrature oscillator (QO) design is obtained using this filter as an application example. The designed filter and QO circuits are simulated through the SPICE program, and some experimental studies are carried out using AD844 ICs to verify the theory.

This paper aims to analyze the wave propagation in functionally graded carbon nanotube-reinforced composite (FG-CNTRC) beams placed on a viscoelastic foundation utilizing an improved first-order shear deformation theory (FSDT). The material properties are derived from the mixture rule. Four carbon nanotube distribution patterns are considered in the analysis. The extended Hamilton’s Principle is utilized to derive the governing wave equations for the CNTRC beam. A comparison between the present theory results and those in the literature is conducted for validation. The wave dispersion investigation is mainly based on the phase and group velocities. The results illustrate the wave propagation responses for the different CNT configurations. In addition, the influence of the CNTs volume fraction, foundation stiffness parameters, and damping coefficient on the wave characteristics is examined.

We establish a consistency result by comparing two independent notions of generalized solutions to a large class of linear hyperbolic first-order PDE systems with constant coefficients, showing that they eventually coincide. The first is the usual notion of weak solutions defined via duality. The second is the new notion of ${𝒟}$-solutions which we recently introduced and arose in connection to the vectorial calculus of variations in $L^{\infty }$ and fully nonlinear elliptic systems. This new approach is a duality-free alternative to distributions and is based on the probabilistic representation of limits of difference quotients.