On the minimal realization of the gyrator by means of nullors and resistors

This paper is a second step in the proof of the conjecture that it is impossible to synthesize a gyrator by means of nullors and linear resistors with fewer than four resistors if only two nullors are permitted, or with fewer than three nullors if only two resistors are permitted. It is proved that a gyrator cannot be realized with only two nullors and two resistors. In a forthcoming paper (third step) it will be proved that a two-nullor, three-resistor gyrator realization cannot be obtained. The proofs are presented in such a way that at the same time a synthesis procedure for minimal nullor-resistor networks is demonstrated.     

On the realization of gyrators by nullors and resistors

It is proved that for the realization of a gyrator by nullors and resistors, at least two nullors and at least two resistors are needed. A generalization is the result that any n-port network possessing both an impedance and an admittance matrix and consisting of nullors and resistors must contain at least n resistors. It is conjectured that a realization of a gyrator with only two nullors requires four resistors and a realization of a gyrator with only two resistors requires three nullors.     

A theory of nonenergic N-ports

A circuit element is nonenergic if the instantaneous power flow into it is always zero. Well-known examples include the ideal diode, transformer, gyrator and circulator. Most of the interesting nonenergic elements are nonlinear N-ports with N ? 2, and many of their properties are quite counterintuitive. For example, there exists a surprisingly large class of nonenergic multiport capacitors and inductors, all of which, it turns out, are nonlinear and reciprocal. Nonenergic linear N-ports, on the other hand, are necessarily resistive and antireciprocal. In this paper, we present a rigorous fundamental theory of nonenergic N-ports that results in a general canonical representation. Special canonical forms are developed for nonenergic resistors, capacitors and inductors, and numerous examples are given.     

回转器基本特性分析及其实现方法

在有源RC网络综合中,常用电阻、电容和运算放大器的综合。电路微型化的趋势和固件的出现,导致使用回转器和理想变压器而不使用电感来进行综合。在分析了回转器原理及其基本特性的基础上,用回转器模拟浮地电感或接地电感,以及用模拟电感来实现二阶带通与低通电路。并研讨了用运算放大器与负电阻来实现回转器网络的方法。     

Synthesis of voltage-transfer matrices with active RC networks embedding nullors

Realizability conditions for the synthesis of multiport voltage-transfer matrices by means of RC transformerless networks embedding either balanced or grounded nullors are systematically described. The results obtained are summarized in two theorems concerning the minimum number of nullors necessary and sufficient to synthesize a given voltage-transfer matrix.     

A new generalized inverter based on the active hybrid

The building block for the new generalized immittance inverter is a 3-port known as the active hybrid network. One of its ports is bidirectional, and matches a design admittance y₀. The second port operates in the send, while the third port operates in the receive direction. The hybrid is constructed from an op-amp and a 5-port network composed of a few resistors and the design admittance y₀. There are two versions of the hybrid: the voltage-inverting (i.h.) and the noninverting hybrid (n.i.h.). The inverter consists of an i.h. and an n.i.h. connected at their unidirectional ports in a loop. The gyration admittances are actual driving-point admittances in the circuit, namely the design admittances y₀, y'₀ of the two hybrids. Such an inverter, when terminated at its output port by a load admittance y, will give at its input port an input admittance y_in = y₀y'₀/y. Expressions are derived for the y parameters of the inverter at higher frequencies, thus accounting for the finite bandwidth of the op-amp. Two special cases are particularly treated, and experimental results are obtained for them. The first is the case of the resistive gyrator, for which y₀ and y'₀ are pure conductances. The second is the case of the capacitive gyrator, for which y₀ and y'₀ are pure capacitive susceptances. The capacitive gyrator is used to produce the supercapacitor, or f.d.n.r., and the results of measurements on a number of f.d.n.r. networks are given.     

Current mode CCII oscillators using grounded capacitors and resistors

New realizations of grounded C, grounded R current mode oscillators using the current conveyor (CCII) are given. The proposed oscillators are classified into two classes depending on the number of feedback loops. In class I, there is a single current feedback loop, whereas in class II, there are two current feedback loops. Class I includes two types and it employs two CCIIs, three capacitors and three or four resistors. Class II employs two CCIIs having two-outputs each, two capacitors and three resistors and has independent control on the condition of oscillation and on the frequency of oscillation by varying two alternative resistors. PSpice simulations are included. Exact analysis based on the parasitic elements of the CCII is carried out indicating that class I has a third order characteristic equation. Class II has the advantage that the effects of the parasitic elements of the CCIIs can be absorbed in the circuit components. © 1998 John Wiley & Sons, Ltd.     

Extension of the normal tree method

The results of this paper are applicable to linear electrical networks that may contain ideal transformers, nullors, independent and controlled sources, resistors, inductors, and capacitors, and, under a topological restriction, gyrators. A relation between summands of some expansion of the network determinant and pairs of conjugate trees is proved, which uncovers the equivalence of known criteria on generic solvability based on matroids and those based on pairs of conjugate trees. New criteria on the solvability of active networks are given. A method to obtain complete sets of generic state co‐ordinates is established, which includes the following extension of the wellknown normal tree method: The generic order of complexity equals the sum of the number of forest capacitors and the number of co–forest inductors in any normal pair of conjugate trees, the latter term being introduced in this paper. The voltages across the forest capacitors together with the currents through the co‐forest inductors may be given initial values independently from each other. Further, a systematic method of augmentation that yields networks of generic index 1 is proposed. All results are expressed in terms of network determinants as well as in terms of network graphs, and all given criteria may be checked by efficient algorithms. Copyright © 1999 John Wiley & Sons, Ltd.     

Circuit Techniques for Improving the Switching Loci of Transistor Switches in Switching Regulators

The use of switching regulator circuits at high power levels and high frequencies requires careful examination and control of the power dissipation during switching, which may be the dominant loss. In this paper it is shown that it is possible to remove most of the switching losses from the switching transistor with two networks, each containing three components: an inductor or a capacitor, a diode, and a resistor. With proper design, the power dissipation in the resistors is less than the switching losses removed from the switching transistor, resulting in some improvement in overall efficiency. In addition, it is possible to obtain a significant further improvement in efficiency by replacing the resistors in the networks with low loss circuits. Each network, one for the reduction of turnoff losses and one for the virtual elimination of turnon losses in the switching transistor, is described in detail. Analytical design procedures are included.     

On the uniqueness of the numerical solution of non‐linearly loaded lossy transmission lines

The purpose of this paper is to investigate the uniqueness of the solution of lossy lines with frequency‐dependent parameters terminated with non‐linear resistors. Several solutions that satisfy the same initial conditions may exist if the terminal resistors are locally active. In these cases the uniqueness of solution is assured adding parasitic capacitances in parallel to the voltage controlled resistors and parasitic inductances in series to the current controlled resistors. In this way, among all the possible solutions, the only one that assures the time continuity of the current and voltage waveforms at the ends of the line is captured. In the light of these results, the properties of numerical models of these distributed circuits based on convolution techniques have been studied, and conditions assuring the uniqueness of the numerical solution have been found. Numerical simulations, when based on qualitative information of this type, enable us to obtain the quantitative properties in an efficient manner. In particular, a simple numerical method that enforces artificially the time continuity of the solution is proposed to circumvent the need of adding parasitics. Copyright © 1999 John Wiley & Sons, Ltd.     

A generalized theorem of Reichert for biquadratic minimum functions

This paper is concerned with a generalized theorem of Reichert for biquadratic minimum functions, which states that any biquadratic minimum function realizable as the impedance of networks with n reactive elements and an arbitrary number of resistors can be realized with n reactive elements and two resistors. First, a series of constraints on networks realizing minimum functions are presented. Furthermore, by discussing the possible resistor edges incident with vertices of the reactive‐element graphs, it is proved that any minimum function realizable as the impedance of networks with three reactive elements and an arbitrary number of resistors can be realized with three reactive elements and two resistors, from which the validity of the case of n = 3 follows. Similarly, the validity of the case of n = 4 is proved. Together with the Bott–Duffin realizations, the generalized theorem of Reichert for biquadratic minimum functions is finally proved. The results of this paper are motivated by passive mechanical control. Copyright © 2016 John Wiley & Sons, Ltd.     

Realizations of fully differential voltage second generation current conveyor with an application

Three novel CMOS realizations for the fully differential voltage second‐generation inverting current conveyor (FDVCCII‐) are proposed in this paper. The first realization has a limited input range, and the other two realizations have a rail to rail input range and show excellent features in linearity and bandwidth. As an application to the FDVCCII‐, a floating gyrator is proposed. A floating inductor is realized using the floating gyrator and it is used in realizing a second‐order low‐pass filter, which is simulated and compared with the ideal result. All circuits are simulated with SPICE using CMOS 0.35µm technology and supply voltages ±1.5V to verify the theoretical results. Copyright © 2008 John Wiley & Sons, Ltd.     

限定燃弧时间试验法

断路器在直接试验线路中试验时,如果试品开断失败,由于燃弧时间过长,试品常遭破坏,会给试品的设计者带来许多麻烦。本文介绍两种试验线路,在其中额外设置了带有并联电容和电阻的辅助开断装置,它可避免过长的燃弧时间和因此而产生的试品爆炸。其中的一种试验线路还能提供测量弧后电流的新途径。     

Order of complexity of rlc networks containing a reactive gyrator

Using a particular expansion of the network determinant, a simple formula is derived giving the total number of natural frequencies of a passive RLC network containing a reactive gyrator. The order of complexity is expressed in terms of the degrees of the polynomials in the gyration impedance and the alteration in the network topology due to gyrator embedding. Quantitative conditions for the order of complexity of the active network exceeding that of the network without the gyrator are obtained. Formulas are also derived for the number of zero and non-zero natural frequencies.     

Floating inductor with two current conveyors

There have been considerable efforts towards the realization of ideal floating inductors where mostly three active blocks are required. The reduction in the number of active blocks to two was however achieved with considerable increase in the number of resistances and passive parameter constraints. The proposed scheme suggests a method to produce a floating inductor with a series negative resistance using two current conveyors, only three resistors and one capacitor, involving only one restrictive constraint. The realized inductor was also used to design a third order Butterworth filter. Experimental results confirm the applicability of the realized immittance.     

The realization of inverse system for circuits containing nullors with applications in chaos synchronization

A very simple method for synthesizing the inverse system of a non-linear non-autonomous circuit containing nullors is proposed. The main application of the procedure is the synchronization of chaos by the inverse system approach. This is illustrated with two examples: the synchronization of a Duffing circuit and a communication scheme by direct chaotic modulation using Chua's circuit. © 1998 John Wiley & Sons, Ltd.     

一种电容补偿型高压电容分压器的设计

根据高压脉冲实验测量的需要,阐述了外带积分器型、电阻补偿型及电容补偿型等几种电容分压器的工作原理,分析了影响各自响应时间的主要因素即对于测量ns量级快前沿高压脉冲信号,使用外带积分器型电容分压器时不宜采用大尺寸的伞式探针结构;使用电阻补偿型电容分压器时对其高压臂大电阻要求较高。在缺少高性能大阻值电阻的情况下,利用高压电容尝试设计并制作了电容补偿型电容分压器,其分压比约为9348,它在一定范围内可通过改变补偿电容值而方便地改变。实验结果与理论计算及PSpice软件的模拟结果基本一致,方波响应时间约为4.4ns,基本达到了设计目的。定标结果表明该分压器可用于测量高功率脉冲调制系统和强流电子束加速器中的高压脉冲。     

High input impedance voltage‐mode first‐order all‐pass sections

This paper proposes six new first‐order voltage‐mode all‐pass sections (VM‐APSs) based on three general topologies. Each circuit uses two differential voltage current conveyors and three grounded passive components. All the circuits possess high input impedance and easy control of pole frequency either by a simple matching of resistors (two equal‐valued resistors) for the three canonical circuits or by a single resistor for three non‐canonical circuits. PSPICE simulation results using real device 0.5µ CMOS parameters are given to validate the proposed circuits. Copyright © 2007 John Wiley & Sons, Ltd.     

Realization of tunable RC-active oscillators using grounded capacitors and voltage amplifiers

A systematic procedure is given to generate a set of tunable RC oscillators, each using two finite gain voltage controlled voltage sources, three resistors and two grounded capacitors. These realizations are shown to be minimal with respect to passive and active elements under the constraint that (one end of) all the capacitors remain grounded. The set consists of four oscillators and is shown to be complete, that is, no additional oscillator circuit can be generated under the given assumptions. A simple approach is then introduced for testing the structures for latch up behaviour. This approach also suggests a way of redesigning the oscillator circuits to render them free of latch up problems, if they exist. Experimental results are found to be in good agreement with the theory.