Ladder Circuit Research Articles

Design of a single flux quantum Σ– Δ A/D converter with a ladder circuit as an on-chip-clock-generating circuit

We investigated an oversampling Σ– Δ A/D converter (ADC) with a large signal-to-noise ratio (∼80 dB or more) and a wide bandwidth (∼100 MHz), which were formed from single flux quantum circuits. The ADC consisted of a second-order lowpass Σ– Δ modulator and a third-order sinc decimation filter. A ladder circuit was utilized to supply the high frequency sampling clock signal of more than 16 GHz to the modulator. The third-order sinc filter was designed from a multistage decimation sinc filter and a multiple integration sinc filter. By combining both sinc filters, the sinc filter operating with a decimation factor of 16 at the high clock frequency of more than 16 GHz could be designed in the chip area of ∼10 × 10 mm 2. Experimentally, we measured the bit rate of the ladder circuit from an average voltage measurement and an oscilloscope observation, and obtained the bit rate of 31 Gbps.

Modeling double-layer capacitor behavior using ladder circuits

The double-layer capacitor (DLC) is a very complex device that is best represented by a distributed parameter system. Many different lumped-parameter equivalent circuits have been proposed for the DLC. An examination into utilizing a ladder circuit to model a DLC is presented. Parameters for different ladder circuits are determined from AC impedance data. Variations in circuit parameters with DC bias and manufacturing have been investigated. The performance of the ladder circuit has been evaluated in slow discharge and pulse load applications.

Frequency behavior of self-similar ladder circuits

The fractal immittance, Y ( ω )∝ ω a or Z ( ω )∝ω − a (0< a <1) with an optional a -value, has been found to be simulated using self-similar ladder circuits with each set of elements, R or C , forming a geometric progression. The optimum bandwidth B op is numerically calculated for a given criterion with respect to the phase angle as a function of the number of rungs n involved in the ladder. B op ≥5 with a phase-angle error of ±1/2° is found to be attainable for a =0.25–0.75 by 18 rungs or less, indicating the availability of the self-similar ladders for the hardware realization of fractal immittance.

Simulation of Fractal Immittance by Ladder Circuits

Fractal immittance FD, expressed by an admittance w α with an optional value of a within the range 0 <a<1, is simulated by ladder circuits with finite numbers of resistors and capacitors starting from the optimized circuit based on the distributed-relaxation-time (DRT) model. Thus designed DRT-equivalent ladder with a = 1/2, e.g., is found to be far more effective than the conventional ladder composed of identical rungs: for the bandwidth of 5 decades with a phase-angle error of ±2°, e.g., the conventional ladder involves 6.426 × 103 identical rungs, while 11 rungs are sufficient for the DRT-equivalent circuit.

Formation of a Large-Scale Structure in a Nonlinear Dissipative System

Dynamic evolution of a small-scale structure to a large-scale structure is studied by a nonlinear dissipative LC ladder circuit. The circuit is described by a Burgers equation in the lowest order. We confirmed that the observed propagation of a shock wave and the confluence of shock waves are well described by the theory. A single hump wave is used to model a small-scale structure. When two single-hump waves with different amplitudes are applied to the circuit, they evolve into a large-scale structure in the course of propagation. Such a formation of a large-scale structure is unique in a nonlinear dissipative system, while the nonlinear dispersive system is known to preserve the nature of small-scale structures even after their interaction as known for solitons.

AN ACTIVELY TUNED SOLID-STATE VIBRATION ABSORBER USING CAPACITIVE SHUNTING OF PIEZOELECTRIC STIFFNESS

A tunable solid-state piezoelectric vibration absorber and an active tuning method were developed and demonstrated. A passive vibration absorber generally acts to minimize structural vibration at a specific frequency associated with either a tonal disturbance or a lightly damped structural vibration mode. Because this frequency is rarely stationary in real applications, damping is usually added to ensure some level of effectiveness over a range of frequencies. Maximum response reductions, however, are achieved only if the absorber is lightly damped and accurately tuned to the frequency of concern. Thus, an actively tuned vibration absorber should perform better than a passive one and, furthermore, could be made lighter. In its simplest form, a vibration absorber consists of a spring–mass combination. A key feature of the tunable vibration absorber described herein is the use of piezoelectric ceramic elements as part of the device stiffness. The effective stiffnesses of these elements were adjusted electrically, using a passive capacitive shunt circuit, to tune the resonance frequency of the device. The tuning range of the absorber is thus bounded by its short- and open-circuit resonance frequencies. An alternative tuning approach might employ resistive shunting, but this would introduce undesirable damping. Another feature of the device is the ability to use the piezoelectric elements as sensors. A control scheme was developed to estimate the desired tuning frequency from the sensor signals, to determine the appropriate shunt capacitance, and then to provide it. The shunt circuit itself was implemented in 10 discrete steps over the tuning range, using a relay-driven parallel capacitor ladder circuit. Experimental results showed a 20 dB maximum, and a 10 dB average improvement in vibration reduction across the tuning range, as compared to a pure passive absorber tuned to the center frequency, with additional benefit extending beyond the tuning range.

Observation of resonant characteristic of synchrotron magnet system

Synchrotron magnets connected in series should be regarded as a ladder circuit. We will show here its clear resonant property. The resonance produces current enhancement at particular locations in the magnet string. For a high field quality of large number of magnet, a theoretical and an experimental knowledge of this property are required. This resonant characteristic in an actual operating synchrotron is presented in this article as a resonant pattern of magnetic field distribution along a synchrotron ring and is compared with the theory.

A practical method for evaluation of ground fault current distribution on double circuit parallel lines

The paper presents an original analytical procedure for quick and, for practical purposes sufficiently accurate evaluation of the principal components of the ground fault current. The procedure is valid for faults at any of the towers of a double 3-phase circuit line with an arbitrary number of spans. The method is obtained by application of relatively simple and exact equations for uniform ladder circuits of any size (for any number of pis, from one to infinity) and for any terminal conditions. The method can be applied to solve several practical problems: the evaluation of the maximum substation grounding system fault current, the selection of a ground wire capable of withstanding the fault currents and the prediction of step and touch voltages near the transmission towers. In the case of a double circuit 3-phase line, the solution of these problems is additionally complicated by the mutual inductive coupling between the two parallel lines.

Experiment on Shock Wave in a Random LC Circuit

Shock wave in a random system has been investigated theoretically and experimentally. A nonlinear LC ladder circuit with random inhomogeneity of linear inductor in series branch has been studied. The circuit is equivalent to a random Toda lattice. It is shown theoretically that wave propagation in the system is described by the Burgers equation in the case of strong randomness with weak nonlinearity. The transition from an oscillatory shock wave to a shock wave has been observed on a random LC ladder circuit experimentally. The velocity and width of shock wave agree with the theoretical prediction from the Burgers equation in a region of strong randomness.

Simulation of resistively terminated LC ladder filters using a new basic cell involving current conveyors

A simple, but general, synthesis method is given for the simulation of resistively terminated LC ladder circuits. The method is based on a new basic cell (BC) introduced in this work. The proposed method converts resistively terminated LC ladder circuits into inductorless active circuits involving only second-generation current conveyors (CCII±), grounded resistors and grounded capacitors. Hence it is suitable for fully integrated circuit design.

On the representation of static hysteresis curves by a PWL ladder circuit

Some important features of static hysteretic phenomena can be suitably represented by a recently proposed ladder circuit model. The elementary cell of this ladder is constituted by a linear capacitor and a non-linear resistor with a proper piecewise linear (PWL) characteristic. With respect to the original formulation, the representation capabilities of the model can be improved by introducing proper generalizations. These generalizations concern the definition of the hysteretic (output) variable and the initial states of the circuit capacitors. After introducing these concepts, this paper addresses the determination of the model parameters that give the best fit of the experimental data of a scalar rate-independent hysteresis. The solution of this identification problem is obtained both for a limit cycle and for a cycle together with its first polarization curve. © 1998 John Wiley & Sons, Ltd.

Practical method for evaluating ground fault current distribution in station, towers and ground wire

The paper presents an original analytical procedure which enables a quick and, for practical purposes sufficiently accurate evaluation of the significant parts of the ground fault current, for a fault at any of the towers of a transmission line of an arbitrary number of spans. The advantages of the method are the simplicity and accuracy of the formulae for solving uniform ladder circuits of any size (from one up to an infinite number of pis) and any terminal conditions. The formulae are obtained by applying the "general equations of the line represented by discrete parameters" on a specific electrical circuit formed by a transmission line ground wire during ground faults. The presented method is suitable for analyses aimed at evaluating the maximum substation grounding system fault current, at selecting the ground wire capable of withstanding the fault currents and at the prediction of step and touch voltages near transmission towers.

Practical method for evaluating ground fault current distribution in station supplied by an unhomogeneous line

The paper presents an analytical procedure which enables a quick and, at the design stage, correct evaluation of the ground fault current distribution, for a fault in a substation supplied by a line composed of two or more uniform and different sections. The advantages of the method are based on the simplicity and accuracy of the formulae for solving uniform lumped parameter ladder circuits of any size and under any terminal conditions. The formulae are obtained by applying the general equations of the line represented by discrete parameters on a specific electrical circuit formed by a transmission line ground wire during ground faults. The paper also derives simple and exact expressions for solving ladder circuits formed by the discretization of underground conductors which are in continuous contact with earth (e.g.: the sheaths of a cable, an interconnecting copper buried in the soil, a pipeline, etc.). The correct prediction of the expected ground fault current parts in soil and neutral conductors is of great importance in designing safe and economical substation grounding installations.

Hierarchical techniques for symbolic analysis of electronic circuits

A hierarchical symbolic analyser (SAGA2) is presented for the analysis of electronic circuits. SAGA2 analyses lumped, linear, or linearised (small-signal) circuits in the S- and Z-domain. For the analysis of large circuits, a hierarchical two-port (multiport) method is proposed that is two to three orders faster than that without using the hierarchical method. A bandpass filter or a 12-stage RC ladder circuit can be analysed in symbolic form within 1 CPU second. Also, the memory used is dramatically reduced.

Analysis for the double staggered ladder circuit

A new type of mm-wave slow wave system, double staggered ladder circuit is analyzed in this paper, by means of “average cavity field method” and three-dimensional finite element method. The influence of the electron beam channel on the dispersion characteristics is discussed. An experimental research is made, the experimental results agree well with the theoretical one.

Static and dynamic hysteretic features in a PWL circuit

The general properties of the static and dynamic hysteretic behaviours of a PWL ladder circuit are described and discussed. These properties are obtained on the basis of some results reported in a previous paper (M.Parodi et al., Int. j. circ. theor. appl., 22, 513 (1994), concerning the static hysteretic behaviour of the same circuit. Despite the non-linearity of the circuit, the main features of its hysteretic behaviour are shown to depend on the parameters of the circuit components in a simple way. Moreover this behaviour is similar to those observed in a large number of experiments. For these reasons, the PWL ladder circuit is taken as the central element of a general circuit model for hysteresis. The structure of this general circuit is described at the end of the paper.

A PWL ladder circuit which exhibits hysteresis

AbstractA circuit model for static hysteresis is presented. the circuit has a ladder structure with linear capacitors and piece wise linear resistors. the model behaviour shows all basic characteristics of static hysteresis phenomena. the model is put into relation with others proposed in the literature. an analysis of the model properties and a detailed comparison with the static Preisach model are made.

T‐versus ABCD‐matrix in circuit analysis

AbstractThe paper describes and compares the wave‐chain and transmission matrix approaches to the calculation of transfer‐function coefficients for ladder circuits (semi‐symbolic analysis). It is found that the wave‐chain matrix approach can be computationally more efficient.

Eigenvalue clustering in compensated parameter identifiers

A class of compensated parameter identifiers is utilized to generate bias-free parameter estimates in the presence of noise disturbance which accounts for the uncertainties in the system. A forward feedback is used to minimize the effect of noise. The observer form of state variable modelling is used to synthesize a ladder circuit whereby the compensated parameter identifiers are asymptotically stable, with rapid convergence. A new technique is applied to derive state feedback that assures the assignment of closed-loop eigenvalues in arbitrary sectors within the unit circle.

Modeling of the distributed gate RC effect in MOSFET's

Scattering parameters of wide MOSFET devices have been measured at the wafer level in the frequency range up to 1 GHz. These scattering parameters are converted to Y-parameters for device characterization and compared with SPICE simulations of L-, Pi -, and T-ladder distributed RC circuits taking into account the effect of distributed gates. Good experimental agreement shows that this effect can be modeled appropriately by multisection RC ladders, especially T-ladder circuits. Differences among ladder circuits in modeling this effect are discussed qualitatively.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>