Resistance-capacitance Ladder Research Articles

Analysis of Fractional Electrical Circuit Containing Two RC Ladder Elements of Different Fractional Orders

Abstract The study addresses the topic of different fractional orders in the context of simulation as well as experiments using real electrical elements of fractional-order circuit. In studying the two solutions of the resistance-capacitance (RC) ladder circuit of appropriate parameters, different fractional orders of the electrical circuit are considered. Two fractional-order (non-integer) elements were designed based on the Continued Fraction Expansion (CFE) approximation method. The CFE method itself was modified to allow free choice of centre pulsation. It was also proposed that when making individual ladder circuits, in the absence of elements with the parameters specified by the program, they should be obtained by connecting commercially available elements in series or parallel. Finally, the theoretical analysis of such a circuit is presented using state-space method and verified experimentally.

Electrical analogy approach to estimate material category from transient thermal response

Material identification based on thermal properties is a commonly used approach of classifying materials into different categories. In this paper, an analytical approach for estimation of two thermal properties under the transient condition and arbitrary ambient temperature is presented for material category identification. The thermal properties are estimated by exploiting the analogy between the one-dimensional thermal conduction in material with the voltage distribution in resistance-capacitance (RC) ladder network. The concept of time delay in the RC ladder network has been used in the thermal domain for deriving simple analytical expressions of thermal diffusivity and thermal conductivity. The proposed approach is simple, has less data related concerns and can identify the material category based on two thermal properties for better certainty. This approach has been verified by simulations and experiments performed on materials of different categories. The approach would be helpful in automated applications related to material identification or handling.

A detailed look at electrical equivalents of uniform electrochemical diffusion using nonuniform resistance–capacitance ladders

This paper discusses equivalent-circuit modeling of the electrochemical impedance corresponding to one-dimensional diffusion in a uniform medium. It argues that, of the several equivalent circuits in use for such modeling, one – namely the nonuniform resistance–capacitance ladder – has attractive properties that are not shared by any other equivalent circuit. Explicit, analytical expressions are derived for the efficient development of this ladder equivalent, which provide advantages compared to computer optimization. Although the context of this work is battery modeling, the results presented can be of value in other fields where diffusion is studied and modeled.

Modeling of Vibrating-Body Field-Effect Transistors Based on the Electromechanical Interactions Between the Gate and the Channel

A coupled analysis method for the mechanical and electrical systems of vibrating-body field-effect transistors (VB-FETs) is described. To accommodate energy transfer between the gate and the FET channel, we represent the FET with a resistance–capacitance ladder circuit and use the Lagrange function to derive motion equations. By solving the equations, we derive the typical electrical characteristics of VB-FETs, namely, the transconductance and the current gain. The results show that the current gain is obtained even above the cutoff frequency of the FET at the antiresonance frequency of the mechanical vibrator. These characteristics strongly depend on the device dimensions and operating conditions. This means that a coupled analysis is helpful for determining an appropriate design of VB-FETs.

Performance study of fractional order integrator using single-component fractional order element

A single-component fractional order element (FOE) is realised and its performance is compared with the conventional FOEs such as cross resistance-capacitance (RC) ladder network and domino ladder network in the analogue domain. The single-component FOE is a capacitive-type probe coated with a porous film of poly-methyl-methacrylate (PMMA) and is dipped in polarisable medium. The fractional exponent of the fabricated single-component FOE and domino ladder can be varied between 0 and 1 whereas that of cross RC ladder realised in this work is 1/2. The performance of fractional order integrator (FOI) using these FOEs is studied in both frequency and time domain by simulation and experimentation. A comparative analysis of the performance of FOI is carried out.

Sensitivity optimization of direct form realization of active-RC all-pole filters

In this paper, a procedure for direct form realization of Active-RC all-pole filters is presented. The filters are based on the resistance-capacitance ladder structure combined with the single operational amplifier and multiple feedback for complex pole realization. Recursive formulas have been developed that determine transfer function coefficients and derivation of transfer function coefficient with respect to filter components. These design equations are developed without knowing filter coefficients in terms of filter components in closed form, and they are necessary and sufficient for the filter design. Performance of these filters base been compared with the classical cascade form realization.

Low-sensitivity, low-power active-RC allpole filters using impedance tapering

A procedure for the design of allpole filters with low sensitivity to component tolerance is presented. The filters are based on resistance-capacitance (RC) ladder structures combined with single operational amplifiers. It is shown that by the use of impedance tapering, in which L-sections of the RC ladder are successively impedance-scaled upwards, from the driving source to the amplifier input, the sensitivity of the filter characteristics to component tolerances can be significantly decreased. Impedance tapering is achieved by the appropriate choice of component values. The design procedure, therefore, adds nothing to the cost of conventional circuits; component count and topology remain unchanged, whereas the component values selected for impedance tapering account for the considerable decrease in tolerance sensitivity.

Realizability constraints for third-order impedance-tapered allpole filters

It is shown that allpole filters of second- and third-order can be significantly desensitized to component tolerances by so-called impedance tapering, i.e., successively impedance-scaling upwards the L-sections of a resistance-capacitance ladder network in the forward and feedback path of a single-amplifier active filter. In order to obtain a realizable filter, certain constraints on the design equations must be observed. These constraints are derived here, and the resulting conditions necessary for the design of realizable third-order impedance tapered allpole filters are given.

Comments on "High-Q Resistance Capacitance Ladder Phase-Shift Networks" and "High-Q Bandpass and Band-Elimination Resistance-Capacitance Ladder Structures

Comments on "High-Q Resistance Capacitance Ladder Phase-Shift Networks" and "High-Q Bandpass and Band-Elimination Resistance-Capacitance Ladder Structures

Author's reply to Comments on 'High-Q Resistance Capacitance Ladder Phase-Shift Networks' and 'High-Q Bandpass and Band-Elimination Resistance-Capacitance Ladder Structures'

Author's reply to Comments on 'High-Q Resistance Capacitance Ladder Phase-Shift Networks' and 'High-Q Bandpass and Band-Elimination Resistance-Capacitance Ladder Structures'

High-Q Resistance-Capacitance Ladder Phase-Shift Networks

Resistance-capacitance ladder lowpass networks, to obtain a phase shift ( \phi ) of 180° between the input and the output, are examined. It is found that there exists a theoretical maximum value of Q , defined by \omega_0/2 |d\phi/d\omega| \omega = \omega_0 where \omega_0 is the frequency at which the phase shift is 180°. This theoretical limit can be approached in actual practice, but never reached. It is attempted to synthesize such networks having as high a Q as possible. In addition, the resulting network possesses the property that the open-circuit input impedance and the short-circuit output admittance are simultaneously maximized. A transformation enables one to get the corresponding highpass structure from the lowpass.

Terminal impedances and transfer functions of ladder networks

Concise mathematical formulas are developed for the input impedances, output impedances and transfer functions of ladder networks containing two kinds of elements only, namely resistance and capacitance or resistance and inductance or capacitance and inductance. A procedure is given for extending these formulas to the most general type of ladder network in which any series or shunt arm may contain all the three types of elements connected in any configuration. As examples of their application, the formulas are used to deduce the design equations of a phase-shift oscillator employing four- and five-section resistance-capacitance ladder networks.