LC Ladder Networks Research Articles

A proposal of short pulse generation using nonlinear LC ladder networks with amplifiers

A proposal of short pulse generation using nonlinear LC ladder networks with amplifiers

A proposal of short pulse generation using nonlinearLC ladder networks with amplifiers

Experimental investigations have been performed on the generation of short pulses using a 60-stage nonlinear LC ladder network with amplifiers to compensate for the network loss. The output amplitude and pulse width at stage 60 were measured to be 4.2 V and 144 ns, respectively, for a rectangular 250 ns input pulse of amplitude 3 V and 250 ns. The dependence of the output waveform on the bias voltage, input pulse width, and amplitude have also been investigated. © 1997 John Wiley & Sons, Inc. Microwave Opt Technol Lett 16: 154–156, 1997.

A proposal of short pulse generation using nonlinear LC ladder networks with amplifiers

A proposal of short pulse generation using nonlinear LC ladder networks with amplifiers

Determination of the impedance matching domain of passive LC ladder networks: Theory and implementation

Impedance matching domain problems of tunable matching networks are described in this paper. A method for determining matchable impedance regions of passive LC ladder networks with any component value ranges is proposed. Matching domains of the most popular II, T and L networks whose component value ranges are arbitrary are determined both analytically and graphically. Computer-aided domain plotting is discussed and various examples are presented. The applications of impedance matching domain problems are also analysed. In the Appendix general mathematical results of addition and inversion impedance transformations involved in the approach are formulated.

Formation of narrow pulses in a nonlinear lossy LC ladder network

We have analyzed the propagation of soliton in a nonlinear lossy LC ladder network by using a novel method called the Fourier Series Analysis Technique. Based on the measured C-V characteristic of the nonlinear capacitor used, we obtained a Korteweg-deVries (KdV) equation with a loss term. Experimental work has been carried out to investigate the effect of applying a DC bias voltage across the nonlinear capacitors on the pulsewidth and peak amplitude of the electrical pulse obtained along the network. A good agreement has been obtained between the theoretical and experimental results.

Narrow pulse formation using nonlinear LC ladder networks

Abstract Soliton propagation in a nonlinear lossy LC ladder network has been studied. We propose a quadratic polynomial expression to model the C-V characteristic of the nonlinear capacitor of the LC ladder network. This fits the experimental C-V data better over a wider range of the applied voltage, compared with the conventionally used formulae. Using this C-V expression, the Korteweg-de Vries (KdV) equation with a loss term has been obtained. This nonlinear equation has been solved by employing a novel technique that is based on Fourier series analysis. We have investigated the effects of bias voltage on the soliton pulse width and peak voltage and found a good agreement between the theoretical and experimental results.

Improved LDI digital filters derived from analog LC ladder filters

Lossless discrete integrator (LDI) digital filters derived from analog LC ladder filters are known to possess low sensitivities of the passband gain with respect to quantizations of the multiplier coefficients. However, previously reported LDI digital filter structures do not generally retain the desired one-to-one correspondence between the LDI digital ladder filter and the original LC analog ladder filter after quantizations of the multiplier coefficients are taken into account. This leads to increased transfer function sensitivities of the LDI digital filter, relative to that of the original LC analog filter. In this paper, it is shown that classical equivalent transformations of the LC ladder network can be used to obtain new LDI ladder structures that do retain (even after coefficient quantizations) the one-to-one correspondence with the LC ladder filter, leading to LDI digital filters having improved performance under coefficient quantizations. These equivalent network transformations also facilitate the design of different types of LDI ladder filters. The obtained LDI filters are suitable for VLSI implementation on a single chip FPGA using one multiplier.

Soliton formation in a nonlinear lossy lc ladder network with quadratic polynomial expression for the c‐v characteristic of the network capacitors

AbstractWe propose a quadratic polynomial expression for the C‐V characteristic of the nonlinear capacitor of the LC ladder network and investigate the soliton propagation in such networks using a modified Korteweg‐de Vries (MKdV) equation. The MKdV equation has been solved by a novel technique which is based on the Fourier‐series analysis. Our theoretical results are in good agreement with experiment. © 1994 John Wiley & Sons, Inc.

Construction of arbitrary transfer functions with complex coefficients using wave digital filters

AbstractThis paper proposes an extension of the real‐coefficient wave digital filter by Fettweis et al. (WDF) to the complex‐coefficient WDF (CWDF) as well as a construction method to realize an arbitrary complex‐coefficient transfer function.The first step of the proposed construction method is to synthesize the lossless reactance circuit containing the imaginary resistors (except for the input terminal) as an analog reference circuit by the continued‐fraction expansion.In this study, the LC ladder network containing imaginary resistors is synthesized as the reference network, realizing the denominator polynomial of the transfer function. Then the state‐variable representation is constructed and the numerator polynomial is realized by determining the tap coefficients to the external output, using the transform matrix.In this process, the reference network is transformed into WCDF, and the tap is formed considering the relation between incident/reflected waves and the terminal voltages. By this procedure, the required transfer function can be realized. Finally, the proposed method is compared to other construction methods and the low‐sensitivity property of the proposed method is demonstrated.

Pulse sharpening in a uniform LC ladder network containing nonlinear ferroelectric capacitors

A new method of pulse sharpening is described in which the risetime of a high-voltage pulse is progressively reduced as it propagates along a uniform lumped-element delay line containing nonlinear ferroelectric capacitors. The capacitors are made from a barium-titanate-based ceramic dielectric whose relative permittivity reduces with applied voltage stress. The resultant drop in capacitance causes the phase velocity of an electrical pulse propagating on the delay line to increase with increasing pulse amplitude. Therefore, the time delay of each section of the line is also amplitude dependent, causing the crest of the pulse to catch up with the low-amplitude portion of its leading edge. In the experiment described, the risetime of the leading edge of a 28-kV voltage pulse was reduced from 280 to 50 ns as it propagated along a 15-section ladder network. It is found that the impedance of the ladder is amplitude dependent, and the problem of matching the line with a nonreactive linear load resistance is discussed. Techniques are described for characterizing the nonlinearity of the capacitors and also for measuring their loss.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

SC simulators of passive two-ports

Abstract A method for synthesizing switched capacitor circuits that simulate passive LC ladder networks is proposed. The circuits are developed by cascading lower order SC active subnetworks which serve the purpose of two port simulators. Experimental results from two circuits that are proposed as examples, are also given.

Generalized ladder synthesis by subnetwork removal

AbstractA general procedure is presented to realize a two‐port impedance matrix by a generalized transformerless LC ladder network including the classical LC ladder structure as a special case. the realization process consists of repeatedly applying a subnetwork removal cycle for which six different cases are to be considered. the feasibility of the various subnetwork removals is characterized by formulating necessary and sufficient conditions on the impedance matrix. the application of the procedure is illustrated by a numerical example.

Linear Phase Emphasis Networks with Gaussian Function

In this paper, a new approach to the practical design and realization methods of linear phase emphasis network, which is applicable to the FM transmission system, is introduced. The methods are based on employing the Gaussian function expressed as a real exponential function exp(P2) realized by the squared amplitude response of a specific two-port passive LC ladder network. They are also based on a time base conversion technique using digital technology which provides a zero phase network.

Linear Phase Networks With Hyperbolic Tangent Function and Their Applications

This paper describes several methods to realize passive and active networks. with linear phase frequency response applicable to the video signal processing circuit especially for the FM transmission system. The methods are based on employing the hyperbolic tangent function realized by using passive LC ladder networks. They are also based on a time base conversion technique which provides the zero phase network. Using these methods, video signal processing circuits with linear phase property such as pre-emphasis and de-emphasis networks for the FM transmission TV system are introduced.

Eigenvalues of LC ladder networks

The system matrix of a resistance-terminated LC ladder network can be derived directly from the scattering-parameter formulation as well as from the wave-chain matrix technique. The two resulting matrices are different in form but have the same eigenvalues, and are thus related by similarity transformations.

On the Synthesis of Resistively Double-Terminated LC Ladder Networks

Resistively double-terminated LC ladder network can be made inherently insensitive to variations of its elements. This article presents a method for the synthesis which, unlike the two existing techniques, does not require the determination of roots of polynomials. Thus, the procedures of calculation are less involved. An example is given.

Numerical algorithm for pole-sensitivity study of LC ladder networks

Pole displacements of LC ladder networks due to parameter variations can be easily and accurately determined by a conceptually simple and computationally efficient algorithm together with the system matrix. The derivation of the algorithm is based on the wave-chain technique. The results will be of interest to sensitivity and optimisation studies of network design problems.

Wave digital filters for second and fourth order basic reactance sections

AbstractOne way to realize a low coefficient sensitivity digital filter is to simulate a resistively terminated LC ladder network. This is called a wave digital filter. However, the transfer functions realized with a resistively terminated LC ladder network are limited. A resistively terminated reactance network realizing an arbitrary transfer function may be synthesized by cascading basic reactance sections. In this paper, we use Brune, Types C, E and D sections with 2‐wire lines as the models for the basic reactance section. These basic sections are represented using modal decomposition by equivalent circuits made of ideal transforming networks (including gyrators for nonreciprocal circuits) and uncoupled lossless lines. Then we derive basic wave digital filters of reciprocal and nonreciprocal second‐order sections and reciprocal fourth‐order sections. the digital filters realized from the basic wave digital filters in the present method do not correspond exactly to the original analog circuit as long as they are constructed with multipliers with finite word length; however, they become low coefficient sensitivity digital filters with as good performance as the wave digital ladder filters.

The analytical transfer functions of wave-digital filters derived from LC ladder prototypes

Based on the wave-chain matrix technique, the paper presents some computationally efficient algorithms for obtaining the polynomial coefficients of the various analytical transfer functions of a class of wave-digital filters derived from the resistance-terminated lossless LC ladder networks, given all the multiplier coefficients. It also describes the numerical methods for computing the multiplier coefficients from the component values of the associated reference filters. The applications of the algorithms in the studies of wave-digital filters are briefly discussed.

Pole sensitivity of all-pole lowpass LC ladder networks

By simple manipulation of the sensitivity relationships for all-pole lowpass LC ladder networks, it is shown that results may be obtained for the sum of pole sensitivities with respect to any inductive or capacitive component. These results are of interest in sensitivity and optimisation studies of these structures.