A Frequency Transformation for Commensurate Transmission-Line Networks

The frequency transformation W=1/S, where S= tanh(/spl gamma/L), is investigated for commensurate transmission-line networks consisting of stubs, resistors, ideal transformers, and unit elements. This transformation takes transmission-line transformers into transmission-line lowpass filters and vice versa, Iowpass (or bandstop) filters into highpass (or band-pass) filters and vice versa, and elliptic-function bandstop filters into elliptic-function bandpass filters and vice versa. The practicality of the transformation lies in the fact that element values of the transformed network are easily related to the corresponding element values of the original network. The transformation is useful because it provides an alternative viewpoint for synthesis, and because it reduces the number of tables of designs needed for various filter types. Several examples of designs using the transformation are given. One design is an unusual narrowband 3-dB directional coupler.     

Synthesis of Cascaded Lossless Commensurate Lines

A scattering transfer matrix factorization based algorithm for cascaded lossless commensurate line synthesis is presented. The characteristic impedances of the extracted commensurate lines and the reflection factors of the remaining networks are formulated in terms of reflection factor coefficients of the whole circuit. There is no need to use root search routines so as to cancel common terms, to get degree reduction. The formulation of the method is explained, and an example is included, to illustrate the implementation of the synthesis algorithm.     

Design of Commensurate Transmission-Line Circuits

Digital computer techniques are developed for the approximation of the periodic frequency characteristics of commensurate transmission-line circuits. For a given periodic delay or loss-derivative function the system function is derived automatically rising a direct method. Any suitable synthesis program will complete the design.     

On Some Integral Relationships for Commensurate Transmission-Line Networks (Short Papers)

Several integral relationships are presented for commensurate transmission-line networks. The integrals focus on the fact that Z(1) for such networks, where Z(S) is the input immittance of the network, is associated with a real or redundant unit element prefacing the network. Three bandwidth restrictions are derived. Some applications of the integral relationships are presented.     

Simplified Analysis of Coupled Transmission-Line Networks

A relatively simple method is presented for analyzing coupled transmission-line networks by using network graphs and graph transformations. The network graph symbolism is easy to draw and to manipulate. All the graphs consist only of inductor, capacitor, and transformer symbols, and straight lines, which represent unit elements. The method of analysis is illustrated by several two-wire-line and multiwire-line examples. Also presented are several new useful transmission-line transformations and a graph equivalent for the general coupled transmission-line network. The graph-transformation method has four principal advantages: 1) explicit open-wire-line equivalent circuits of coupled line networks can be obtained relatively easily and without knowledge of network synthesis techniques; 2) the form of equivalent circuits can often be obtained without using any algebra; 3) at each step of the analysis, a positive-real network in graph form is available; consequently, in many analysis problems several equivalent circuits for the same network are derived; and 4) multiport networks are as easily dealt with as two-port networks.     

Analysis of Certain Transmission-Line Networks in the Time Domain

Many linear components in nondispersive transmission line are made up solely of commensurate lengths of line of various characteristic impedances. Such components have impulse responses that are a series of equispaced impulses, and, as a result, their frequency responses can be written as a Fourier series. Given the period and coefficients of the Fourier series describing the frequency response, the time response of the circuit to any pulse can be written down immediately as a sum of replicas of the applied pulse, each replica having an amplitude given by the coefficient of a term in the series, and occurring at a time determined by the period of that term of the series. The pulse responses of stepped transmission-line transformers, backward-coupling hybrids, and branch-line hybrids are determined and, after assuming a simple applied-pulse shape, are plotted.     

Computer-Aided Analysis and Design of Networks Containing Commensurate and Noncommensurate Delay Lines

Several computer programs are described for the analysis and synthesis of networks containing transmision lines, lumped resistors, voltage sources and current sources. There are no restrictions on the topology of the networks and degenerate elements can also be included. In the noncommensurate case the transmission lines could have different delays and thus the degree of freedom for each network is doubled. State-space techniques are used to formulate the solution to the problem and the high degree of generality was achieved by using topological methods to derive the state equations. Several examples are given.     

Analysis and Sensitivity Evaluation of 2p-Port Cascaded Networks

An exact analysis approach for efficiently evaluating the response and its sensitivities with respect to all design parameters for cascaded 2p-port networks is presented for any value of p. It is illustrated via a quasi-optical bandpass filter.     

The Synthesis of Coupled Transmission Line All-Pass Networks in Cascades of 1 to n

A homogeneous coupled line configuration realizing the characteristics of an all-pass network in the distributed network sense is useful for delay equalization in the UHF range. All-pass networks of first and second order are presented, while nth-order networks may be realized directly or built out of first- and second-order networks, analogous to the lumped-constant element network technique.     

Normal Transmission-Line Networks and Their Lumped LC Presentation

A previous result is extended and a new presentation is described for Richards' transmission-line (TL) networks. The new presentation is in a lumped LC form; therefore, classical analysis and synthesis techniques are directly applicable. The class of networks for which this presentation is possible is studied in detail. This class of networks, called normal TL networks, is found to be a necessary and sufficient condition for driving-point immittance functions to be rational positive real functions of /spl lambda/ =tanh /spl tau//spl rho/. The effectiveness of this representation is further demonstrated by applying it to graph-transformation analysis method. It simplifies the procedure considerably and reveals additional physical insight into the TL network.     

Exact Simulation and Sensitivity Analysis of Multiplexing Networks

This paper presents a novel approach to the simulation and sensitivity analysis of multiplexing networks. All computations are performed efficiently utilizing the concept of forward and reverse analysis which is elegant and effective in cascaded circuit analysis. Formulas are derived for such responses as input or output reflection coefficient, common port and channel output port return losses, insertion loss, gain slope, and group delay. Exact sensitivities w.r.t. all variables of interest, including frequency, are evaluated. The fundamental assumption is that the transmission matrices for the individual components of the network and their sensitivities w.r.t. possible variables inside them are available. An explicit algorithm is provided describing the details of the computational aspects of our theory. The formulas are applied to the optimal design of practical contiguous or noncontiguous band multiplexer consisting of multicavity filters distributed along a waveguide manifold. An example of optimizing a practical 12 channel, 12-GHz contiguous band multiplexer without dummy channels, which is the state-of-the-art structure used as the output multiplexer in satellite transponders, is presented.     

Design of Transmission-Line Reactance Networks for Equalizer Applications

Synthesis techniques are presented for realizing arbitrary transmission-line reactance functions in four common forms of arrays of coupled lines, together with minor variations of these forms. These are two types of interdigital lines and dual forms of half-wave parallel-coupled lines. Design examples are presented for each form of coupled-line network and variations. Although the synthesis procedures are developed from the point of view of applications to equalizers, the procedures are completely general.     

Exact Delay Analysis of Packet-Switching Concentrating Networks

We present an exact delay analysis for a packet-switching concentrating system consisting of an arbitrary number of active stations connected in tandem by unidirectional, asynchronous transmission lines, all with identical transmission rate. Packetized messages from exogenous sources enter the system at every station, are handled from station to station in a store-and-forward fashion, and exit at the downstream end; there are no intermediate departures. The service discipline at each station is either FCFS, fixed priority, or alternating priority, the transmission of a packet is not interrupted while in progress. We assume that the packets have identical length (in bits), that the sources are independent and that each source generates batch Poisson traffic. The FCFS case was solved by Kaplan [7] and Shalmon and Kaplan [19]. Here we analyze the priority disciplines. For the packets and messages from each source, we obtain the steady-state moment generating functions for their end-to-end waiting times. We offer simple formulas for the corresponding mean waiting times, and show that the Poisson approximation for departures is unreliable. The analysis for all three disciplines generalizes to the case where the line capacities are nonincreasing in the direction of the flow, and for the priority disciplines, it further generalizes to a concentrating tree network, and to an arrival process somewhat more general than batch Poisson.     

Gain-Bandwidth Limitations and Synthesis of Single-Stub Bandpass Transmission-Line Structures

Gain-bandwidth limitations and synthesis of a class of bandpass transmission-line structures with a single shunted stub and n cascaded commensurate lines are presented in this paper. With a shunt shorted stub as the reactive constraint, the optimum gain bandwidth is derived for an ideal bandpass gain characteristic. Explicit gain-bandwidth and synthesis results have been obtained for the class of single-stub cascaded line structures with one and two cascaded lines for both maximally flat and Chebyshev characteristics. For the general case of n cascaded lines approximate gain-bandwidth limitations have also been derived. The explicit results including gain-bandwidth limitations and element values can be used for the design of this class of bandpass transmission-line networks for broad-band matching of the reactive constraint as well as impedance transformation.     

波分复用环网中带内串扰的精确分析

分析了波分复用 (WDM)全光通信环网中的串扰起因 ,指出单纤 WDM环网中的串扰分析可以简化为单一串扰源的情况。接着从接收机检测光电流的概率分布函数出发 ,给出了单一串扰源的精确误码率表达式 ,串扰功率代价的分析结果与实验测量非常吻合。     

Analysis and Design Procedure of Transmission-Line Transformers

Transmission-line transformers are devices used to match RF and microwave devices, to make the conversion balanced-unbalanced, or both things simultaneously. Transmission-line transformers are mandatory at frequencies where traditional magnetic coupling transformers do not operate properly. In this paper, a procedure to design transmission-line transformers with different configurations is presented. The procedure is based on the theoretical analysis of the device and has been validated via experimental study.     

Synthesis of Even-Order Equally Terminated Transmission-Line Bandstop Filters

An exact synthesis procedure for the design of even-order equally terminated transmission-line bandstop filters is described. The method is optimum in the sense that it does not introduce redundant unit elements into the network. The final network is obtained in the form of a cascade of unit elements and shunt open-circuited stubs.