126319448
IDENTIFICATION OF EQUIVALENT CIRCUIT BASED ON POLYGON NETWORK FOR NONRECIPROCAL LOSSY N-PORT DEVICE
In this paper, a technique to identify/synthesize an equivalent circuit of nonreciprocal lossy N -port device is presented. The technique joins the classical procedure discussed in the ’60s to the polygon network recently proposed in the literature, which permits to draw an equivalent circuit for reciprocal lossless N -port device in a very simple way. The identification is applied to two microwave devices, a reciprocal lossy iris in WR90 waveguide and a 3-port nonreciprocal lossy circulator. The proposed equivalent circuit could give some information about the agreement of the manufactured device and its design, which usually is developed in the hypothesis of ideal lossless components.
106526329
Principles of Microwave Circuits
* Chapter 1: Introduction * Chapter 2: Electromagnetic waves * Chapter 3: Waveguides as transmission lines * Chapter 4: Elements of network theory * Chapter 5: General microwave circuit theorems * Chapter 6: Waveguide circuit elements * Chapter 7: Resonant cavities as microwave circuit elements * Chapter 8: Radial transmission lines * Chapter 9: Waveguide junctions with several arms * Chapter 10: Mode transformations * Chapter 11: Dielectrics in waveguides * Chapter 12: The symmetry of waveguide junctions
51630730
On the Physical Realizability of Linear Non-Reciprocal Networks
The necessary and sufficient conditions are given that a matrix with arbitrary complex number elements be the impedance, admittance or scattering matrix of a physical linear reciprocal or non-reciprocal network. A canonical form for non-reciprocal network synthesis is presented which applies to any linear n-terminal pair (n-port) system at any fixed frequency. If the network is passive the only circuit element required in addition to lossless inductors, capacitors, transformers and positive resistors is the gyrator. If the network is active, negative resistors and gyrators must be used in addition to conventional passive elements. Some discussion of matrixes with frequency variable elements is also given.
110338667
The Scattering Matrix in Network Theory
This paper gives an introductory treatment of the concept and uses of scattering methods in network problems. The scattering parameter description for linear networks is defined and the utility of this formalism for problems involving power flow in terminated networks is discussed. Examples of scattering computations for transformer 4-ports, transformerless impedance matching networks and transducers with parasitic capacitance are given. The physical realizability requirements for linear lumped networks in the frequency domain are presented in scattering terms, and some extensions to the realizability of distributed networks are briefly discussed.
51645998
Network Synthesis with Negative Resistors
The development of new solid-state active elements, such as variable-capacitor diodes and tunnel diodes, has stimulated the network theorist to consider the negative resistor as an additional basic circuit element to be included in problems of linear network analysis and synthesis. In this paper it is first shown that if the negative resistor is added to the usual set of lumped passive building blocks, then it is possible to represent as a network any linear relation between n-port voltages and currents prescribed in terms of real, rational functions of a complex-frequency variable. This leads to the synthesis of some novel pathologic circuits which have neither immittance nor scattering representations, such as a one-port, which is simultaneously an open circuit and a short circuit (v=i=0, the "nullator"), and the linear network in which voltages and currents at the ports are completely arbitrary (the "norator," the unique, linear nonreciprocal, one-port). These elements are shown to be basic linear circuit building blocks. The second part of the paper considers the synthesis in the frequency domain of a real, rational n×n immitance matrix in which pole locations and pole multiplicities are completely arbitrary. It is shown that such a matrix can always be realized with lossless elements and at most n positive and n negative resistors.
110536631
Application of Scattering Matrices to the Synthesis of n Ports
Scattering matrices are applied to the synthesis of finite passive n -ports ( n -terminal pair networks) with frequency dependence. A realizability theorem for scattering matrices is shown and an n -port is synthesized as a nondissipative network terminated in resistances. By considering the various numbers of resistance terminations and introducing the notion of generalized minimum phase shift, the relation among all the equivalent networks with a prescribed scattering matrix is studied. Reciprocal or nonreciprocal networks containing the minimum number of reactances or the minimum number of reactances and resistances are generally treated.
122759408
Bounded Real Scattering Matrices and the Foundations of Linear Passive Network Theory
In this paper the most general linear, passive, time-invariant n -port (e.g., networks which may be both distributed and non-reciprocal) is studied from an axiomatic point of view, and a completely rigorous theory is constructed by the systematic use of theorems of Bochner and Wiener. An n -port \Phi is defined to be an operator in H_n , the space of all n -vectors whose components are measurable functions of a real variable t, (- \infty (and as such need not be single-valued). Under very weak conditions on the domain of \Phi , it is shown that linearity and passivity imply causality. In every case, \Phi_a , the n -port corresponding to \phi augmented by n series resistors is always causal ( \Phi is the "augmented network," Fig. 2). Under the further assumptions that the domain of \Phi_a is dense in Hilbert space and \phi is time-invariant, it is proved that \Phi possesses a frequency response and defines an n \times n matrix S(z) (the scattering matrix) of a complex variable z = \omega + i\beta with the following properties: 1) S(z) is analytic in Im z > 0 ; 2) Q(z) = I_n - S^{\ast}(z)S(z) is the matrix of a non-negative quadratic form for all z in the strict upper half-plane and almost all \omega . Conversely, it is also established that any such matrix represents the scattering description of a linear, passive, time-invariant n -port \Phi such that the domain of \Phi_a contains all of Hilbert space. Such matrices are termed "bounded real scattering matrices" and are a generalization of the familiar positive-real immittance matrices. When \Phi and \Phi^{-1} are single-valued, it is possible to define two auxiliary positive-real matrices Y(z) and Z(z) , the admittance and impedance matrices of \Phi , respectively, which either exist for all z in Im z > 0 and almost all \omega or nowhere. The necessary and sufficient conditions for an m>n \times n matrix A_{n}(z) to represent either the scattering or immittance description of a linear, passive, time-invariant n -port \Phi are derived in terms of the real frequency behavior of A_{n}(\omega) . Necessary and sufficient conditions for \Phi_a to admit the representation i(t) = \int_{-\infty}^{\infty} dW_{n}(\tau)e(t - {\tau}) for all integrable e(t) in its domain are given in terms of S(z) . The last section concludes with a discussion concerning the nature of the singularities of S(z) and the possible extension of the theory to active networks.
111028198
Direct Single Frequency Synthesis from a Prescribed Scattering Matrix
This paper presents two techniques for synthesizing an n-port (at a single frequency) directly from its normalized scattering matrix without recourse to its associated impedance matrix. Both methods depend on standard matrix canonic forms. In the first one, all the loss is extracted immediately in the form of n resistors and the problem is reduced to the synthesis of a lossless 2n-port. The second makes use of the Jordan decomposition of a matrix and leads to a hybrid mixture of ideal transformers, reactances, gyrators and resistors. The only elements required for a complete synthesis are ideal transformers, lossless capacitors, inductors, and gyrators, and positive and negative resistors. It is shown that synthesis from a prescribed scattering matrix requires, in general, irrational operations (computation of eigenvectors, eigenvalues, etc.) whereas synthesis from a prescribed impedance matrix (if it exists) can be achieved with rational operations alone.
10489773
Simple, Fast, and Effective Identification of an Equivalent Circuit of a Waveguide Junction With $N$ Ports
A simple, drawable, and efficient equivalent circuit is proposed to represent a discontinuity/junction with N ports. The circuit is based on N transmission lines connected to the sides of a polygon with N side. N( N-1)/2 susceptances are placed on the sides and on the inner diagonals of the polygon. The circuit modularity permits to identify the N( N+1)/2 electrical parameters in a simple way. In fact, the lengths of the N transmission lines are obtained solving a system of N polynomial equations and the N( N-1)/2 susceptances are obtained solving a simple linear equation system. The proposed circuit is used to evaluate the equivalent circuit of some directional couplers in the horizontal plane and of a 3-D six-port coupler acting on the horizontal and vertical planes.
6367908
An Equivalent Circuit for Discontinuities Exciting Evanescent Accessible Modes
An equivalent circuit for discontinuities exciting evanescent accessible modes is proposed. The key feature of this equivalent circuit is its capability for simplification if a port relative to an accessible evanescent mode is matched, or connected to a very long line. Circuit drawing is simple, fast, and based on a regular polygon with as many susceptances as the sides and diagonals. Each side is connected with a line of electrical length θk to the terminal ports, and if the port refers to an evanescent accessible mode, a series reactance is added. This reactance is the key to the evanescent part of the circuit because it is able to cancel the effect of the evanescent mode if the relative port is matched or connected to a very long evanescent line, reducing the complexity of the circuit by one degree. With the help of the proposed equivalent circuit, we can define some approximating functions for the elements of a circuit representing a post in a waveguide, which can be used to speed up the optimization of complex structures, like filters or diplexers, based on posts.
17499190
Circuit Approach to the Analysis of Microwave Discontinuities
Abstract—An equivalent circuit based on propagating and evanescent accessible modes is discussed and the numerical values of its elements (susceptances and electrical length) are obtained starting from the knowledge of the generalized scattering matrix S of microwave discontinuities. A database of the circuit elements is then defined in the frequency and geometric ranges of the analyzed discontinuities and is used to evaluate the generalized scattering matrix for values not contained in the database, with very simple formulas for any number of circuit ports. The obtained S matrices can be used to analyze very complex structures such as iris-based filters and manifold filters.
16609246
An equivalent circuit for thick centered irises in rectangular waveguide
An equivalent circuit for thick centered irises in rectangular waveguide, exciting evanescent accessible modes, is proposed. Starting from the numerical evaluation of the scattering matrix of the iris, we can define some approximating functions for the elements of the circuit representing the iris, which can be used to speed up the optimization of complex structures, like filters or diplexers, based on irises.
55080300
Reconstruction of the S-Matrix of n-Port Waveguide Reciprocal Devices from 2-Port VNA Measurements
Two approaches to reconstruct the S-matrix of N -port waveguide reciprocal devices from 2-port S-matrix measurements are proposed and discussed. The main advantage of the proposed approaches is that measurements are done always at the same two ports, without moving the device. The remaining N -2 ports are loaded with different loads, either matched or short. The first approach, based on a manipulation of the 2-port S-matrices, requires N -2 matched and two other loads, while the second approach, based on the evaluation of an equivalent circuit, requires N -2 short and two other loads. The measurement technique is based on standard loads (short, shift and matched) in the waveguide calibration kit of the 2-port VNA.