Lossless One-port Research Articles

Principles of Lossless Adjustable One-Ports

This paper explores the possibility of constructing two-terminal mechanical devices (one-ports) which are lossless and adjustable. To be lossless, the device must be passive (i.e., not requiring a power supply) and nondissipative. To be adjustable, a parameter of the device should be freely variable in real time as a control input. For the simplest lossless one-ports, the spring and inerter, the question is whether the stiffness and inertance may be varied freely in a lossless manner. We will show that the typical laws which have been proposed for adjustable springs and inerters are necessarily active, and that it is not straightforward to modify them to achieve losslessness, or indeed, passivity. By means of a physical construction using a lever with moveable fulcrum, we will derive device laws for adjustable springs and inerters which satisfy a formal definition of losslessness. We further provide a construction method which does not require a power supply for physically realizable translational and rotary springs and inerters. The analogous questions for lossless adjustable electrical devices are examined.

Modelling of 2-D Real Rational Reactance Functions. A Parameter-Based Approach

Summary Lossless (reactive) one-ports are of great importance in the field of linear network theory. This statement also applies for the two-dimensional (2-D) case, where the design of corresponding impedance or admittance functions is a much more challenging task. In this paper a model for 2-D real rational reactance functions is introduced which is a rational function in p 1 and p 2 where the coefficients are functions of parameters. The following features make it best suited for the computer based design of lossless one-ports, namely no dependencies between the real valued parameters, coverage of the whole class of 2-D real rational reactance functions, and the coefficients are polynomials in the parameters. The synthesis of 2-D lossless networks and skew symmetric matrices form the basis of our considerations.

Relationship between group delay and stored energy in microwave filters

In this paper, an expression for the time average stored energy (t.a.s.e.) in a passive lossless two-port is derived in terms of its scattering parameters. In particular, it is shown that the t.a.s.e. in a passive lossless reciprocal symmetrical or antimetrical two-port is proportional to the group delay. One implication of this result is that the t.a.s.e., which is linked to the power-handling capability in many passive filters used in practice, is proportional to the group delay of the filter. This rigorous derivation is based on a variational theorem, which has been used in the past to prove energy storage results for passive lossless one-ports and periodic two-ports.

A parametric representation for k-variable Schur polynomials

A parametric representation for k-variable polynomials with prescribed partial degrees is given, where the coefficients are functions of real parameter vectors. For these parameters, simple conditions which are sufficient to guarantee that the corresponding polynomials are widest-sense Schur are established. Simple necessary and sufficient conditions are introduced in the two-variable case so that the corresponding polynomials are scattering Schur. The synthesis of two-dimensional lossless one-ports and a parametric representation of constant unitary matrices form the basis of these considerations. >

Generalized Chebyshev band-pass prototype filters

Band-pass prototype filters are presented having an equiripple passband with single transmission zero at the origin, an odd number of transmission zeros at infinity and a multiple even number at a finite real frequency in one of the stopbands near the corresponding band edge. These prototypes can be easily and accurately synthesized using the alternating pole technique. The application of the alternating pole technique leads to the construction of a reactance (admittance) function. Thus the synthesis of a doubly terminated prototype network is reduced to the synthesis of a lossless one-port network of much lower degree with very little loss of accuracy.

Canonic structures for lossless one-ports

Necessary and sufficient topological conditions for a lossless 1-port to be canonic have been discovered and proved. All the currently known canonic structures, comprising the classical Foster and Cauer forms and the five more recently discovered networks, are special cases of the general class of canonic 1-ports described here.

On the canonic cascade synthesis for lossless one-ports

The problem of finding all possible canonic cascade syntheses for lossless one-ports Is considered. Without being able to solve it in general, the following steps in this direction are presented. For the purpose of a systematic search for canonic LC -cells a topological criterion is given which eliminates all nonminimal LC -cells, i.e. those with more elements than is their degree. Another topological criterion serves to detect a large number of minimal LC -cells that are not canonic. On the other hand, in order to prove an LC -cell to be canonic the synthesis problem is divided into a linear and a nonlinear part. A bridged T of degree 4 serves as an example to show how to prove the existence of a solution for the nonlinear equations and how to generate from it a canonic synthesis, using theorems about the linear part. Some of the material is new, some can be found piecewise elsewhere but is reproduced and adapted here for the sake of a unified and coherent presentation. In particular, apart from the bridged T already mentioned, seven different new nontrivial canonic LC -cells are listed.

Single-transistor all-pass networks

A network configuration consisting of a resistive twoport bridged by a lossless one-port is considered. It is shown that in certain cases this configuration is capable of realizing a voltage transfer function equal to that of a constant-resistance passive lattice. As a special case, conditions are derived on the two-port parameters for the structure to be all pass. It is determined that a single transistor suffices to realize the two-port network, thus resulting in a very simple all-pass structure; only one coil, one capacitor, and one transistor are necessary to realize a second-degree all-pass voltage transfer function. Higher order transfer functions can be realized by adding an <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">LC</tex> branch per each additional second-order factor to the same transistor circuit. In the second-order case, losses in the coil can be compensated. In higher order realizations coil losses cannot be compensated, but a design technique which achieves an arbitrarily close approximation to the desired all-pass transfer-function is presented. Methods of cascading lower order sections are discussed and experimental results are given.

Realisation of an open circuit as a lossless one-port

In signal processing, a network having no loss and no gain is often required to avoid attenuation of the signal below a given threshold value, and also to prevent overloading of following stages. A very broadband 1-port network is described, and it is hoped that the technique employed may be applied to 2-port networks after further research.

The Physical Meaning of Compactness

A lossless twoport N, whose impedances z_{11}, z_{12} , and z_{22} possess poles at the complex frequencies s = \pm j\omega_p , is considered. It is shown that the algebraic alternatives of compactness, or lack of compactness, for the z_{ij} at s = \pm j\omega_p correspond directly to the physical alternatives of whether or not a pair of N's natural oscillations at the frequency \omega = \omega_p are scaled replicas of one another throughout N. A secondary result of the paper is called the Energy Theorem. This theorem assumes that the natural oscillations of a lossless oneport have been excited by a unit impulse of current, and states that each impedance residue of the oneport is proportional to the energy stored in the corresponding one of these oscillations.