Brune Sections Research Articles

Design of multiband matching ladders without mutual coupling using parametric representation of Brune functions

In this study, a semianalytical method for the design of mutual coupling free multiband matching networks is introduced. A new parametric representation of Brune functions is used for the construction of multiband ladder network topologies without mutual induction. The method involves the use of Fujisawa's constraints for low pass ladders having finite transmission zeros, in a parametric representation of driving point impedance function resulting in mutual inductance free Brune sections. The developed parametric representation is incorporated with Real Frequency Techniques to design matching networks with a plurality of pass bands. Several illustrative design examples are presented to validate the method.

Brune sections in the non-stationary case

Rational J-inner-valued functions which are J-inner with respect to the unit circle ( J being a matrix which is both self-adjoint and unitary) play an important role in interpolation theory and are extensively utilized in signal processing for filtering purposes and in control for minimal sensitivity ( H ∞ feedback). Any such function is a product of three kinds of elementary factors, each of them having a unique singularity outside the unit disk, inside the unit disk and on the unit circle, respectively. Counterparts of the first kind have already been studied in the context of non-stationary systems, when analytic functions are replaced by upper triangular operators. The purpose of the present work is to study the non-stationary analogues of the factors of the third kind. One main difficulty is that one leaves the realm of bounded upper triangular operators and considers unbounded operators. Yet, as is the case for a number of special clases of non-stationary systems, all the systems under consideration are finitely specified, and the computations are done recursively on a finite set of state space data. We consider the particular case, where the operator given is of the IVI type (that is, it is time-invariant both for small and large indices, and is time-varying in between). The theory results in a rather general factorization theorem that generalizes the time-invariant case to finitely specified, time-varying systems.

Synthesis of lossy reflection-mode prototype networks with symmetrical and asymmetrical characteristics

A modified synthesis procedure for lossy reflection-mode prototype networks is presented. The resultant one-port filters are composed of a cascade of Brune or Triplet sections realising symmetrical and asymmetrical transfer functions, respectively. The Brune sections of symmetrical reflection functions have progressively decreasing resonator Q and the prototypes are suitable for dual-mode realisation. Tables of element values are provided for elliptic function filters up to degree six. Numerical examples are also presented for both types of transfer function.

On a generalization of the Szego-Levinson recurrence and its application in lossless inverse scattering

Predictor polynomials corresponding to nested Toeplitz matrices are known to be connected by the Szego-Levinson recurrence relation. A generalization of that result, where the relevant reduction process for Toeplitz matrices (of decreasing order) is defined by an elementary one-parameter linear transformation, is addressed. The descending and ascending versions of the corresponding generalized Szego-Levinson recurrence relations are discussed in detail. In particular, these relations are shown to be essentially the same as the extraction formulas for canonical Schur and Brune sections in the Dewilde-Dym (1984) recursive solution of the lossless inverse scattering problem. Some extensions of the Levinson algorithm for linear prediction and of the Schur-Cohn algorithm for polynomial stability test are presented. >

Design of switched-capacitor and wave digital filters with linear phase and high amplitude selectivity

A design technique, and the associated algorithm, are presented for selective linear-phase low-pass and high-pass sampled data filters. The resulting filter transfer functions are particularly suitable for realization as leap-frog lossless discrete integrator (LDI) switched-capacitor structures and also in wave digital form. Due to the specific form of the transfer function, the filters generally have no lumped-element counterparts. The technique leads to an optimum compromise between amplitude selectively and passband phase linearity under the restriction of a prescribed form of the transfer function, and allows the use of finite j omega -axis zeros of transmission for achieving high amplitude selectivity. The transfer functions presented are also capable of realization as distributed microwave filters, but these require the use of coupled-wire networks in the form of distributed Brune sections, if j omega -axis zeros of transmission are introduced. >

Generalised lattice transformation for crystal filters

Crystal lattice filters are usually based on the transformation of a lowpass Brune section to a second-order lattice section. This letter describes a generalisation, which transforms n Brune sections simultaneously into a lattice of order 2n, and which offers advantages for high-order filters, or filters with complex transmission zeros.

On the Transformerless Synthesis of Reactance Two-Ports of Degree Four or Less

This paper deals with the transformerless synthesis of reactive immittance matrices that are compact and whose elements are of degree four or less. In reference to the well-known necessary condition for transformerless networks, it is shown that there exist transformerless equivalent networks for the Darlington section, the cascade of two Brune sections with attenuation poles on the real and imaginary axes, and the cascade of two Brune sections with attenuation poles on the imaginary axis. These results are applied to transformerless one-port synthesis.

Bridge-network synthesis

The paper deals with the equivalence of a bridge section to either a Darlington D section or two Brune sections, and with the extraction of this bridge section from a general reactance and an impedance function. Theorems specifying the necessary and sufficient conditions for section extraction are given in terms of the impedance function.

Synthesis of Distributed Elliptic-Function Filters from Lumped-Constant Prototypes

A synthesis procedure for distributed elliptic-function filters utilizing published tables of lumped-constant elliptic-function filters has been devised. It is dependent upon the application of a new generalized transformation for distributed networks. The filters often require the realization of distributed Brune sections, and several novel practical realizations are given both for general and degenerate Brune (i.e., Foster) sections. Examples are given of elliptic function stop band and pass band filters having both wide and narrow bandwidths, and experimental results show good agreement with theory.

Realisation of microwave brune sections

Microwave Brune sections are used for realisation of real-frequency zeros of transmission. Previous realisations of this section involve inconvenient structures, and two new realisations are described which possess considerable practical advantages.