Acoustical Analysis of a General Network of Multi- Port Elements — An Impedance Matrix Approach
نویسندگان
چکیده
The present work deals with a generalized algorithm for analyzing a network of linear passive acoustic filters having multi-port elements which are interconnected to each other in an arbitrary manner through their respective ports or through general 2-port elements. A multi-port element is characterized by an impedance [Z] matrix, and the junctions through which these multi-port elements are connected are characterized by conditions of continuity of acoustic pressure and mass velocity. A connectivity matrix is written for the entire network, wherein the interconnections of the elements are taken care of by proper bookkeeping of the acoustic state variables. The acoustic pressures at the external nodes (at the network terminations) are related to mass velocity at the external ports by inversion of the connectivity matrix to obtain the global impedance matrix, characterizing the entire network. This characterization thereby offers a generalized formulation for dealing with a network of multi-port elements. Generalized expressions are obtained for determination of the acoustic performance parameters (Transmission loss (TL), Insertion loss (IL), and Level Difference (LD)) for a multi-port system in terms of the [Z] matrix and scattering [S] matrix. A simple method is proposed for evaluation of the [Z] matrices by means of the axial plane wave theory to characterize long chamber mufflers for a uniform area, conical and exponential duct having an arbitrary number of ports, whilst the ports can be located on the end faces as well as on the side surfaces. The [Z] matrices characterizing each of these multi-port elements are then used to analyze arbitrary networks of such multi-port elements, and the results are compared with those obtained by 3-D FEA and also against the existing literature.
منابع مشابه
The Classical n-Port Resistive Synthesis Problem
Introduction An n-port resistive network is an n-port circuit consisting of only passive resistors, which is an important class of passive networks. An n-port resistive network is usually characterized by its impedance or admittance matrix. Since there are no reactive elements, passivity and reciprocity imply that the impedance and admittance matrices of n-port resistive networks must be nonneg...
متن کاملComment on two-port network analysis and modeling of a balanced armature receiver.
Models for acoustic transducers, such as loudspeakers, mastoid bone-drivers, hearing-aid receivers, etc., are critical elements in many acoustic applications. Acoustic transducers employ two-port models to convert between acoustic and electromagnetic signals. This study analyzes a widely-used commercial hearing-aid receiver ED series, manufactured by Knowles Electronics, Inc. Electromagnetic tr...
متن کاملComputational Cost Reduction for N+2 Order Coupling Matrix Synthesis Based on Desnanot-Jacobi Identity
Matrix inversion is routinely performed in computational engineering, with coupling matrix filter synthesis considered here as just one of many example applications. When calculating the elements of the inverse of a matrix, the determinants of the submatrices are evaluated. The recent mathematical proof of the Desnanot–Jacobi (also known as the ‘‘Lewis Carol’’) identity shows how the determinan...
متن کاملMulti Attribute Analysis of a Novel Compact UWB Antenna with Via-fed Elements for Dual Band Notch Function (RESEARCH NOTE)
A compact microstrip-fed antenna with dual notched bands is proposed. First, a simple basic configuration is presented for Ultra Wide Band (UWB) applications and then the dual band notched structure is extended from the UWB one. The basic structure of the UWB antenna consists of a simple square radiating patch and a ground plane with a wide square slot on back of the substrate. A semi-circle sh...
متن کاملEven Mode Network Model for Multi-band and Compact Modified Rectangular Microstrip Antennas
The multi-port network model is a simpler tool to analyze microstrip antennas on thinner substrates. While analyzing modified shaped microstrip antennas, the multi-port network model consists of larger number of segments which increases the complexity of the model. In this paper, first multi-port network models of multi-band and compact modified rectangular microstrip antennas are discussed. Fu...
متن کامل