Eq Circuit Parameters From Admittance

Eq Circuit Parameters From Admittance - WE3D-5 LUMPED...

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WE3D-5 LUMPED ELEMENT EQUIVALENT CIRCUIT PARAMETER EXTRACTION OF DISTRIBUTED MICROWAVE CIRCUITS VIA TLM SIMULATION Peter Russer’, Mario Righi’, Channabasappa Eswarappa2 and Wolfgang J.R. Hoefer’ Ferdinand-Braun-Institut fur Hochstfrequenztechnik Rudower Chaussee 5, 12489 Berlin, Germany and Lehrstuhl fur Hochfrequenztechnik Technische Universitat Miinchen, Arcisstrasse 21 D-80333 Munchen, Germany NSERC/MPR Teltech Research Chair in RF Engineering, University of Victoria, Victoria, B.C., Canada V8W 3P6 ABSTRACT A method for generation of lumped element equivalent circuits and the corresponing systems of ordinary differ- ential equations for distributed microwave circuits is pre- sented. Starting with a TLM analysis of a distributed multiport circuit the impulse response functions for re- flection and transmission between the ports are computed. After Laplace-transforming the impulse functions numer- ically the poles are extracted within a specified domain of the complex frequency plane. From these poles canon- ical equivalent circuits representing the branches of the lumped element equivalent circuit are derived directly. By this way the topology as well as the parameters of the lumped element equivalent circuit are determined. The method is demonstrated in modeling of distributed one- port and multiport circuits. INTRODUCTION The transmission hie matrix (TLM) method is a powerful method for modeling distributed microwave circuits [l]. Analyzing the pulse traiisniission and reflection behaviour in time domain provides the complete frequency doma.in information for a broad frequency band after Fourier or Laplace transforinatioii Diakoptics allows the analysis of complex distributed circuits by subdividing the circuit into subcircuits [a]. The set of all the impulse reflec- tion and transmission responses constitutes the complete description of the subcircuit. In the traditional applica- tion of time domain diakoptics in TLM the connection of the subcircuits requires the convolution of the response functions. The storage of the response functions in nu- merical form requires large memory, and performing the numerical convolutions requires considerable computing time. This problem is encountered especially in cases where the subcircuits exhibit a high Q factor and the impulse responses, consequently, decay slowly with time. An alternative way to describe the subcircuits is to find an equivalent system of equations or an equivalent subcircuit exhibiting, within a specified range of frequen- cies, the same signal transmission behaviour as the sub- circuit to be modeled. The restriction of the model to a finite range of frequencies allows to model the subcir- cuit by a system of ordinary differential equations or by a lumped element circuit. Lumped element modeling has
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Eq Circuit Parameters From Admittance - WE3D-5 LUMPED...

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