06-Distributed - EE 541, Fall 2009: Course Notes #6...

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EE 541, Fall 2009: Course Notes #6 Distributed Circuit Models and Applications Dr. John Choma Professor of Electrical Engineering University of Southern California Ming Hsieh Department of Electrical Engineering University Park: Mail Code: 0271 Los Angeles, California 90089–0271 213–740–4692 [USC Office] 213–740–8677 [USC Fax] [email protected] ABSTRACT: This report addresses the models, electrical properties, and fundamental applica- tions of distributed transmission lines. The concepts underpinning such metrics as characteristic impedance and propagation coefficient are defined and assiduously scrutinized. The report concluded with a brief introduction of active distributed structures. Original: December 2002
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Course Notes #6 University of Southern California John Choma August 2006 192 Distributed Circuits 1.0. INTRODUCTION When the signal frequencies imposed on an active or passive network are small so that their associated wavelengths are large, the classic lumped circuit approximation applies to all circuit level analyses conducted on the network. This lumped circuit presumption is comforting from several perspectives. For example, it allows branch elements of the circuit undergoing study to be identified unambiguously, and it permits a straightforward analytical definition of the volt-ampere properties of these elements. As a corollary to this branch identification attribute, the interconnection of these branches pinpoints the junctions and nodes of the circuit, thereby enabling a systematic application of the Kirchhoff laws to determine circuit equilibrium. More- over and virtually by definition, the lumped circuit approximation supports the tacit presumption that the current flowing into one terminal of a two-terminal branch element is, at any instant of time, precisely the same as the current that resultantly flows out of the branch. In effect, the large signal wavelengths associated with modest frequencies permeate the branch uniformly so that said branch can be viewed as a kind of a “giant node,” for which the algebraic sum of cur- rents is necessarily zero. A final and related engineering comfort level is that the voltages with respect to any reference node along any length of interconnect are, at any instant of time, identi- cal and independent of the actual line length. Subcircuit #1 + V 2 I 2 I 2 + V 1 I 2 I 2 P a c k g i n Subcircuit #2 + V 4 I 4 I 4 + V 3 I 3 I 3 (a). Subcircuit #1 + V 2 I 2 I 2 + V 1 I 2 I 2 Subcircuit #2 + V 4 I 4 I 4 + V 3 I 3 I 3 (b). I t e r o M d l Fig. (1). (a). An Abstraction Of Electrical Subcircuits And Packaging Connected Together With Wir- ing Or Metallization For Which Distributed Resistance, Inductance, And Capacitance Cannot Be Ignored. (b). An Abstraction Of Two Port Models Interposed To Account For The Elec- trical Effects Of Distributed Interconnect Impedances.
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06-Distributed - EE 541, Fall 2009: Course Notes #6...

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