329lect28 - 28 Introduction to distributed circuits Last...

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Unformatted text preview: 28 Introduction to distributed circuits Last lecture we learned that voltage and current variations on TLs are governed by telegraphers equations and their dAlembert solutions the latter can be expressed explicitly as +- Wire 2 Wire 1 +- f ( t ) R g R L I ( z, t ) V ( z, t ) z l Source ckt Transmission line Load Z o I ( z, t ) V ( z, t ) = V + ( t- z v ) + V- ( t + z v ) and I ( z, t ) = V + ( t- z v ) Z o- V- ( t + z v ) Z o in terms of v = 1 LC and Z o = L C and V + ( t ) and V- ( t ) labeling signal waveforms propagated in + z and- z directions, respectively. We will next solve a sequence of distributed circuit problems containing TL segments and two terminal elements such as resistors and voltage (or current) sources. In solving the problems, we will apply the usual rules of lumped circuit analysis at element terminals and treat the TLs in terms of dAlembert solutions above. Consider a TL with a characteristic impedance Z o extending from z = 0 to z = l , where a two-terminal source circuit (e.g., a receiving antenna) modeled by a Thevenin equivalent with voltage f ( t ) and resistance 1 R g is connected between the TL terminals at z = 0 and a load (e.g., a receiver circuit) modeled by a resistance R L terminates the line at z = l (see margin). +- Wire 2 Wire 1 +- f ( t ) R g R L I ( z, t ) V ( z, t ) z l Source ckt Transmission line Load Z o I ( z, t ) We want to determine voltage and current signals V ( t ) and I ( t ) on the TL and the load in terms of source signal f ( t ) . Let us simplify the problem posed above by having R g = 0 f ( t ) = u ( t ) R L = Z o in which case the circuit takes the simplified form in the margin. Circuit 1: +- +- u ( t ) Z o I ( z, t ) V ( z, t ) z l Z o I ( z, t ) Now applying KVL at z = 0 we have u ( t ) = V + ( t ) + V- ( t ) ....
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This note was uploaded on 06/20/2011 for the course ECE 329 taught by Professor Kim during the Spring '08 term at University of Illinois, Urbana Champaign.

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329lect28 - 28 Introduction to distributed circuits Last...

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