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# PP11 - Texas State University-San Marcos Ingram School of...

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Unformatted text preview: Texas State University-San Marcos Ingram School of Engineering EE3340: Fields and Waves so L Vx ‘r t u N 5 Practice Problem 11: Ampere’s Circuital Law NAME: DATE: An important problem in digital communications is crosstalk, the unintentional coupling of signals from one transmission line to a different line. Stray magnetic ﬁelds that extend from one line to another can cause crosstalk. This problem should help you to see why unbalanced transmission lines can have more severe crosstalk than balanced lines. Figure (a) below shows a current source driving a current I into Wire #1. The current goes to a load resistor RL and then returns to the source through a ground plane that is very far away. Assume that Wire #2 is a separate sensitive circuit that will be disturbed by any stray magnetic ﬁelds. This is an unbalanced circuit because the current goes out from the source on a wire and returns via the ground plane. :I‘k‘ H1? “2 Tb nun PLAN! >> a 1 Figure (a) Using Ampere’s circuital law (ignore any current induced in Wire #2), calculate the magnetic ﬁeld intensity magnitude IHAI at Wire #2, which is a distance R away from Wire #1. Express your answer algebraically in terms of R and I (this is a simple result). Next, suppose we change the circuit to a balanced one. Balanced transmission lines have symmetry and are basically independent of ground. Figure (b) shows how the Figure (b) current source drives current I toward the load on one of a pair of wires spaced a short distance d apart and the same current ﬂows back along the other wire in the pair. If R is now the distance between the center of the balanced wire pair and Wire #2 of the sensitive circuit, derive an algebraic expression for the magnetic ﬁeld strength magnitude IHBl at Wire #2. (This is just the sum of the ﬁeld strengths from the individual wires in Pair #1). Finally, ﬁnd the balanced—to—unbalanced ﬁeld strength ratio IHBIIIHAI as a function of the ratio d/R between pair spacing d and pair—to-wire-#2 distance R. This shows why balanced transmission lines are better at reducing magnetic—ﬁeld interference than unbalanced lines. in; I 4 I__ ;%(/———““i"*%) (Film Li) ...
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PP11 - Texas State University-San Marcos Ingram School of...

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