ece107_set2_nbg

# ece107_set2_nbg - ECE 107 Electromagnetism Set 2...

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1 ECE 107: Electromagnetism Set 2: Transmission lines Instructor: Prof. Vitaliy Lomakin Department of Electrical and Computer Engineering University of California, San Diego, CA 92093

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2 Outline Transmission Lines for Communications General description Lumped element model Transmission line equations Wave propagation in transmission lines Lossless transmission lines Reflection from loads and standing waves Input impedance and concepts of matching
3 General description (1) Electromagnetic Transmission Lines (TLs) are structures or media that transfer energy/ information between two points by means of electromagnetic fields. TL is a two-port network, where each port consists of two terminals

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4 General description (2) Examples of transmission lines
Why 50 Ohms? General description (3)

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General description (4) l v(t) ~ c As the switch is closed a voltage (and current) pulse moves down the wire. Time to travel length of wire is l /c. If voltage is not varying at this time scale then the system equilibrates such that the wire is at a constant voltage and no current flowing. However if the voltage varies at a frequency comparable to this time then the system is not in equilibrium. Close switch at t = 0 Close the switch attaching the battery to two wires
General description (5) Propagating signal can be thought of in terms of fields E and H or voltage V and current I. = 2 1 2 , 1 l d E V C = Q/V + + + + + + + + + + + + - - - - - - - - - - - - electo- statics magneto- statics

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8 General description (8) How is a TL different from an electric circuit? Consider the following structure: When , i.e. the voltage does not depend on the length of the connecting wires When is not too small , i.e. the voltage depends on the length of the wires! What is low and high frequency regime? Look at ! If low frequency (no delay). If high frequency (large delay). 0 BB AA V V ω = ω 0 ( ) cos( ( )) BB AA V V t l c V t l c ω = = 2 ~ l c l l ω π λ λ = ~1 or 1 l l λ λ ? 1 l λ = response delay
General description (7) 60 Hz l = 5000 km Data rate 1 GHz (30 cm) Rise times 100 psec l ~ 1 – 30 cm circuit TL circuit TL

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10 General description (9) Types of TLs Transverse electromagnetic (TEM) TLs: Electric AND magnetic field are normal to the propagation direction Higher-order TLs: There are electric or/and magnetic field components in the propagation direction