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HW 8 Solutions

# HW 8 Solutions - Z represents the amount of power absorbed...

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Chapter 2: Solutions 2.1 Fill in the blanks: (a) A microstrip line is a type of transmission line that is made by etching or milling away the top conductor on a conventional printed circuit board. (b) The symmetrical stripline and the coaxial cable are two examples of transmission lines that have complete field and signal confinement. (c) When the transit time of a printed circuit board causes delays in pulses that threaten the synchronization of a high speed circuit, we call this effect latency . (d) Three ways to increase Z 0 for a coaxial line are to decrease the radius of the inner conductor, increase the radius of the outer conductor, or decrease the permittivity of the dielectric material. 2.2 True or false: (a) If two transmission lines have the same per-unit-length capacitance, they will have the same characteristic impedance Z 0 . FALSE (b) The microstrip transmission line is made from a printed circuit board with etched traces above the dielectric and a ground plane on the bottom. TRUE (c) The characteristic impedance

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Unformatted text preview: Z represents the amount of power absorbed and converted to heat by the transmission line. FALSE 2.4 Fill in the following table of transmission line parameters, where each row corresponds to a unique transmission line. L C Z v p a. 1 F/m 50 ! b. ! c. 200 ! 1 ! 10 7 m/s d. 200 H/m 4 ! 10 7 m/s e. 75 ! 2.4 ! 10 8 m/s 2.9 The following represent invalid solutions of the transmission line differential equations. Explain why each is impossible for a linear transmission line in terms of basic physical properties (i.e., characteristic impedance, pulse shape, attenuation, velocity of propagation, etc.) No credit will be given for purely mathematical answers. (a) v ( z , t ) = 100 cos 2 ! ft &amp;quot; z ( ) + 50sin 2 ft + z ( ) i ( z , t ) = 5 cos 2 ft &amp;quot; z ( ) &amp;quot; 5sin 2 ft + z ( ) (b) v ( z , t ) = 20 sin t ! 5 z ( ) t ! 5 z i ( z , t ) = sin t ! 5 z ( ) (c) v ( z , t ) = 75exp ! t ! z 2 ( ) + 75exp ! t + z 2 2 &amp;quot; # \$ % &amp;amp; ' i ( z , t ) = exp ! t ! z 2 ( ) ! exp ! t + z 2 2 &amp;quot; # \$ % &amp;amp; '...
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