Introduction_FEM_4

# Introduction_FEM_4 - b • a = 1 5 ⇒ cot 1 = 1 2 cos 2 =...

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Lecture 4: Characteristic Impedance Calculations of Microstrip Transmission Lines Prof. Jin-Fa Lee

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Computation of Area A = 1 2 abs x 1 x 0 y 1 y 0 x 2 x 0 y 2 y 0 = 1 2 x 1 x 0 ( ) y 2 y 0 ( ) x 2 x 0 ( ) y 1 y 0 ( ) Computation of co-tangents a = x 1 x 0, y 1 y 0 ( ) x 1 x 0 ( ) 2 + y 1 y 0 ( ) 2 b = x 2 x 1, y 2 y 1 ( ) x 2 x 1 ( ) 2 + y 2 y 1 ( ) 2 c = x 0 x 2, y 0 y 2 ( ) x 0 x 2 ( ) 2 + y 0 y 2 ( ) 2 θ 0 = cos 1 a c ( ) cot 0 1 = cos 1 b a ( ) cot 1 2 = cos 1 c b ( ) cot 2

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a = 1,1 ( ) 2 b = 1,0 ( ) c = 0, 1 ( ) cos θ 0 = a c = 1 2 cot 0 = 1 cos 1 = b a = 1 2 cot 1 = 1 cos 2 = c b = 0 cot 2 = 0 S 4 = cot 0 2 0 0 0 0 1 1 0 1 1 + cot 1 2 1 0 1 0 0 0 1 0 1 = 0.5 0 0.5 0 0.5 0.5 0.5 0.5 1

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0 1 φ 1 0 1 1 2 × 0.5 0 0.5 0 0.5 0.5 0.5 0.5 1 A = 2 0 0 0 0 0 0 + 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 = 2 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 f = 1.0 0 + 1.0 0 0 0 = 1.0 1.0 0 0 0
a = 1,0 ( ) b = 2.5,5.0 ( ) 2.5 2 + 5 2 = 1 5 1,2 ( ) c = 0, 1 ( ) cos θ 0 = a c = 0 cot 0 = 0 cos 1 =

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Unformatted text preview: b • a = 1 5 ⇒ cot 1 = 1 2 cos 2 = − c • b = 2 5 ⇒ cot 2 = 2 S = cot 1 2 1 − 1 − 1 1 ⎡ ⎣ ⎢ ⎢ ⎢ ⎤ ⎦ ⎥ ⎥ ⎥ + cot 2 2 1 − 1 − 1 1 ⎡ ⎣ ⎢ ⎢ ⎢ ⎤ ⎦ ⎥ ⎥ ⎥ = 1 4 1 − 1 − 1 1 ⎡ ⎣ ⎢ ⎢ ⎢ ⎤ ⎦ ⎥ ⎥ ⎥ + 1 − 1 − 1 1 ⎡ ⎣ ⎢ ⎢ ⎢ ⎤ ⎦ ⎥ ⎥ ⎥ = 1.25 − 1 − 0.25 − 1 1 − 0.25 0.25 ⎡ ⎣ ⎢ ⎢ ⎢ ⎤ ⎦ ⎥ ⎥ ⎥...
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## This note was uploaded on 10/21/2010 for the course ECE 715 taught by Professor Unknown during the Fall '09 term at Ohio State.

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Introduction_FEM_4 - b • a = 1 5 ⇒ cot 1 = 1 2 cos 2 =...

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