Step 4_exerciseN°1_john jairo valencia Rojas.docx

Universidad Nacional Abierta y a Distancia  – UNAD Escuela de Ciencias C iencias Básicas Tecnologías e Ingenierías-ECBTI Curso: Teoria electromagnetica y Ondas Unity III

 Step  Step 4- Wave Wavegui des - E lect lectrr i c pa par ameter ter s in i n tra tr ansmi nsmi ssio ssi on line li ness

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 J ohn J ai ro Vale Valencia ncia R ojas C od: 9432 943264 6428 28

G r oup: up: 2030580_2 2030580_24 4

Tutor Tutor : Wilm Wi lme er H er nan nan Gutié Guti ér r ez

 - UNAD OPEN AND DI STANCE STANCE NATI ONAL UNI UNI VE RSI TY  -

Palmi Palmi r a ( V alle) lle)  April  Apri l /30/ 30/2018 2018

Universidad Nacional Abierta y a Distancia  – UNAD Escuela de Ciencias Básicas Tecnologías e Ingenierías-ECBTI Curso: Teoria electromagnetica y Ondas Unity III

1. A lossless transmission line has a characteristic impedance of  = 60Ω and the load at the end of the line has an impedance of  = 45 + 95Ω. Using the Smith Chart, find: a. Reflection coefficient Γ (magnitude and phase), and the VSWR.  b. The input impedance if the line is 0.75 long. c. The length of the line, necessary to make the input impedance real and the value of the impedance in this point.

SOLUCION

 Normalizing the load impedance  .

 =

  

=

45 + 95Ω 60Ω

= 0,8 + 1,6

We place the previous value in Smith's Letter, we draw a straight line that starts in 1.0 and go through  = 0,8 + 1.6 The straight line is extended until you cut the peripheral circle, we can read the "Origin of   Which in this case is

 = .



At this moment we draw a circle, centered on 1.0 and passing through  . This circle intersects the horizontal axis, on the right side at point 6 .0. This value is the system VSWR.

 = 6,0 To determine the value of de  = 0.75   , a distance of 0.75   Long can be moved over the peripheral circle from Z_ (N) and we arrive at the point 0.424   Long  A straight line is drawn that starts at en 0.424    and reaches the center of the chart at 1.0, the intersection with the VSWR circle determines the value of  = 0.75  .

0.172  Long + 0.75   = 0.924  

Universidad Nacional Abierta y a Distancia  – UNAD Escuela de Ciencias Básicas Tecnologías e Ingenierías-ECBTI Curso: Teoria electromagnetica y Ondas Unity III

Because a distance of. 0.5 is a complete return to the Charter, the integer multiples of. 0.5 of the value obtained, in this case:

0.924    − 0.5   = 0.424  

 0.75   = 0.5 − 0.25

The previous value is normalized; therefore, the real value will be:

   0.75      0.5    0.25   60  

 

The reflection coefficient is read directly from Smith's Letter. The following is done: a vertical straight line is drawn, which starts at the intersection of the VSWR   circle and the horizontal axis on the right side and ends in parameters of the radial scale. In this scale we obtain the magnitude and the phase is on the peripheral circle, graduated in degrees.

we have that the coefficient of reflection has the value:

 = .  °