Download presentation

Presentation is loading. Please wait.

Published byEssence Easter Modified over 2 years ago

1
16.360 Lecture 7 Last lecture Standing wave Input impedance i(z) = V(z) = V 0 ( ) + + e jzjz - e -j z (e(e + V0V0 Z0Z0 e jzjz ) |V(z)| = | V 0 | | | + e -j z |||| e jzjz + e jrjr = | V 0 | [ 1+ | |² + 2| |cos(2 z + r )] + 1/2 |i(z)| = | V 0 | /|Z0|| | + e -j z |||| e jzjz - e jrjr = | V 0 |/|Z 0 | [ 1+ | |² - 2| |cos(2 z + r )] + 1/2

2
16.360 Lecture 7 Special cases 1.Z L = Z 0, = 0 = | V 0 | + |V(z)| 2. Z L = 0, short circuit, = -1 |V(z)| |V0| + - -3 /4- /2- /4 = | V 0 | [ 2 + 2cos(2 z + )] + 1/2 |V(z)| 2|V0| + - -3 /4- /2- /4 3. Z L = , open circuit, = 1 = | V 0 | [ 2 + 2cos(2 z )] + 1/2 |V(z)| 2|V0| + - -3 /4- /2- /4

3
16.360 Lecture 7 Voltage maximum and minimum | V 0 | [ 1+ | |], + |V(z)| max = when 2 z + r = 2n . | V 0 | [ 1 - | |], + |V(z)| min = when 2 z + r = (2n+1) . Voltage standing-wave ratio VSWR or SWR 1 - | | |V(z)| min S |V(z)| max = 1 + | | S = 1, when = 0, S = , when | | = 1,

4
16.360 Lecture 7 Input impudence Vg(t) VLVL A z = 0 B l ZLZL z = - l Z0Z0 ViVi Zg IiIi Z in (z) = V(z) I(z) = + + e jzjz e -j z V0V0 ( ) + - e jzjz e V0V0 ( ) Z0Z0 = + (1 e j2 z ) - (1 e j2 z ) Z0Z0 + (1 e -j2 l ) - (1 e -j2 l ) Z0Z0 Z in (-l) =

5
16.360 Lecture 7 Today: special cases short circuit line open circuit line quarter-wave transformer matched transmission line

6
16.360 Lecture 7 short circuit line Z L = 0, = -1, S = Vg(t) VLVL A z = 0 B l Z L = 0 z = - l Z0Z0 Zg IiIi Z in sc i(z) = V(z) = V 0 ) - e jzjz + (e(e -j z (e(e + V0V0 Z0Z0 e jzjz ) = -2jV 0 sin( z) + = 2V 0 cos( z)/Z 0 + Z in = V(-l) i(-l) = jZ 0 tan( l)

7
16.360 Lecture 7 short circuit line Z in = V(-l) i(-l) = jZ 0 tan( l) If tan( l) >= 0, the line appears inductive,j L eq = jZ 0 tan( l), If tan( l) <= 0, the line appears capacitive,1/j C eq = jZ 0 tan( l), l = 1/ [ - tan (1/ C eq Z 0 )], The minimum length results in transmission line as a capacitor:

8
16.360 Lecture 7 An example: tan ( l) = - 1/ C eq Z 0 = -0.354, Choose the length of a shorted 50- lossless line such that its input impedance at 2.25 GHz is equivalent to the reactance of a capacitor with capacitance Ceq = 4pF. The wave phase velocity on the line is 0.75c. Solution: Vp = ƒ, = 2 / = 2 ƒ/Vp = 62.8 (rad/m) l = tan (-0.354) + n , = -0.34 + n ,

9
16.360 Lecture 7 open circuit line Z L = 0, = 1, S = Vg(t) VLVL A z = 0 B l Z L = z = - l Z0Z0 Zg IiIi Z in oc i(z) = V(z) = V 0 ) + e jzjz - (e(e -j z (e(e + V0V0 Z0Z0 e jzjz ) = 2V 0 cos( z) + = 2jV 0 sin( z)/Z 0 + Z in = V(-l) i(-l) = -jZ 0 cot( l) oc

10
16.360 Lecture 7 Application for short-circuit and open-circuit Network analyzer Measure Z in oc Z in sc and Calculate Z 0 Measure S paremeters Z in = -jZ 0 cot( l) oc Z in = jZ 0tan ( l) sc =Z0Z0 Z in sc Z in oc Calculate l = -jZ0Z0 Z in sc Z in oc

11
16.360 Lecture 7 Line of length l = n /2 = Z L tan( l) = tan((2 / )(n /2)) = 0, + (1 e -j2 l ) - (1 e -j2 l ) Z0Z0 Z in (-l) = Any multiple of half-wavelength line doesn’t modify the load impedance.

12
16.360 Lecture 7 Quarter-wave transformer l = /4 + n /2 = Z 0 ²/Z L l = (2 / )( /4 + n /2) = /2, + (1 e -j2 l ) - (1 e -j2 l ) Z0Z0 Z in (-l) = + (1 e -j ) - (1 e -j ) Z0Z0 = (1 + ) Z0Z0 (1 - ) =

13
16.360 Lecture 7 An example: A 50- lossless tarnsmission is to be matched to a resistive load impedance with Z L = 100 via a quarter-wave section, thereby eliminating reflections along the feed line. Find the characteristic impedance of the quarter-wave tarnsformer. Z L = 100 /4 Z 01 = 50 Z in = Z 0 ²/Z L = 50 Z 0 = (Z in Z L ) = (50*100) ½ ½

14
16.360 Lecture 7 Matched transmission line: 1.Z L = Z 0 2. = 0 3.All incident power is delivered to the load.

15
16.360 Lecture 7 Next lecture: Power flow on a lossless transmission line

Similar presentations

OK

Darryl Michael/GE CRD Fields and Waves Lesson 1.2 SINE WAVES ON TRANSMISSION LINES.

Darryl Michael/GE CRD Fields and Waves Lesson 1.2 SINE WAVES ON TRANSMISSION LINES.

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on op amp circuits formula Ppt on taj hotel mumbai Ppt on marine ecosystem Ppt on diode as rectifier circuits Ppt on osmosis and diffusion Ppt on human resource recruitment Ppt on artificial intelligence for speech recognition Ppt on tamper resistant electrical outlets Ppt on event handling in javascript what is a number Ppt on forex market