1 / 14

16.360 Lecture 8

16.360 Lecture 8. Last lecture. short circuit line open circuit line quarter-wave transformer matched transmission line. +. V 0. Z 0. j  z. j  z. -j  z. -j  z. e. ( e. e. ( e. 16.360 Lecture 8. short circuit line. B. I i. A. Zg. Vg(t). sc. Z 0. V L. Z in.

glyn
Download Presentation

16.360 Lecture 8

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. 16.360 Lecture 8 • Last lecture • short circuit line • open circuit line • quarter-wave transformer • matched transmission line

  2. + V0 Z0 jz jz -jz -jz e (e e (e 16.360 Lecture 8 short circuit line B Ii A Zg Vg(t) sc Z0 VL Zin ZL = 0 l z = - l z = 0 ZL= 0, = -1, S =  + V(z) = V0 ) - = -2jV0sin(z) + + i(z) = ) = 2V0cos(z)/Z0 V(-l) Zin = jZ0tan(l) = i(-l)

  3. -1 l = 1/[- tan (1/CeqZ0)], 16.360 Lecture 8 short circuit line V(-l) Zin = jZ0tan(l) = i(-l) • If tan(l) >= 0, the line appears inductive, jLeq= jZ0tan(l), • If tan(l) <= 0, the line appears capacitive, 1/jCeq= jZ0tan(l), • The minimum length results in transmission line as a capacitor:

  4. + = 2V0cos(z) + V0 Z0 jz jz -jz -jz e (e e (e 16.360 Lecture 8 open circuit line B Ii A Zg Vg(t) oc Z0 VL Zin ZL =  l z = - l z = 0 ZL= 0, = 1, S =  + V(z) = V0 ) + - i(z) = ) = 2jV0sin(z)/Z0 V(-l) oc Zin = -jZ0cot(l) = i(-l)

  5. oc sc Zin Zin • Measure and sc oc = -jZ0cot(l) = jZ0tan(l) Zin Zin oc sc sc oc Zin Zin Zin Zin Z0 = Z0 = -j 16.360 Lecture 8 Application for short-circuit and open-circuit • Network analyzer • Measure S paremeters • Calculate Z0 • Calculate l

  6. -j2l -j2l e e + - (1 (1   ) ) Z0 16.360 Lecture 8 Transmission line of length l = n/2 tan(l) = tan((2/)(n/2)) = 0, Zin(-l) = = ZL Any multiple of half-wavelength line doesn’t modify the load impedance.

  7. (1 - ) Z0 (1 + ) -j2l -j2l e e - + (1 (1   ) ) Z0 16.360 Lecture 8 Quarter-wave transformer l = /4 + n/2 l = (2/)(/4 + n/2) = /2 , -j  e +  ) (1 Zin(-l) = = Z0 = -j  e -  (1 ) = Z0²/ZL

  8. 16.360 Lecture 8 Matched transmission line: • ZL = Z0 •  = 0 • All incident power is delivered to the load.

  9. - + + V0 V0 V0 Z0 Z0 Z0 -jz jz -jz e e (e 16.360 Lecture 8 Today: Power flow on a lossless transmission line • Instantaneous power • Time-average power jz + e V(z) = V0() +  - i(z) = )  At load z = 0, the incident and reflected voltages and currents: i i + V = V0 i = r - r V = V0 i =

  10. 16.360 Lecture 8 • Instantaneous power i i i P(t) = v(t) i(t) = Re[V exp(jt)] Re[ i exp(jt)] + + + + = Re[|V0|exp(j )exp(jt)] Re[|V0|/Z0 exp(j )exp(jt)] + + = (|V0|²/Z0) cos²(t +  ) r r r P(t) = v(t) i(t) = Re[V exp(jt)] Re[ i exp(jt)] - + - + = Re[|V0|exp(j )exp(jt)] Re[|V0|/Z0 exp(j )exp(jt)] + + = - ||²(|V0|²/Z0) cos²(t +  + r)

  11. 1 T + + (|V0|²/Z0) cos²(t +  )dt 16.360 Lecture 8 • Time-average Time-domain approach: i T  T i Pav = P (t)dt = 2 0 0 + = (|V0|²/2Z0) r + Pav = -||² (|V0|²/2Z0) Net average power: i r Pav + Pav = Pav + = (1-||²) (|V0|²/2Z0)

  12. 16.360 Lecture 8 • Time-average Phasor-domain approach Pav = (½)Re[V i*] i + + Pav = (1/2) Re[V0 V0*/Z0] = (|V0|²/2Z0) r + Pav = -||² (|V0|²/2Z0) + Pav = (1-||²) (|V0|²/2Z0)

  13. 16.360 Lecture 8 Next lecture • The Smith Chart

More Related