Sinusoidal Steady-state Analysis of Transmission Lines

Question 1

steady state

Answer 1

transients have settled

Question 2

Most RF signals are

Answer 2

Narrowband, their bandwidth is only 1-2% of their center frequency

Question 3

Fourier analysis allows us to

Answer 3

extend to narrowband to wideband or baseband signals

Question 4

Propagation constant

Answer 4

γ = α +jβ (1/m)

Question 5

Attenuation constant

Answer 5

α (Np/m), the sine wave decays with α, measure of the attenuation of the amplitude of the fields in electromagnetic wave propagation

Question 6

Phase constant

Answer 6

β (rad/m), 2pi/λ, As the wave moves forward, its phase may undergo variations, and this factor that indicates this variation

Question 7

Attenuation increases with

Answer 7

frequency

Question 8

Line attenuation

Answer 8

10log[Pin/Pout], 8.686αL (dB). Often quoted in dB/m

Question 9

Lossless medium attenuation and phase

Answer 9

α = 0 and β = ω√L’C’

Question 10

Standing wave cause

Answer 10

Counter propagating sine waves with different amplitudes and phases due to the reflection at the load will lead to standing waves on the line

Question 11

Standing wave maximum

Answer 11

2βz + ∠ΓL = (2n)π

Question 12

Standing wave minimum

Answer 12

2βz + ∠ΓL = (2n+1)π

Question 13

VSWR

Answer 13

Voltage standing wave ratio, a real number that tells us how close we are to a match

Question 14

Return Loss

Answer 14

-20log|ΓL| (dB)

Question 15

Power delivered to the load

Answer 15

A fraction of the available power will be delivered to the load, the rest will be reflected and turned to heat in the transmission line, unless there is a perfect match

Question 16

Power available at the load

Answer 16

(|V+|^2)/2Zo

Question 17

Wave impedance

Answer 17

the ratio of the voltage to current at any point along a (potentially mismatched) transmission line

Question 18

Distortion will occur on a transmission line unless

Answer 18

the antennation constant (amplitude distortion) and propagation speed (phase distortion) are independent of frequency.

Question 19

An infinite lossy line will appear

Answer 19

matched, but very little power may be reaching the load

Question 20

Impedance special cases

Answer 20

1) when d = nλ/2, tan(npi) = 0 We will see the load again Z(d) = ZL
2) when d = (2n+1)λ/4, tan() -> infinity and we have impedance inversion Z(d) = (Zo^2)/ZL
3) Short Circuit Load
4) Open Circuit Load

Question 21

Impedance of a quarter waveform transformer

Answer 21

Z0A = √Z0RL

Question 22

Short Circuit Stub

Question 23

Open Circuit Stub

Question 24

Distortion less conditon

Answer 24

R’/L’ = G’/C’