Transient Analysis of Transmission Lines

Question 1

Transmission Line

Answer 1

A collection of one or more conductors and dielectrics that impose boundary conditions on the EM wave equations, effectively guiding waves along the length of the line

Question 2

Electrically Small

Answer 2

dmax &laquo_space;λ/2pi (low-loss medium)

Question 3

TEM

Answer 3

Transverse electromagnetic, E and B are perpendicular to the direction of propagation. TEM lines have electrically small cross-sections

Question 4

Quasi-static approximations conditions

Answer 4

TEM lines have electrically small cross sections that permits quasi-static approximations

Question 5

MQS

Answer 5

magneto-quasi-static approximation - displacement currents have a negligible impact on the magnetic field

Question 6

EQS

Answer 6

electro-quasi-static approximation - time-varying magnetic fields have a negligible impact on the electric field. The E-field is assumes to be irrotational/conservative)

Question 7

Losses in the line are due to

Answer 7

current flow in the line, both conduction and displacement currents

Question 8

R’

Answer 8

(ohms/m) - loss due to conduction current flow (conductor losses, skin effect)

Question 9

G’

Answer 9

(S/m) - loss due to displacement currents

Question 10

Lossless line

Answer 10

R’=0 and G’=0

Question 11

Zo

Answer 11

Characteristic Impedance = √(L’/C’)

Question 12

V-

Answer 12

Is the reverse travelling wave along the transmission line, it is equal to the forward travelling component V= multiplied with the reflection coefficient

Question 13

Short circuit termination

Answer 13

RL = 0 and ΓL = -1

Question 14

Matched termination

Answer 14

RL = Z0 and ΓL = 0

Question 15

Open circuit termination

Answer 15

RL = ∞ and ΓL = +1

Question 16

How to calculate the reflection coefficient

Answer 16

Where you’re going minus where you’re coming from

Question 17

What occurs when there are non zero reflection coefficients at both the load and the generator

Answer 17

Reflections go on indefinitely with the line voltage asymptotically approaches a steady state value, this value should approach what you would get from DC analysis

Question 18

When is it
reasonable to ignore transmission line effects when analyzing the circuit:

Answer 18

l≪ λ/10
​

Question 19

Wavelength equation

Answer 19

λ = c/f
​

Question 20

quasi-static approximation

Answer 20

The quasi-static approximation implies that the equation of continuity can be written as ∇ ⋅ J = 0 and that the time derivative of the electric displacement ∂D/∂t can be disregarded in Maxwell-Ampère’s law

Question 21

L’

Answer 21

Inductance per unit length of the line (H/m), defined from MQS

Question 22

C’

Answer 22

Capacitance per unit length of the line (F/m), defined from EQS

Question 23

When the length is not electrically small

Answer 23

we can break it into electrically small segments Δz in z (length)

Question 24

How were the telegrapher’s equations derived?

Answer 24

Look at the voltages on the input and output of one electrically small segment of transmission line. The two voltages are related by the voltage drop across the series elements. Rearrange and take the limit as Δz goes to 0

Question 25

Where is the tx line does the EM travel

Answer 25

through the dielectric surrounding the conductors

Question 26

TDR

Answer 26

Time Domain Reflectometry - Analyzing the transient response of a Tx line is a common way to assess/diagnose damage

Question 27

How does TDR work?

Answer 27

Apply a high speed voltage step (sub-nanosecond) and monitor the response of the line at the input. Record with a high speed scope over a time interval and convert to distance.

Question 28

TDR Response for a matched line

Answer 28

V(t) = Vg/2 for all of z >0

Question 29

TDR Response for a break halfway down the line

Answer 29

V(t) = Vg/2 for all of z >l/2 then V(t) = 0 for short or V(t) = Vg for open

Question 30

TDR response capacitive load

Answer 30

Short circuit at load and charging curve up to Vg. Approaches steady state with a time constant of ZoC

Question 31

TDR response inductive load

Answer 31

Open circuit at load and curve down to 0. Approaches steady state with a time constant of L/Zo

Question 32

VNA

Answer 32

Vector Network Analyzer, measures the complex Scattering- or S-parameters of RF components in the frequency
domain

Question 33

Steady state for Bounce Diagram

Answer 33

V = (VgRL)/Rg+RL

Question 34

TDR response mismatched loading

Answer 34

For RL>Zo the voltage will be in between Vg/2 and Vg

For RL<Zo the voltage will be in between 0 and Vg/2

Question 35

The characteristic impedance on a transmission line can be calculated by ratio of

Answer 35

forward travelling voltage to forward travelling current on the line