Lossless Transmission Lines (Part-III)

|Ĩ_max|

(i)

|Ĩ_min|

(ii)

|Ṽ_max|

(1)

|Ṽ_min|

(2)

d_min

(3)

d_max

(4)

d = -z

Distance from the Load (The alternative coordinate system)

2βd - θ_r = 2nπ

Constructive Interference Condition: Condition where incident and reflected waves are in-phase

2βd - θ_r = (2n + 1)π

Destructive Interference Condition: Condition where incident and reflected waves are in phase opposition

|Ṽ_max| = (1 + |Γ|)|V0^+|

Maximum Standing-Wave Voltage: Largest voltage magnitude along the transmission line

|Ṽ_min| = (1 - |Γ|)|V0^+|

Minimum Standing-Wave Voltage: Smallest voltage magnitude along the transmission line

λ/2

Standing-Wave Repetition Period: Spatial repetition period of a standing-wave pattern ___

maxima, maxima

Voltage ______ correspond to current minima, and voltage minima correspond to current ______

Z_L = Z_0

Matched Transmission Line: A transmission line with no reflected wave because …

Γ = 0

Reflection coefficient of the Matched Transmission Line

Matched Line

Short-Circuited Line

Z_L = 0

Load Impedance of a short circuited line

Open-Circuited Line

Γ = -1

Reflection Coefficient of a short-circuited line

Z_L = ∞

Load Impedance of a open-circuited line

Γ = 1

Reflection Coefficient of a open-circuited line

No-Reflection Condition

Condition in which no standing waves exist because there is no reflected wave: Γ = 0

Purely Reactive Load

A load containing only reactance (inductive or capacitive), for which: |Γ| = 0

Voltage Maximum Location Condition

Condition for locations where voltage magnitude is maximum: (2β(d_max)) - θ_r = 2nπ

d_max = ((θ_r) + (2nπ))/(2β)

Voltage Maximum Location: Distance from the load where the voltage magnitude reaches a maximum

d_max = ((θ_r)λ)/(4π) + (nλ)/2

Voltage Maximum Location Using Wavelength: Voltage maximum position written in terms of wavelength

Voltage Minimum Location Condition

Condition for locations where voltage magnitude is minimum:
(2β(d_min)) - θ_r = (2n + 1)π

λ/4

Spacing Between Adjacent Voltage Maximum and Minimum: Distance separating adjacent voltage maxima and minima ___

d_min = d_max ± (λ/4)

Voltage Minimum Position Rule: Relationship between the first voltage minimum and voltage maximum

Voltage Standing-Wave Ratio (VSWR)

Ratio of maximum voltage magnitude to minimum voltage magnitude

S = |Ṽ_max|/|Ṽ_min|

Mathematical Representation of Voltage Standing-Wave Ratio (VSWR)

S = (1 + |Γ|)/(1 - |Γ|)

VSWR in Terms of Reflection Coefficient: Expression relating standing-wave ratio to reflection coefficient magnitude

S = 1

Matched-Line VSWR: Standing-wave ratio for a perfectly matched line (Γ = 0)

S = ∞

Complete Reflection VSWR: Standing-wave ratio when total reflection occurs (Γ = 1)

Γ = |Γ|e^(j(θ_r))

Phase Angle of Reflection Coefficient: Angular component of the complex reflection coefficient

Standing-Wave Envelope

The curve traced by the maxima and minima of the standing-wave pattern along the transmission line

Wave Impedance

Ratio of total voltage to total current at a distance d from the load on a lossless transmission line

Z(d)

Symbol to represent the wave impedance

Z(d) = Ṽ(d)/Ĩ(d)

Mathematical Representation of Wave Impedance