MAYURBHANJ SCHOOL OF ENGINEERING � LAXMIPOSI ,BARIPADA,757107
Prepared by Er. Viswanath Behera (Lecturer E & TC Engineering Department)
Subject – WAVE PROPAGATION & BROADBAND COMMUNICATION ENGINEERING
Chapter – 2 – TRANSMISSION LINES
Topic – Transmission Line
Semester – 5th
Branch – Electronics & Telecommunication
AY-2021-2022, WINTER-2021
FUNDAMINTAL OF TRANSMISSION LINE
Definition: Transmission lines are the conductors that serve as a path for transmitting (sending) electrical waves (energy) through them. These basically forms a connection between transmitter and receiver in order to permit signal transmission.
TYPE OF TRANSMISSION LINE
3
Transmission-Line Theory
We need transmission-line theory whenever the length of a line is significant compared to a wavelength.
4
Transmission Line
2 conductors
4 per-unit-length parameters:
C = capacitance/length [F/m]
L = inductance/length [H/m]
R = resistance/length [Ω/m]
G = conductance/length [ /m or S/m]
Ω
Δz
5
Transmission Line (cont.)
+ + + + + + +
- - - - - - - - - -
x
x
x
B
Note: There are equal and opposite currents on the two conductors.
(We only need to work with the current on the top conductor, since we have chosen to put all of the series elements there.)
+
-
+
-
6
Transmission Line (cont.)
+
-
+
-
7
Wavenumber Notation
8
Characteristic Impedance Z0
so
Assumption: A wave is traveling in the positive z direction.
(Note: Z0 is a number, not a function of z.)
9
Use first Telegrapher’s Equation:
so
Hence
Characteristic Impedance Z0 (cont.)
Recall:
10
From this we have:
Use:
Characteristic Impedance Z0 (cont.)
Both are in the first quadrant
(principal square root)
11
Hence, we have
Characteristic Impedance Z0 (cont.)
12
Backward-Traveling Wave
so
A wave is traveling in the negative z direction.
Note:
The reference directions for voltage and current are chosen the same as for the forward wave.
z
13
General Case
A general superposition of forward and backward traveling waves:
Most general case:
z
14
Guided wavelength:
Phase velocity:
Summary of Basic TL formulas
15
Lossless Case
so
(independent of freq.)
(real and independent of freq.)
16
Lossless Case (cont.)
If the medium between the two conductors is lossless and homogeneous (uniform) and is characterized by (ε, μ), then (proof given later):
The speed of light in a dielectric medium is
Hence, we have that:
In the lossless case the phase velocity does not depend on the frequency, and it is always equal to the speed of light (in the material).
(proof given later)
and
17
At the load (d = 0):
Terminated Transmission Line (cont.)
At any point on the line(d > 0):
Thank You