Unit 1 : Transmission Line Theory
Session Meta Data
Author Ramprabhu S
Version No. 1.1
Release Date 12-12-2019
Reviewer
Revision History
Date of Revision Details Version Number
12 Dec 2019 1.1
Session Objectives
To introduce the general solution of transmission
lines
Session Outcomes
At the end of the session, students will be able to
Understand the general solution of transmission
lines
Outline
General solution of transmission lines
Input impedance of transmission line
Physical significance of transmission line
Transfer impedance of transmission line
Transmission line equations
• A transmission line is a structure that transfers
electromagnetic energy from one point to the other.
• The parameters of the transmission line is
distributed throughout the length of the line.
• Depending upon the
operating wavelength, the
transmission line is modeled as lumped T section.
Transmission line equations
• One such section is shown below
ds s
IS I Zds
IR
dI
Eg E Yds ZR
Transmission line equations
• The elemental section shown is of length ds and
carries a current I. The series impedance being Z
ohms per unit, the series impedance is Zds ohms.
• The voltage drop in the length ds is
dE I Zds
dE
IZ ...(1)
ds
Transmission line equations
• The shunt admittance of the line is Y mhos per unit
length, so that the admittance of the element of line
is Yds mhos.
• The current dI that flows across the line or from
one conductor to the other is
dI EYds
dI
EY ... (2)
ds
Transmission line equations
• Differentiating equations 1 and 2 with respect
to s, is given by
d2E
2
ZY E ... (3)
ds
d2I
2
ZY I ... (4)
ds
• The above equations are called Telegrapher’s
Equations.
Transmission line equations
• The solution to the above differential equations are
obtained as
E Ae Zy
Be Zy
...(5)
I Ce
Zy
De Zy
...(6)
• The constants A, B, C and D are obtained by simple
manipulation.
Transmission line equations
• The general solution to the transmission line is
E ER cosh ZY s IR Z0 sinh ZY s
ER
I I R cosh ZY s sinh ZY s
Z0
Input impedance of transmission line
• The voltage and current at any point on the transmission
line can be determined.
• The input impedance of the transmission line is
determined from these equations as
where γ is the propagation constant, ZR is the load
impedance and l is the length of the transmission line.
Physical significance of
transmission line equations
• If the length of the line is infinite, i.e., l=∞, The
input impedance is ZS= Z0
• If the length is finite and ZR=Z0, then ZS= Z0 .
Thus, the characteristic impedance is the input
impedance of an infinitely long line.
•When ZR=Z0, the line is perfectly terminated.
Transfer impedance of transmission line
Transfer Impedance is defined as the ratio
between sending-end voltage and receiving-end
current.
ES
It is expressed as Z T
IR
From transmission line equations, the transfer
impedance is obtained as
ZT Z R cosh l Zo sinh l
Summary
• Transmission is a metallic medium through which
EM wave is transmitted.
• Using the transmission line equations the various
parameters of the line can be determined.
• The transmission line is said to be correctly
terminated if the load impedance is equal to the
characteristic impedance of the line.
Test Your Understanding
• Derive the expression for voltage and current in a
transmission line.
• What is transfer impedance ? Derive the expression
for transfer impedance of a transmission line.
References
1. John D Ryder, “Networks, lines and fields”, 2nd
Edition, Prentice Hall India, 2015.
2. Mathew M. Radmanesh, “Radio Frequency &
Microwave Electronics”, Pearson Education Asia,
Second Edition, 2002.
