EC8651 – Transmission Lines and
RF Systems
UNIT – I
TRANSMISSION LINE THEORY
General theory of Transmission lines - the
transmission line - general solution - The infinite line
- Wavelength, velocity of propagation - Waveform
distortion - the distortion-less line - Loading and
different methods of loading - Line not terminated
in Z0 - Reflection coefficient - calculation of current,
voltage, power delivered and efficiency of
transmission - Input and transfer impedance - Open
and short circuited lines - reflection factor and
GENERAL THEORY OF TRANSMISSION LINES
• A Transmission line is a device designed to guide electrical energy from one
point to another, i.e., to transfer the output RF energy from a transmitter to
an antenna.
• This energy will not travel through normal electrical wire without great
losses.
• Although the antenna can be connected directly to the transmitter, the
antenna is usually located some distance away from the transmitter.
• The transmitter is located inside a radio room and its associated antenna is
mounted somewhere away from transmitter.
• A transmission line is used to connect the transmitter and the antenna.
• The purpose of transmission line is to transfer the energy output of the
transmitter to the antenna with the least possible power loss which
depends on the special physical and electrical characteristics (impedance
and resistance) of the transmission line.
Transmission Line Theory
• The electrical characteristics of a two-wire transmission line
depend primarily on the construction of the line.
• The two-wire line acts like a long capacitor and the change of its
capacitive reactance is noticeable as the frequency applied to it is
changed.
• Since the long conductors have a magnetic field about them when
electrical energy is being passed through them, they also exhibit
the properties of inductance.
• The values of inductance and capacitance presented depend on
the various physical factors are:
– type of line used,
– dielectric in the line and
– length of the line.
• The effects of the inductive and capacitive reactance of the line
depend on the frequency applied.
• Since no dielectric is perfect, electrons manage to
move from one conductor to the other through the
dielectric.
• Each type of two-wire transmission line also has a
conductance value and it represents the value of the
current flow that may be expected through the
insulation,
• If the line is uniform (all values equal at each unit
length), then one small section of the line may
represent several feet.
• This illustration of a two-wire transmission line will be
used throughout the discussion of transmission lines.
• It should be noted that the principles presented apply
• A transmission line has the properties of
inductance, capacitance, and resistance just as the
more conventional circuits have.
• Usually, however, the constants in conventional
circuits are lumped into a single device or
component.
• A coil of wire has the property of inductance.
• When a certain amount of inductance is needed in a
circuit, a coil of the proper dimensions is inserted.
• The inductance of the circuit is lumped into the one
component.
• Two metal plates separated by a small space, can
be used to supply the required capacitance for a
circuit.
• In such a case, most of the capacitance of the
circuit is lumped into this one component.
• Similarly, a fixed resistor can be used to supply a
certain value of circuit resistance as a lumped sum.
• Ideally, a transmission line would also have its
constants of inductance, capacitance, and
resistance lumped together.
• Unfortunately, this is not the case. Transmission
line constants are as described in the following
paragraphs.
Distributed Constants
• Transmission line constants, called distributed
constants, are spread along the entire length of the
transmission line and cannot be distinguished
separately.
• The amount of inductance, capacitance, and
resistance depends on the
– length of the line,
– size of the conducting wires,
– spacing between the wires and
– dielectric (air or insulating medium) between the wires.
• The electrical lines which are used to transmit the
electrical waves along them are represented as
• The parameters of a transmission line are:
– Resistance(R),
– Inductance (L),
– Capacitance (C) and
– Conductance (G).
• Hence transmission line is called distributed network.
• Resistance (R) is defined as the loop resistance per unit
length of the wire. Unit : ohm/Km
• Inductance (L) is defined as the loop inductance per unit
length of the wire. Unit: Henry/Km
• Capacitance (C) is defined as the loop capacitance per
unit length of the wire. Unit :Farad/Km
• Conductance(G) is defined as the loop conductance per
unit length of the wire. Unit: mho/Km
• Since the line constants R, L, C and G are
distributed through the entire length of the
line, they are called as distributed elements.
• They are also called as primary constants.
• The secondary constants of a line are:
– Characteristic Impedance
– Propagation Constant
Application of transmission lines.
• They are used to transmit signal i.e. EM Waves from
one point to another.
• They can be used for impedance matching purpose.
• They can be used as circuit elements like inductors,
capacitors.
• They can be used as stubs by properly adjusting
their lengths.
• Wavelength of a line is the distance the wave travels
along the line while the phase angle is changing
through 2π radians.
• Characteristic impedance is the impedance
measured at the sending end of the line.
• It is given by Z0 = Z/Y,
– where Z = R + jwL is the series impedance
– Y = G + jwC is the shunt admittance.
Propagation constant
• It is defined as the natural logarithm of the ratio
of the sending end current or voltage to the
receiving end current or voltage of the line.
• It gives the manner in the wave is propagated
along a line and specifies the variation of voltage
and current in the line as a function of distance.
• Propagation constant is a complex quantity and is
expressed as γ = α + j β
• The real part is called the attenuation constant
whereas the imaginary part of propagation
constant is called the phase constant.
