Unit 2
High Frequency Transmission Lines
Power and impedance
measurement on transmission lines
Session Meta Data
Author Ramprabhu S
Version No. 1.1
Release Date 14-01-2020
Reviewer
Revision History
Date of Revision Details Version Number
14 Jan 2020 1.1
Session Objectives
To introduce the concepts of power and
impedance measurement of transmission lines.
Session Outcomes
At the end of the session, students will be able to
Measure the power and impedance on a
transmission line .
Outline
Power measurement
Impedance measurement
Power measurement
The expressions for the voltage and current on
the dissipation less line as
Voltage and current phasor diagram
It can be seen that the voltage and current phasors
are drawn in this Fig with phasors A and B being
proportional to E and I respectively.
Power measurement
At voltage maximum points, the incident and reflected
voltage waves are in phase. From the phasor diagram, it
is noted that the line 1∠0° is proportional to the
incident voltage and |K|∠Φ-2βs is proportional to the
reflected voltage. The in-phase condition is required for
Emax, so that
Similarly at a current maximum, the incident and
reflected current waves must also be in phase Imax, so
that
Power measurement
From the above equations, it can be seen that
Since a change to the values at voltage and current
minima requires only the reversal of phase of the
reflected waves or a minus sign in front of |K|, it can be
seen that a similar value for Ro can be derived as
Power measurement
It may be seen that a voltage maximum and a current
minimum occur at the same point on the line. At such a
point the current and voltage are in phase or if the
impedance of the line is measured looking toward the
load, the impedance seen will be resistive.
The resistive impedance seen at a voltage loop is
Power measurement
Since the voltage and current are again in phase at a
current loop, the resistive impedance seen there may be
identified as
Power measurement
The power passing a voltage loop is the power
effectively flowing into a resistance Rmax at voltage Emax,
so that
The same value of power must also pass the current
loop, effectively flowing into a resistance Rmin at
voltage Emin, since there is no line dissipation, so that
Power measurement
The expression for power passing along the line is given
as
The power may also be expressed as
These expressions permit easy measurements of power
flow on a line of negligible losses.
Power measurement
• In many lines, especially those of coaxial
construction, the dielectric strength or the voltage
breakdown of the line dielectric limits the voltage on
the line and thus fixes the maximum power that may
be transmitted.
• For a given maximum line voltage, the above
equation shows that the greatest amount of power will
be transmitted if |Emax|= |Emin|, or the line is operated
as a smooth line without standing waves and with an
Ro termination.
• For the greatest transfer of power from line to load to
operate the line with an Ro termination, provided the
line is sufficiently long that the output image
impedance is substantially Ro.
Impedance measurement
• The unknown value of a load impedance ZR connected
to a transmission line may be determined by standing-
wave measurements on the open-wire or slotted line.
• The characteristic impedance Ro of the line must be
known or calculated, and measurements must be made
of the standing-wave ratio S and the distance s' from
the load to the nearest point of voltage minimum.
• At the point of voltage minimum it has been shown
that
Impedance measurement
• At any point on a line,
so that at the point of voltage minimum, distant s' from
the load,
Impedance measurement
Solution for ZR gives
The above equation gives the measurement of load
impedance. The point of a voltage minimum is
measured rather than a voltage maximum because it is
usually possible to determine the exact point of
minimum voltage with greater accuracy.
Summary
• The expression for power passing along the line
is given as
Test Your Understanding
• How to measure power and impedance on 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.
