MadSci Network: Physics |
Greetings Hashu:
Reference:
S. Ramo, J. R. Winnery, T. Van Duzer,
Fields and Waves in Communication Electronics
John Wiley & Sons, New York, 1965
The measurement of standing waves is an important parameter in physics
and
engineering for determining the wavelength that a wave generator
produces
and for measuring the efficiency of power transfer from the wave
generator
to a load at the termination of a transmission line. Standing waves
are
generated in many ways including acoustic (sound) waves in organ
pipes,
horns and in stringed instruments; in radio frequency transmission
lines;
in microwave waveguides and in light waves in fiber optic transmission
lines.
In this answer I'll use radio waves as an example; however, the basic
concepts described here pertain to all forms of standing waves.
One of the most common uses for observing standing waves is to measure
the
efficiency of power transfer from a radio transmitter to a radiating
antenna. A typical instrument for measuring standing waves is called a
Slotted Line. This instrument usually consists of a coaxial
cable
fabricated with a small slot, that is many wavelengths long, placed in
the
outer metallic sheath of the cable. A calibrated radio receiver
connected to
a small antenna probe, that can move along the line, is inserted into
the slot to measure the voltage at various points along the cable. In
this
way we can measure the voltage of the maximum and minimum points along
the
cable. The distance between two minimum points of the standing wave
gives a
very accurate measurement of one half of the wavelength of the
transmitter
within the cable. The wavelength inside a cable is usually about 60%
of the
wavelength in air because of the dielectric materials used to support
the
center conductor of a coaxial cable.
In the Mad Science Archives I have discussed how standing waves
are generated
in answer to the following question:
Wed Jan 22 00:13:27 1997
When waves collide, do both kinds of interference occur?
http:
//www.madsci.org/posts/archives/mar97/853194471.Ph.r.html
In this answer I have presented a plot of the interference between two
waves
traveling in opposite directions as they produce a standing wave. This
answer
also has a simple program in BASIC that can be used to generate
the plots.
In a radio frequency (RF) transmitter/antenna system, if the antenna
is a
perfect
design and all of the transmitter power is radiated into space, there
would be
no reflected wave to produce a standing wave in the transmission line.
In this
case our slotted line would measure a constant AC voltave all along
the
transmission line. However, if the antenna acts like a short circuit
then all
of the transmitter power wound be reflected back from the antenna to
the
transmitter. In this case we would measure a standing wave that ranges
from a
maximum voltage every one half wavelength to node points also spaced
every one
half wavelength along the line. At these node points we would measure
zero
voltage. This is the condition demonstrated in the BASIC plot.
Real antennas are not designed to be short circuits and they are also
not perfect
and do not radiate 100 % of the transmitted power. Thus some power is
always
reflected
from an antenna and a measurable standing wave is produced; however
the minimum
node points of voltage along the standing wave do not go all the way
to zero voltage.
To measure the efficiency of an antenna to radiate RF power we measure
the peak
voltage along the standing wave and the minimum voltage along the
standing wave
and divide the peak voltage by the minimum voltage. This data
determines the
Voltage Standing Wave Ratio (VSWR). By using the following
formula
the
VSWR can give us an accurate measure of how much power is radiated by
the antenna
and how much power is reflected from the antenna and wasted:
Power reflected / Power transmitted = [ (VSWR-1) / (VSWR+1)] ^2
Thus if the minimum voltage we measure is one half of the peak voltage
we
measure the VSWR = 2.0
Placing this VSWR in the power formula gives : [(2-1) / (2+1)]^2 =
(1/3)^2 = 1/9
Thus an antenna with a VSWR of 2.0 radiates 8/9 (88.9%) of the
transmitter power
and reflects 1/9 (11.1 %) of wasted transmitter power. In practice an
antenna with
a VSWR less than 2.0 is considered a good antenna design. An antenna
with a VSWR = 1.0 would be be perfect and radiate 100% of the
transmitter power.
If the VSWR were measured to be 4.0, the power formula gives 9/25.
This antenna
reflects 36% of the transmitter power and radiates only 64% of the
transmitter
power. If this were a high power transmitter, a 36% reflection would
probably
damage the transmitter circuitry. In this case radio engineers must
design matching
circuits between the transmitter and the antenna if poor antennas must
be used in
a particular application.
Measuring the VSWR and the distance of the VSWR nodes from the antenna
also
enables radio engineers to determine very accurately the electrical
resistance
and impedance characteristics of the antenna or any other type of
load. However,
this technique is much to complex to discuss in this forum and takes
up several
chapters in the referenced text book.
In answer to your question any standing wave, including sound
waves,
radio waves,
microwaves or light waves, are caused by wasted power that is
reflected from the
load in a given application. However, all practical devices and
circuits produce
reflections and measuring the standing wave ratio characteristics of
devices
is very
valuable in determining the operating parameters and efficiency of a
device
in a given application.
Best regards Your Mad Scientist
Adrian Popa
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