MadSci Network: Physics
Query:

Re: Do standing waves transfer energy?

Date: Sat Jan 24 17:30:42 2004
Posted By: Adrian E. Popa, Laboratory Director Emeritus
Area of science: Physics
ID: 1074768555.Ph
Message:



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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