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This module covers the idea of voltage standing wave ratio (VSWR).

A standing wave pattern

In making this plot , we have made use of the fact that the propagation constant can also be expressed as 2 , and so for the independent variable, instead of showing s in meters or whatever, we normalize the distance away from the load to the wavelengthof the excitation signal, and hence show distance in wavelengths. What we are showing here is called a standing wave . There are places along the line where the magnitude of the voltage V s has a maximum value. This is where V + and V - are adding up in phase with one another, and places where there is a voltage minimum, where V + and V - add up out of phase. Since V - V + , the maximum value of the standing wave pattern is 1 times V + and the minimum is 1 times V + . Note that anywhere on the line, the voltage is still oscillating at t , and so it is not a constant, it is just that the magnitude of the oscillating signal changes as we move down the line. If we were to put an oscilloscope across theline, we would see an AC signal, oscillating at a frequency .

A number of considerable interest is the ratio of the maximum voltage amplitude to the minimum voltage amplitude,called the voltage standing wave ratio , or VSWR for short. It is easy to see that:

VSWR 1 1
Note that because 0 1 , VSWR 1 .

Although looks like the standing wave pattern is more or less sinusoidal, if we increase to 0.8, we see that it most definitely is not. There is also a temptation to say that the spacing between minima (ormaxima) of the standing wave pattern is , the wavelength of the signal, but a closer inspection of either or , shows that in fact the spacing between features is only half a wavelength, or 2 . Why is this? Well, s goes as -2 s and 2 , and so every time s increases by 2 , s decreases by 2 and we have come one full cycle on the way V s behaves.

Standing wave pattern with a larger reflection coefficient

Now let's go back to the Crank Diagram . At the position shown, we are at a voltage maximum, and Z s Z 0 just equals the VSWR.
Z s V max Z 0 VSWR 1 1
Note also that at this particular point, that the voltage and current phasors are in phase with one another (lined up in thesame direction) and hence the impedance must be real or resistive.

We can move further down the line, and now the V s phasor starts shrinking, and the I s phasor starts to get bigger .

Moving further down the line

Moving further down the line from a V max
If we move even further down the line, we get to a point wherethe current phasor is now at a maximum value, and the voltage phasor is at a minimum value . We are now at a voltage minimum, the impedance is again real (the voltageand current phasors are lined up with one another, so they must be in phase) and
Z s V min 1 VSWR 1 1

Moving even further down the line

Crank diagram at a V min
The only problem we have here is that except at a voltage minimum or maximum, finding Z s from the crank diagram is not very straightforward, since the voltage and current are out of phase, and dividing thetwo vectors becomes somewhat tedious.

Questions & Answers

I only see partial conversation and what's the question here!
Crow Reply
what about nanotechnology for water purification
RAW Reply
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
what is the stm
Brian Reply
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
How we are making nano material?
what is a peer
What is meant by 'nano scale'?
What is STMs full form?
scanning tunneling microscope
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Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
what is differents between GO and RGO?
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
what is Nano technology ?
Bob Reply
write examples of Nano molecule?
The nanotechnology is as new science, to scale nanometric
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
Stoney Reply
why we need to study biomolecules, molecular biology in nanotechnology?
Adin Reply
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
what school?
biomolecules are e building blocks of every organics and inorganic materials.
anyone know any internet site where one can find nanotechnology papers?
Damian Reply
sciencedirect big data base
Introduction about quantum dots in nanotechnology
Praveena Reply
what does nano mean?
Anassong Reply
nano basically means 10^(-9). nanometer is a unit to measure length.
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
Damian Reply
absolutely yes
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Akash Reply
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How can I make nanorobot?
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Smarajit Reply
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Source:  OpenStax, Introduction to physical electronics. OpenStax CNX. Sep 17, 2007 Download for free at http://cnx.org/content/col10114/1.4
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