# 6.5 Standing waves/vswr

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

In making this plot , we have made use of the fact that the propagation constant  can also be expressed as $\frac{2\pi }{}$ , 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 $\left|V(s)\right|$ 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 $\left|{V}^{-}\right|=\left|{}_{}\right|\left|{V}^{+}\right|$ , the maximum value of the standing wave pattern is $1+\left|{}_{}\right|$ times $\left|{V}^{+}\right|$ and the minimum is $1-\left|{}_{}\right|$ times $\left|{V}^{+}\right|$ . Note that anywhere on the line, the voltage is still oscillating at $e^{it}$ , 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:

$\mathrm{VSWR}=\frac{1+\left|\right|}{1-\left|\right|}$
Note that because $\left|{}_{}\right|\in \left[0 , 1\right]$ , $\mathrm{VSWR}\in \left\{1\right\}$ .

Although looks like the standing wave pattern is more or less sinusoidal, if we increase $\left|\right|$ 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 $\frac{}{2}$ . Why is this? Well, $(s)$ goes as $-2s$ and $=\frac{2\pi }{}$ , and so every time $s$ increases by $\frac{}{2}$ , $(s)$ decreases by $2\pi$ and we have come one full cycle on the way $\left|V(s)\right|$ behaves.

Now let's go back to the Crank Diagram . At the position shown, we are at a voltage maximum, and $\frac{Z(s)}{{Z}_{0}}$ just equals the VSWR.
$\frac{Z({s}_{{V}_{\mathrm{max}}})}{{Z}_{0}}=\mathrm{VSWR}=\frac{1+\left|{}_{}\right|}{1-\left|{}_{}\right|}$
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 .

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
$Z({s}_{{V}_{\mathrm{min}}})=\frac{1}{\mathrm{VSWR}}=\frac{1-\left|{}_{}\right|}{1+\left|{}_{}\right|}$
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.

where we get a research paper on Nano chemistry....?
nanopartical of organic/inorganic / physical chemistry , pdf / thesis / review
Ali
what are the products of Nano chemistry?
There are lots of products of nano chemistry... Like nano coatings.....carbon fiber.. And lots of others..
learn
Even nanotechnology is pretty much all about chemistry... Its the chemistry on quantum or atomic level
learn
da
no nanotechnology is also a part of physics and maths it requires angle formulas and some pressure regarding concepts
Bhagvanji
hey
Giriraj
Preparation and Applications of Nanomaterial for Drug Delivery
revolt
da
Application of nanotechnology in medicine
what is variations in raman spectra for nanomaterials
ya I also want to know the raman spectra
Bhagvanji
I only see partial conversation and what's the question here!
what about nanotechnology for water purification
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
Damian
yes that's correct
Professor
I think
Professor
Nasa has use it in the 60's, copper as water purification in the moon travel.
Alexandre
nanocopper obvius
Alexandre
what is the stm
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
Rafiq
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
Damian
How we are making nano material?
what is a peer
What is meant by 'nano scale'?
What is STMs full form?
LITNING
scanning tunneling microscope
Sahil
how nano science is used for hydrophobicity
Santosh
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
Rafiq
what is differents between GO and RGO?
Mahi
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
Rafiq
if virus is killing to make ARTIFICIAL DNA OF GRAPHENE FOR KILLED THE VIRUS .THIS IS OUR ASSUMPTION
Anam
analytical skills graphene is prepared to kill any type viruses .
Anam
Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
Hafiz
what is Nano technology ?
write examples of Nano molecule?
Bob
The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
Is there any normative that regulates the use of silver nanoparticles?
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
why we need to study biomolecules, molecular biology in nanotechnology?
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
why?
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
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