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How to find the load impedence using the Smith Chart and VSWR circle.

Let's move on to some other Smith Chart applications. Suppose, somehow, we can obtain a plot of V s on a line with some unknown load on it. The data might look like . What can we tell from this plot? Well, V max 1.7 and V min 0.3 which means

VSWR 1.7 0.3 5.667
and hence
Γ VSWR 1 VSWR 1 4.667 6.667 0.7

A standing wave pattern

Since r s Γ , we can plot r s on the Smith Chart, as shown here . We do this by setting the compass at a radius of 0.7 and drawing a circle! Now, Z L Z 0 is somewhere on this circle. We just do not know where yet! There is more information to begleaned from the VSWR plot however.

The vswr circle

Firstly, we note that the plot has a periodicity of about 10 cm. This means thatλthe wavelength of the signal on the line is 20 cm. Why? According to this equation, V s goes as φ s and φ s θ Γ 2 β s and β 2 λ , thus V s goes as 4 s λ . Thus each λ 2 , we are back to where we started.

Secondly, we note that there is a voltage minima at about 2.5 cm away from the load. Where on would we expect to find a voltage minima? It would be where r s has a phase angle of 180 ° or point "A" shown in here . The voltage minima is always where the VSWR circle passes through the real axis on the left hand side. (Conversely a voltagemaxima is where the circle goes through the real axis on the right hand side.) We don't really care about Z s Z 0 at a voltage minima, what we want is Z s 0 Z 0 , the normalized load impedance. This should be easy! If we start at "A" and go 2.5 20 0.125 λ towards the load we should end up at the point corresponding to Z L Z 0 . The arrow on the mini-Smith Chart says "Wavelengths towards generator" If we start at A, and want to go towards the load , we had better go around the opposite direction from the arrow. (Actually, as you can see on a real Smith Chart, there are arrows pointing in both directions, and they are appropriately marked for yourconvenience.)

Location of a vmin

So we start at "A" go 0.125 λ in a counter-clockwise direction, and mark a new point "B" which represents our Z L Z 0 which appears to be about 0.35 -0.95 or so . Thus, the load in this case (assuming a 50 Ω line impedance) is a resistor, again by co-incidence of about 50 Ω , in series with a capacitor with a negative reactance of about 47.5 Ω . Note that we could have started at the minima at 12.5 cm or even 22.5 cm, and then have rotated 12.5 20 0.625 λ or 22.5 20 1.125 λ towards the load. Since λ 2 0.5 λ means one complete rotation around the Smith Chart, we would have ended up at the same spot, with the same Z L Z 0 that we already have! We could also have started at a maxima, at say 7.5 cm, marked our starting point on the right handside of the Smith chart, and then we would go 0.375 λ counterclockwise and again, we'd end up at "B".

Moving from vmin to the load

Now, here is another example. In this case the VSWR 1.5 0.5 3 , which means Γ 0.5 and we get a circle as shown in . The wavelength λ 2 25 10 30 cm . The first minima is thus a distance of 10 30 0.333 λ from the load. So we again start at the minima, "A" and now rotate as distance 0.333 λ towards the load .

Another standing wave pattern

The vswr circle

Questions & Answers

Application of nanotechnology in medicine
what is variations in raman spectra for nanomaterials
Jyoti Reply
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.
Damian
yes that's correct
Professor
I think
Professor
what is the stm
Brian Reply
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?
LITNING Reply
what is a peer
LITNING Reply
What is meant by 'nano scale'?
LITNING Reply
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
what is Nano technology ?
Bob Reply
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?
Damian Reply
what king of growth are you checking .?
Renato
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
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
Adin
why?
Adin
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
anyone know any internet site where one can find nanotechnology papers?
Damian Reply
research.net
kanaga
sciencedirect big data base
Ernesto
Introduction about quantum dots in nanotechnology
Praveena Reply
hi
Loga
what does nano mean?
Anassong Reply
nano basically means 10^(-9). nanometer is a unit to measure length.
Bharti
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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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