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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

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
how to know photocatalytic properties of tio2 nanoparticles...what to do now
Akash Reply
it is a goid question and i want to know the answer as well
characteristics of micro business
for teaching engĺish at school how nano technology help us
Do somebody tell me a best nano engineering book for beginners?
s. Reply
there is no specific books for beginners but there is book called principle of nanotechnology
what is fullerene does it is used to make bukky balls
Devang Reply
are you nano engineer ?
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
what is the actual application of fullerenes nowadays?
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
what is the Synthesis, properties,and applications of carbon nano chemistry
Abhijith Reply
Mostly, they use nano carbon for electronics and for materials to be strengthened.
is Bucky paper clear?
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
so some one know about replacing silicon atom with phosphorous in semiconductors device?
s. Reply
Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure.
Do you know which machine is used to that process?
how to fabricate graphene ink ?
for screen printed electrodes ?
What is lattice structure?
s. Reply
of graphene you mean?
or in general
in general
Graphene has a hexagonal structure
On having this app for quite a bit time, Haven't realised there's a chat room in it.
how did you get the value of 2000N.What calculations are needed to arrive at it
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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