6.11 Finding zl

 Page 1 / 1
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, $V(\mathrm{max})=1.7$ and $V(\mathrm{min})=0.3$ which means

$\mathrm{VSWR}=\frac{1.7}{0.3}=5.667$
and hence
$\left|\Gamma \right|=\frac{\mathrm{VSWR}-1}{\mathrm{VSWR}+1}=\frac{4.667}{6.667}=0.7$
Since $\left|r(s)\right|=\left|\Gamma \right|$ , 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, $\frac{{Z}_{L}}{{Z}_{0}}$ is somewhere on this circle. We just do not know where yet! There is more information to begleaned from the VSWR plot however. 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, $\left|V(s)\right|$ goes as $\cos \phi (s)$ and $\phi (s)={\theta }_{\Gamma }-2\beta s$ and $\beta =\frac{2\pi }{\lambda }$ , thus $\left|V(s)\right|$ goes as $\cos \left(\frac{4\pi s}{\lambda }\right)$ . Thus each $\frac{\lambda }{2}$ , 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 $\frac{Z(s)}{{Z}_{0}}$ at a voltage minima, what we want is $\frac{Z(s=0)}{{Z}_{0}}$ , the normalized load impedance. This should be easy! If we start at "A" and go $\frac{2.5}{20}=0.125\lambda$ towards the load we should end up at the point corresponding to $\frac{{Z}_{L}}{{Z}_{0}}$ . 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.)

So we start at "A" go $0.125\lambda$ in a counter-clockwise direction, and mark a new point "B" which represents our $\frac{{Z}_{L}}{{Z}_{0}}$ which appears to be about $0.35+-0.95i$ or so . Thus, the load in this case (assuming a $50\Omega$ line impedance) is a resistor, again by co-incidence of about $50\Omega$ , in series with a capacitor with a negative reactance of about $47.5\Omega$ . Note that we could have started at the minima at 12.5 cm or even 22.5 cm, and then have rotated $\frac{12.5}{20}=0.625\lambda$ or $\frac{22.5}{20}=1.125\lambda$ towards the load. Since $\frac{\lambda }{2}=0.5\lambda$ means one complete rotation around the Smith Chart, we would have ended up at the same spot, with the same $\frac{{Z}_{L}}{{Z}_{0}}$ 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 $0.375\lambda$ counterclockwise and again, we'd end up at "B". Now, here is another example. In this case the $\mathrm{VSWR}=\frac{1.5}{0.5}=3$ , which means $\left|\Gamma \right|=0.5$ and we get a circle as shown in . The wavelength $\lambda =2(25-10)=30\mathrm{cm}$ . The first minima is thus a distance of $\frac{10}{30}=0.333\lambda$ from the load. So we again start at the minima, "A" and now rotate as distance $0.333\lambda$ towards the load .

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
anyone know any internet site where one can find nanotechnology papers?
research.net
kanaga
sciencedirect big data base
Ernesto
Introduction about quantum dots in nanotechnology
what does nano mean?
nano basically means 10^(-9). nanometer is a unit to measure length.
Bharti
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
absolutely yes
Daniel
how to know photocatalytic properties of tio2 nanoparticles...what to do now
it is a goid question and i want to know the answer as well
Maciej
characteristics of micro business
Abigail
for teaching engĺish at school how nano technology help us
Anassong
Do somebody tell me a best nano engineering book for beginners?
there is no specific books for beginners but there is book called principle of nanotechnology
NANO
what is fullerene does it is used to make bukky balls
are you nano engineer ?
s.
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.
Tarell
what is the actual application of fullerenes nowadays?
Damian
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.
Tarell
what is the Synthesis, properties,and applications of carbon nano chemistry
Mostly, they use nano carbon for electronics and for materials to be strengthened.
Virgil
is Bucky paper clear?
CYNTHIA
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
NANO
so some one know about replacing silicon atom with phosphorous in semiconductors device?
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.
Harper
Do you know which machine is used to that process?
s.
how to fabricate graphene ink ?
for screen printed electrodes ?
SUYASH
What is lattice structure?
of graphene you mean?
Ebrahim
or in general
Ebrahim
in general
s.
Graphene has a hexagonal structure
tahir
On having this app for quite a bit time, Haven't realised there's a chat room in it.
Cied
how did you get the value of 2000N.What calculations are needed to arrive at it
Privacy Information Security Software Version 1.1a
Good
Got questions? Join the online conversation and get instant answers!         By 