# 6.12 Matching

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Using the Smith Chart to match the appropriate circuit elements to a line.

This gets us to "B", and we find that $\frac{{Z}_{L}()}{{Z}_{0}()}=1+1.2i$ .Now this is a very interesting

result. Suppose we take the load off the line, and add, in series, an additional capacitor, whose reactance is $\frac{1}{j\times \omega \times C}=-(i\times 1.2{Z}_{0})$ .

The capacitor and the inductor just cancel each other out (series resonance) and so the apparent load for the line is just ${Z}_{0}()$ , the magnitude of the reflection coefficient (Γ)= 0 and the $\mathrm{VSWR}=1.0$ ! All of the energy flowing down the line is coupled to the load resistor, and nothing is reflected back towards the load.

We were lucky that the real part of $\frac{{Z}_{L}()}{{Z}_{0}()}=1$ . If there were not that case, we would not be able to "match" the load to the line, right? Not completely. Let'sconsider another example. The next figure shows a line with a ${Z}_{0}()=50$ , terminated with a $25(Ω)$ resistor. ${\Gamma }_{L}()=\frac{-1}{3}$ , and we end up with the VSWR circle shown in the subsequent figure .

How could we match this load? We could add another 25Ω in series with the first resistor, but if we want to maximize thepower we deliver to the first one, this would not be a very satisfactory approach. Let's move down the line a ways. If we goto point "B", we find that

at this spot, $\frac{{Z}_{s}()}{{Z}_{0}()}=1+0.8i$ . Once again we have an impedance with a normalized real part equals 1! How far do we go? It looks like it's a littlemore than $0.15(\lambda )$ . If we add a negative reactance in series with the line at this point, with a normalized value of $-(0.8i)$ , then from that point on back to the generator, the line would "look" like it was terminated with a matched load.

There's one awkward feature to this solution, and that is we have to cut the line to insert the capacitor. It would be a loteasier if we could simply add something across the line, instead of having to cut it. This is easily done, if we go over into theadmittance world.

what is variations in raman spectra for nanomaterials
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
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
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 did you get the value of 2000N.What calculations are needed to arrive at it
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Berger describes sociologists as concerned with
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