# 7.1 Principle components

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Helps the user understand the various components in NFC and their mathematical significance. Very useful for discussions presented in the next module.

An NFC system consists of a passive network (the card/circuit with information) and an active circuit. We must also take into account the environment surrounding the device. A working knowledge of these three componenents is essential to understanding the inner mechanics of near field communication.

## The active circuit

The active circuit has a transmitting antenna that broadcasts RF waves and a number of electrodes that read values corresponding to how the environment reacts to the RF waves. All the processing power is centered in this active circuit and that is where the decoding will take place. This would be considered the reader in the traditional sense. In the following mathematical discussion, the electrode voltages of the active circuit will be values in a vector v1.

## The passive network

The passive network consists of a series of electrodes which are attached to impedances with values of infinity or zero (open/closed switches). This network might be located inside a phone or other device and is associated with the client side identification. The configuration of the passive network uniquely identifies the user, and thus, our problem becomes one of reverse engineering in which we try to determine the impedances. In our analysis, the passive network voltages are stored in the vector v1 and the impedances are represented by the matrix Y1. Since we are assuming no mutual impedances, this is a diagonal matrix. Rather than using infinity, we have represented the open switches with the very high impedance value of 10,000 ohms.

## The environment

The “evil channel” is our environment. It converts our beautiful binary impedances into ugly complex voltages. It is our job to understand its effects and make sure that our output is decipherable. The channel matrix we used was given to us and was measured experimentally. It can be modeled by a large square matrix which is of size N x N where N is the total number of voltages (in this case 41). The matrix is labeled Ys and is divided into 9 separate matrices, each representing the mutual interaction of different elements in our matrix.

For example, the elements in matrix W12 would reperesent how the electrodes with voltages v1 interact with the electrodes with voltages v2. Consequently, our answer lies in simplifying this matrix and trying to nullify it’s effect on the input (the Y1 matrix).

## Problem analysis

As previously stated, the relationship between input impedences and output voltages is non-linear by nature. Thus, our task will be to find some underlying patterns between input and output so that we may adequately decode the voltage values. When presented with a problem as open-ended as this, a number of techniques can be employed. We must make a preliminary analysis of the data through the use of well-constructed plots and principle component analysis.

can someone help me with some logarithmic and exponential equations.
20/(×-6^2)
Salomon
okay, so you have 6 raised to the power of 2. what is that part of your answer
I don't understand what the A with approx sign and the boxed x mean
it think it's written 20/(X-6)^2 so it's 20 divided by X-6 squared
Salomon
I'm not sure why it wrote it the other way
Salomon
I got X =-6
Salomon
ok. so take the square root of both sides, now you have plus or minus the square root of 20= x-6
oops. ignore that.
so you not have an equal sign anywhere in the original equation?
Commplementary angles
hello
Sherica
im all ears I need to learn
Sherica
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Tamia
what is a good calculator for all algebra; would a Casio fx 260 work with all algebra equations? please name the cheapest, thanks.
a perfect square v²+2v+_
kkk nice
algebra 2 Inequalities:If equation 2 = 0 it is an open set?
or infinite solutions?
Kim
The answer is neither. The function, 2 = 0 cannot exist. Hence, the function is undefined.
Al
y=10×
if |A| not equal to 0 and order of A is n prove that adj (adj A = |A|
rolling four fair dice and getting an even number an all four dice
Kristine 2*2*2=8
Differences Between Laspeyres and Paasche Indices
No. 7x -4y is simplified from 4x + (3y + 3x) -7y
is it 3×y ?
J, combine like terms 7x-4y
im not good at math so would this help me
yes
Asali
I'm not good at math so would you help me
Samantha
what is the problem that i will help you to self with?
Asali
how do you translate this in Algebraic Expressions
Need to simplify the expresin. 3/7 (x+y)-1/7 (x-1)=
. After 3 months on a diet, Lisa had lost 12% of her original weight. She lost 21 pounds. What was Lisa's original weight?
what's the easiest and fastest way to the synthesize AgNP?
China
Cied
types of nano material
I start with an easy one. carbon nanotubes woven into a long filament like a string
Porter
many many of nanotubes
Porter
what is the k.e before it land
Yasmin
what is the function of carbon nanotubes?
Cesar
what is nanomaterials​ and their applications of sensors.
what is nano technology
what is system testing?
preparation of nanomaterial
Yes, Nanotechnology has a very fast field of applications and their is always something new to do with it...
what is system testing
what is the application of nanotechnology?
Stotaw
In this morden time nanotechnology used in many field . 1-Electronics-manufacturad IC ,RAM,MRAM,solar panel etc 2-Helth and Medical-Nanomedicine,Drug Dilivery for cancer treatment etc 3- Atomobile -MEMS, Coating on car etc. and may other field for details you can check at Google
Azam
anybody can imagine what will be happen after 100 years from now in nano tech world
Prasenjit
after 100 year this will be not nanotechnology maybe this technology name will be change . maybe aftet 100 year . we work on electron lable practically about its properties and behaviour by the different instruments
Azam
name doesn't matter , whatever it will be change... I'm taking about effect on circumstances of the microscopic world
Prasenjit
how hard could it be to apply nanotechnology against viral infections such HIV or Ebola?
Damian
silver nanoparticles could handle the job?
Damian
not now but maybe in future only AgNP maybe any other nanomaterials
Azam
can nanotechnology change the direction of the face of the world
At high concentrations (>0.01 M), the relation between absorptivity coefficient and absorbance is no longer linear. This is due to the electrostatic interactions between the quantum dots in close proximity. If the concentration of the solution is high, another effect that is seen is the scattering of light from the large number of quantum dots. This assumption only works at low concentrations of the analyte. Presence of stray light.
the Beer law works very well for dilute solutions but fails for very high concentrations. why?
how did you get the value of 2000N.What calculations are needed to arrive at it
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