# 3.20 Analog signal processing problems

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Problems Dealing with Analog Signal Processing

## Simple circuit analysis

For each circuit shown in [link] , the current $i$ equals $\cos (2\pi t)$ .

1. What is the voltage across each element and what is the voltage $v$ in each case?
2. For the last circuit, are there element values that make the voltage $v$ equal zero for all time? If so, what element values work?
3. Again, for the last circuit, if zero voltage were possible, what circuit element could substitute for the capacitor-inductor series combination that would yield the same voltage?

## Solving simple circuits

1. Write the set of equations that govern Circuit A's behavior.
2. Solve these equations for ${i}_{1}()$ : In other words, express this current in terms ofelement and source values by eliminating non-source voltages and currents.
3. For Circuit B, find the value for ${R}_{\text{L}}$ that results in a current of 5 A passing through it.
4. What is the power dissipated by the load resistor ${R}_{\text{L}}$ in this case?

## Equivalent resistance

For each of the following circuits , find the equivalent resistance using series and parallel combination rules.

Calculate the conductance seen at the terminals for circuit (c) in terms of each element's conductance.Compare this equivalent conductance formula with the equivalent resistance formula you found for circuit (b).How is the circuit (c) derived from circuit (b)?

## Superposition principle

One of the most important consequences of circuit laws is the Superposition Principle : The current or voltage defined for any element equals the sum of thecurrents or voltages produced in the element by the independent sources. This Principle has importantconsequences in simplifying the calculation of ciruit variables in multiple source circuits.

1. For the depicted circuit , find the indicated current using any technique you like (youshould use the simplest).
2. You should have found that the current $i$ is a linear combination of the two source values: $i={C}_{1}(){v}_{\mathrm{in}}()+{C}_{2}(){i}_{\mathrm{in}}()$ . This result means that we can think of the current asa superposition of two components, each of which is due to a source. We can find each component by settingthe other sources to zero. Thus, to find the voltage source component, you can set the current source tozero (an open circuit) and use the usual tricks. To find the current source component, you would set thevoltage source to zero (a short circuit) and find the resulting current. Calculate the total current $i$ using the Superposition Principle. Is applying the SuperpositionPrinciple easier than the technique you used in part (1)?

## Current and voltage divider

Use current or voltage divider rules to calculate the indicated circuit variables in [link] .

## Thévenin and mayer-norton equivalents

Find the Thévenin and Mayer-Norton equivalentcircuits for the following circuits .

## Detective work

In the depicted circuit , the circuit ${N}_{1}()$ has the v-i relation ${v}_{1}()=3{i}_{1}()+7$ when ${i}_{s}()=2$ .

1. Find the Thévenin equivalent circuit for circuit ${N}_{2}()$ .
2. With ${i}_{s}()=2$ , determine $R$ such that ${i}_{1}()=-1$ .

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 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
Abigail
for teaching engĺish at school how nano technology help us
Anassong
How can I make nanorobot?
Lily
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
how can I make nanorobot?
Lily
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 By      By  By Sam Luong  By