# 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 ${i}_{1}()=-1$ .

#### Questions & Answers

what is Nano technology ?
Bob Reply
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?
Damian Reply
what king of growth are you checking .?
Renato
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
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
Adin
why?
Adin
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?
Damian Reply
research.net
kanaga
sciencedirect big data base
Ernesto
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.
Bharti
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
Daniel
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
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?
s. Reply
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
Devang Reply
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
Abhijith Reply
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?
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.
Harper
Do you know which machine is used to that process?
s.
how to fabricate graphene ink ?
SUYASH Reply
for screen printed electrodes ?
SUYASH
What is lattice structure?
s. Reply
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
Smarajit Reply
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Source:  OpenStax, Fundamentals of electrical engineering i. OpenStax CNX. Aug 06, 2008 Download for free at http://legacy.cnx.org/content/col10040/1.9
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