# 3.20 Analog signal processing problems  (Page 6/6)

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## A circuit problem

You are given the depicted circuit .

1. Find the differential equation relating the output voltage to the source.
2. What is the impedance “seen” by the capacitor?

## Analog computers

Because the differential equations arising in circuits resemble those that describemechanical motion, we can use circuit models to describe mechanical systems. An ELEC 241 student wants tounderstand the suspension system on his car. Without a suspension, the car's body moves in concert with the bumpsin the raod. A well-designed suspension system will smooth out bumpy roads, reducing the car's vertical motion. Ifthe bumps are very gradual (think of a hill as a large but very gradual bump), the car's vertical motion shouldfollow that of the road. The student wants to find a simple circuit that will model the car's motion. He istrying to decide between two circuit models ( [link] ).

Here, road and car displacements are represented by the voltages ${v}_{\mathrm{road}}(t)$ and ${v}_{\mathrm{car}}(t)$ , respectively.

1. Which circuit would you pick? Why?
2. For the circuit you picked, what will be the amplitude of the car's motion if the road has adisplacement given by ${v}_{\mathrm{road}}(t)=1+\sin (2t)$ ?

## Transfer functions and circuits

You are given the depicted network .

1. Find the transfer function between ${V}_{\mathrm{in}}$ and ${V}_{\mathrm{out}}$ .
2. Sketch the magnitude and phase of your transferfunction. Label important frequency, amplitude and phase values.
3. Find ${v}_{\mathrm{out}}(t)$ when ${v}_{\mathrm{in}}(t)=\sin (\frac{t}{2}+\frac{\pi }{4})$ .

## Fun in the lab

You are given an unopenable box that has two terminals sticking out. You assume the box contains a circuit. Youmeasure the voltage $\sin (t+\frac{\pi }{4})$ across the terminals when nothing is connected to them and the current $\sqrt{2}\cos t$ when you place a wire across the terminals.

1. Find a circuit that has these characteristics.
2. You attach a 1 H inductor across the terminals. What voltage do you measure?

## Dependent sources

Find the voltage ${v}_{\mathrm{out}}$ in each of the depicted circuits .

## Operational amplifiers

Find the transfer function between the source voltage(s) andthe indicated output voltage for the circuits shown in [link] .

## Op-amp circuit

The following circuit is claimed to serve a useful purpose.

1. What is the transfer function relating the complex amplitude of the output signal, the current ${I}_{\mathrm{out}}$ , to the complex amplitude of the input, the voltage ${V}_{\mathrm{in}}$ ?
2. What equivalent circuit does the load resistor ${R}_{L}$ see?
3. Find the output current when ${v}_{\mathrm{in}}={V}_{0}e^{-\left(\frac{t}{\tau }\right)}$ .

## Why op-amps are useful

The circuit of a cascade of op-amp circuits illustrate the reason whyop-amp realizations of transfer functions are so useful.

1. Find the transfer function relating the complexamplitude of the voltage ${v}_{\mathrm{out}}(t)$ to the source. Show that this transfer function equals the product of each stage's transfer function.
2. What is the load impedance appearing across the first op-amp's output?
3. [link] illustrates that sometimes “designs” can go wrong. Find the transferfunction for this op-amp circuit , and then show that it can't work! Why can't it?

## Operational amplifiers

Consider the depicted circuit .

1. Find the transfer function relating the voltage ${v}_{\mathrm{out}}(t)$ to the source.
2. In particular, ${R}_{1}=530\Omega$ , ${C}_{1}=1\mathrm{\mu F}$ , ${R}_{2}=5.3\mathrm{k\Omega }$ , ${C}_{2}=0.01\mathrm{\mu F}$ , and ${R}_{3}={R}_{4}=5.3\mathrm{k\Omega }$ . Characterize the resulting transfer function anddetermine what use this circuit might have.

## Designing a bandpass filter

We want to design a bandpass filter that has transferthe function $H(f)=10\frac{i\times 2\pi f}{(i\frac{f}{{f}_{l}}+1)(i\frac{f}{{f}_{h}}+1)}$ Here, ${f}_{l}$ is the cutoff frequency of the low-frequency edge of the passband and ${f}_{h}$ is the cutoff frequency of the high-frequency edge. We want ${f}_{l}=1\mathrm{kHz}$ and ${f}_{h}=10\mathrm{kHz}$ .

1. Plot the magnitude and phase of this frequency response. Label important amplitude and phase valuesand the frequencies at which they occur.
2. Design a bandpass filter that meets thesespecifications. Specify component values.

## Pre-emphasis or de-emphasis?

In audio applications, prior to analog-to-digital conversion signals are passed throughwhat is known as a pre-emphasis circuit that leaves the low frequencies alone but provides increasinggain at increasingly higher frequencies beyond some frequency ${f}_{0}$ . De-emphasis circuits do the opposite and are applied after digital-to-analog conversion. Afterpre-emphasis, digitization, conversion back to analog and de-emphasis, the signal's spectrumshould be what it was.

The op-amp circuit here has been designed for pre-emphasis or de-emphasis (Samantha can'trecall which).

1. Is this a pre-emphasis or de-emphasis circuit? Find the frequency ${f}_{0}$ that defines the transition from low to highfrequencies.
2. What is the circuit's output when the input voltage is $\sin (2\pi ft)$ , with $f=4\mathrm{kHz}$ ?
3. What circuit could perform the opposite function to your answer for the first part?

## Active filter

Find the transfer function of the depicted active filter .

## This is a filter?

You are given a circuit .

1. What is this circuit's transfer function? Plot the magnitude and phase.
2. If the input signal is the sinusoid $\sin (2\pi {f}_{0}t)$ , what will the output be when ${f}_{0}$ is larger than the filter's “cutoff frequency”?

This circuit served as a transducer, converting light energy into a voltage ${v}_{\mathrm{out}}$ . The photodiode acts as a current source, producing a current proportional to the light intesityfalling upon it. As is often the case in this crucial stage, the signals are small and noise can be aproblem. Thus, the op-amp stage serves to boost the signal and to filter out-of-band noise.

1. Find the transfer function relating light intensity to ${v}_{\mathrm{out}}$ .
2. What should the circuit realizing the feedbackimpedance ${Z}_{f}$ be so that the transducer acts as a 5 kHz lowpass filter?
3. A clever engineer suggests an alternative circuit to accomplish the same task. Determine whether the idea works or not. If itdoes, find the impedance ${Z}_{\mathrm{in}}$ that accomplishes the lowpass filtering task. If not, show why it does not work.

## Reverse engineering

The depicted circuit has been developed by the TBBG Electronics design group. They are trying to keep itsuse secret; we, representing RU Electronics, have discovered the schematic and want to figure out theintended application. Assume the diode is ideal.

1. Assuming the diode is a short-circuit (it has been removed from the circuit), what is the circuit'stransfer function?
2. With the diode in place, what is the circuit's outputwhen the input voltage is $\sin (2\pi {f}_{0}t)$ ?
3. What function might this circuit have?

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
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
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