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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 road t and v 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 road t 1 2 t ?

Transfer functions and circuits

You are given the depicted network .

  1. Find the transfer function between V in and V out .
  2. Sketch the magnitude and phase of your transferfunction. Label important frequency, amplitude and phase values.
  3. Find v out t when v in t t 2 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 t 4 across the terminals when nothing is connected to them and the current 2 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 out in each of the depicted circuits .

Circuit a

Circuit b

Operational amplifiers

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

Op-amp a

Op-amp b

Op-amp c

Op-amp d

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 out , to the complex amplitude of the input, the voltage V in ?
  2. What equivalent circuit does the load resistor R L see?
  3. Find the output current when v in V 0 t τ .

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 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 out t to the source.
  2. In particular, R 1 530 Ω , C 1 1 μF , R 2 5.3 , C 2 0.01 μF , and R 3 R 4 5.3 . 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 2 f f f l 1 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 kHz and f h 10 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 2 f t , with f 4 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 2 f 0 t , what will the output be when f 0 is larger than the filter's “cutoff frequency”?

Optical receivers

In your optical telephone, the receiver circuit had the form shown .

This circuit served as a transducer, converting light energy into a voltage v 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 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 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 2 f 0 t ?
  3. What function might this circuit have?

Questions & Answers

how can chip be made from sand
Eke Reply
is this allso about nanoscale material
are nano particles real
Missy Reply
Hello, if I study Physics teacher in bachelor, can I study Nanotechnology in master?
Lale Reply
no can't
where is the latest information on a no technology how can I find it
where we get a research paper on Nano chemistry....?
Maira Reply
nanopartical of organic/inorganic / physical chemistry , pdf / thesis / review
what are the products of Nano chemistry?
Maira Reply
There are lots of products of nano chemistry... Like nano coatings.....carbon fiber.. And lots of others..
Even nanotechnology is pretty much all about chemistry... Its the chemistry on quantum or atomic level
no nanotechnology is also a part of physics and maths it requires angle formulas and some pressure regarding concepts
Preparation and Applications of Nanomaterial for Drug Delivery
Hafiz Reply
Application of nanotechnology in medicine
has a lot of application modern world
what is variations in raman spectra for nanomaterials
Jyoti Reply
ya I also want to know the raman spectra
I only see partial conversation and what's the question here!
Crow Reply
what about nanotechnology for water purification
RAW Reply
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
yes that's correct
I think
Nasa has use it in the 60's, copper as water purification in the moon travel.
nanocopper obvius
what is the stm
Brian Reply
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
How we are making nano material?
what is a peer
What is meant by 'nano scale'?
What is STMs full form?
scanning tunneling microscope
how nano science is used for hydrophobicity
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
what is differents between GO and RGO?
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
analytical skills graphene is prepared to kill any type viruses .
Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
what is Nano technology ?
Bob Reply
write examples of Nano molecule?
The nanotechnology is as new science, to scale nanometric
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
Privacy Information Security Software Version 1.1a
Answers please
Nikki 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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