# 3.20 Analog signal processing problems  (Page 5/6)

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## A testing circuit

The simple circuit here was given on a test.

When the voltage source is $\sqrt{5}\sin t$ , the current $i(t)=\sqrt{2}\cos (t-\arctan 2-\frac{\pi }{4})$ .

1. What is voltage ${v}_{\mathrm{out}}(t)$ ?
2. What is the impedance $Z$ at the frequency of the source?

## Black-box circuit

You are given a circuit that has two terminals for attaching circuit elements.

When you attach a voltage source equaling $\sin t$ to the terminals, the current through the source equals $4\sin (t+\frac{\pi }{4})-2\sin (4t)$ . When no source is attached (open-circuited terminals),the voltage across the terminals has the form $A\sin (4t+\phi )$ .

1. What will the terminal current be when you replace thesource by a short circuit?
2. If you were to build a circuit that was identical (from the viewpoint of the terminals) to the givenone, what would your circuit be?
3. For your circuit, what are $A$ and $\phi$ ?

## Solving a mystery circuit

Sammy must determine as much as he can about a mystery circuit by attaching elements to the terminal andmeasuring the resulting voltage. When he attaches a 1Ω resistor to the circuit's terminals, he measuresthe voltage across the terminals to be $3\sin t$ . When he attaches a 1F capacitor across the terminals,the voltage is now $3\sqrt{2}\sin (t-\frac{\pi }{4})$ .

1. What voltage should he measure when he attaches nothing to the mystery circuit?
2. What voltage should Sammy measure if he doubled the size of the capacitor to 2 F and attached it to thecircuit?

The depicted circuit has a transfer function between the output voltage and the source equal to $H(f)=\frac{-8\pi ^{2}f^{2}}{8\pi ^{2}f^{2}+4+i\times 6\pi f}$ .

1. Sketch the magnitude and phase of the transfer function.
2. At what frequency does the phase equal $\frac{\pi }{2}$ ?
3. Find a circuit that corresponds to this loadimpedance. Is your answer unique? If so, show it to be so; if not, give another example.

## Analog “hum” rejection

“Hum” refers to corruption from wall socket power that frequently sneaks intocircuits. “Hum” gets its name because it sounds like a persistent humming sound. We want to finda circuit that will remove hum from any signal. A Rice engineer suggests using a simple voltage divider circuit consisting of two series impedances.

1. The impedance ${Z}_{1}$ is a resistor. The Rice engineer must decide between two circuits for the impedance ${Z}_{2}$ . Which of these will work?
2. Picking one circuit that works, choose circuit elementvalues that will remove hum.
3. Sketch the magnitude of the resulting frequency response.

## An interesting circuit

1. For the circuit shown in [link] , find the transfer function.
2. What is the output voltage when the input has the form ${i}_{\mathrm{in}}=5\sin (2000\pi t)$ ?

## A simple circuit

You are given the depicted circuit .

1. What is the transfer function between the source and the output voltage?
2. What will the voltage be when the source equals $\sin t$ ?
3. Many function generators produce a constant offset in addition to a sinusoid. If the source equals $1+\sin t$ , what is theoutput voltage?

## An interesting and useful circuit

The depicted circuit has interesting properties, which are exploited in high-performance oscilloscopes.

The portion of the circuit labeled "Oscilloscope" represents the scope's input impedance. ${R}_{2}=1\mathrm{M\Omega }$ and ${C}_{2}=30\mathrm{pF}$ (note the label under the channel 1 input in the lab'soscilloscopes). A probe is a device to attach an oscilloscope to a circuit, and it has theindicated circuit inside it.

1. Suppose for a moment that the probe is merely a wire and that the oscilloscope is attached to a circuitthat has a resistive Thévenin equivalent impedance. What would be the effect of theoscilloscope's input impedance on measured voltages?
2. Using the node method, find the transfer function relating the indicated voltage to the source whenthe probe is used.
3. Plot the magnitude and phase of this transfer function when ${R}_{1}=9\mathrm{M\Omega }$ and ${C}_{1}=2\mathrm{pF}$ .
4. For a particular relationship among the elementvalues, the transfer function is quite simple. Find that relationship and describe what is so specialabout it.
5. The arrow through ${C}_{1}$ indicates that its value can be varied. Select the value for this capacitor to make the specialrelationship valid. What is the impedance seen by the circuit being measured for this special value?

Application of nanotechnology in medicine
what is variations in raman spectra for nanomaterials
I only see partial conversation and what's the question here!
what about nanotechnology for water purification
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
Damian
yes that's correct
Professor
I think
Professor
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
if virus is killing to make ARTIFICIAL DNA OF GRAPHENE FOR KILLED THE VIRUS .THIS IS OUR ASSUMPTION
Anam
analytical skills graphene is prepared to kill any type viruses .
Anam
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
hi
Loga
what does nano mean?
nano basically means 10^(-9). nanometer is a unit to measure length.
Bharti
how did you get the value of 2000N.What calculations are needed to arrive at it
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