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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

A golfer on a fairway is 70 m away from the green, which sits below the level of the fairway by 20 m. If the golfer hits the ball at an angle of 40° with an initial speed of 20 m/s, how close to the green does she come?
Aislinn Reply
cm
tijani
what is titration
John Reply
what is physics
Siyaka Reply
A mouse of mass 200 g falls 100 m down a vertical mine shaft and lands at the bottom with a speed of 8.0 m/s. During its fall, how much work is done on the mouse by air resistance
Jude Reply
Can you compute that for me. Ty
Jude
what is the dimension formula of energy?
David Reply
what is viscosity?
David
what is inorganic
emma Reply
what is chemistry
Youesf Reply
what is inorganic
emma
Chemistry is a branch of science that deals with the study of matter,it composition,it structure and the changes it undergoes
Adjei
please, I'm a physics student and I need help in physics
Adjanou
chemistry could also be understood like the sexual attraction/repulsion of the male and female elements. the reaction varies depending on the energy differences of each given gender. + masculine -female.
Pedro
A ball is thrown straight up.it passes a 2.0m high window 7.50 m off the ground on it path up and takes 1.30 s to go past the window.what was the ball initial velocity
Krampah Reply
2. A sled plus passenger with total mass 50 kg is pulled 20 m across the snow (0.20) at constant velocity by a force directed 25° above the horizontal. Calculate (a) the work of the applied force, (b) the work of friction, and (c) the total work.
Sahid Reply
you have been hired as an espert witness in a court case involving an automobile accident. the accident involved car A of mass 1500kg which crashed into stationary car B of mass 1100kg. the driver of car A applied his brakes 15 m before he skidded and crashed into car B. after the collision, car A s
Samuel Reply
can someone explain to me, an ignorant high school student, why the trend of the graph doesn't follow the fact that the higher frequency a sound wave is, the more power it is, hence, making me think the phons output would follow this general trend?
Joseph Reply
Nevermind i just realied that the graph is the phons output for a person with normal hearing and not just the phons output of the sound waves power, I should read the entire thing next time
Joseph
Follow up question, does anyone know where I can find a graph that accuretly depicts the actual relative "power" output of sound over its frequency instead of just humans hearing
Joseph
"Generation of electrical energy from sound energy | IEEE Conference Publication | IEEE Xplore" ***ieeexplore.ieee.org/document/7150687?reload=true
Ryan
what's motion
Maurice Reply
what are the types of wave
Maurice
answer
Magreth
progressive wave
Magreth
hello friend how are you
Muhammad Reply
fine, how about you?
Mohammed
hi
Mujahid
A string is 3.00 m long with a mass of 5.00 g. The string is held taut with a tension of 500.00 N applied to the string. A pulse is sent down the string. How long does it take the pulse to travel the 3.00 m of the string?
yasuo Reply
Who can show me the full solution in this problem?
Reofrir 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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