# 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?

what is math number
x-2y+3z=-3 2x-y+z=7 -x+3y-z=6
Need help solving this problem (2/7)^-2
x+2y-z=7
Sidiki
what is the coefficient of -4×
-1
Shedrak
the operation * is x * y =x + y/ 1+(x × y) show if the operation is commutative if x × y is not equal to -1
An investment account was opened with an initial deposit of $9,600 and earns 7.4% interest, compounded continuously. How much will the account be worth after 15 years? Kala Reply lim x to infinity e^1-e^-1/log(1+x) given eccentricity and a point find the equiation Moses Reply 12, 17, 22.... 25th term Alexandra Reply 12, 17, 22.... 25th term Akash College algebra is really hard? Shirleen Reply Absolutely, for me. My problems with math started in First grade...involving a nun Sister Anastasia, bad vision, talking & getting expelled from Catholic school. When it comes to math I just can't focus and all I can hear is our family silverware banging and clanging on the pink Formica table. Carole I'm 13 and I understand it great AJ I am 1 year old but I can do it! 1+1=2 proof very hard for me though. Atone hi Adu Not really they are just easy concepts which can be understood if you have great basics. I am 14 I understood them easily. Vedant hi vedant can u help me with some assignments Solomon find the 15th term of the geometric sequince whose first is 18 and last term of 387 Jerwin Reply I know this work salma The given of f(x=x-2. then what is the value of this f(3) 5f(x+1) virgelyn Reply hmm well what is the answer Abhi If f(x) = x-2 then, f(3) when 5f(x+1) 5((3-2)+1) 5(1+1) 5(2) 10 Augustine how do they get the third part x = (32)5/4 kinnecy Reply make 5/4 into a mixed number, make that a decimal, and then multiply 32 by the decimal 5/4 turns out to be AJ how Sheref can someone help me with some logarithmic and exponential equations. Jeffrey Reply sure. what is your question? ninjadapaul 20/(×-6^2) Salomon okay, so you have 6 raised to the power of 2. what is that part of your answer ninjadapaul I don't understand what the A with approx sign and the boxed x mean ninjadapaul it think it's written 20/(X-6)^2 so it's 20 divided by X-6 squared Salomon I'm not sure why it wrote it the other way Salomon I got X =-6 Salomon ok. so take the square root of both sides, now you have plus or minus the square root of 20= x-6 ninjadapaul oops. ignore that. ninjadapaul so you not have an equal sign anywhere in the original equation? ninjadapaul hmm Abhi is it a question of log Abhi 🤔. Abhi I rally confuse this number And equations too I need exactly help salma But this is not salma it's Faiza live in lousvile Ky I garbage this so I am going collage with JCTC that the of the collage thank you my friends salma Commplementary angles Idrissa Reply hello Sherica im all ears I need to learn Sherica right! what he said ⤴⤴⤴ Tamia hii Uday hi salma hi Ayuba Hello opoku hi Ali greetings from Iran Ali salut. from Algeria Bach hi Nharnhar A soccer field is a rectangle 130 meters wide and 110 meters long. The coach asks players to run from one corner to the other corner diagonally across. What is that distance, to the nearest tenths place. Kimberly Reply Jeannette has$5 and \$10 bills in her wallet. The number of fives is three more than six times the number of tens. Let t represent the number of tens. Write an expression for the number of fives.
What is the expressiin for seven less than four times the number of nickels
How do i figure this problem out.
how do you translate this in Algebraic Expressions
why surface tension is zero at critical temperature
Shanjida
I think if critical temperature denote high temperature then a liquid stats boils that time the water stats to evaporate so some moles of h2o to up and due to high temp the bonding break they have low density so it can be a reason
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Need to simplify the expresin. 3/7 (x+y)-1/7 (x-1)=
. After 3 months on a diet, Lisa had lost 12% of her original weight. She lost 21 pounds. What was Lisa's original weight?