Category Archives: ECET 345

ECET 345 Week 1 Homework latest

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ECET 345 Week 1 Homework latest

1.Express the following numbers in Cartesian (rectangular) form.
2.Express the following numbers in polar form. Describe the quadrant of the complex plane, in which the complex number is located.
3.(a) A continuous-time sine wave has a frequency of 60 Hz, an amplitude of 117 V, and an initial phase of π/4 radians. Describe this signal in a mathematical form using the Sin function.
4. A sinusoidal signal described by 50 Cos (20πt + π/4) passes through a linear time invariant (LTI) system that applies a gain of 1.5 and a phase lag of π/2 radians to the signal. Write the mathematical expression that describes the signal that will come out of the LTI system.
5.A sinusoidal signal described by 20 Cos (2πt + π/4) passes through a linear time invariant (LTI) system that applies a gain of 2 and a time delay of 0.125 seconds to the signal. Write the mathematical expression that describes the signal that will come out of the LTI system.
6. Apply the principle of superposition to determine whether the following systems are linear. Sketch what the plot of the function looks like.
7. A continuous time system, described by y(t) = 5 Cos (2*π*20*t + π/2), is sampled at a rate 320 Hz.
8. Sketch the odd and even part of the following discrete signal. (See pages 13–14 of the text.)
9. Express the signal given in Problem 8 as the sum of the following

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ECET 345 Week 1 Lab Signal Observation And Recreation (100% Score) latest

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ECET 345 Week 1 Lab Signal Observation And Recreation (100% Score) latest

Objective:
Using a Tower system and supplied HCS12-based program, experimentally observe the closest equivalent of four key signals (impulse, sinusoidal, exponential, and square wave) on the oscilloscope and then create them in MATLAB.
Equipment list:
• Tower System with ADCDAC board
• Oscilloscope
• Three BNC to alligator
• One PC running CodeWarrior 5.9
• MATLAB
• 2.0 mm flathead screwdriver

ECET 345 Week 1 Lab
1. How does an experimental approximation of an impulse differ from an ideal impulse?
2.  A step input is applied to the following circuit at time t = 0. What will the output waveform look like? What is the significance of the time constant for the circuit? How will the observed waveform change as the value of capacitor is increased?
3. How does a sine wave differ from a cosine wave?
4. With the knowledge you gained in the theory section, how can an exponentially growing sinusoid be generated? Can a physical system generate an exponentially growing sinusoid?
5. In finance, what does the growth curve of a compound interest savings account look like over time
6. Create a MATLAB code that generates an amplitude modulated (AM) signal with a 1 Hz information frequency and a 100 Hz carrier frequency, with the carrier amplitude equal to 1.0 and the information frequency amplitude equal to 0.9. The general form of an AM signal is
where Ac is the amplitude of the carrier, Ai is the amplitude of the information signal, ωi is the frequency of the information signal in radians/second, ωc is the frequency of the carrier signal in radians/second, and t is time. Plot the graph over the time period of 0 to 2 seconds. Give meaningful labels to the X and Y axis as well as a title to the graph
7. Take the signal generated in the previous question and find the signal spectrum using the tools you have learned in earlier labs. Paste the signal spectrum and code below. (Hint: Use the method of finding the signal spectrum of a signal that was shown in Lab 1.) Give meaningful labels to the X and Y axis as well as a title to the graph.

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ECET 345 Week 2 Homework latest

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ECET 345 Week 2 Homework latest

1.Redraw the following schematics with the impedance of each of the element shown in Laplace domain. Then determine the overall impedance of the entire circuit between the two ends of the shown circuit and express it in Laplace domain as a ratio of two polynomials in s, with the coefficients of the highest power if s in the numerator and denominator are made unity. (Follow the method outlined in the lecture to determine the impedances of elements in Laplace domain and then use the formulas for combining impedances in series and parallel.)
2. (a) Apply Laplace transform to the following differential equation and express it as an algebraic equation in s.
3. An RC circuit with an initial condition is shown below. The toggle switch is closed at t = 0. Assuming that a current i(t) flows clockwise in the circuit, Write the integral equation that governs the behavior of the circuit current and solve it for the current in the circuit i(t) and voltage across the capacitor as a function of time using Laplace transforms. Note the polarity of the initial condition as marked in the figure. (Take help from the document “Solving RC, RLC, and RL Circuits Using Laplace Transforms” (located in Doc Sharing) and the Week 2 Lecture to see how initial conditions are entered in Laplace domain.)
4. The voltage in a circuit, expressed in Laplace domain, is given by the questions below.
5.An RLC circuit is shown below. There is an initial voltage of 5 V on the capacitor, with polarity as marked in the circuit. The switch is closed at t = 0 and a current i(t) is assumed to flow clockwise. Write the integral-differential equation of this circuit using Kirchoff’s method (sum of all voltages around a loop is zero). Apply Laplace transform as outlined in the lecture for Week 2 and in the document “Solving RC, RLC, and RL Circuits Using Laplace Transforms” (located in Doc Sharing) and write i(s) in Laplace transform notation. Express the denominator with the coefficient of the highest power of s unity. Then invert to obtain the current in time domain, i(t).

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ECET 345 Week 2 Lab Response Of Rc Circuits (100% Score) latest

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ECET 345 Week 2 Lab Response Of Rc Circuits (100% Score) latest

Objective of the lab experiment: 

The objective of this experiment is to experimentally measure the  step response of an RC circuit and compare it to response prediced using MATLAB

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ECET 345 Week 3 Homework latest

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ECET 345 Week 3 Homework latest

The transfer function of a circuit is given by
Express the transfer function in a form in which the coefficients of the highest power ofs are unity in both numerator and denominator.
What is the characteristic equation of the system? (Hint: see this week’s lecture for a definition of characteristic equation.)
Determine the order of the transfer function.
Determine where the poles and zeroes of the system are located.
____________
Using MATLAB, plot the pole zero map and the Bode plot of the two transfer functions and paste the graphs below. Identify and briefly discuss the differences between the Bode plot of the two transfer functions.

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ECET 345 Week 3 Lab Transfer Function Analysis Of Continuous Systems latest

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ECET 345 Week 3 Lab Transfer Function Analysis Of Continuous Systems latest

Objective of the lab experiment:
The objective of this experiment is to create continuous (s domain) transfer functions in MATLAB and explore how they can be manipulated to extract relevant data.
We shall first present an example of how MATLAB is used for s (Laplace) domain analysis, and then the student shall be required to perform specified analysis on a given circuit.

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ECET 345 Week 4 Homework latest

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ECET 345 Week 4 Homework latest

1.   A shiny metal disk with a dark spot on it, as shown in figure below, is rotating clockwise at 100 revolutions/second in a dark room. A human observer uses a strobe that flashes 99 times/second to observe the spot on the metal disk (a strobe is a flashing light whose rate of flashing can be varied). The spot appears to the human observer as if it is rotating slowly
2. (a) A system samples a sinusoid of frequency 480 Hz at a rate of 100 Hz and writes the sampled signal to its output without further modification. Determine the frequency that the sampling system will generate in its output.
3. The spectrum of an analog signal is shown below, containing . Such a signal is sampled by an ideal impulse sampler at a 100 Hz rate. List the first 10 positive frequencies that will be produced by the replication. (Hint: Follow the method outlined in the lecture for spectrum replication of sampled signals.)
4. The spectrum of an analog signal is shown below. It is sampled, with an ideal impulse sampler, at a rate of 200 Hz
5. Determine the Z transform of the signal,, shown below using the basic definition of Z transform . All values not shown can be assumed to be zero.
6. a) A simulation diagram is shown below. Determine the difference equation associated with the diagram.
7. An analog signal is given by f(t) = t  (i.e., it increases linearly with time and is thus is a unit ramp.) It is convolved with a second signal, g(t), which is of the form g(t) = 1 (i.e., it has a constant value of 1 or is a unit step function). The two signals are shown below. 

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ECET 345 Week 4 Lab Experimental Observation Of Aliasing (100% Score) latest

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ECET 345 Week 4 Lab Experimental Observation Of Aliasing (100% Score) latest

Objective of the lab experiment:
The objective of this experiment is to observe the effect of aliasing in a discrete sampling system and to measure how aliasing alters the frequency of an input signal that is beyond the Nyquist limit. This lab can also be used to quantitatively and qualitatively observe the effect of an antialiasing filter, even though we do not do so in this exercise.

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ECET 345 Week 5 ilab Convolution Of Signals Solution (100% Score) latest

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ECET 345 Week 5 ilab Convolution Of Signals Solution (100% Score) latest

Objective of the lab experiment:
The objective of this experiment is to demonstrate how the convolution is used to process signals entering a system. 

1. Convolution in the time domain is equivalent to what mathematical operation in the frequency domain?
2. When we convolve the triangular 10 Hz input with the impulse response of the 50 Hz low-pass filter, why is it that the peaks of output become rounded and not a sharp point as in the input triangular function?
3. Why is it that we get no (or very little) output when we convolve the 60 Hz sinusoid with the impulse response of the filter?
4. When we apply the 10 Hz output, which is within the pass band of the filter, we see that we get nearly the same sinusoid in the output except for a time delay. How is the time delay a signal experiences as it passes through a system related to the phase characteristic of the system response? 

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ECET 345 Week 6 Homework latest

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ECET 345 Week 6 Homework latest

1.Find the z-transform x(z) of x(n) = . Hint: Follow the method used in the lecture for Week 6. Also, when evaluating the numerical value of a trig function, keep in mind that the arguments of trig functions are always in radians and not in degrees.
2. Find the system transfer function of a causal LSI system whose impulse response is given by and express the result in positive powers of z. Hint: The transfer function is just the z-transform of impulse response. However, we must first convert the power of -0.5 from (n – 1) to (n – 2) by suitable algebraic manipulation.
3. Express the following signal, x(n), in a form such that z-transform tables can be applied directly. In other words, write it in a form such that the power of 0.25 is (n-1) and the argument of sin is also expressed with a (n-1) multiplier.
4. The transfer function of a system is given below. Find its impulse response in n-domain. Hint: First expand using partial fraction expansion and then perform its inversion using z-transform tables
5. The transfer function of a system is given by
6. A simulation diagram is shown below. We apply a unit impulse to such a system. Determine the numerical values of the first three outputs. You are free to use MATLAB where appropriate or do it entirely by hand.

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