Knowledge Integration Module 2 Fall 2016

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1 Knowledge Integration Module 2 Fall

2 Basic Information: The knowledge integration module 2 or KI-2 is a vehicle to help you better grasp the commonality and correlations between concepts covered in ECE 311, 331 and 341 during LSM 3 and 4. All activities relevant to the KI-2 should be performed as a group (you should have received an telling you who your group members are). The grade for KI-2 will be counted as grade for Laboratory assignment 3 for ECE 331, grade for Assignment #6 for ECE 311, and Homework Assignment 9 for ECE 341. The KI report should be electronically submitted to ECE 331 TA Lang Yang by midnight on Sunday 6 th November. In course of this KI activity every group will need to tackle a specific design scenario. Each group needs to take their group number (say x) and y = (x mod 8)+1 will be the number of the design scenario (1 to 8) you have to consider from the Appendix. Continuing with our analysis of different blocks of a radio system, in this KI we will focus on the audio signal processing performed at the backend of radio systems. Specifically, we will analyze a subsystem consisting of an amplifier driving a speaker. Activities A. Amplifier Design You are required to build the following MOSFET amplifier circuit. As you can see this is a two stage amplifier. The source V b represents a biasing voltage and forms a design parameter. The values of V b that will be used by the different groups is given in the design variation Tables I-III listed in the appendix. For activities other than C you can replace the speaker with a 10Ω resistor. The pinout diagrams for the two different MOSFETs can be seen below. 2

3 Questions: What is the amplifier topology of the first transistor (common source, common gate, source follower)? What is the amplifier topology of the second transistor? (common source, common gate, source follower)? What could be a possible reason for using the second stage of the amplifier? B. Building and Analyzing the Speaker Gather the following materials: A foam plate A piece of paper Two business cards or a piece of cardstock paper Copper wire, AWG 32 (enameled) Tape Glue (hot glue works well) A cylindrical neodymium magnet A piece of cardboard 1) Cut two strips of paper so that their widths are equal and slightly less than the height of the magnet. 2) Roll one of the strips of paper over the magnet and tape the paper into a cylinder. 3) Roll the second paper strip over the first one and tape it into cylinder as well. 4) Remove the magnet and inner paper cylinder and glue the outer paper cylinder at the center of the bottom of the foam plate. 5) If you have cardstock paper, cut it into two approximately 2 x 3 cards. 6) Fold the business cards or cardstock cards into an M shape. 7) Align the cards in parallel on the plate around the magnet allowing at least an inch of separation. 8) After the glue has dried, put the inner paper cylinder back in the outer paper cylinder. Note: Do not keep the speakers on for more than 5 mins at a stretch. You can find detailed instructions with a video at: Follow the steps above. Your speaker frame should look like the one below without the coil of wires or the magnets attached. You will use this lab-made ( home-made ) speaker to conduct the associated ECE331- and ECE311- based experiments with the amplifier-speaker circuit from the top of this document. 3

4 B.1: Testing the effect of the total number of wire turns, N, in the winding 1) Take at least 1.5 m of wire. 2) Place the magnet back in the cylindrical strips. 3) Wind approximately 25 turns of wire around the paper cylinders and then remove the magnet and the inner cylinder. 4) Attach the output of the amplifier circuit from this KI to the input of the coil through a 4Ω power resistor (used to prevent blowing out the amplifier due to too large of a current). 5) Glue the magnet down onto the cardboard. 6) Place the cylinder and wire coil loop over the magnet and tape the cards to the cardboard. 7) Using a sound spectrum analyzer app on your phone, a function generator, and your speaker with a winding composed of 25 wire turns and measure the volume in db. Repeat it with increasing number of wire turns till 50 in step of 5. Generate a graph from the results. Set the function generator to a constant frequency between 400 Hz and 15,000 Hz, well within the human hearing range. (NOTE: Keep your phone the same distance away from the speaker for all db measurements.) (You can remove the plate speaker in between every measurement.) Apps: For Android: For Apple: Questions: 1) What does the slope of this graph represent? 2) What kind of relationship exists between the sound intensity and N (linear, quadratic, etc.)? 3) Based on this setup, what kind of relationship do you think exists between the magnetic flux density, B, and N? 4) You should not be increasing the length of the coil too much for the fixed number (25) of turns in the wire explain why. 5) Why does the drawn input current increase with time? B.2: Testing the effect of current magnitude 1) Increase the current I flowing through the circuit by increasing the amplitude of the sine wave with the function generator while holding N constant at their most effective values from parts A and B, respectively. 2) Repeat 7 from part A while varying the voltage. Questions: 1) What does the slope of this graph represent? 2) What kind of relationship exists between the sound intensity and the intensity of current, I, flowing through the coil? 3) Based on this setup, what kind of relationship do you think exists between the magnetic flux density and the current intensity of the coil, I? 4

5 B.3: Testing the effect of the magnetic core 1) Holding the three quantities from A, B, and C, so N, and I, constant, exchange the magnets from a neodymium magnet to a ceramic magnet and measure the db level for both, noting which core has a higher db level. Questions: 1) Based on what you know about permanent magnets and magnetic materials, why does the type of magnet used change the volume of sound produced? 2) Based on what you have seen from the experiments above, derive an equation relating the magnetic flux density, B, of a coil and some or all of the quantities above (N, I, and the remnant magnetic flux density, B r, of the core material). 5

6 C. Amplifier Response to Pure Tones Based on their group number, each group will choose a design variation from Table I. C1. Response to single tones (individual sinusoids): Generate a sinusoidal signal using the function generator with amplitude A 1 and frequency f 0 and use it as the input V in of the amplifier circuit in Fig. 1. The bias voltage V b is set to the value provided in Table I for each group. Capture and view the output of the amplifier on the oscilloscope (time domain). What do you see? Is the output also a pure single tone? Based on the time domain signal, what would you expect to see in the frequency domain? Connect the output of the amplifier to the speaker and write down your observations. View the output using the spectrum analyzer. Does the output agree with your prediction? If there is a discrepancy, provide a possible explanation. C2. Frequency response: Send a sinusoidal signal through the amplifier with amplitude A 1 and frequency ω 1 and view the output on the oscilloscope. Measure the peak-to-peak voltages of the input and output and calculate the magnitude of the frequency response using the following equation: H(jω 1 ) = v pp,out v pp,in Repeat this process for the six different frequencies specified in Table I to collect a total of six data points for the magnitude H(jω). Assume that the system has a single-pole response, i.e. the frequency response of the system is of the form H(jω) = α α, for α>0 and β>0. Then fit a function H(jω) = to the six data points that 1+βjω 1+β 2 ω2 you have obtained for H(jω) by using the Curve Fitting Tool (Apps->Curve Fitting) in MATLAB. Use the list of your frequencies as your x data, and the list of your 6 frequency response magnitude values as the y-data. Set the equation type to Custom Equation and enter alpha/sqrt(1+beta^2*x^2) as your equation. Report your values of α and β found in the Results panel of the window. Plot the fitted curve with the frequency axis in Hz. Find the 3 db cutoff frequency of the amplifier, i.e., the frequency ω c for which H(jω c ) = α α. Plot the magnitude spectrum H(jω) = and mark with vertical bars the 2 1+β 2 ω2 ω = ω c. Using your fitted value for β, also plot the phase of the frequency response H(jω). Include both the magnitude and phase plots in your report. In MATLAB abs(.) and angle(.) give magnitude and phase of a complex number respectively. C3. Distortion: Now send a sinusoidal signal with the same frequency ω 0 but with amplitude A 2. What does the time domain signal look like? Is this a pure sinusoid? What do you expect to see in the frequency domain? View the output using the spectrum analyzer and verify your prediction. Can you explain why the result from the frequency analyzer is different for the two amplitudes A 1 and A 2? 6

7 D. Fourier Analysis of a Periodic Input Based on their group number, each group will choose a design variation from Table II. For the periodic wave x(t) that corresponds to your design variation, do the following: D1. Theoretical spectrum: Compute the Fourier series coefficients of x(t) by evaluating a k = 1 T x(t)e jkω0t dt. <T> The waveform x(t) is real and even. What type of symmetry do you expect for the Fourier series coefficients a k? Plot the Fourier series coefficients, corresponding to the first K=10 harmonics (a 10, a 9,, a 9, a 10 ), in MATLAB using the stem(.) command. Do you see a particular symmetry? Next, plot the magnitude a k of the line spectrum (Fourier series coefficients) using stem(.) and abs(.) commands in MATLAB. Label the horizontal axis in units of Hz. Include both plots in your report. D2. Comparison with the measured spectrum: Now generate the periodic signal x(t) with the function generator and view the input signal on the oscilloscope. On the right hand side of the GUI panel, set Base: 75us/div, which should set the sampling rate to fs=10mhz. Import the oscilloscope data into MATLAB and find and plot its magnitude spectrum. Let s call the imported signal xt. Here is a code that generates its spectrum Xf and plots Xf : Xf =fftshift(fft(xt)); Xfmag=abs(Xf); N=length(Xfmag); f = -fs/2+fs/n:fs/n:fs/2; figure; plot(f,xfmag); xlabel( Frequency [Hz] ); ylabel( Magnitude Spectrum ); %calculates the spectrum of xt %calculates the magnitude spectrum of xt %Gives the number of points in the spectrum %Gives the frequency range in Hz over which the %spectrum is calculated. The parameter fs is the %sampling rate in Hz, which can be found at the %top of the oscillator screen for xt. %Plots the magnitude spectrum In the plot, the zero frequency is at the center of the plot. Do the height and location of the peaks in the magnitude spectrum calculated for the oscilloscope trace match the theoretical magnitude spectrum a k, and the corresponding frequency harmonics from D1? Overlay the two plots (Fourier Series vs. Xmag of oscilloscope trace). Include both plots in your report. D3. Signal approximation: Now build up a superposition of harmonics as K x(t) a k e jkω 0t k= K for different values of K (1, 2, 3, 5, 10, 20), using the Fourier series coefficients that you calculated in D1. Plot the resulting signals and overlay them on top of the periodic square waveform generated by the signal generator after importing it to MATLAB. How well does the finite superposition of harmonics (truncated Fourier series) match the periodic square waveform generated by the signal generator for each value of K? Does the accuracy improve with increasing K? Do you see the Gibbs phenomenon? Include all plots in your report. 7

8 E. Amplifier Response to a Periodic Input Based on their group number, each group will choose a design variation from Table III. When looking up your design variation, note that the waveform x(t) for this part is identical to the waveform you had in your design variation in part D. E1. Theoretical signal and system analysis: In part C2, you found an approximate frequency response H(jω) = α for the amplifier. Suppose that x(t) (with Fourier series coefficients a 1+βjω k that you calculated in part D1) is now the input to such mathematical amplifier. The output y(t) will of course be periodic. Let s call the Fourier series coefficients of the output b k. What is the connection between b k and H(jω) and a k? Is it b k = H(jkω 0 )a k? If yes, show analytically why this is the case. Then, using the relationship that you just proved, determine b k. Plot the magnitude and phase of b k on different plots and include them in your report. E2. Matching with measurements: Generate the periodic signal x(t) using the function generator. Send the signal through the actual amplifier and view the output using the oscilloscope. Import the oscilloscope data (output signal, call it yt) into MATLAB and find its spectrum Yf using a similar code as in D2. Plot both the magnitude Yf and phase <Yf of your output spectrum, and compare them with the magnitude and phase of the mathematically predicted b k s from E1. Do they match? You can use the angle(yf) to calculate the phase of Yf. Include all of your plots in the report. 8

9 APPENDIX Design Variations for Activity C, D, and E: NOTE: Use frequency (f) when using function generator/spectrum analyzer, but use angular frequency (ω=2πf) when computing Fourier Series C (Table I) Var. Bias (V b ) A 1 A 2 f 0 f 1 f 2 f 3 f 4 f 5 f 6 # V 10 mv 400 mv 1 khz 20 khz 60 khz 150 khz 250 khz 750 khz 2 MHz # V 10 mv 500 mv 5 khz 30 khz 90 khz 200 khz 400 khz 1 MHz 3 MHz # V 15 mv 400 mv 1 khz 20 khz 60 khz 150 khz 250 khz 750 khz 2 MHz # V 15 mv 500 mv 5 khz 30 khz 90 khz 200 khz 400 khz 1 MHz 3 MHz #5 1.2 V 10 mv 400 mv 1 khz 20 khz 60 khz 150 khz 250 khz 750 khz 2 MHz #6 1.2 V 10 mv 500 mv 5 khz 30 khz 90 khz 200 khz 400 khz 1 MHz 3 MHz #7 1.2 V 15 mv 400 mv 1 khz 20 khz 60 khz 150 khz 250 khz 750 khz 2 MHz #8 1.2 V 15 mv 500 mv 5 khz 30 khz 90 khz 200 khz 400 khz 1 MHz 3 MHz D (Table II) Variation A 1 f 0 Waveform #1 10 mv 40 khz 1 #2 10 mv 60 khz 2 #3 15 mv 40 khz 3 #4 15 mv 60 khz 4 #5 10 mv 40 khz 1 #6 10 mv 60 khz 2 #7 15 mv 40 khz 3 #8 15 mv 60 khz 4 E (Table III) Variations Bias (V b ) A 1 f 0 Waveform # V 10 mv 40 khz 1 # V 10 mv 60 khz 2 # V 15 mv 40 khz 3 # V 15 mv 60 khz 4 #5 1.2 V 10 mv 40 khz 1 #6 1.2 V 10 mv 60 khz 2 #7 1.2 V 15 mv 40 khz 3 #8 1.2 V 15 mv 60 khz 4 9

10 Waveforms for C and D 10

11 Presentation/Report Details for KI-2 KI Reports: KI Reports are all due by Sunday midnight (11/6, 23:59 PM). This is to ensure that you have enough time to study for the assessment examinations. Please send an electronic copy of the report to the ECE 331 TA Lang Yang ( All s must have in the subject line KI1-<Your-Name>-<CSUID>". Please include all your group member names, CSUIDs, as well as which courses (ECE 311, 331, and 341) you are currently enrolled in on the cover of report. You may follow the lab report writing format uses in ECE 331, and make sure that all questions you were assigned will be answered. Team Presentations: The following presentation schedule is to be followed. Monday (3:00 PM-4:15 PM, Scott 101): Teams 2, 6, 24 and 10 will present Tuesday (9:30 AM-10:45 AM, Clarke A 202): Teams 13, 18, 20, and 21 will present For your reference, the following page in IEEE has valuable resources to help you develop your presentation skills ( When preparing your presentations, keep in mind the following: 1) You have mins to presentation time followed by 3-5 mins of QnA time. This time limit will be strongly enforced. Questions may be posed by both faculty and your peers. You must your design variations for part B of the KI questions along with any relevant or interesting materials that you may have relevant to part C and D. 2) You need to visualize yourself as professors seeking to inform the entire class about what you learned from the KI activities. Thus, you are strongly encouraged to add any interesting observation, insights, or even a newer perspective to established theory that you may have gained from the activities. Please try to relate this new knowledge to the concepts covered in the three courses. At this point it is perfectly acceptable if your attempts to explain your new knowledge is not refined. 3) Each group will be evaluated by their peers. Peer evaluation forms are uploaded in CANVAS along with this document. As a group presenting on Monday or Tuesday, please make it a point to go through the peer evaluation form. This form states exactly the criteria your presentation will be graded on. 4) Note that not all group members have to speak during the presentation. 5) You will be graded both on the technical insight and communication skills. 1

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