Lab 4.docx

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ECE 10CL Lab 4 Lab 4: Sinusoidal Steady State (continued) Required Parts: Quantity Part Name Shop Part Number 1 TL074 Quad Op Amp 74 1 10 mH inductor MHI10 2 .05 μ F Leaded Capacitor CC.05 3 100 Ohm 1/4W, Resistor QWR100 1 200 Ohm 1/4W, Resistor QWR200 1 1 kOhm 1/4W, Resistor QWR1K 1 2 kOhm 1/4W, Resistor QWR2K 1 10 kOhm 1/4W, Resistor QWR10K Objectives: Part 1: ● Understand how to create a square wave using sinusoidal waves ● Construct a non-inverting summing amplifier ● Create a square wave using 2 sinusoids and the summing amplifier Part 2: ● Construct a Resonant LC Bandpass filter ● Learn how to perform a frequency sweep and use a spectrum analyzer Step 1: PreLab [Paper] 1.1 Using Fourier series expansion, it can be shown that a square wave, x(t) , with frequency, can be decomposed into sinusoids using the following formula 𝑓 0 , . 𝑥(?) = (4/π) 𝑛=1,3,5,… ∞ ∑ (1/𝑛) ?𝑖𝑛(2π𝑛𝑓 0 ?) where n is the harmonic number. In this lab, you will approximate the square wave using only the first two harmonics, n = 1, 3 . The square wave will be approximated by: . 𝑥(?) ≈4/π [?𝑖𝑛(2π𝑓 0 ?) + (1/3)?𝑖𝑛(6π𝑓 0 ?) ] 1

ECE 10CL Lab 4 1.2 Consider the circuit of a non-inverting summing amplifier circuit in Figure 1 and derive the relation between the inputs (V A , V B , V C ) and output voltages (find transfer function) [RP1] . 1.3 Analyze the non-inverting summing amplifier in Figure 1. This circuit is used to sum 3 input signals. Simplify the relation between the input and output voltages in RP1 using the following values: R1 = R2 = R3 = R0 = 100Ω and Rf = 200Ω [RP2] . Figure 1 Non-inverting Summing Amplifier 1.4 In Part 2 of this lab, you will construct a “resonant” LC bandpass filter (Figure 2). The filter will only allow signals at the resonant frequency to pass through. For example, if you input a 1kHz square wave into a 5kHz resonant bandpass filter , the resulting output will be a sinusoid at 5kHz . From Prelab part 1.1, we know that a square wave can be represented as an infinite sum of sinusoids. As such, when the input is a square wave (sum of sinusoids), the resonant bandpass filter “cancels” all sinusoids except for the one at the filter’s resonant frequency. 1.5 Calculate a reasonable capacitor value for a LC bandpass “resonant” filter (Figure 2) at 10kHz, (given an inductor value of 10mH). How can you construct this capacitor value out of the capacitors you have [RP3] ? The tank oscillator (LC in parallel in Figure 2) is followed by a non-inverting amplifier stage to boost the output voltage of the 2

ECE 10CL Lab 4 filtered signal (boost gain = 1+ , use R = 2kΩ as the feedback resistor). The resonance 𝑅 1𝑘 frequency is given by: in 𝑓 0 = 1/(2π 𝐿𝐶 ) Figure 2 LC bandpass resonant filter Step 2: In-Lab [Breadboard] (Bolded parts need to be demonstrated to TA) Part 1: 2.1 Construct a non-inverting summing amplifier with 2 inputs using the values specified in the pre-lab. Power the Op-amp +/-Vcc at +/-5V and verify its functionality by summing two 1V DC signals and checking that the output matches the expected output from the pre-lab. 2.2 Set the first input as a 10kHz sinusoid with amplitude and leave the 2nd input 4/π unconnected. Observe and screencap the output of the summing amplifier [RP4] . 2.3 Now, set the second input as a 30kHz sinusoid with amplitude observe the 4/(3π) output of the summing amplifier. Does it look like a square wave? What could you do to make it resemble a square wave more closely? What is your adjustment and how much [RP5] ? Take a screenshot of the output that looks more closely like the square wave after the adjustment [RP6] . Part 2: 2.4 Construct the resonant LC bandpass filter shown in Figure 2 with resonant frequency of 10kHz. 3

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ECE 10CL Lab 4 2.5 The function generator has a frequency sweep function that allows you to choose 2 frequencies and a duration. The board will “sweep” all frequencies between the 2 limits in the time duration specified. 2.6 To test that your resonant LC bandpass filter is functioning correctly, input a +/- 1Vpp sine wave with a linear “sweep” from 1kHz to 50kHz into the filter and record the frequency at which there is a maximum amplitude output Vpp (verify that the resonant frequency matches the target frequency, i.e., 10 kHz). To do this, use Scope 1 on the input signal and Scope 2 on the output signal. As the sweep progresses from 1kHz to 50kHz, the output signal should increase in Vpp when near the resonant frequency. Record this maximum output Vpp and the frequency it occurs at [RP7] . ( Hint : use Sweep to observe a high-level progression of output amplitude, then you can quit the Sweep mode and use manual frequency adjustment to find that maximum amplitude and the frequency it occurs, i.e. sweep by hand.) 2.7 Screencap the oscilloscope image displaying both the input signal and the output sinusoid at the resonant frequency [RP8] . 2.8 Switch the input to a +/- 0.5Vpp, 10kHz square wave. Observe and screen-capture the output waveform [RP9] . Why is the filter changing a square wave into a sinusoid [RP10] ? 2.9 Using the FFT view (MATH function) on the oscilloscope, observe and screencap the magnitude vs. frequency plot of the filter. There should be one frequency with a large spike and the rest should look like noise. Why is this? What frequency does this occur at [RP11] ? 2.10 Did the lab TA check-off all of the bolded parts [RP12] ? 4

ECE 10CL Lab 4 Report Rubrics [100 Points]: ● Introduction: Brieﬂy explain the goals and steps. [5 points] ● Results [85 points] ○ RP 1 [15 points] ○ RP 2 [5 points] ○ RP 3 [5 points] ○ RP 4 [5 points] ○ RP 5 [5 points] ○ RP 6 [5 points] ○ RP 7 [5 points] ○ RP 8 [5 points] ○ RP 9 [5 points] ○ RP 10 [5 points] ○ RP 11 [5 points] ○ RP 12 [20 points] ● Conclusion [5 points] ● Clear format [5 points] ○ When submitting on Gradescope, please assign “Clear format” to every page. ○ We expect all figures (and tables) to be numbered and titled properly. 5