Lab 4

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Electrical Engineering

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Jan 9, 2024

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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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