Lab 9 – Introduction to RC Circuits in the Time and Frequency-Domains

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Northeastern University *

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2150

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Electrical Engineering

Date

Dec 6, 2023

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pdf

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7

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Lab 9 – Introduction to RC Circuits in the Time and Frequency-Domains Student: Celine Habr Instructor: Dr. Iman Salama Lab Partner: Mateo Wu Chen November 6, 2023
1. Introduction The goal of this experiment was to examine how alternating current (AC) voltage signals impact a resistor-capacitor (RC) circuit. Initially, a function generator was linked to an RC circuit to create a square wave. The charge and discharge of the capacitor, which led to a decay in the signal, was monitored using an oscilloscope. Subsequently, the experiment continued with the identical setup, but with a sine wave input, to investigate how the frequency of the signal influenced the voltage across the capacitor and to note the variances between the capacitor's voltage and that of the source. 2. Results 2.1 Part 1: Transient Signals With An Rc Circuit With Square Waves Firstly, we connected the function generator to a 20 kΩ resistor in series with a 0.1 μF capacitor – the circuit diagram for this is seen in figure 1 , while the actual built circuit is figure 2 . The function generator was then set to produce a 1V amplitude square wave with a DC offset of 1V. Figure 1: Simple RC circuit used for this lab where R is 20 kΩ and C is 0.1 μF Source: Dr. Iman Salama. “Lab 9 - Getting started with Analog to Digital Conversion and Sampling.” Northeastern University. 23 October 2023.
Figure 2: Completed RC circuit on protoboard with oscilloscope connected across the capacitor and to the signal generator. We then determined the frequency that should be used to observe the exponential decay behavior of the voltage across the capacitor by first finding the time constant τ. In this circuit, , where R is the equivalent resistance in the circuit, being 20kΩ, and C is the capacitance τ = 𝑅𝐶 of the capacitor, 0.1 μF. Hence, the time constant τ for this circuit was In order to see the capacitor fully charge and discharge, the 2000 × 0. 1 × 10 −6 = 0. 002 ?. period of the wave should be at least 10 times the value of τ, so T = 0.02s. Therefore, the frequency was set to ? = 1 0.2 = 50 𝐻𝑧.
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