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Calculate the cutoff frequency, f and Yout at the cutoff frequency, fc for R1 = 100 www VIN = 100 mvp-p for all frequencies C1 = 0.022uf Output

Calculate the cutoff frequency, f and Yout at the cutoff frequency, fc for R1 = 100 www VIN = 100 mvp-p for all frequencies C1 = 0.022uf Output

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
Section: Chapter Questions
Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...
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**Title: Calculating Cutoff Frequency and Output Voltage** --- **Objective:** Calculate the cutoff frequency, \( f_c \), and the output voltage, \( V_{\text{out}} \), at the cutoff frequency for the given RC circuit. **Components:** - **Resistor (R1):** 10 Ω - **Capacitor (C1):** 0.022 µF - **Input Voltage (\( V_{\text{IN}} \)):** 100 mV peak-to-peak **Circuit Diagram Description:** The diagram shows a simple RC low-pass filter circuit. The input voltage source \( V_{\text{IN}} \) is connected in series with a resistor (R1), followed by a capacitor (C1) connected in parallel to the output terminal. The circuit is designed to allow the calculation of the cutoff frequency and the output voltage at that frequency. --- **Analysis:** 1. **Calculate the Cutoff Frequency (\( f_c \)):** The cutoff frequency for an RC circuit is given by: \[ f_c = \frac{1}{2\pi R_1 C_1} \] Substituting \( R_1 = 10 \, \Omega \) and \( C_1 = 0.022 \, \mu\text{F} \): \[ f_c = \frac{1}{2\pi \times 10 \times 0.022 \times 10^{-6}} \] 2. **Determine the Output Voltage (\( V_{\text{out}} \)) at \( f_c \):** At the cutoff frequency, the output voltage is approximately 0.707 times the input voltage due to the -3dB point in the frequency response of the filter. \[ V_{\text{out}} = 0.707 \times V_{\text{IN}} \] Given the input voltage is 100 mV peak-to-peak, calculate the output voltage using the above relationship. --- Upon completion of these calculations, you'll have determined the cutoff frequency and output voltage for this low-pass filter configuration, providing insight into its behavior in filtering signals.
Transcribed Image Text:**Title: Calculating Cutoff Frequency and Output Voltage** --- **Objective:** Calculate the cutoff frequency, \( f_c \), and the output voltage, \( V_{\text{out}} \), at the cutoff frequency for the given RC circuit. **Components:** - **Resistor (R1):** 10 Ω - **Capacitor (C1):** 0.022 µF - **Input Voltage (\( V_{\text{IN}} \)):** 100 mV peak-to-peak **Circuit Diagram Description:** The diagram shows a simple RC low-pass filter circuit. The input voltage source \( V_{\text{IN}} \) is connected in series with a resistor (R1), followed by a capacitor (C1) connected in parallel to the output terminal. The circuit is designed to allow the calculation of the cutoff frequency and the output voltage at that frequency. --- **Analysis:** 1. **Calculate the Cutoff Frequency (\( f_c \)):** The cutoff frequency for an RC circuit is given by: \[ f_c = \frac{1}{2\pi R_1 C_1} \] Substituting \( R_1 = 10 \, \Omega \) and \( C_1 = 0.022 \, \mu\text{F} \): \[ f_c = \frac{1}{2\pi \times 10 \times 0.022 \times 10^{-6}} \] 2. **Determine the Output Voltage (\( V_{\text{out}} \)) at \( f_c \):** At the cutoff frequency, the output voltage is approximately 0.707 times the input voltage due to the -3dB point in the frequency response of the filter. \[ V_{\text{out}} = 0.707 \times V_{\text{IN}} \] Given the input voltage is 100 mV peak-to-peak, calculate the output voltage using the above relationship. --- Upon completion of these calculations, you'll have determined the cutoff frequency and output voltage for this low-pass filter configuration, providing insight into its behavior in filtering signals.
Expert Solution
Step 1: Question analysis:

For the given circuit calculation of cutoff frequency fc and Vout at cutoff frequency fc.

Electrical Engineering homework question answer, step 1, image 1

  • This given circuit is a series RC circuit.

Hence,

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