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Consider a transfer function given by G(s) = 1/(s+1). What is the gain (in dB) at the input frequency of 2.0 Hz that is predicted by the asymptotic approximation? Keep three significant figures.

Consider a transfer function given by G(s) = 1/(s+1). What is the gain (in dB) at the input frequency of 2.0 Hz that is predicted by the asymptotic approximation? Keep three significant figures.

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
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SOLVE CAREFULLY!! Please Write Clearly and Box the final Answer Hint : Pay attention to values given
**Problem Statement:** Consider a transfer function given by \( G(s) = \frac{1}{(s+1)} \). What is the gain (in dB) at the input frequency of 2.0 Hz that is predicted by the asymptotic approximation? Keep three significant figures. [ **Answer Box:** ] **Explanation:** The problem involves calculating the gain in decibels (dB) for a given transfer function \( G(s) \) at a specified input frequency. The transfer function provided is \( G(s) = \frac{1}{(s+1)} \), where \( s \) represents the complex frequency variable. To find the gain in dB at 2.0 Hz using the asymptotic approximation, you would typically convert the frequency to the complex \( s \)-domain by using \( s = j\omega \), where \( \omega \) is the angular frequency (\( \omega = 2\pi f \) and \( f = 2.0 \) Hz). Follow these steps: 1. Substitute \( s = j\omega \) into the transfer function. 2. Calculate the magnitude of \( G(j\omega) \). 3. Convert the magnitude to decibels using the formula \( \text{Gain (dB)} = 20 \log_{10}(\text{Magnitude}) \). 4. Use asymptotic approximation methods if specified. The numerical calculations and asymptotic approximations are typically executed in computational exercises or systems analysis contexts.
Transcribed Image Text:**Problem Statement:** Consider a transfer function given by \( G(s) = \frac{1}{(s+1)} \). What is the gain (in dB) at the input frequency of 2.0 Hz that is predicted by the asymptotic approximation? Keep three significant figures. [ **Answer Box:** ] **Explanation:** The problem involves calculating the gain in decibels (dB) for a given transfer function \( G(s) \) at a specified input frequency. The transfer function provided is \( G(s) = \frac{1}{(s+1)} \), where \( s \) represents the complex frequency variable. To find the gain in dB at 2.0 Hz using the asymptotic approximation, you would typically convert the frequency to the complex \( s \)-domain by using \( s = j\omega \), where \( \omega \) is the angular frequency (\( \omega = 2\pi f \) and \( f = 2.0 \) Hz). Follow these steps: 1. Substitute \( s = j\omega \) into the transfer function. 2. Calculate the magnitude of \( G(j\omega) \). 3. Convert the magnitude to decibels using the formula \( \text{Gain (dB)} = 20 \log_{10}(\text{Magnitude}) \). 4. Use asymptotic approximation methods if specified. The numerical calculations and asymptotic approximations are typically executed in computational exercises or systems analysis contexts.
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