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For the cirouit below: A. Obtain an expression for H(w) = Vo/Vs in standard form. B. Sketch the bode plots for the magnitude and phase of H(w), given that R1 =1k, R2 =4k, and C=1pF. O. What type of filter is it? What is its maximum gain? What is the cutoff frequency? R2 R1 V.

For the cirouit below: A. Obtain an expression for H(w) = Vo/Vs in standard form. B. Sketch the bode plots for the magnitude and phase of H(w), given that R1 =1k, R2 =4k, and C=1pF. O. What type of filter is it? What is its maximum gain? What is the cutoff frequency? R2 R1 V.

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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Please && thank you! Please use "jw" notation if possible as that is easier for me to understand, for now. 

### Transcription and Explanation for Educational Website **Problem Statement:** **For the circuit below:** **A.** Obtain an expression for \( H(\omega) = \frac{V_o}{V_s} \) in standard form. **B.** Sketch the bode plots for the magnitude and phase of \( H(\omega) \), given that \( R1 = 1k\Omega \), \( R2 = 4k\Omega \), and \( C = 1\mu F \). **C.** What type of filter is it? What is its maximum gain? What is the cutoff frequency? **Circuit Diagram Description:** The circuit consists of an operational amplifier in a feedback configuration. The input voltage \( V_s \) is applied across a resistor \( R1 \) and a capacitor \( C \) in series. The feedback resistor \( R2 \) connects the output voltage \( V_o \) to the inverting input of the op-amp. The non-inverting input of the op-amp is grounded. **Explanation of Components:** - \( R1 \): A resistor with a resistance of \( 1k\Omega \). - \( R2 \): A feedback resistor with a resistance of \( 4k\Omega \). - \( C \): A capacitor with a capacitance of \( 1\mu F \). **Analysis:** 1. **Expression for \( H(\omega) \):** The expression for the transfer function \( H(\omega) \), which is the ratio of the output voltage \( V_o \) to the input voltage \( V_s \), needs to be derived based on the circuit's configuration. 2. **Bode Plots:** Bode plots are graphical representations that show how the gain (magnitude) and phase of the transfer function \( H(\omega) \) vary with frequency. The task involves sketching these plots for the given component values. 3. **Filter Type, Maximum Gain, and Cutoff Frequency:** - **Filter Type:** Determine the type of filter (e.g., low-pass, high-pass, band-pass, or band-stop). - **Maximum Gain:** Identify the maximum amplification provided by the filter. - **Cutoff Frequency:** Calculate the frequency at which the filter's gain drops by 3 dB from its maximum value. This circuit requires an understanding of operational amplifier behavior, frequency response analysis
Transcribed Image Text:### Transcription and Explanation for Educational Website **Problem Statement:** **For the circuit below:** **A.** Obtain an expression for \( H(\omega) = \frac{V_o}{V_s} \) in standard form. **B.** Sketch the bode plots for the magnitude and phase of \( H(\omega) \), given that \( R1 = 1k\Omega \), \( R2 = 4k\Omega \), and \( C = 1\mu F \). **C.** What type of filter is it? What is its maximum gain? What is the cutoff frequency? **Circuit Diagram Description:** The circuit consists of an operational amplifier in a feedback configuration. The input voltage \( V_s \) is applied across a resistor \( R1 \) and a capacitor \( C \) in series. The feedback resistor \( R2 \) connects the output voltage \( V_o \) to the inverting input of the op-amp. The non-inverting input of the op-amp is grounded. **Explanation of Components:** - \( R1 \): A resistor with a resistance of \( 1k\Omega \). - \( R2 \): A feedback resistor with a resistance of \( 4k\Omega \). - \( C \): A capacitor with a capacitance of \( 1\mu F \). **Analysis:** 1. **Expression for \( H(\omega) \):** The expression for the transfer function \( H(\omega) \), which is the ratio of the output voltage \( V_o \) to the input voltage \( V_s \), needs to be derived based on the circuit's configuration. 2. **Bode Plots:** Bode plots are graphical representations that show how the gain (magnitude) and phase of the transfer function \( H(\omega) \) vary with frequency. The task involves sketching these plots for the given component values. 3. **Filter Type, Maximum Gain, and Cutoff Frequency:** - **Filter Type:** Determine the type of filter (e.g., low-pass, high-pass, band-pass, or band-stop). - **Maximum Gain:** Identify the maximum amplification provided by the filter. - **Cutoff Frequency:** Calculate the frequency at which the filter's gain drops by 3 dB from its maximum value. This circuit requires an understanding of operational amplifier behavior, frequency response analysis
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