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For the phase shift oscillator below, and assuming no loading effects:  What is the resonant frequency in kHz? (Please provide derivation). Thanks

For the phase shift oscillator below, and assuming no loading effects:  What is the resonant frequency in kHz? (Please provide derivation). Thanks

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
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1. For the phase shift oscillator below, and assuming no loading effects:
 What is the resonant frequency in kHz?

(Please provide derivation). Thanks

**Op-Amp Circuit with Low-Pass Filter Network** **Description:** The above image shows an operational amplifier (op-amp) circuit utilizing the TLV2471 op-amp, configured with a low-pass filter network. This type of circuit is common in electronics for applications such as signal conditioning, where it helps to filter out high-frequency noise or to smoothen the output signal. **Components and Connections:** 1. **Operational Amplifier (Op-Amp) - TLV2471:** - The circuit uses a TLV2471 op-amp, which is powered by a +5V supply. - The non-inverting input (+) of the op-amp is connected to a 2.5V reference voltage. - The inverting input (-) of the op-amp is connected to a feedback resistor \( R_F \) and a ground resistor \( R_G \). 2. **Feedback and Ground Resistor Network:** - \( R_F \): Feedback resistor connected between the output of the op-amp and the inverting input. - \( R_G \): Ground resistor connected between the inverting input and ground. 3. **Low-Pass Filter Network:** - The circuit includes a series of 10 kΩ resistors (R) and 10 nF capacitors (C) in a low-pass filter configuration. Each resistor is followed by a capacitor connected to ground, forming three RC sections in series. - These RC sections are vital in filtering high-frequency components from the output signal, allowing only the lower frequency signals to pass through to the final output (\( V_{OUT} \)). **Explanation:** - **Operation of the Op-Amp Circuit:** The op-amp works to amplify the input signal, which is set by the reference voltage of 2.5V at the non-inverting input. The feedback network helps to stabilize the gain of the op-amp. - **Low-Pass Filter Function:** Each RC section of the low-pass filter network progressively attenuates higher frequency signals more, such that by the end of the network, the output signal at \( V_{OUT} \) is largely free of high-frequency noise. This is useful for applications where a clean and stable signal is required. This type of circuit is commonly used in analog signal processing to achieve desired filtering characteristics, ensuring that only the necessary signal frequencies are passed through while unwanted noise is minimized.
Transcribed Image Text:**Op-Amp Circuit with Low-Pass Filter Network** **Description:** The above image shows an operational amplifier (op-amp) circuit utilizing the TLV2471 op-amp, configured with a low-pass filter network. This type of circuit is common in electronics for applications such as signal conditioning, where it helps to filter out high-frequency noise or to smoothen the output signal. **Components and Connections:** 1. **Operational Amplifier (Op-Amp) - TLV2471:** - The circuit uses a TLV2471 op-amp, which is powered by a +5V supply. - The non-inverting input (+) of the op-amp is connected to a 2.5V reference voltage. - The inverting input (-) of the op-amp is connected to a feedback resistor \( R_F \) and a ground resistor \( R_G \). 2. **Feedback and Ground Resistor Network:** - \( R_F \): Feedback resistor connected between the output of the op-amp and the inverting input. - \( R_G \): Ground resistor connected between the inverting input and ground. 3. **Low-Pass Filter Network:** - The circuit includes a series of 10 kΩ resistors (R) and 10 nF capacitors (C) in a low-pass filter configuration. Each resistor is followed by a capacitor connected to ground, forming three RC sections in series. - These RC sections are vital in filtering high-frequency components from the output signal, allowing only the lower frequency signals to pass through to the final output (\( V_{OUT} \)). **Explanation:** - **Operation of the Op-Amp Circuit:** The op-amp works to amplify the input signal, which is set by the reference voltage of 2.5V at the non-inverting input. The feedback network helps to stabilize the gain of the op-amp. - **Low-Pass Filter Function:** Each RC section of the low-pass filter network progressively attenuates higher frequency signals more, such that by the end of the network, the output signal at \( V_{OUT} \) is largely free of high-frequency noise. This is useful for applications where a clean and stable signal is required. This type of circuit is commonly used in analog signal processing to achieve desired filtering characteristics, ensuring that only the necessary signal frequencies are passed through while unwanted noise is minimized.
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