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Consider the output voltage measured across the resistor in the circuit shown below.   a. Find the transfer function for the filter circuit above (??/??) as a function of jω. (Leave R and C as variables) b. Transpose the transfer function to a Magnitude and Phase , that is |?(??)|??? form. c. Approximate the magnitude and phase of H(jω) as ω approaches 0; and as ω approaches infinity.

Consider the output voltage measured across the resistor in the circuit shown below.   a. Find the transfer function for the filter circuit above (??/??) as a function of jω. (Leave R and C as variables) b. Transpose the transfer function to a Magnitude and Phase , that is |?(??)|??? form. c. Approximate the magnitude and phase of H(jω) as ω approaches 0; and as ω approaches infinity.

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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Consider the output voltage measured across the resistor in the circuit shown below.

 

a. Find the transfer function for the filter circuit above (??/??) as a function of jω. (Leave R and C as variables)

b. Transpose the transfer function to a Magnitude and Phase , that is |?(??)|??? form.

c. Approximate the magnitude and phase of H(jω) as ω approaches 0; and as ω approaches infinity.

d. If R = 4000 ohms, C = 2.5uF what is the corner frequency ω0 in rad/s.

e. What is the corner frequency, f0 in Hz?

f. Is this a high pass or low pass filter?

g. What is the passband gain of the circuit in [dB].

h. Assuming C does not change, choose R for a cut off frequency of 50Hz.

 

This is an electrical circuit diagram commonly used in the study of alternating current (AC) circuits. The circuit consists of the following components: 1. **AC Voltage Source (\(\tilde{V}_i\))**: Represented by a circle with a plus and minus sign, indicating the polarity of the voltage. This source provides an input alternating voltage \(\tilde{V}_i\) to the circuit. 2. **Resistor (R)**: Located next to the voltage source, it is depicted by a zig-zag line. The resistor is used to regulate the current flow in the circuit. The voltage across the resistor is labeled as \(\tilde{V}_o\), with the plus and minus signs indicating the polarity. 3. **Capacitor (C)**: Shown as two parallel lines located after the resistor, this component stores electrical energy in an electric field. The capacitor is in series with the resistor, forming an RC circuit. The diagram represents a simple RC circuit used to study the behavior of capacitors and resistors in AC circuits, such as the phase relationship between voltage and current and the frequency response of the circuit.
Transcribed Image Text:This is an electrical circuit diagram commonly used in the study of alternating current (AC) circuits. The circuit consists of the following components: 1. **AC Voltage Source (\(\tilde{V}_i\))**: Represented by a circle with a plus and minus sign, indicating the polarity of the voltage. This source provides an input alternating voltage \(\tilde{V}_i\) to the circuit. 2. **Resistor (R)**: Located next to the voltage source, it is depicted by a zig-zag line. The resistor is used to regulate the current flow in the circuit. The voltage across the resistor is labeled as \(\tilde{V}_o\), with the plus and minus signs indicating the polarity. 3. **Capacitor (C)**: Shown as two parallel lines located after the resistor, this component stores electrical energy in an electric field. The capacitor is in series with the resistor, forming an RC circuit. The diagram represents a simple RC circuit used to study the behavior of capacitors and resistors in AC circuits, such as the phase relationship between voltage and current and the frequency response of the circuit.
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