+v R, Rz ovo Rf2 1.+ Redrawthe circuit-equivalentwhenoperatingat-a-DCvoltage(OHz).1 VerifyusingKCL-that-the circuit-operation-will-be-that-ofa-non-invertingamplifier.1 2.→ Redrawthe circuit-equivalentat veryhigh-frequencies.-Verifythat Voutisshorted.-(Hint.-Note: the reactance at-the non-invertinginputat-extremelyhighfrequencies.-What-will-bethe- voltage at that-node?-What-doesthis-meanforthe voltage at-Rf2?)¶1 3.+ Let-C1= C2.Calculate the valuesofC1-and-C2-for-a-cut-off frequency of500-Hz-if-R1-and-R2. are-33kohm-and-choosereasonable valuesof Rf1and-RF2•50-thatthe-gain-at-low-frequenciesis. 4-dB.--1 75
+v R, Rz ovo Rf2 1.+ Redrawthe circuit-equivalentwhenoperatingat-a-DCvoltage(OHz).1 VerifyusingKCL-that-the circuit-operation-will-be-that-ofa-non-invertingamplifier.1 2.→ Redrawthe circuit-equivalentat veryhigh-frequencies.-Verifythat Voutisshorted.-(Hint.-Note: the reactance at-the non-invertinginputat-extremelyhighfrequencies.-What-will-bethe- voltage at that-node?-What-doesthis-meanforthe voltage at-Rf2?)¶1 3.+ Let-C1= C2.Calculate the valuesofC1-and-C2-for-a-cut-off frequency of500-Hz-if-R1-and-R2. are-33kohm-and-choosereasonable valuesof Rf1and-RF2•50-thatthe-gain-at-low-frequenciesis. 4-dB.--1 75
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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![### Circuit Analysis and Design
**Cut-off Frequency Formula:**
The cut-off frequency for the circuit is given by:
\[
f_C = \frac{1}{2 \pi \sqrt{R_1 R_2 C_1 C_2}}
\]
**Circuit Diagram Explanation:**
The circuit diagram represents an operational amplifier configuration with associated resistors and capacitors. The components are labeled as \( R_1, R_2, C_1, C_2, R_{f1}, \) and \( R_{f2} \). The operational amplifier has a feedback loop connecting the output \( V_0 \) to its inverting input.
**Steps for Analysis:**
1. **DC Operation:**
- Redraw the circuit equivalent when operating at DC voltage (0 Hz).
- Verify using Kirchhoff’s Current Law (KCL) that the circuit operates as a non-inverting amplifier.
2. **High-Frequency Analysis:**
- Redraw the circuit equivalent at very high frequencies.
- Verify that \( V_{\text{out}} \) is shorted.
- Hint: Analyze the reactance at the non-inverting input at extremely high frequencies.
- Determine the voltage at that node and its implications for the voltage at \( R_{f2} \).
3. **Component Selection:**
- Let \( C_1 = C_2 \).
- Calculate \( C_1 \) and \( C_2 \) for a cut-off frequency of 500 Hz if \( R_1 \) and \( R_2 \) are 33 kΩ.
- Select reasonable values for \( R_{f1} \) and \( R_{f2} \) to achieve a low-frequency gain of 4 dB.
4. **Simulation:**
- Use Multisim to simulate the circuit and repeat steps 4 and 5 of Part 1.
- Produce a Bode Plot using the AC Sweep function.
- Identify the type of response curve and the roll-off rate.
This analysis guides the study of circuit behavior across different frequencies and helps in designing filter circuits with specific cut-off frequencies and gain characteristics.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fff3dd3d4-8cf8-4e80-9073-dd7d9c77d352%2Fc2d0c5ee-0b5e-48a6-9092-c11a093cb4ce%2Fw7fubj_processed.png&w=3840&q=75)
Transcribed Image Text:### Circuit Analysis and Design
**Cut-off Frequency Formula:**
The cut-off frequency for the circuit is given by:
\[
f_C = \frac{1}{2 \pi \sqrt{R_1 R_2 C_1 C_2}}
\]
**Circuit Diagram Explanation:**
The circuit diagram represents an operational amplifier configuration with associated resistors and capacitors. The components are labeled as \( R_1, R_2, C_1, C_2, R_{f1}, \) and \( R_{f2} \). The operational amplifier has a feedback loop connecting the output \( V_0 \) to its inverting input.
**Steps for Analysis:**
1. **DC Operation:**
- Redraw the circuit equivalent when operating at DC voltage (0 Hz).
- Verify using Kirchhoff’s Current Law (KCL) that the circuit operates as a non-inverting amplifier.
2. **High-Frequency Analysis:**
- Redraw the circuit equivalent at very high frequencies.
- Verify that \( V_{\text{out}} \) is shorted.
- Hint: Analyze the reactance at the non-inverting input at extremely high frequencies.
- Determine the voltage at that node and its implications for the voltage at \( R_{f2} \).
3. **Component Selection:**
- Let \( C_1 = C_2 \).
- Calculate \( C_1 \) and \( C_2 \) for a cut-off frequency of 500 Hz if \( R_1 \) and \( R_2 \) are 33 kΩ.
- Select reasonable values for \( R_{f1} \) and \( R_{f2} \) to achieve a low-frequency gain of 4 dB.
4. **Simulation:**
- Use Multisim to simulate the circuit and repeat steps 4 and 5 of Part 1.
- Produce a Bode Plot using the AC Sweep function.
- Identify the type of response curve and the roll-off rate.
This analysis guides the study of circuit behavior across different frequencies and helps in designing filter circuits with specific cut-off frequencies and gain characteristics.
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