Design a first-order, low-pass, active filter with cutoff frequency equal to 2200 rad/s and gain in the passing region equal to 19 dB. You need to calculate the value of the resistor R₁, given that the capacitor that you must use in the design is C = 3 nF.
Design a first-order, low-pass, active filter with cutoff frequency equal to 2200 rad/s and gain in the passing region equal to 19 dB. You need to calculate the value of the resistor R₁, given that the capacitor that you must use in the design is C = 3 nF.
Introductory Circuit Analysis (13th Edition)
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ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
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![**Design a first-order, low-pass, active filter with cutoff frequency equal to 2200 rad/s and gain in the passing region equal to 19 dB. You need to calculate the value of the resistor \( R_1 \), given that the capacitor that you must use in the design is \( C = 3 \text{ nF} \).**
**Diagram Explanation:**
- The circuit diagram shows a first-order, low-pass, active filter.
- It consists of an operational amplifier with input voltage \( V_{\text{in}} \) and output voltage \( V_{\text{out}} \).
- Resistor \( R_1 \) is connected in series with the input voltage.
- Capacitor \( C \) is parallel to the resistor \( R_2 \), which is connected from the inverting input of the op-amp to the output.
- The non-inverting input of the op-amp is grounded.
**Hint:** The relationship between the gain in dB and in linear scale is:
\[ H_{\text{dB}} = 20 \log_{10} |H|. \]
**Answer:** \( R_1 = \_\_\_ \)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F77548912-c51c-4c9d-8b51-f3905a3bec75%2Fe58dc6d4-0b4f-4211-a3db-8fcfd125dbe9%2Fce8fbw9_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Design a first-order, low-pass, active filter with cutoff frequency equal to 2200 rad/s and gain in the passing region equal to 19 dB. You need to calculate the value of the resistor \( R_1 \), given that the capacitor that you must use in the design is \( C = 3 \text{ nF} \).**
**Diagram Explanation:**
- The circuit diagram shows a first-order, low-pass, active filter.
- It consists of an operational amplifier with input voltage \( V_{\text{in}} \) and output voltage \( V_{\text{out}} \).
- Resistor \( R_1 \) is connected in series with the input voltage.
- Capacitor \( C \) is parallel to the resistor \( R_2 \), which is connected from the inverting input of the op-amp to the output.
- The non-inverting input of the op-amp is grounded.
**Hint:** The relationship between the gain in dB and in linear scale is:
\[ H_{\text{dB}} = 20 \log_{10} |H|. \]
**Answer:** \( R_1 = \_\_\_ \)
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