1) The canonica nonical form for a band-reject filter is 2 sa wa + Wo O S² + BS a) Show that a m Hi band - reject filter : R un 3$L 2 + w₂² series RLC is a Š V/SC O b) Express bandwidth, center frequency and Quality Factor in terms of R, L,C. c) Determine the magnitude gain | Ht (jw)|
1) The canonica nonical form for a band-reject filter is 2 sa wa + Wo O S² + BS a) Show that a m Hi band - reject filter : R un 3$L 2 + w₂² series RLC is a Š V/SC O b) Express bandwidth, center frequency and Quality Factor in terms of R, L,C. c) Determine the magnitude gain | Ht (jw)|
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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![**Transcription:**
1) The canonical form for a band-reject filter is
\[
\frac{s^2 + \omega_0^2}{s^2 + \beta s + \omega_0^2}
\]
a) Show that a series RLC is a band-reject filter:
A circuit diagram is shown with the following components:
- A series combination of a resistor (R), an inductor (3L), and a capacitor (1/3C) arranged horizontally.
- There are two nodes: the input node and the output node.
- The circuit depicts a traditional RLC series network.
b) Express bandwidth, center frequency, and quality factor in terms of R, L, C.
c) Determine the magnitude gain \(|H(j\omega)|\).
**Explanation of Diagram:**
The diagram illustrates a series RLC circuit which includes:
- **Resistor (R):** Placed horizontally on one side.
- **Inductor (3L):** Placed in the middle of the series path.
- **Capacitor (1/3C):** Also in the series path, connected horizontally.
This configuration is typically used to create a band-reject or notch filter, which attenuates a specific range of frequencies and allows others to pass through.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F93e18a88-13ba-47d2-8c84-ec9d29397d2a%2Fd84e8bc8-6c38-4568-9c14-03d31f58fae3%2Ffxygvg_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Transcription:**
1) The canonical form for a band-reject filter is
\[
\frac{s^2 + \omega_0^2}{s^2 + \beta s + \omega_0^2}
\]
a) Show that a series RLC is a band-reject filter:
A circuit diagram is shown with the following components:
- A series combination of a resistor (R), an inductor (3L), and a capacitor (1/3C) arranged horizontally.
- There are two nodes: the input node and the output node.
- The circuit depicts a traditional RLC series network.
b) Express bandwidth, center frequency, and quality factor in terms of R, L, C.
c) Determine the magnitude gain \(|H(j\omega)|\).
**Explanation of Diagram:**
The diagram illustrates a series RLC circuit which includes:
- **Resistor (R):** Placed horizontally on one side.
- **Inductor (3L):** Placed in the middle of the series path.
- **Capacitor (1/3C):** Also in the series path, connected horizontally.
This configuration is typically used to create a band-reject or notch filter, which attenuates a specific range of frequencies and allows others to pass through.
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