To determine Plot the maximum gain decibels versus α when ω = 0 for the circuit designed in Problem 15.61. Explanation Given data: The value of α varies from 0 to 1 in increment of 0.1 . From the Problem 15.61, The maximum gain value is 14 dB and the gain value is 11 dB . The value of the center frequency ( f o ) is 50 Hz . The value of the resistor ( R 1 ) is 10 k Ω . The value of the resistor ( R 2 ) is 50 k Ω . Formula used: Write the expression to calculate the angular center frequency. ω o = 2 π f o (1) Here, f o is the value of the center frequency in hertz. Write the expression to calculate the center frequency of the bass volume control circuit. ω o = 1 R 2 C 1 (2) Here, R 2 is the value of the resistor 2, and C 1 is the value of the capacitor 1. Calculation: The Bass volume control circuit is drawn as Figure 1. Write the transfer function equation of the bass volume control circuit. H ( j ω ) = − ( R 1 + α R 2 + j ω R 1 R 2 C 1 ) R 1 + ( 1 − α ) R 2 + j ω R 1 R 2 C 1 (3) The maximum gain is obtained when ω is equal to zero. That is, ω = 0 . Substitute 0 for ω in equation (3) to find H ( j 0 ) . H ( j 0 ) = − ( R 1 + α R 2 + j ( 0 ) R 1 R 2 C 1 ) R 1 + ( 1 − α ) R 2 + j ( 0 ) R 1 R 2 C 1 = − ( R 1 + α R 2 + 0 ) R 1 + ( 1 − α ) R 2 + 0 = − ( R 1 + α R 2 ) R 1 + ( 1 − α ) R 2 Take magnitude on both sides of the above equation to find | H ( j 0 ) | . | H ( j 0 ) | = | − ( R 1 + α R 2 ) R 1 + ( 1 − α ) R 2 | = | − ( R 1 + α R 2 ) | | ( R 1 + ( 1 − α ) R 2 ) | = ( − ( R 1 + α R 2 ) ) 2 ( R 1 + ( 1 − α ) R 2 ) 2 | H ( j 0 ) | = ( R 1 + α R 2 ) ( R 1 + ( 1 − α ) R 2 ) (4) The equation (4) is the magnitude of the transfer function of the circuit with a maximum gain that is at ω = 0 . Assume α = 1 and substitute in equation (4) to find | H ( j 0 ) | . | H ( j 0 ) | = ( R 1 + ( 1 ) R 2 ) ( R 1 + ( 1 − 1 ) R 2 ) = R 1 + R 2 R 1 + 0 | H ( j 0 ) | = R 1 + R 2 R 1 (5) Given that the maximum gain value is 14 dB , therefore the equation (5) becomes, 20 log ( R 1 + R 2 R 1 ) = 14 dB log ( R 1 + R 2 R 1 ) = 14 20 dB log ( R 1 + R 2 R 1 ) = 0.7 dB Simplify the above equation. R 1 + R 2 R 1 = 10 0.7 dB R 1 + R 2 R 1 = 5 R 1 + R 2 = 5 R 1 Rearrange the above equation to find R 2 . R 2 = 5 R 1 − R 1 = 4 R 1 Substitute equation (1) in equation (2). 2 π f o = 1 R 2 C 1 Rearrange the above equation to find C 1 . C 1 = 1 2 π f o R 2 Substitute 50 Hz for f o and 50 k Ω for R 2 in above equation to find C 1 . C 1 = 1 2 π ( 50 Hz ) ( 50 k Ω ) = 1 2 π ( 50 ) ( 50 × 10 3 ) Ω ⋅ Hz { ∵ 1 k = 10 3 } = 63.66 × 10 − 9 1 ( 1 F ) { ∵ 1 F = 1 1 Ω ⋅ 1 Hz } = 63.66 nF { ∵ 1 n = 10 − 9 } From the obtained capacitor value, the standard value is taken for the following calculation. C 1 = 64 nF Substitute 10 k Ω for R 1 and 50 k Ω for R 2 in equation (5) to find | H ( j 0 ) | . | H ( j 0 ) | = ( 10 k Ω ) + ( 50 k Ω ) 10 k Ω = 60 k Ω 10 k Ω = 6 Find the above value in decibel. | H ( j 0 ) | dB = 20 log ( 6 ) dB = 15.56 dB The given base volume control circuit has 15.56 dB gain which can survive and works efficiently for the given maximum gain of 14 dB . Calculate the center frequency of the circuit using the obtained standard values. Substitute 50 k Ω for R 2 and 64 nF for C 1 in equation (2) to find ω o . ω o = 1 ( 50 k Ω ) ( 64 nF ) = 1 ( 50 × 10 3 ) ( 64 × 10 − 9 ) Ω ⋅ F { ∵ 1 k = 10 3 , 1 n = 10 − 9 } = 1 ( 3.2 × 10 − 3 ) Ω ⋅ ( s Ω ) { ∵ 1 F = 1 s 1 Ω } = 312

10th Edition

ISBN: 9781292060545

Author: James W. Nilsson, Susan Riedel

Publisher: Pearson Education Limited

See similar textbooks

Concept explainers

Filter

A filter is a device or process which removes some of the unwanted features or components like frequencies from a signal in signal processing. The feature of filters is the complete or partial suppression of some part of the signal, and filtering is a cl…

Videos

Question

Chapter 15, Problem 63P

To determine

Plot the maximum gain decibels versus α when ω=0 for the circuit designed in Problem 15.61.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 15, Problem 62P

Chapter 15, Problem 64P

Students have asked these similar questions

kΩ

NO AI PLEASE

Chapter 15 Solutions

Electric Circuits, Global Edition

Ch. 15.1 - Compute the values for R2 and C that yield a...Ch. 15.1 - Prob. 2AP Ch. 15.2 - Prob. 3AP Ch. 15.4 - Prob. 4AP Ch. 15.5 - Prob. 5AP Ch. 15.5 - Prob. 6AP Ch. 15 - Prob. 1P Ch. 15 - Prob. 2P Ch. 15 - Prob. 3P Ch. 15 - Prob. 4P

Ch. 15 - Prob. 5P Ch. 15 - Use the result of Problem 15.5 to find the...Ch. 15 - Repeat Problem 15.6, using the circuit shown in...Ch. 15 - Prob. 8P Ch. 15 - Prob. 10P Ch. 15 - Prob. 11P Ch. 15 - Prob. 12P Ch. 15 - Prob. 13P Ch. 15 - Prob. 14P Ch. 15 - Prob. 17P Ch. 15 - Prob. 18P Ch. 15 - Prob. 19P Ch. 15 - Prob. 20P Ch. 15 - Prob. 21P Ch. 15 - Scale the inductor and capacitor in Fig. P9.66 so...Ch. 15 - Prob. 24P Ch. 15 - Prob. 25P Ch. 15 - Prob. 26P Ch. 15 - Prob. 27P Ch. 15 - Prob. 30P Ch. 15 - Design a parallel band reject filter with a center...Ch. 15 - Show that the circuit in Fig. P15.32 behaves as a...Ch. 15 - For circuits of resistors, capacitors, Inductors,...Ch. 15 - Prob. 34P Ch. 15 - Prob. 35P Ch. 15 - Prob. 36P Ch. 15 - Prob. 37P Ch. 15 - Prob. 38P Ch. 15 - Prob. 39P Ch. 15 - Prob. 40P Ch. 15 - Prob. 41P Ch. 15 - Using 250 nF capacitors and ideal op amps, design...Ch. 15 - Prob. 46P Ch. 15 - Prob. 47P Ch. 15 - Prob. 48P Ch. 15 - Use 20 nF capacitors in the circuit in Fig. 15.27...Ch. 15 - The purpose of this problem is to guide you...Ch. 15 - Assume the circuit analyzed in Problem 15.48 is...Ch. 15 - The purpose of this problem is to develop the...Ch. 15 - Prob. 56P Ch. 15 - Prob. 57P Ch. 15 - Prob. 58P Ch. 15 - Prob. 59P Ch. 15 - Prob. 60P Ch. 15 - Prob. 61P Ch. 15 - Prob. 62P Ch. 15 - Plot the maximum gain in decibels versus α when ω...Ch. 15 - Prob. 64P

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, electrical-engineering and related others by exploring similar questions and additional content below.

Similar questions

SEE MORE QUESTIONS

Recommended textbooks for you

Introductory Circuit Analysis (13th Edition)
Electrical Engineering
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:PEARSON
Delmar's Standard Textbook Of Electricity
Electrical Engineering
ISBN:9781337900348
Author:Stephen L. Herman
Publisher:Cengage Learning
Programmable Logic Controllers
Electrical Engineering
ISBN:9780073373843
Author:Frank D. Petruzella
Publisher:McGraw-Hill Education
Fundamentals of Electric Circuits
Electrical Engineering
ISBN:9780078028229
Author:Charles K Alexander, Matthew Sadiku
Publisher:McGraw-Hill Education
Electric Circuits. (11th Edition)
Electrical Engineering
ISBN:9780134746968
Author:James W. Nilsson, Susan Riedel
Publisher:PEARSON
Engineering Electromagnetics
Electrical Engineering
ISBN:9780078028151
Author:Hayt, William H. (william Hart), Jr, BUCK, John A.
Publisher:Mcgraw-hill Education,

Introductory Circuit Analysis (13th Edition)

Electrical Engineering

ISBN:9780133923605

Author:Robert L. Boylestad

Publisher:PEARSON

Delmar's Standard Textbook Of Electricity

Electrical Engineering

ISBN:9781337900348

Author:Stephen L. Herman

Publisher:Cengage Learning

Programmable Logic Controllers

Electrical Engineering

ISBN:9780073373843

Author:Frank D. Petruzella

Publisher:McGraw-Hill Education

Fundamentals of Electric Circuits

Electrical Engineering

ISBN:9780078028229

Author:Charles K Alexander, Matthew Sadiku

Publisher:McGraw-Hill Education

Electric Circuits. (11th Edition)

Electrical Engineering

ISBN:9780134746968

Author:James W. Nilsson, Susan Riedel

Publisher:PEARSON

Engineering Electromagnetics

Electrical Engineering

ISBN:9780078028151

Author:Hayt, William H. (william Hart), Jr, BUCK, John A.

Publisher:Mcgraw-hill Education,

SEE MORE TEXTBOOKS

What is Filter & Classification of Filters | Four Types of Filters | Electronic Devices & Circuits; Author: SimplyInfo;https://www.youtube.com/watch?v=9x1Sjz-VPSg;License: Standard Youtube License