Answered: Magnitude (Gain in dB) NO -20 -30…

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...

See similar textbooks

Related questions

Question

The MATLAB code is going well but the last part in bandpass, the legend that is supposed to tell the color of both lower and upper-frequency cutoff does not align with each other. As such I need help

My Matlab code:

% Define frequency range for the plot

f = logspace(1, 5, 500); % Frequency range from 10 Hz to 100 kHz

w = 2 * pi * f; % Angular frequency

% Parameters for the filters

R = 1e3; % Resistance in ohms (1 kΩ)

C = 1e-6; % Capacitance in farads (1 μF)

L = 0.1; % Inductance in henries (chosen for proper bandpass response)

% Compute cutoff frequencies

f_cutoff_RC = 1 / (2 * pi * R * C); % RC low-pass/high-pass cutoff

f_resonance = 1 / (2 * pi * sqrt(L * C)); % Resonant frequency of RLC

Q_factor = (1/R) * sqrt(L/C); % Quality factor of the circuit

% Band-pass filter cutoff frequencies

f_lower_cutoff = f_resonance / (sqrt(1 + 1/(4*Q_factor^2)) + 1/(2*Q_factor));

f_upper_cutoff = f_resonance / (sqrt(1 + 1/(4*Q_factor^2)) - 1/(2*Q_factor));

% Define Transfer Functions

H_low = 1 ./ (1 + 1i * w * R * C); % Low-pass filter (RC)

H_high = (1i * w * R * C) ./ (1 + 1i * w * R * C); % High-pass filter (RC)

H_band = (R ./ (R + 1i*w*L + 1./(1i*w*C))); % Band-pass filter (RLC series)

% Normalize the gain for Low-pass and High-pass filters

H_low_normalized = abs(H_low) / max(abs(H_low));

H_high_normalized = abs(H_high) / max(abs(H_high));

H_band_dB = 20 * log10(abs(H_band) / max(abs(H_band)));

% Create Figure

figure('Position', [100, 100, 800, 600]);

% ---- Low-pass Filter ----

subplot(3,1,1);

semilogx(f, H_low_normalized, 'b', 'LineWidth', 1.5);

hold on;

line([f_cutoff_RC f_cutoff_RC], [0, 0.707], 'Color', 'r', 'LineStyle', '--'); % Mark cutoff

title('Low-pass Filter Magnitude Response (Normalized)');

xlabel('Frequency (Hz)');

ylabel('Magnitude (Normalized Gain)');

grid on;

legend('Low-pass Filter', sprintf('Cutoff = %.2f Hz', f_cutoff_RC));

ylim([0 1.1]); % Ensure visibility

hold off;

% ---- High-pass Filter ----

subplot(3,1,2);

semilogx(f, H_high_normalized, 'r', 'LineWidth', 1.5);

hold on;

line([f_cutoff_RC f_cutoff_RC], [0, 0.707], 'Color', 'r', 'LineStyle', '--'); % Mark cutoff

title('High-pass Filter Magnitude Response (Normalized)');

xlabel('Frequency (Hz)');

ylabel('Magnitude (Normalized Gain)');

grid on;

legend('High-pass Filter', sprintf('Cutoff = %.2f Hz', f_cutoff_RC));

ylim([0 1.1]);

hold off;

% ---- Band-pass Filter ----

subplot(3,1,3);

semilogx(f, H_band_dB, 'g', 'LineWidth', 1.5);

hold on;

% Mark -3dB reference line

yline(-3, 'k--');

% Mark lower cutoff frequency

line([f_lower_cutoff f_lower_cutoff], [-40, -3], 'Color', 'r', 'LineStyle', '--');

text(f_lower_cutoff, -3, sprintf('Lower Cutoff: %.2f Hz', f_lower_cutoff), ...

'VerticalAlignment', 'bottom', 'HorizontalAlignment', 'right', 'FontSize', 10);

% Mark upper cutoff frequency

line([f_upper_cutoff f_upper_cutoff], [-40, -3], 'Color', 'b', 'LineStyle', '--');

text(f_upper_cutoff, -3, sprintf('Upper Cutoff: %.2f Hz', f_upper_cutoff), ...

'VerticalAlignment', 'bottom', 'HorizontalAlignment', 'left', 'FontSize', 10);

% Plot the band-pass filter magnitude response with labels, legend, and cutoff frequencies.

title('Band-pass Filter Magnitude Response (dB)');

xlabel('Frequency (Hz)');

ylabel('Magnitude (Gain in dB)');

grid on;

legend('Band-pass Filter', sprintf('Lower Cutoff = %.2f Hz', f_lower_cutoff), ...

sprintf('Upper Cutoff = %.2f Hz', f_upper_cutoff));

ylim([-40 5]);

hold off;

Magnitude (Gain in dB)
NO
-20
-30
Magnitude (Normalized Gain) Magnitude (Normalized Gain)
101
0
5
101
5
102
102
0
Lower Cutoff: 145.80 Hz
-10
Low-pass Filter Magnitude Response (Normalized)
103
Frequency (Hz)
High-pass Filter Magnitude Response (Normalized)
103
Frequency (Hz)
Band-pass Filter Magnitude Response (dB)
↑
104
104
Low-pass Filter
-Cutoff 159.15 Hz
High-pass Filter
-Cutoff 159.15 Hz
Upper Cutoff: 1737.35 Hz
Band-pass Filter
-Lower Cutoff = 145.80 Hz
Upper Cutoff 1737.35 Hz
-40
101
102
103
104
Frequency (Hz)
105
105
105

Expert Solution

Step by step

Solved in 2 steps with 2 images

SEE SOLUTION Check out a sample Q&A here

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

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