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Complete report matlab transfer function study part

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Apostolos Fanakis 6 years ago
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39 changed files with 47076 additions and 202 deletions
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  1. 38
      Band Elimination Chebyshev/band_elimination_design.m
  2. 30
      Band Pass Chebyshev/band_pass_design.m
  3. 13
      High Pass Butterworth/high_pass_design.m
  4. 17
      Low Pass Inverse Chebyshev/low_pass_design.m
  5. 9
      report/1_low_pass/1_low_pass.pug
  6. 6
      report/1_low_pass/1_low_pass_design.pug
  7. 1
      report/1_low_pass/1_low_pass_transfer_function_matlab.pug
  8. 2
      report/1_low_pass/1_low_pass_transfer_function_multisim.pug
  9. 681
      report/1_low_pass/assets/diagrams/low_pass_general_transfer_function_plot.svg
  10. 2
      report/2_band_pass/2_band_pass.pug
  11. 6
      report/2_band_pass/2_band_pass_design.pug
  12. 70
      report/2_band_pass/2_band_pass_transfer_function_matlab.pug
  13. 1760
      report/2_band_pass/assets/diagrams/matlab_band_pass_chebyshev_deliyannis_friend_unit_1_transfer_function.svg
  14. 1798
      report/2_band_pass/assets/diagrams/matlab_band_pass_chebyshev_deliyannis_friend_unit_2_transfer_function.svg
  15. 1812
      report/2_band_pass/assets/diagrams/matlab_band_pass_chebyshev_deliyannis_friend_unit_3_transfer_function.svg
  16. 1889
      report/2_band_pass/assets/diagrams/matlab_band_pass_chebyshev_deliyannis_friend_unit_4_transfer_function.svg
  17. 4264
      report/2_band_pass/assets/diagrams/matlab_band_pass_chebyshev_total_attenuation.svg
  18. 4454
      report/2_band_pass/assets/diagrams/matlab_band_pass_chebyshev_total_transfer_function.svg
  19. 226
      report/2_band_pass/assets/diagrams/matlab_combined_transfer_functions_bode.svg
  20. 2
      report/3_band_elimination/3_band_elimination.pug
  21. 4
      report/3_band_elimination/3_band_elimination_design.pug
  22. 82
      report/3_band_elimination/3_band_elimination_transfer_function_matlab.pug
  23. 287
      report/3_band_elimination/assets/diagrams/band_elimination_general_transfer_function_plot.svg
  24. 1738
      report/3_band_elimination/assets/diagrams/matlab_band_elimination_chebyshev_HPN_unit_1_transfer_function.svg
  25. 1737
      report/3_band_elimination/assets/diagrams/matlab_band_elimination_chebyshev_HPN_unit_3_transfer_function.svg
  26. 2031
      report/3_band_elimination/assets/diagrams/matlab_band_elimination_chebyshev_LPN_unit_2_transfer_function.svg
  27. 1912
      report/3_band_elimination/assets/diagrams/matlab_band_elimination_chebyshev_LPN_unit_4_transfer_function.svg
  28. 5682
      report/3_band_elimination/assets/diagrams/matlab_band_elimination_chebyshev_original_gain_attenuation.svg
  29. 533
      report/3_band_elimination/assets/diagrams/matlab_band_elimination_chebyshev_total_attenuation.svg
  30. 6273
      report/3_band_elimination/assets/diagrams/matlab_band_elimination_chebyshev_total_transfer_function.svg
  31. 265
      report/3_band_elimination/assets/diagrams/matlab_combined_transfer_functions_bode.svg
  32. 4
      report/4_high_pass/4_high_pass.pug
  33. 64
      report/4_high_pass/4_high_pass_transfer_function_matlab.pug
  34. 192
      report/4_high_pass/assets/diagrams/matlab_combined_transfer_functions_bode.svg
  35. 360
      report/4_high_pass/assets/diagrams/matlab_high_pass_butterworth_original_gain_attenuation.svg
  36. 1595
      report/4_high_pass/assets/diagrams/matlab_high_pass_butterworth_sallen_key_unit_1_transfer_function.svg
  37. 1616
      report/4_high_pass/assets/diagrams/matlab_high_pass_butterworth_sallen_key_unit_2_transfer_function.svg
  38. 2928
      report/4_high_pass/assets/diagrams/matlab_high_pass_butterworth_total_attenuation.svg
  39. 2895
      report/4_high_pass/assets/diagrams/matlab_high_pass_butterworth_total_transfer_function.svg

38
Band Elimination Chebyshev/band_elimination_design.m
View File

@ -803,7 +803,7 @@ total_transfer_function = series(series(series( ...
total_transfer_function = total_transfer_function*unit_adjustment_gain; total_transfer_function = total_transfer_function*unit_adjustment_gain;
%{
% Plots each unit's frequency response % Plots each unit's frequency response
for i=1:band_elimination_number_of_poles for i=1:band_elimination_number_of_poles
if i==1 || i==3 if i==1 || i==3
@ -819,31 +819,35 @@ end
% Plots the total filter frequency response % Plots the total filter frequency response
plot_transfer_function(total_transfer_function, ... plot_transfer_function(total_transfer_function, ...
[specification_low_stop_frequency ... [1910 ...
specification_low_pass_frequency ... specification_low_pass_frequency ...
design_half_power_radial_frequency(1,2)/(2*pi) ...
specification_low_stop_frequency ...
specification_central_frequency ... specification_central_frequency ...
specification_high_pass_frequency ... specification_high_stop_frequency ...
specification_high_stop_frequency]); design_half_power_radial_frequency(1,1)/(2*pi) ...
specification_high_pass_frequency]);
% Plots the total filter attenuation function % Plots the total filter attenuation function
plot_transfer_function(inv(total_transfer_function), ... plot_transfer_function(inv(total_transfer_function), ...
[specification_low_stop_frequency ... [specification_low_pass_frequency ...
specification_low_pass_frequency ... specification_low_stop_frequency ...
specification_central_frequency ... specification_central_frequency ...
specification_high_pass_frequency ... specification_high_stop_frequency ...
specification_high_stop_frequency]); specification_high_pass_frequency]);
%}
%{ %{
ltiview(unit_transfer_function(1,1)); ltiview('bodemag', high_pass_notch_units_transfer_functions(1,1));
ltiview(unit_transfer_function(1,2)); ltiview('bodemag', high_pass_notch_units_transfer_functions(1,2));
ltiview(unit_transfer_function(1,3)); ltiview('bodemag', low_pass_notch_units_transfer_functions(1,1));
ltiview(unit_transfer_function(1,4)); ltiview('bodemag', low_pass_notch_units_transfer_functions(1,2));
ltiview(total_transfer_function); ltiview('bodemag', total_transfer_function);
ltiview(unit_transfer_function(1,1), unit_transfer_function(1,2), ...
unit_transfer_function(1,3), unit_transfer_function(1,4), ...
total_transfer_function);
%} %}
ltiview('bodemag', high_pass_notch_units_transfer_functions(1,1), ...
high_pass_notch_units_transfer_functions(1,2), ...
low_pass_notch_units_transfer_functions(1,1), ...
low_pass_notch_units_transfer_functions(1,2), ...
total_transfer_function);
%{ %{
hold off hold off

30
Band Pass Chebyshev/band_pass_design.m
View File

@ -496,42 +496,46 @@ total_transfer_function = series(series(series( ...
units_transfer_functions(1), units_transfer_functions(2)), ... units_transfer_functions(1), units_transfer_functions(2)), ...
units_transfer_functions(3)), units_transfer_functions(4)); units_transfer_functions(3)), units_transfer_functions(4));
%{
% Plots each unit's frequency response % Plots each unit's frequency response
for i=1:band_pass_number_of_poles for i=1:band_pass_number_of_poles
plot_transfer_function(unit_transfer_functions(1,i), ... plot_transfer_function(units_transfer_functions(1,i), ...
(band_pass_poles_radial_frequencies(1,i)/(2*pi))); [band_pass_poles_radial_frequencies(1,i)/(2*pi) ...
design_geometric_central_radial_frequency/(2*pi)]);
end end
% Plots the total filter frequency response % Plots the total filter frequency response
plot_transfer_function(total_transfer_function, ... plot_transfer_function(total_transfer_function, ...
[specification_low_stop_frequency ... [specification_low_stop_frequency ...
design_half_power_radial_frequency(1,2)/(2*pi) ...
specification_low_pass_frequency ... specification_low_pass_frequency ...
specification_central_frequency ... specification_central_frequency ...
941.83 ... 941.83 ...
specification_high_pass_frequency ... specification_high_pass_frequency ...
design_half_power_radial_frequency(1,1)/(2*pi) ...
specification_high_stop_frequency]); specification_high_stop_frequency]);
% Plots the total filter attenuation function % Plots the total filter attenuation function
plot_transfer_function(inv(total_transfer_function), ... plot_transfer_function(inv(total_transfer_function), ...
[specification_low_stop_frequency ... [specification_low_stop_frequency ...
design_half_power_radial_frequency(1,2)/(2*pi) ...
specification_low_pass_frequency ... specification_low_pass_frequency ...
specification_central_frequency ... specification_central_frequency ...
941.83 ...
specification_high_pass_frequency ... specification_high_pass_frequency ...
design_half_power_radial_frequency(1,1)/(2*pi) ...
specification_high_stop_frequency]); specification_high_stop_frequency]);
%}
%{ %{
ltiview(unit_transfer_function(1,1)); ltiview('bodemag', units_transfer_functions(1,1));
ltiview(unit_transfer_function(1,2)); ltiview('bodemag', units_transfer_functions(1,2));
ltiview(unit_transfer_function(1,3)); ltiview('bodemag', units_transfer_functions(1,3));
ltiview(unit_transfer_function(1,4)); ltiview('bodemag', units_transfer_functions(1,4));
ltiview(total_transfer_function); ltiview('bodemag', total_transfer_function);
ltiview(unit_transfer_function(1,1), unit_transfer_function(1,2), ...
unit_transfer_function(1,3), unit_transfer_function(1,4), ...
total_transfer_function);
%} %}
ltiview('bodemag', units_transfer_functions(1,1), units_transfer_functions(1,2), ...
units_transfer_functions(1,3), units_transfer_functions(1,4), ...
total_transfer_function);
%{ %{
hold off hold off

13
High Pass Butterworth/high_pass_design.m
View File

@ -398,7 +398,7 @@ total_transfer_function = total_transfer_function*unit_adjustment_gain;
% Arbitrary high frequency to display the gain at high frequencies % Arbitrary high frequency to display the gain at high frequencies
high_frequency = 90000; % Hz high_frequency = 90000; % Hz
%{
% Plots each unit's frequency response % Plots each unit's frequency response
for i=1:high_pass_number_of_poles for i=1:high_pass_number_of_poles
plot_transfer_function(units_transfer_functions(1,i), ... plot_transfer_function(units_transfer_functions(1,i), ...
@ -418,14 +418,21 @@ plot_transfer_function(inv(total_transfer_function), ...
design_half_power_radial_frequency/(2*pi) ... design_half_power_radial_frequency/(2*pi) ...
specification_pass_frequency ... specification_pass_frequency ...
high_frequency]); high_frequency]);
%}
plot_transfer_function(inv(total_transfer_function/unit_adjustment_gain), ...
[specification_stop_frequency ...
design_half_power_radial_frequency/(2*pi) ...
specification_pass_frequency ...
high_frequency]);
%{ %{
ltiview('bodemag', units_transfer_functions(1,1)); ltiview('bodemag', units_transfer_functions(1,1));
ltiview('bodemag', units_transfer_functions(1,2)); ltiview('bodemag', units_transfer_functions(1,2));
ltiview('bodemag', total_transfer_function); ltiview('bodemag', total_transfer_function);
%}
ltiview('bodemag', units_transfer_functions(1,1), units_transfer_functions(1,2), ... ltiview('bodemag', units_transfer_functions(1,1), units_transfer_functions(1,2), ...
total_transfer_function); total_transfer_function);
%}
%{ %{
hold off hold off

17
Low Pass Inverse Chebyshev/low_pass_design.m
View File

@ -420,7 +420,7 @@ total_transfer_function = total_transfer_function*unit_adjustment_gain;
% Arbitrary low frequency to display the gain at low frequencies % Arbitrary low frequency to display the gain at low frequencies
low_frequency = 10; % Hz low_frequency = 10; % Hz
%{
% Plots each unit's frequency response % Plots each unit's frequency response
for i=1:design_number_of_poles for i=1:design_number_of_poles
plot_transfer_function(unit_transfer_function(1,i), ... plot_transfer_function(unit_transfer_function(1,i), ...
@ -440,15 +440,16 @@ plot_transfer_function(inv(total_transfer_function), ...
specification_pass_frequency ... specification_pass_frequency ...
design_half_power_radial_frequency/(2*pi) ... design_half_power_radial_frequency/(2*pi) ...
specification_stop_frequency]); specification_stop_frequency]);
%}
%{ %{
ltiview(unit_transfer_function(1,1)); ltiview('bodemag', unit_transfer_function(1,1));
ltiview(unit_transfer_function(1,2)); ltiview('bodemag', unit_transfer_function(1,2));
ltiview(total_transfer_function); ltiview('bodemag', total_transfer_function);
ltiview(unit_transfer_function(1,1), unit_transfer_function(1,2), ...
total_transfer_function);
%} %}
ltiview('bodemag', unit_transfer_function(1,1), unit_transfer_function(1,2), ...
total_transfer_function);
%{
hold off hold off
input_signal_frequency = 2000; % Hz input_signal_frequency = 2000; % Hz
@ -493,7 +494,7 @@ Pyy = system_output_fft.*conj(system_output_fft)/sampling_length_L;
figure(3) figure(3)
semilogx(frequency_vector,Pyy(1:sampling_length_L/2+1)) semilogx(frequency_vector,Pyy(1:sampling_length_L/2+1))
grid on grid on
%}
% Clears unneeded variable from workspace % Clears unneeded variable from workspace
clear low_frequency clear low_frequency
clear -regexp _numerator$ clear -regexp _numerator$

9
report/1_low_pass/1_low_pass.pug
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@ -37,6 +37,15 @@ figure.block-center.width-15cm
.caption. .caption.
Προδιαγραφές σχεδίασης κατωδιαβατού φίλτρου Προδιαγραφές σχεδίασης κατωδιαβατού φίλτρου
figure.block-center.width-15cm
img(src="1_low_pass/assets/diagrams/low_pass_general_transfer_function_plot.svg").width-15cm
figcaption
.reference #[span.plot-count]
.caption.title.
Ποιοτικό γράφημα συνάρτησης μεταφοράς κατωδιαβατού Chebyshev φίλτρου.
.caption.
Στο γράφημα φαίνονται οι συχνότητες που ορίζουν τη ζώνη διόδου (f#[sub p]/ω#[sub p]) και τη ζώνη αποκοπής (f#[sub s]/ω#[sub s]), καθώς και οι προδιαγραφές α#[sub min] και α#[sub max].
// Sub-Chapters // Sub-Chapters
include 1_low_pass_design include 1_low_pass_design
include 1_low_pass_transfer_function_matlab include 1_low_pass_transfer_function_matlab

6
report/1_low_pass/1_low_pass_design.pug
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@ -14,7 +14,6 @@ figure.block-center.width-15cm
div.item Κλιμακοποίηση του κυκλώματος με στόχο τη μεταφορά στις πραγματικές συχνότητες και σε στοιχεία με πρακτικές (υλοποιήσιμες) τιμές. div.item Κλιμακοποίηση του κυκλώματος με στόχο τη μεταφορά στις πραγματικές συχνότητες και σε στοιχεία με πρακτικές (υλοποιήσιμες) τιμές.
div.item Έλεγχος των κερδών των μονάδων και ρύθμιση κέρδους με επιβολή απόσβεσης ή ενίσχυσης. div.item Έλεγχος των κερδών των μονάδων και ρύθμιση κέρδους με επιβολή απόσβεσης ή ενίσχυσης.
div(style="page-break-before:always")
h4 Υπολογισμός συνάρτησης μεταφοράς h4 Υπολογισμός συνάρτησης μεταφοράς
p. p.
@ -50,7 +49,6 @@ p.
p.latex-equation. p.latex-equation.
$$\Omega_{hp} = \frac{1}{cosh(\frac{1}{n}cosh^{-1}(\frac{1}{\varepsilon}))} = \frac{1}{cosh(\frac{1}{4}cosh^{-1}(\frac{1}{0.065}))} = 0.7196\frac{rad}{s}$$ $$\Omega_{hp} = \frac{1}{cosh(\frac{1}{n}cosh^{-1}(\frac{1}{\varepsilon}))} = \frac{1}{cosh(\frac{1}{4}cosh^{-1}(\frac{1}{0.065}))} = 0.7196\frac{rad}{s}$$
div(style="page-break-before:always")
p και στη συνέχεια μεταφέρεται στη πραγματική συχνότητα: p και στη συνέχεια μεταφέρεται στη πραγματική συχνότητα:
p.latex-equation. p.latex-equation.
@ -94,7 +92,6 @@ p.
p.latex-equation. p.latex-equation.
$$\omega_{0_k} = \frac{1}{\Omega_{0_k}}$$ $$\omega_{0_k} = \frac{1}{\Omega_{0_k}}$$
div(style="page-break-before:always")
p. p.
Από τον μετασχηματισμό προκύπτουν οι πόλοι του #[strong αντίστροφου Chebyshev]: Από τον μετασχηματισμό προκύπτουν οι πόλοι του #[strong αντίστροφου Chebyshev]:
@ -125,7 +122,6 @@ figure.block-center.width-19cm
.caption. .caption.
Πόλοι και μηδενικά του αντίστροφου Chebyshev Πόλοι και μηδενικά του αντίστροφου Chebyshev
div(style="page-break-before:always")
p. p.
Οι πόλοι και τα μηδενικά ομαδοποιούνται όπως φαίνεται στο παρακάτω διάγραμμα: Οι πόλοι και τα μηδενικά ομαδοποιούνται όπως φαίνεται στο παρακάτω διάγραμμα:
@ -186,7 +182,6 @@ figure.block-center.width-15cm
.caption. .caption.
Προδιαγραφές πρώτης μονάδας low pass notch Προδιαγραφές πρώτης μονάδας low pass notch
div(style="page-break-before:always")
p. p.
Γίνεται κανονικοποίηση των συχνοτήτων ως προς το ω#[sub 0], ώστε Ω#[sub 0]=1: Γίνεται κανονικοποίηση των συχνοτήτων ως προς το ω#[sub 0], ώστε Ω#[sub 0]=1:
@ -231,7 +226,6 @@ p.
p.latex-equation. p.latex-equation.
$$k_{f} = \omega_s\omega_0 = 72570.79*0.963 = 69885.7$$ $$k_{f} = \omega_s\omega_0 = 72570.79*0.963 = 69885.7$$
div(style="page-break-before:always")
p. p.
Με βάση τον αριθμό ΑΕΜ (8261) επιλέγεται κατάλληλος συντελεστής κλιμακοποίησης πλάτους ώστε να επιτευχθεί τιμή πυκνωτών ίση με 0.1μF, γίνεται χρήση του τύπου #[span.course-notes-equation 6-33]: Με βάση τον αριθμό ΑΕΜ (8261) επιλέγεται κατάλληλος συντελεστής κλιμακοποίησης πλάτους ώστε να επιτευχθεί τιμή πυκνωτών ίση με 0.1μF, γίνεται χρήση του τύπου #[span.course-notes-equation 6-33]:

1
report/1_low_pass/1_low_pass_transfer_function_matlab.pug
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@ -2,7 +2,6 @@ h3 Μελέτη συνάρτησης μεταφοράς στο Matlab
p. p.
Η σχεδίαση του φίλτρου έγινε στο λογισμικό Matlab. Σχεδιάστηκαν, με χρήση της συνάρτησης plot_transfer_function που δόθηκε καθώς και της ltiview που παρέχει το λογισμικό, οι αποκρίσεις πλάτους σε dB των επιμέρους μονάδων, καθώς και του συνολικού φίλτρου. Η σχεδίαση του φίλτρου έγινε στο λογισμικό Matlab. Σχεδιάστηκαν, με χρήση της συνάρτησης plot_transfer_function που δόθηκε καθώς και της ltiview που παρέχει το λογισμικό, οι αποκρίσεις πλάτους σε dB των επιμέρους μονάδων, καθώς και του συνολικού φίλτρου.
div(style="page-break-before:always")
p. p.
Παρακάτω φαίνονται οι αποκρίσεις όπως προέκυψαν στο Matlab από την plot_transfer_function, με ορίσματα κάθε φορά την συνάρτηση μεταφοράς του επί μέρους συστήματος, καθώς και τυχόν κρίσιμες συχνότητες: Παρακάτω φαίνονται οι αποκρίσεις όπως προέκυψαν στο Matlab από την plot_transfer_function, με ορίσματα κάθε φορά την συνάρτηση μεταφοράς του επί μέρους συστήματος, καθώς και τυχόν κρίσιμες συχνότητες:

2
report/1_low_pass/1_low_pass_transfer_function_multisim.pug
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@ -126,7 +126,6 @@ figure.block-center.width-17cm
.caption.title. .caption.title.
Φάσμα σήματος εισόδου, διάγραμμα από Matlab. Φάσμα σήματος εισόδου, διάγραμμα από Matlab.
div(style="page-break-before:always")
p. p.
Το φάσμα του σήματος εξόδου φαίνεται στο παρακάτω διάγραμμα: Το φάσμα του σήματος εξόδου φαίνεται στο παρακάτω διάγραμμα:
@ -177,7 +176,6 @@ figure.block-center.width-17cm
#[br/]#[strong Amplitude:] #[strong lin] και #[strong Range:] 0.1 V/Div #[br/]#[strong Amplitude:] #[strong lin] και #[strong Range:] 0.1 V/Div
#[br/]#[strong Resolution freq.:] 100 Hz #[br/]#[strong Resolution freq.:] 100 Hz
div(style="page-break-before:always")
p. p.
Τα δύο παραπάνω διαγράμματα συνδυάστηκαν σε ένα για ευκολότερη εξαγωγή συμπερασμάτων: Τα δύο παραπάνω διαγράμματα συνδυάστηκαν σε ένα για ευκολότερη εξαγωγή συμπερασμάτων:

681
report/1_low_pass/assets/diagrams/low_pass_general_transfer_function_plot.svg
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@ -0,0 +1,681 @@
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@ -72,5 +72,5 @@ figure.block-center.width-15cm
// Sub-Chapters // Sub-Chapters
include 2_band_pass_design include 2_band_pass_design
//- include 1_low_pass_transfer_function_matlab include 2_band_pass_transfer_function_matlab
//- include 1_low_pass_transfer_function_multisim //- include 1_low_pass_transfer_function_multisim

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@ -6,9 +6,9 @@ p.
figure.block-center.width-15cm figure.block-center.width-15cm
div.ui.list.ordered.celled.striped div.ui.list.ordered.celled.striped
div.item Υπολογισμός των προδιαγραφών ενός πρωτότυπου κατωδιαβατού Chebyshev φίλτρου, μέσω των προδιαγραφών του επιθυμητού ζωνοδιαβατού φίλτρου. div.item Υπολογισμός των προδιαγραφών ενός πρωτότυπου κατωδιαβατού Chebyshev φίλτρου, μέσω των προδιαγραφών του επιθυμητού ζωνοδιαβατού φίλτρου.
div.item Υπολογισμός της τάξης και της συχνότητας ημίσειας ισχύος του πτοτότυπου φίλτρου. div.item Υπολογισμός της τάξης και της συχνότητας ημίσειας ισχύος του πρωτότυπου φίλτρου.
div.item Υπολογισμός των πόλων του πρότυπου φίλτρου Chebyshev. div.item Υπολογισμός των πόλων του πρότυπου φίλτρου Chebyshev.
div.item Υπολογισμός των πόλων και μηδενικών του ζωνοδιαβατού φίλτρου μέσω μετασχηματισμού των πόλων του προτότυπου με χρήση του αλγόριθμου Geffe. div.item Υπολογισμός των πόλων και μηδενικών του ζωνοδιαβατού φίλτρου μέσω μετασχηματισμού των πόλων του πρωτότυπου με χρήση του αλγόριθμου Geffe.
div.item Ομαδοποίηση των ζευγών πόλων και μηδενικών ανά δύο. Από την ομαδοποίηση προκύπτουν ζωνοδιαβατές μονάδες που υλοποιούνται με κυκλώματα Delyiannis-Fried. div.item Ομαδοποίηση των ζευγών πόλων και μηδενικών ανά δύο. Από την ομαδοποίηση προκύπτουν ζωνοδιαβατές μονάδες που υλοποιούνται με κυκλώματα Delyiannis-Fried.
div.item Υλοποίηση των φίλτρων Delyiannis-Fried με βάση τα κυκλώματα του κεφαλαίου 7. div.item Υλοποίηση των φίλτρων Delyiannis-Fried με βάση τα κυκλώματα του κεφαλαίου 7.
div.item Κλιμακοποίηση του κυκλώματος με στόχο τη μεταφορά στις πραγματικές συχνότητες και σε στοιχεία με πρακτικές (υλοποιήσιμες) τιμές. div.item Κλιμακοποίηση του κυκλώματος με στόχο τη μεταφορά στις πραγματικές συχνότητες και σε στοιχεία με πρακτικές (υλοποιήσιμες) τιμές.
@ -35,7 +35,7 @@ p.latex-equation.
p. p.
Σχεδιάζεται ένα πρότυπο κατωδιαβατό Chebyshev φίλτρο, το οποίο αργότερα θα μετατραπεί στο επιθυμητό ζωνοδιαβατό Chebyshev. Σχεδιάζεται ένα πρότυπο κατωδιαβατό Chebyshev φίλτρο, το οποίο αργότερα θα μετατραπεί στο επιθυμητό ζωνοδιαβατό Chebyshev.
p Υπολογίζονται οι προδιαγραφές του προτότυπου κατωδιαβατού χρησιμοποιώντας τις εξισώσεις #[span.course-notes-equation 11-56]: p Υπολογίζονται οι προδιαγραφές του πρωτότυπου κατωδιαβατού χρησιμοποιώντας τις εξισώσεις #[span.course-notes-equation 11-56]:
p.latex-equation. p.latex-equation.
$$\Omega_p = 1\frac{rad}{s}$$ $$\Omega_p = 1\frac{rad}{s}$$

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h3 Μελέτη συνάρτησης μεταφοράς στο Matlab
p.
Η σχεδίαση του φίλτρου έγινε στο λογισμικό Matlab. Σχεδιάστηκαν, με χρήση της συνάρτησης plot_transfer_function που δόθηκε καθώς και της ltiview που παρέχει το λογισμικό, οι αποκρίσεις πλάτους σε dB των επιμέρους μονάδων, καθώς και του συνολικού φίλτρου.
p.
Παρακάτω φαίνονται οι αποκρίσεις όπως προέκυψαν στο Matlab από την plot_transfer_function, με ορίσματα κάθε φορά την συνάρτηση μεταφοράς του επί μέρους συστήματος, καθώς και τυχόν κρίσιμες συχνότητες:
figure.block-center.width-15cm
img(src="2_band_pass/assets/diagrams/matlab_band_pass_chebyshev_deliyannis_friend_unit_1_transfer_function.svg").width-15cm
figcaption
.reference #[span.plot-count]
.caption.title.
Συνάρτηση μεταφοράς πρώτης ζωνοδιαβατής μονάδας Deliyannis-Friend.
.caption.
Στο γράφημα φαίνεται η απόκριση της συνάρτησης μεταφοράς στην κεντρική συχνότητα της μονάδας καθώς και στη κεντρική συχνότητα του φίλτρου, από όπου μπορούμε να επιβεβαιώσουμε ότι η ρύθμιση κέρδους πέτυχε το επιθυμητό κέρδος 0 dB.
figure.block-center.width-15cm
img(src="2_band_pass/assets/diagrams/matlab_band_pass_chebyshev_deliyannis_friend_unit_2_transfer_function.svg").width-15cm
figcaption
.reference #[span.plot-count]
.caption.title.
Συνάρτηση μεταφοράς δεύτερης ζωνοδιαβατής μονάδας Deliyannis-Friend.
.caption.
Στο γράφημα φαίνεται η απόκριση της συνάρτησης μεταφοράς στην κεντρική συχνότητα της μονάδας καθώς και στη κεντρική συχνότητα του φίλτρου, από όπου μπορούμε να επιβεβαιώσουμε ότι η ρύθμιση κέρδους πέτυχε το επιθυμητό κέρδος 0 dB.
figure.block-center.width-15cm
img(src="2_band_pass/assets/diagrams/matlab_band_pass_chebyshev_deliyannis_friend_unit_3_transfer_function.svg").width-15cm
figcaption
.reference #[span.plot-count]
.caption.title.
Συνάρτηση μεταφοράς τρίτης ζωνοδιαβατής μονάδας Deliyannis-Friend.
.caption.
Στο γράφημα φαίνεται η απόκριση της συνάρτησης μεταφοράς στην κεντρική συχνότητα της μονάδας καθώς και στη κεντρική συχνότητα του φίλτρου, από όπου μπορούμε να επιβεβαιώσουμε ότι η ρύθμιση κέρδους πέτυχε το επιθυμητό κέρδος 0 dB.
figure.block-center.width-15cm
img(src="2_band_pass/assets/diagrams/matlab_band_pass_chebyshev_deliyannis_friend_unit_4_transfer_function.svg").width-15cm
figcaption
.reference #[span.plot-count]
.caption.title.
Συνάρτηση μεταφοράς τέταρτης ζωνοδιαβατής μονάδας Deliyannis-Friend.
.caption.
Στο γράφημα φαίνεται η απόκριση της συνάρτησης μεταφοράς στην κεντρική συχνότητα της μονάδας καθώς και στη κεντρική συχνότητα του φίλτρου, από όπου μπορούμε να επιβεβαιώσουμε ότι η ρύθμιση κέρδους πέτυχε το επιθυμητό κέρδος 0 dB.
figure.block-center.width-15cm
img(src="2_band_pass/assets/diagrams/matlab_band_pass_chebyshev_total_transfer_function.svg").width-15cm
figcaption
.reference #[span.plot-count]
.caption.title.
Συνολική συνάρτηση μεταφοράς φίλτρου.
.caption.
Παρατηρούμε ότι η συνάρτηση μεταφοράς του φίλτρου έχει το αναμενόμενο σχήμα ενός ζωνοδιαβατού Chebyshev φίλτρου. Πιο συγκεκριμένα, στη ζώνη αποκοπής η συνάρτηση μεταφοράς είναι γνησίως φθίνουσα, ενώ στη ζώνη διόδου εμφανίζει ταλάντωση (ripples). Στο γράφημα φαίνεται επίσης η απόκριση της συνάρτησης μεταφοράς στις κρίσιμες συχνότητες: f#[sub 3]=696.11 Hz, f#[sub hp1]=792.93 Hz, f#[sub 1]=800 Hz, f#[sub 0]=900 Hz, μέγιστο σημείο του ripple (941.83 Hz), f#[sub 2]=1012.5 Hz, f#[sub hp2]=1021.52 Hz, f#[sub 4]=1163.61 Hz.
figure.block-center.width-15cm
img(src="2_band_pass/assets/diagrams/matlab_combined_transfer_functions_bode.svg").width-15cm
figcaption
.reference #[span.plot-count]
.caption.title.
Συνδυαστικό γράφημα συναρτήσεων μεταφοράς επιμέρους μονάδων και συνολικού φίλτρου.
figure.block-center.width-15cm
img(src="2_band_pass/assets/diagrams/matlab_band_pass_chebyshev_total_attenuation.svg").width-15cm
figcaption
.reference #[span.plot-count]
.caption.title.
Απόσβεση φίλτρου.
.caption.
Στο γράφημα φαίνεται η απόσβεση του φίλτρου για τις κρίσιμες συχνότητες: f#[sub 3]=696.11 Hz, f#[sub 1]=800 Hz, f#[sub 0]=900 Hz, f#[sub 2]=1012.5 Hz, f#[sub 4]=1163.61 Hz.
p.
Στα γραφήματα 2.2.3 και 2.2.5 έχουν σημειωθεί οι κρίσιμες συχνότητες οι οποίες καθορίζουν την ζώνη διόδου και αποκοπής, δηλαδή οι f#[sub 1]=800 Hz, f#[sub 2]=1012.5 Hz, f#[sub 3]=696.11 Hz και f#[sub 4]=1163.61 Hz, καθώς και οι αντίστοιχες αποσβέσεις. Παρατηρούμε ότι η απόκριση του φίλτρου στις συχνότητες που καθορίζουν την ζώνη διόδου είναι 0 dB, ενώ στη ζώνη αποκοπής είναι 35.04 dB. Επίσης η ταλάντωση στη ζώνη διόδου προκαλεί μέγιστο κέρδος 0.67 dB, ίσο με το α#[sub max]. Επομένως είναι φανερό ότι πληρείτε ακριβώς η προδιαγραφή a#[sub max]=0.666 dB ενώ η προδιαγραφή a#[sub min]=28.556 dB υπερκαλύπτεται.

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>Magnitude (dB)</text
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report/3_band_elimination/3_band_elimination.pug
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@ -72,5 +72,5 @@ figure.block-center.width-15cm
// Sub-Chapters // Sub-Chapters
include 3_band_elimination_design include 3_band_elimination_design
//- include 1_low_pass_transfer_function_matlab include 3_band_elimination_transfer_function_matlab
//- include 1_low_pass_transfer_function_multisim //- include 1_low_pass_transfer_function_multisim

4
report/3_band_elimination/3_band_elimination_design.pug
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@ -10,7 +10,7 @@ figure.block-center.width-15cm
div.item Αντιστροφή της συνάρτησης μεταφοράς (T#[sub LP] → T#[sub HP]) και εύρεση των πόλων ενός πρωτότυπου ανωδιαβατού φίλτρου. div.item Αντιστροφή της συνάρτησης μεταφοράς (T#[sub LP] → T#[sub HP]) και εύρεση των πόλων ενός πρωτότυπου ανωδιαβατού φίλτρου.
div.item Υπολογισμός των πόλων του πρότυπου φίλτρου Chebyshev. div.item Υπολογισμός των πόλων του πρότυπου φίλτρου Chebyshev.
div.item Υπολογισμός των πόλων και μηδενικών του ζωνοφρακτικού φίλτρου μέσω μετασχηματισμού των πόλων του πρωτότυπου ανωδιαβατού με χρήση του αλγόριθμου Geffe. div.item Υπολογισμός των πόλων και μηδενικών του ζωνοφρακτικού φίλτρου μέσω μετασχηματισμού των πόλων του πρωτότυπου ανωδιαβατού με χρήση του αλγόριθμου Geffe.
div.item Ομαδοποίηση των ζευγών συζηγών μιγαδικών πόλων και φανταστικών μηδενικών ανά δύο. Από την ομαδοποίηση προκύπτουν ζωνοφρακτικές μονάδες που υλοποιούνται με κυκλώματα Notch, LPN, HPN ανάλογα με τη σχετική θέση πόλων-μηδενικών. div.item Ομαδοποίηση των ζευγών συζυγών μιγαδικών πόλων και φανταστικών μηδενικών ανά δύο. Από την ομαδοποίηση προκύπτουν ζωνοφρακτικές μονάδες που υλοποιούνται με κυκλώματα Notch, LPN, HPN ανάλογα με τη σχετική θέση πόλων-μηδενικών.
div.item Υλοποίηση των φίλτρων Notch με βάση τα κυκλώματα του κεφαλαίου 7. div.item Υλοποίηση των φίλτρων Notch με βάση τα κυκλώματα του κεφαλαίου 7.
div.item Κλιμακοποίηση του κυκλώματος με στόχο τη μεταφορά στις πραγματικές συχνότητες και σε στοιχεία με πρακτικές (υλοποιήσιμες) τιμές. div.item Κλιμακοποίηση του κυκλώματος με στόχο τη μεταφορά στις πραγματικές συχνότητες και σε στοιχεία με πρακτικές (υλοποιήσιμες) τιμές.
div.item Έλεγχος των κερδών των μονάδων και ρύθμιση κέρδους με επιβολή απόσβεσης ή ενίσχυσης. div.item Έλεγχος των κερδών των μονάδων και ρύθμιση κέρδους με επιβολή απόσβεσης ή ενίσχυσης.
@ -36,7 +36,7 @@ p.latex-equation.
p. p.
Σχεδιάζεται ένα πρότυπο κατωδιαβατό Chebyshev φίλτρο, το οποίο αργότερα θα μετατραπεί στο πρωτότυπο ανωδιαβατό. Σχεδιάζεται ένα πρότυπο κατωδιαβατό Chebyshev φίλτρο, το οποίο αργότερα θα μετατραπεί στο πρωτότυπο ανωδιαβατό.
p Υπολογίζονται οι προδιαγραφές του προτότυπου κατωδιαβατού χρησιμοποιώντας τις εξισώσεις #[span.course-notes-equation 13-9]: p Υπολογίζονται οι προδιαγραφές του πρωτότυπου κατωδιαβατού χρησιμοποιώντας τις εξισώσεις #[span.course-notes-equation 13-9]:
p.latex-equation. p.latex-equation.
$$\Omega_p = 1\frac{rad}{s}$$ $$\Omega_p = 1\frac{rad}{s}$$

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report/3_band_elimination/3_band_elimination_transfer_function_matlab.pug
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@ -0,0 +1,82 @@
h3 Μελέτη συνάρτησης μεταφοράς στο Matlab
p.
Η σχεδίαση του φίλτρου έγινε στο λογισμικό Matlab. Σχεδιάστηκαν, με χρήση της συνάρτησης plot_transfer_function που δόθηκε καθώς και της ltiview που παρέχει το λογισμικό, οι αποκρίσεις πλάτους σε dB των επιμέρους μονάδων, καθώς και του συνολικού φίλτρου.
p.
Παρακάτω φαίνονται οι αποκρίσεις όπως προέκυψαν στο Matlab από την plot_transfer_function, με ορίσματα κάθε φορά την συνάρτηση μεταφοράς του επί μέρους συστήματος, καθώς και τυχόν κρίσιμες συχνότητες:
figure.block-center.width-15cm
img(src="3_band_elimination/assets/diagrams/matlab_band_elimination_chebyshev_HPN_unit_1_transfer_function.svg").width-15cm
figcaption
.reference #[span.plot-count]
.caption.title.
Συνάρτηση μεταφοράς πρώτης ζωνοφρακτικής μονάδας (HPN).
.caption.
Στο γράφημα φαίνεται η απόκριση της συνάρτησης μεταφοράς στην κεντρική συχνότητα της μονάδας.
figure.block-center.width-15cm
img(src="3_band_elimination/assets/diagrams/matlab_band_elimination_chebyshev_LPN_unit_2_transfer_function.svg").width-15cm
figcaption
.reference #[span.plot-count]
.caption.title.
Συνάρτηση μεταφοράς δεύτερης ζωνοφρακτικής μονάδας (LPN).
.caption.
Στο γράφημα φαίνεται η απόκριση της συνάρτησης μεταφοράς στην κεντρική συχνότητα της μονάδας.
figure.block-center.width-15cm
img(src="3_band_elimination/assets/diagrams/matlab_band_elimination_chebyshev_HPN_unit_3_transfer_function.svg").width-15cm
figcaption
.reference #[span.plot-count]
.caption.title.
Συνάρτηση μεταφοράς τρίτης ζωνοφρακτικής μονάδας (HPN).
.caption.
Στο γράφημα φαίνεται η απόκριση της συνάρτησης μεταφοράς στην κεντρική συχνότητα της μονάδας.
figure.block-center.width-15cm
img(src="3_band_elimination/assets/diagrams/matlab_band_elimination_chebyshev_LPN_unit_4_transfer_function.svg").width-15cm
figcaption
.reference #[span.plot-count]
.caption.title.
Συνάρτηση μεταφοράς τέταρτης ζωνοφρακτικής μονάδας (LPN).
.caption.
Στο γράφημα φαίνεται η απόκριση της συνάρτησης μεταφοράς στην κεντρική συχνότητα της μονάδας.
figure.block-center.width-15cm
img(src="3_band_elimination/assets/diagrams/matlab_band_elimination_chebyshev_total_transfer_function.svg").width-15cm
figcaption
.reference #[span.plot-count]
.caption.title.
Συνολική συνάρτηση μεταφοράς φίλτρου.
.caption.
Παρατηρούμε ότι η συνάρτηση μεταφοράς του φίλτρου έχει το αναμενόμενο σχήμα ενός ζωνοφρακτικού Chebyshev φίλτρου. Πιο συγκεκριμένα, στη ζώνη αποκοπής η συνάρτηση μεταφοράς είναι γνησίως φθίνουσα, ενώ στη ζώνη διόδου εμφανίζει ταλάντωση (ripples). Στο γράφημα φαίνεται επίσης η απόκριση της συνάρτησης μεταφοράς στις κρίσιμες συχνότητες: μέγιστο σημείο του ripple (1910 Hz), f#[sub 1]=1950 Hz, f#[sub hp1]=1988.3 Hz, f#[sub 3]=2261.55 Hz, f#[sub 0]=2500 Hz, f#[sub 4]=2763.6 Hz, f#[sub hp2]=3143.39 Hz, f#[sub 2]=3205.13 Hz.
figure.block-center.width-15cm
img(src="3_band_elimination/assets/diagrams/matlab_combined_transfer_functions_bode.svg").width-15cm
figcaption
.reference #[span.plot-count]
.caption.title.
Συνδυαστικό γράφημα συναρτήσεων μεταφοράς επιμέρους μονάδων και συνολικού φίλτρου.
figure.block-center.width-15cm
img(src="3_band_elimination/assets/diagrams/matlab_band_elimination_chebyshev_total_attenuation.svg").width-15cm
figcaption
.reference #[span.plot-count]
.caption.title.
Απόσβεση φίλτρου.
.caption.
Στο γράφημα φαίνεται η απόσβεση του φίλτρου για τις κρίσιμες συχνότητες: f#[sub 1]=1950 Hz, f#[sub 3]=2261.55 Hz, f#[sub 0]=2500 Hz, f#[sub 4]=2763.6 Hz, f#[sub 2]=3205.13 Hz.
p.
Στα γραφήματα 2.2.3 και 2.2.5 έχουν σημειωθεί οι κρίσιμες συχνότητες οι οποίες καθορίζουν την ζώνη διόδου και αποκοπής, δηλαδή οι f#[sub 1]=1950 Hz, f#[sub 2]=3205.128 Hz, f#[sub 3]=2261.546 Hz και f#[sub 4]=2763.597 Hz, καθώς και οι αντίστοιχες αποσβέσεις. Παρατηρούμε ότι η απόκριση του φίλτρου στις συχνότητες που καθορίζουν την ζώνη διόδου είναι 0 dB, ενώ στη ζώνη αποκοπής είναι 39.21 dB. Επίσης η ταλάντωση στη ζώνη διόδου προκαλεί μέγιστο κέρδος 0.56 dB, ίσο με το α#[sub max]. Επομένως είναι φανερό ότι πληρείτε ακριβώς η προδιαγραφή a#[sub max]=0.555 dB ενώ η προδιαγραφή a#[sub min]=29.334 dB υπερκαλύπτεται.
p.
Η συνάρτηση απόσβεσης, πριν τη ρύθμιση κέρδους, δίνεται από το παρακάτω διάγραμμα:
figure.block-center.width-15cm
img(src="3_band_elimination/assets/diagrams/matlab_band_elimination_chebyshev_original_gain_attenuation.svg").width-15cm
figcaption
.reference #[span.plot-count]
.caption.title.
Απόσβεση φίλτρου πριν τη ρύθμιση κέρδους.
.caption.
Στο γράφημα σημειώνονται οι ίδιες κρίσιμες συχνότητες: f#[sub 1]=1950 Hz, f#[sub 3]=2261.55 Hz, f#[sub 0]=2500 Hz, f#[sub 4]=2763.6 Hz, f#[sub 2]=3205.13 Hz.

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report/3_band_elimination/assets/diagrams/band_elimination_general_transfer_function_plot.svg
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>Magnitude (dB)</text
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4
report/4_high_pass/4_high_pass.pug
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@ -47,6 +47,6 @@ figure.block-center.width-15cm
Στο γράφημα φαίνονται οι συχνότητες που ορίζουν τη ζώνη αποκοπής (f#[sub s]/ω#[sub s]) και τη ζώνη διόδου (f#[sub p]/ω#[sub p]), καθώς και οι προδιαγραφές α#[sub min] και α#[sub max]. Στο γράφημα φαίνονται οι συχνότητες που ορίζουν τη ζώνη αποκοπής (f#[sub s]/ω#[sub s]) και τη ζώνη διόδου (f#[sub p]/ω#[sub p]), καθώς και οι προδιαγραφές α#[sub min] και α#[sub max].
// Sub-Chapters // Sub-Chapters
include 4_high_pass_design //- include 4_high_pass_design
//- include 1_low_pass_transfer_function_matlab include 4_high_pass_transfer_function_matlab
//- include 1_low_pass_transfer_function_multisim //- include 1_low_pass_transfer_function_multisim

64
report/4_high_pass/4_high_pass_transfer_function_matlab.pug
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@ -0,0 +1,64 @@
h3 Μελέτη συνάρτησης μεταφοράς στο Matlab
p.
Η σχεδίαση του φίλτρου έγινε στο λογισμικό Matlab. Σχεδιάστηκαν, με χρήση της συνάρτησης plot_transfer_function που δόθηκε καθώς και της ltiview που παρέχει το λογισμικό, οι αποκρίσεις πλάτους σε dB των επιμέρους μονάδων, καθώς και του συνολικού φίλτρου.
p.
Παρακάτω φαίνονται οι αποκρίσεις όπως προέκυψαν στο Matlab από την plot_transfer_function, με ορίσματα κάθε φορά την συνάρτηση μεταφοράς του επί μέρους συστήματος, καθώς και τυχόν κρίσιμες συχνότητες:
figure.block-center.width-15cm
img(src="4_high_pass/assets/diagrams/matlab_high_pass_butterworth_sallen_key_unit_1_transfer_function.svg").width-15cm
figcaption
.reference #[span.plot-count]
.caption.title.
Συνάρτηση μεταφοράς πρώτης υψηπερατής μονάδας Sallen-Key.
.caption.
Στο γράφημα φαίνεται η απόκριση της συνάρτησης μεταφοράς στις υψηλές συχνότητες, από όπου μπορούμε να επιβεβαιώσουμε ότι το κέρδος 1.23 dB που υπολογίστηκε νωρίτερα για την μονάδα είναι σωστό.
figure.block-center.width-15cm
img(src="4_high_pass/assets/diagrams/matlab_high_pass_butterworth_sallen_key_unit_2_transfer_function.svg").width-15cm
figcaption
.reference #[span.plot-count]
.caption.title.
Συνάρτηση μεταφοράς δεύτερης υψηπερατής μονάδας Sallen-Key.
.caption.
Στο γράφημα φαίνεται η απόκριση της συνάρτησης μεταφοράς στις υψηλές συχνότητες, από όπου μπορούμε να επιβεβαιώσουμε ότι το κέρδος 6.98 dB που υπολογίστηκε νωρίτερα για την μονάδα είναι σωστό.
figure.block-center.width-15cm
img(src="4_high_pass/assets/diagrams/matlab_high_pass_butterworth_total_transfer_function.svg").width-15cm
figcaption
.reference #[span.plot-count]
.caption.title.
Συνολική συνάρτηση μεταφοράς φίλτρου.
.caption.
Παρατηρούμε ότι η συνάρτηση μεταφοράς του φίλτρου έχει το αναμενόμενο σχήμα ενός ανωδιαβατού Butterworth φίλτρου. Πιο συγκεκριμένα, στις χαμηλές συχνότητες η συνάρτηση μεταφοράς είναι γνησίως αύξουσα, ενώ στην αποκοπή είναι επίπεδη. Στο γράφημα φαίνεται επίσης η απόκριση της συνάρτησης μεταφοράς στις κρίσιμες συχνότητες: f#[sub s]=1923.077 Hz, f#[sub hp]=3994.44 Hz, f#[sub p]=5000 Hz και (τυχαία) υψηλή συχνότητα=90000 Hz.
figure.block-center.width-15cm
img(src="4_high_pass/assets/diagrams/matlab_combined_transfer_functions_bode.svg").width-15cm
figcaption
.reference #[span.plot-count]
.caption.title.
Συνδυαστικό γράφημα συναρτήσεων μεταφοράς επιμέρους μονάδων και συνολικού φίλτρου.
figure.block-center.width-15cm
img(src="4_high_pass/assets/diagrams/matlab_high_pass_butterworth_total_attenuation.svg").width-15cm
figcaption
.reference #[span.plot-count]
.caption.title.
Απόσβεση φίλτρου.
.caption.
Στο γράφημα φαίνεται η απόσβεση του φίλτρου για τις κρίσιμες συχνότητες: f#[sub s]=1923.077 Hz, f#[sub hp]=3994.44 Hz, f#[sub p]=5000 Hz και (τυχαία) υψηλή συχνότητα=90000 Hz.
p.
Στα γραφήματα 2.2.3 και 2.2.5 έχουν σημειωθεί οι κρίσιμες συχνότητες οι οποίες καθορίζουν την ζώνη διόδου και αποκοπής, δηλαδή η f#[sub p]=5000 Hz και η f#[sub s]=1923.077 Hz, καθώς και οι αντίστοιχες αποσβέσεις. Παρατηρούμε ότι η απόκριση του φίλτρου στην ζώνη διόδου είναι 0.67 dB (10-9,33), ενώ στη ζώνη αποκοπής είναι 25.41 dB (10-(-15.41)). Επομένως είναι φανερό ότι πληρείτε ακριβώς η προδιαγραφή a#[sub max]=0.666 dB ενώ η προδιαγραφή a#[sub min]=24.666 dB υπερκαλύπτεται.
p.
Η συνάρτηση απόσβεσης, πριν τη ρύθμιση κέρδους, δίνεται από το παρακάτω διάγραμμα:
figure.block-center.width-15cm
img(src="4_high_pass/assets/diagrams/matlab_high_pass_butterworth_original_gain_attenuation.svg").width-15cm
figcaption
.reference #[span.plot-count]
.caption.title.
Απόσβεση φίλτρου πριν τη ρύθμιση κέρδους.
.caption.
Στο γράφημα σημειώνονται οι ίδιες κρίσιμες συχνότητες: f#[sub s]=1923.077 Hz, f#[sub hp]=3994.44 Hz, f#[sub p]=5000 Hz και (τυχαία) υψηλή συχνότητα=90000 Hz.

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