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+00.511.522.533.544.55Time (s)#10-3-1.5-1-0.500.511.5Voltage (V)Oscilloscope plot diff --git a/Low Pass Inverse Chebyshev/Multisim/low_pass_inversed_chebyshev_oscilloscope_input_sig.svg b/Low Pass Inverse Chebyshev/Multisim/low_pass_inversed_chebyshev_oscilloscope_input_sig.svg new file mode 100644 index 0000000..761f140 --- /dev/null +++ b/Low Pass Inverse Chebyshev/Multisim/low_pass_inversed_chebyshev_oscilloscope_input_sig.svg @@ -0,0 +1,299 @@ + + +00.511.522.533.544.55Time (s)#10-3-1.5-1-0.500.511.5Voltage (V)Oscilloscope plot diff --git a/Low Pass Inverse Chebyshev/Multisim/low_pass_inversed_chebyshev_oscilloscope_output_sig.svg b/Low Pass Inverse Chebyshev/Multisim/low_pass_inversed_chebyshev_oscilloscope_output_sig.svg new file mode 100644 index 0000000..2540601 --- /dev/null +++ b/Low Pass Inverse Chebyshev/Multisim/low_pass_inversed_chebyshev_oscilloscope_output_sig.svg @@ -0,0 +1,299 @@ + + +00.511.522.533.544.55Time (s)#10-3-1.5-1-0.500.511.5Voltage (V)Oscilloscope plot diff --git a/Low Pass Inverse Chebyshev/Multisim/low_pass_inversed_chebyshev_spectrum_analyzer_combined_input_output.svg b/Low Pass Inverse Chebyshev/Multisim/low_pass_inversed_chebyshev_spectrum_analyzer_combined_input_output.svg new file mode 100644 index 0000000..321dcd0 --- /dev/null +++ b/Low Pass Inverse Chebyshev/Multisim/low_pass_inversed_chebyshev_spectrum_analyzer_combined_input_output.svg @@ -0,0 +1,347 @@ + + +00.20.40.60.811.21.41.61.82Frequency (Hz)#10400.10.20.30.40.50.60.70.8Amplitude (V)Spectrum analyzer plotInput spectrumOutput spectrum diff --git a/Low Pass Inverse Chebyshev/Multisim/low_pass_inversed_chebyshev_spectrum_analyzer_input.csv b/Low Pass Inverse Chebyshev/Multisim/low_pass_inversed_chebyshev_spectrum_analyzer_input.csv new file mode 100644 index 0000000..cc9ec9b --- /dev/null +++ b/Low Pass Inverse Chebyshev/Multisim/low_pass_inversed_chebyshev_spectrum_analyzer_input.csv @@ -0,0 +1,513 @@ +X--Trace 1::[Signal],Y--Trace 1::[Signal],,X--Trace 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+42600,1.18135e-012,,0,0 +42700,1.6383e-012,,0,0 +42800,0.000403511,,0,0 +42900,1.59766e-012,,0,0 +43000,1.0461e-012,,0,0 +43100,1.57257e-012,,0,0 +43200,0.000438586,,0,0 +43300,1.60161e-012,,0,0 +43400,1.05036e-012,,0,0 +43500,1.58016e-012,,0,0 +43600,0.000148952,,0,0 +43700,1.55794e-012,,0,0 +43800,1.09483e-012,,0,0 +43900,1.58794e-012,,0,0 +44000,0.000609852,,0,0 +44100,1.81082e-012,,0,0 +44200,1.35363e-012,,0,0 +44300,1.77862e-012,,0,0 +44400,0.000911478,,0,0 +44500,1.54243e-012,,0,0 +44600,1.1014e-012,,0,0 +44700,1.59605e-012,,0,0 +44800,0.000213056,,0,0 +44900,1.64451e-012,,0,0 +45000,1.08672e-012,,0,0 +45100,1.58756e-012,,0,0 +45200,0.000264707,,0,0 +45300,1.56707e-012,,0,0 +45400,1.04147e-012,,0,0 +45500,1.59423e-012,,0,0 +45600,0.000564739,,0,0 +45700,1.68192e-012,,0,0 +45800,1.18638e-012,,0,0 +45900,1.62772e-012,,0,0 +46000,0.000354486,,0,0 +46100,1.55999e-012,,0,0 +46200,1.16408e-012,,0,0 +46300,1.61253e-012,,0,0 +46400,0.000390128,,0,0 +46500,1.62198e-012,,0,0 +46600,1.17753e-012,,0,0 +46700,1.67132e-012,,0,0 +46800,0.000542337,,0,0 +46900,1.61378e-012,,0,0 +47000,1.04766e-012,,0,0 +47100,1.54455e-012,,0,0 +47200,0.000273379,,0,0 +47300,1.58919e-012,,0,0 +47400,1.06746e-012,,0,0 +47500,1.61839e-012,,0,0 +47600,0.000209467,,0,0 +47700,1.58324e-012,,0,0 +47800,1.07587e-012,,0,0 +47900,1.49712e-012,,0,0 +48000,0.00087145,,0,0 +48100,1.73186e-012,,0,0 +48200,1.34274e-012,,0,0 +48300,1.83518e-012,,0,0 +48400,0.000672807,,0,0 +48500,1.62463e-012,,0,0 +48600,1.12734e-012,,0,0 +48700,1.57701e-012,,0,0 +48800,0.000131179,,0,0 +48900,1.60155e-012,,0,0 +49000,1.06801e-012,,0,0 +49100,1.60349e-012,,0,0 +49200,0.000434859,,0,0 +49300,1.57927e-012,,0,0 +49400,1.04637e-012,,0,0 +49500,1.58019e-012,,0,0 +49600,0.00042711,,0,0 +49700,1.62917e-012,,0,0 +49800,1.17756e-012,,0,0 +49900,1.68155e-012,,0,0 +50000,0.000189843,,0,0 +50100,1.73045e-012,,0,0 +50200,1.23696e-012,,0,0 +50300,1.60485e-012,,0,0 +50400,0.000793218,,0,0 +50500,1.52186e-012,,0,0 +50600,1.12513e-012,,0,0 +50700,1.64624e-012,,0,0 +50800,0.000469957,,0,0 +50900,1.63177e-012,,0,0 +51000,1.06462e-012,,0,0 +51100,1.55452e-012,,0,0 diff --git a/Low Pass Inverse Chebyshev/Multisim/low_pass_inversed_chebyshev_spectrum_analyzer_output.svg b/Low Pass Inverse Chebyshev/Multisim/low_pass_inversed_chebyshev_spectrum_analyzer_output.svg new file mode 100644 index 0000000..c24ff9b --- /dev/null +++ b/Low Pass Inverse Chebyshev/Multisim/low_pass_inversed_chebyshev_spectrum_analyzer_output.svg @@ -0,0 +1,325 @@ + + +00.20.40.60.811.21.41.61.82Frequency (Hz)#10400.10.20.30.40.50.60.70.8Amplitude (V)Spectrum analyzer plot diff --git a/Low Pass Inverse Chebyshev/Multisim/multisim_csv_plot.m b/Low Pass Inverse Chebyshev/Multisim/multisim_csv_plot.m index 0a91b1c..4c064c2 100644 --- a/Low Pass Inverse Chebyshev/Multisim/multisim_csv_plot.m +++ b/Low Pass Inverse Chebyshev/Multisim/multisim_csv_plot.m @@ -1,4 +1,5 @@ -multisim = csvread('low_pass_inversed_chebyshev_bode_plot.csv', 1, 0); +%{ +multisim = csvread('low_pass_inversed_chebyshev_bode_plotter.csv', 1, 0); % Create figure figure1 = figure('Name','Bode plot','Color',[1 1 1]); @@ -8,7 +9,6 @@ hold(axes1,'on'); % Create semilogx semilogx(multisim(:, 1),20*log10(multisim(:, 2)),'Color',[1 0.501960813999176 0]); - xlabel('Frequency (Hz)'); ylabel('Gain (dB)'); ylim(axes1,[-90 10]); @@ -17,3 +17,125 @@ set(axes1,'Color',[0 0 0],'GridAlpha',0.5,'GridColor',[1 1 1],... 'GridLineStyle',':','MinorGridAlpha',0.5,'MinorGridColor',[1 1 1],'TickDir',... 'both','TickLength',[0.004 0.0025],'XColor',[0 0 0],'XGrid','on',... 'XMinorTick','on','XScale','log','YColor',[0 0 0],'YGrid','on'); + +%======================================================================================= + +multisim = csvread('low_pass_inversed_chebyshev_oscilloscope.csv', 1, 0); + +% Create figure +figure1 = figure('Name','Oscilloscope plot','Color',[1 1 1]); +axes1 = axes('Parent',figure1); +hold(axes1,'on'); + +plot(multisim(:, 1),multisim(:, 2),'Color',[1 0.501960813999176 0]); + +xlabel('Time (s)'); +ylabel('Voltage (V)'); +ylim(axes1,[-1.5 1.5]); +xlim(axes1,[-1e-05 0.005]); +title('Oscilloscope plot') +set(axes1,'Color',[0 0 0],'GridAlpha',0.5,'GridColor',[1 1 1],... + 'GridLineStyle',':','MinorGridAlpha',0.5,'MinorGridColor',[1 1 1],'TickDir',... + 'both','TickLength',[0.004 0.0025],'XColor',[0 0 0],'XGrid','on',... + 'XMinorTick','on','YColor',[0 0 0],'YGrid','on'); + +%======================================================================================= + +% Create figure +figure1 = figure('Name','Oscilloscope plot','Color',[1 1 1]); +axes1 = axes('Parent',figure1); +hold(axes1,'on'); + +plot(multisim(:, 4),multisim(:, 5),'Color',[0 0.5 0]); + +xlabel('Time (s)'); +ylabel('Voltage (V)'); +ylim(axes1,[-1.5 1.5]); +xlim(axes1,[-1e-05 0.005]); +title('Oscilloscope plot') +set(axes1,'Color',[0 0 0],'GridAlpha',0.5,'GridColor',[1 1 1],... + 'GridLineStyle',':','MinorGridAlpha',0.5,'MinorGridColor',[1 1 1],'TickDir',... + 'both','TickLength',[0.004 0.0025],'XColor',[0 0 0],'XGrid','on',... + 'XMinorTick','on','YColor',[0 0 0],'YGrid','on'); + +%======================================================================================= + +% Create figure +figure1 = figure('Name','Oscilloscope plot','Color',[1 1 1]); +axes1 = axes('Parent',figure1); +hold(axes1,'on'); + +plot(multisim(:, 1),multisim(:, 2),'Color',[1 0.501960813999176 0]); +plot(multisim(:, 4),multisim(:, 5),'Color',[0 0.5 0]); + +xlabel('Time (s)'); +ylabel('Voltage (V)'); +ylim(axes1,[-1.5 1.5]); +xlim(axes1,[-1e-05 0.005]); +title('Oscilloscope plot') +set(axes1,'Color',[0 0 0],'GridAlpha',0.5,'GridColor',[1 1 1],... + 'GridLineStyle',':','MinorGridAlpha',0.5,'MinorGridColor',[1 1 1],'TickDir',... + 'both','TickLength',[0.004 0.0025],'XColor',[0 0 0],'XGrid','on',... + 'XMinorTick','on','YColor',[0 0 0],'YGrid','on'); +%} +%======================================================================================= + +multisim = csvread('low_pass_inversed_chebyshev_spectrum_analyzer_input.csv', 1, 0); + +% Create figure +figure1 = figure('Name','Spectrum analyzer plot','Color',[1 1 1]); +axes1 = axes('Parent',figure1); +hold(axes1,'on'); + +plot(multisim(:, 1),multisim(:, 2),'Color',[1 0.501960813999176 0]); + +xlabel('Frequency (Hz)'); +ylabel('Amplitude (V)'); +ylim(axes1,[0 0.8]); +xlim(axes1,[0 20000]); +title('Spectrum analyzer plot') +set(axes1,'Color',[0 0 0],'GridAlpha',0.5,'GridColor',[1 1 1],... + 'GridLineStyle',':','MinorGridAlpha',0.5,'MinorGridColor',[1 1 1],'TickDir',... + 'both','TickLength',[0.004 0.0025],'XColor',[0 0 0],'XGrid','on',... + 'XMinorTick','on','YColor',[0 0 0],'YGrid','on'); + +%======================================================================================= + +multisim2 = csvread('low_pass_inversed_chebyshev_spectrum_analyzer_output.csv', 1, 0); + +% Create figure +figure1 = figure('Name','Spectrum analyzer plot','Color',[1 1 1]); +axes1 = axes('Parent',figure1); +hold(axes1,'on'); + +plot(multisim2(:, 1),multisim2(:, 2),'Color',[0 0.5 0]); + +xlabel('Frequency (Hz)'); +ylabel('Amplitude (V)'); +ylim(axes1,[0 0.8]); +xlim(axes1,[0 20000]); +title('Spectrum analyzer plot') +set(axes1,'Color',[0 0 0],'GridAlpha',0.5,'GridColor',[1 1 1],... + 'GridLineStyle',':','MinorGridAlpha',0.5,'MinorGridColor',[1 1 1],'TickDir',... + 'both','TickLength',[0.004 0.0025],'XColor',[0 0 0],'XGrid','on',... + 'XMinorTick','on','YColor',[0 0 0],'YGrid','on'); + +%======================================================================================= + +% Create figure +figure1 = figure('Name','Spectrum analyzer plot','Color',[1 1 1]); +axes1 = axes('Parent',figure1); +hold(axes1,'on'); + +plot(multisim(:, 1),multisim(:, 2),'Color',[1 0.501960813999176 0]); +plot(multisim2(:, 1),multisim2(:, 2),'Color',[0 0.5 0]); + +xlabel('Frequency (Hz)'); +ylabel('Amplitude (V)'); +ylim(axes1,[0 0.8]); +xlim(axes1,[0 20000]); +title('Spectrum analyzer plot') +set(axes1,'Color',[0 0 0],'GridAlpha',0.5,'GridColor',[1 1 1],... + 'GridLineStyle',':','MinorGridAlpha',0.5,'MinorGridColor',[1 1 1],'TickDir',... + 'both','TickLength',[0.004 0.0025],'XColor',[0 0 0],'XGrid','on',... + 'XMinorTick','on','YColor',[0 0 0],'YGrid','on'); \ No newline at end of file diff --git a/Low Pass Inverse Chebyshev/low_pass_inversed_chebyshev_combined_input_output_sig.svg b/Low Pass Inverse Chebyshev/low_pass_inversed_chebyshev_combined_input_output_sig.svg new file mode 100644 index 0000000..f378d76 --- /dev/null +++ b/Low Pass Inverse Chebyshev/low_pass_inversed_chebyshev_combined_input_output_sig.svg @@ -0,0 +1,266 @@ + + +00.511.522.533.544.55Time (s)#10-3-0.200.20.40.60.811.2Voltage (V)Filter response to square waveInput signalOutput signal diff --git a/Low Pass Inverse Chebyshev/low_pass_inversed_chebyshev_input_spectrum.svg b/Low Pass Inverse Chebyshev/low_pass_inversed_chebyshev_input_spectrum.svg new file mode 100644 index 0000000..26b28c0 --- /dev/null +++ b/Low Pass Inverse Chebyshev/low_pass_inversed_chebyshev_input_spectrum.svg @@ -0,0 +1,446 @@ + + +10-210-1100101102103104105Frequency (Hz)00.511.522.533.544.55Trivial unit#105Input signal spectrum diff --git a/Low Pass Inverse Chebyshev/low_pass_inversed_chebyshev_input_spectrum_zoom.svg b/Low Pass Inverse Chebyshev/low_pass_inversed_chebyshev_input_spectrum_zoom.svg new file mode 100644 index 0000000..a079a3b --- /dev/null +++ b/Low Pass Inverse Chebyshev/low_pass_inversed_chebyshev_input_spectrum_zoom.svg @@ -0,0 +1,241 @@ + + +103104Frequency (Hz)00.511.522.533.544.55Trivial unit#105Input signal spectrum diff --git a/Low Pass Inverse Chebyshev/low_pass_inversed_chebyshev_output_spectrum.svg b/Low Pass Inverse Chebyshev/low_pass_inversed_chebyshev_output_spectrum.svg new file mode 100644 index 0000000..f552f32 --- /dev/null +++ b/Low Pass Inverse Chebyshev/low_pass_inversed_chebyshev_output_spectrum.svg @@ -0,0 +1,439 @@ + + +10-210-1100101102103104105Frequency (Hz)00.511.522.533.544.5Trivial unit#105Output signal spectrum diff --git a/Low Pass Inverse Chebyshev/low_pass_inversed_chebyshev_output_spectrum_zoom.svg b/Low Pass Inverse Chebyshev/low_pass_inversed_chebyshev_output_spectrum_zoom.svg new file mode 100644 index 0000000..db66887 --- /dev/null +++ b/Low Pass Inverse Chebyshev/low_pass_inversed_chebyshev_output_spectrum_zoom.svg @@ -0,0 +1,241 @@ + + +103104Frequency (Hz)00.511.522.533.544.55Trivial unit#105Output signal spectrum diff --git a/report/0_intro/0_intro.pug b/report/0_intro/0_intro.pug index 7294948..b9d9e7a 100644 --- a/report/0_intro/0_intro.pug +++ b/report/0_intro/0_intro.pug @@ -46,7 +46,7 @@ figure.block-center.width-15cm tbody tr td πόλος - td Μπορεί να εννοείται ζεύγος συζηγών πόλων #[br/](έναντι ενός, μοναδικού πόλου) + td Μπορεί να εννοείται ζεύγος συζυγών πόλων #[br/](έναντι ενός, μοναδικού πόλου) tr td LP td Low pass filter @@ -68,4 +68,9 @@ figure.block-center.width-15cm figcaption .reference #[span.table-count] .caption. - Ειδικοί όροι που χρησιμοποιούνται + Ειδικοί όροι που χρησιμοποιούνται. + +br/ +br/ +p. + #[strong Σημείωση:] Τα διάγραμμα των οργάνων του Multisim παράχθηκαν στο Matlab, ωστόσο οι τιμές εξάχθηκαν από το Multisim. Αυτό έγινε για παραγωγή καλύτερης ποιότητας διαγραμμάτων σε σχέση με άλλες μεθόδους όπως screenshot. Μετά την διεξαγωγή των πειραμάτων, χρησιμοποιήθηκε το view "Grapher" του Multisim, από το οποίο αποκτήθηκαν αρχεία comma separated values (.csv) για κάθε όργανο, τα οποία περιείχαν τις τιμές των αποτελεσμάτων. Έπειτα τα αρχεία χρησιμοποιήθηκαν στο Matlab για την παραγωγή όμορφων διαγραμμάτων σε μορφή scalable vector graphics (.svg) τα οποία παραμένουν αναλλοίωτα στη μεγέθυνση. diff --git a/report/1_low_pass/1_low_pass.pug b/report/1_low_pass/1_low_pass.pug index 455e6e6..85e2d42 100644 --- a/report/1_low_pass/1_low_pass.pug +++ b/report/1_low_pass/1_low_pass.pug @@ -5,7 +5,7 @@ br/ // Chapter description/introduction p. - Με βάση το ΑΕΜ (8261), υπολογίστηκαν οι προδιαγραφές του κατωδιαβατού φίλτρου προς σχεδίαση: + Με βάση τον αριθμό ΑΕΜ (8261), υπολογίστηκαν οι προδιαγραφές του κατωδιαβατού φίλτρου προς σχεδίαση: figure.block-center.width-15cm table.ui.celled.table.teal.striped.center.aligned diff --git a/report/1_low_pass/1_low_pass_design.pug b/report/1_low_pass/1_low_pass_design.pug index 8451e6d..124cb6c 100644 --- a/report/1_low_pass/1_low_pass_design.pug +++ b/report/1_low_pass/1_low_pass_design.pug @@ -14,10 +14,11 @@ 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 Έλεγχος των κερδών των μονάδων και ρύθμιση κέρδους με επιβολή απόσβεσης ή ενίσχυσης. +div(style="page-break-before:always") h4 Υπολογισμός συνάρτησης μεταφοράς p. - Αρχικά σχεδιάζεται ένα πρότυπο κατωδιαβατό Chebyshev φίλτρο, το οποίο αργότερα να μετατραπεί στο επιθυμητό αντίστροφο Chebyshev. + Αρχικά σχεδιάζεται ένα πρότυπο κατωδιαβατό Chebyshev φίλτρο, το οποίο αργότερα θα μετατραπεί στο επιθυμητό αντίστροφο Chebyshev. p Γίνεται κανονικοποίηση των συχνοτήτων ώστε να επιτευχθεί Ω#[sub s]=1 rad/s: @@ -49,6 +50,7 @@ p. p.latex-equation. $$\Omega_{hp} = \frac{1}{cosh(\frac{1}{n}cosh^{-1}(\frac{1}{\varepsilon}))} = \frac{1}{cosh(\frac{1}{4}cosh^{-1}(\frac{1}{0.065}))} = 0.7196\frac{rad}{s}$$ +div(style="page-break-before:always") p και στη συνέχεια μεταφέρεται στη πραγματική συχνότητα: p.latex-equation. @@ -92,12 +94,13 @@ p. p.latex-equation. $$\omega_{0_k} = \frac{1}{\Omega_{0_k}}$$ +div(style="page-break-before:always") p. Από τον μετασχηματισμό προκύπτουν οι πόλοι του #[strong αντίστροφου Chebyshev]: p.latex-equation. - $$\text{Pole 1: } \Omega_0 = 0.963 \text{, }Q = 0.582$$ - $$\text{Pole 2: } \Omega_0 = 0.748 \text{, }Q = 1.809$$ + $$\text{Pole 1: } \omega_0 = 0.963 \text{, }Q = 0.582$$ + $$\text{Pole 2: } \omega_0 = 0.748 \text{, }Q = 1.809$$ p. Κατά τον μετασχηματισμό προκύπτουν επίσης, με βάση την εξίσωση #[span.course-notes-equation 9-143]: @@ -122,6 +125,7 @@ figure.block-center.width-19cm .caption. Πόλοι και μηδενικά του αντίστροφου Chebyshev +div(style="page-break-before:always") p. Οι πόλοι και τα μηδενικά ομαδοποιούνται όπως φαίνεται στο παρακάτω διάγραμμα: @@ -182,6 +186,7 @@ figure.block-center.width-15cm .caption. Προδιαγραφές πρώτης μονάδας low pass notch +div(style="page-break-before:always") p. Γίνεται κανονικοποίηση των συχνοτήτων ως προς το ω#[sub 0], ώστε Ω#[sub 0]=1: @@ -221,11 +226,12 @@ p.latex-equation. p #[strong Κλιμακοποίηση] p. - Γίνεται κλιμακωποίηση των στοιχείων της μονάδας για να μεταφερθούν οι συχνότητες στις πραγματικές τιμές. Επιλέγεται: + Γίνεται κλιμακoποίηση των στοιχείων της μονάδας για να μεταφερθούν οι συχνότητες στις πραγματικές τιμές. Επιλέγεται: p.latex-equation. $$k_{f} = \omega_s\omega_0 = 72570.79*0.963 = 69885.7$$ +div(style="page-break-before:always") 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]: @@ -350,7 +356,7 @@ p.latex-equation. p #[strong Κλιμακοποίηση] p. - Γίνεται κλιμακωποίηση των στοιχείων της μονάδας για να μεταφερθούν οι συχνότητες στις πραγματικές τιμές. Επιλέγεται: + Γίνεται κλιμακoποίηση των στοιχείων της μονάδας για να μεταφερθούν οι συχνότητες στις πραγματικές τιμές. Επιλέγεται: p.latex-equation. $$k_{f} = \omega_s\omega_0 = 72570.79*0.7484 = 54311.9$$ @@ -417,7 +423,7 @@ p. Με βάση τον αριθμό ΑΕΜ (8261) πραγματοποιείται ρύθμιση κέρδους με στόχο την επίτευξη κέρδους 0 dB στις χαμηλές συχνότητες. p. - Κατά την υλοποίηση των μονάδων Fried διαπιστώθηκε ότι κάθε μονάδα εισάγει μία απόσβεση. Κάτι το οποίο ήταν αναμενόμενο με βάση τη θεωρεία των μονάδων αυτών. Το συνολικό κέρδος που εισάγουν οι μονάδες είναι: + Κατά την υλοποίηση των μονάδων Fried διαπιστώθηκε ότι κάθε μονάδα εισάγει ένα κέρδος. Κάτι το οποίο ήταν αναμενόμενο με βάση τη θεωρεία των μονάδων αυτών. Το συνολικό κέρδος που εισάγουν οι μονάδες είναι: p.latex-equation. $$k = k_{low}^1k_{low}^2 = 0.4411*4.2573 = 1.878$$ @@ -477,4 +483,4 @@ figure.block-center.width-19cm figcaption .reference #[span.plot-count] .caption. - Κύκλωμα κατωδιαβατού φίλτρου \ No newline at end of file + Κύκλωμα κατωδιαβατού φίλτρου diff --git a/report/1_low_pass/1_low_pass_transfer_function_matlab.pug b/report/1_low_pass/1_low_pass_transfer_function_matlab.pug index 04657be..29fe8e3 100644 --- a/report/1_low_pass/1_low_pass_transfer_function_matlab.pug +++ b/report/1_low_pass/1_low_pass_transfer_function_matlab.pug @@ -1,12 +1,13 @@ 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. Επίσης η συνολική απόκριση του φίλτρου ελέγχθηκαν σε σήμα εισόδου που καθόρισε η εκφώνηση. + 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. - Παρακάτω φαίνονται οι αποκρίσεις όπως προέκυψαν στο Matlab από την plot_transfer_function, με ορίσματα κάθε φορά την συνάρτηση μεταφοράς των επί μέρους συστημάτων, 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: -figure.block-center.width-19cm - img(src="1_low_pass/assets/diagrams/matlab_low_pass_inverse_chebyshev_notch_unit_1_transfer_function.svg").width-19cm +figure.block-center.width-15cm + img(src="1_low_pass/assets/diagrams/matlab_low_pass_inverse_chebyshev_notch_unit_1_transfer_function.svg").width-15cm figcaption .reference #[span.plot-count] .caption.title. @@ -14,8 +15,8 @@ figure.block-center.width-19cm .caption. Παρατηρούμε ότι η μονάδα, ορθώς, έχει χαμηλότερη απόκριση στις υψηλές συχνότητες σε σχέση με τις χαμηλές. Στο γράφημα φαίνεται επίσης η απόκριση της συνάρτησης μεταφοράς στις χαμηλές συχνότητες, από όπου μπορούμε να επιβεβαιώσουμε ότι το κέρδος -7,1 dB που υπολογίστηκε νωρίτερα για την μονάδα είναι σωστό. -figure.block-center.width-19cm - img(src="1_low_pass/assets/diagrams/matlab_low_pass_inverse_chebyshev_notch_unit_2_transfer_function.svg").width-19cm +figure.block-center.width-15cm + img(src="1_low_pass/assets/diagrams/matlab_low_pass_inverse_chebyshev_notch_unit_2_transfer_function.svg").width-15cm figcaption .reference #[span.plot-count] .caption.title. @@ -23,8 +24,8 @@ figure.block-center.width-19cm .caption. Παρατηρούμε ότι η μονάδα, ορθώς, έχει χαμηλότερη απόκριση στις υψηλές συχνότητες σε σχέση με τις χαμηλές. Στο γράφημα φαίνεται επίσης η απόκριση της συνάρτησης μεταφοράς στις χαμηλές συχνότητες, από όπου μπορούμε να επιβεβαιώσουμε ότι το κέρδος 12,6 dB που υπολογίστηκε νωρίτερα για την μονάδα είναι σωστό. -figure.block-center.width-19cm - img(src="1_low_pass/assets/diagrams/matlab_low_pass_inverse_chebyshev_total_transfer_function.svg").width-19cm +figure.block-center.width-15cm + img(src="1_low_pass/assets/diagrams/matlab_low_pass_inverse_chebyshev_total_transfer_function.svg").width-15cm figcaption .reference #[span.plot-count] .caption.title. @@ -32,15 +33,15 @@ figure.block-center.width-19cm .caption. Παρατηρούμε ότι η συνάρτηση μεταφοράς του φίλτρου έχει το αναμενόμενο σχήμα ενός κατωδιαβατού αντίστροφου Chebyshev φίλτρου. Πιο συγκεκριμένα, στις χαμηλές συχνότητες η συνάρτηση μεταφοράς είναι επίπεδη, ενώ στην αποκοπή εμφανίζει ταλάντωση (ripples). Μάλιστα ο αριθμός των ripples (δύο) είναι σωστός με βάση τη τάξη του φίλτρου (τέταρτης τάξης) και τη θεωρία του αντίστροφου Chebyshev. Στο γράφημα φαίνεται επίσης η απόκριση της συνάρτησης μεταφοράς στις κρίσιμες συχνότητες: (τυχαία) χαμηλή συχνότητα=10 Hz, f#[sub p]=5500 Hz, f#[sub hp]=8313.16 Hz και f#[sub s]=11550 Hz. -figure.block-center.width-19cm - img(src="1_low_pass/assets/diagrams/matlab_combined_transfer_functions_bode.svg").width-19cm +figure.block-center.width-15cm + img(src="1_low_pass/assets/diagrams/matlab_combined_transfer_functions_bode.svg").width-15cm figcaption .reference #[span.plot-count] .caption.title. - Συνδυαστηκό γράφημα συναρτήσεων μεταφοράς επιμέρους μονάδων και συνολικού φίλτρου. + Συνδυαστικό γράφημα συναρτήσεων μεταφοράς επιμέρους μονάδων και συνολικού φίλτρου. -figure.block-center.width-19cm - img(src="1_low_pass/assets/diagrams/matlab_low_pass_inverse_chebyshev_total_attenuation.svg").width-19cm +figure.block-center.width-15cm + img(src="1_low_pass/assets/diagrams/matlab_low_pass_inverse_chebyshev_total_attenuation.svg").width-15cm figcaption .reference #[span.plot-count] .caption.title. @@ -49,16 +50,16 @@ figure.block-center.width-19cm Στο γράφημα φαίνεται η απόσβεση του φίλτρου για τις κρίσιμες συχνότητες: (τυχαία) χαμηλή συχνότητα=10 Hz, f#[sub p]=5500 Hz, f#[sub hp]=8313.16 Hz και f#[sub s]=11550 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]=5500 Hz και η f#[sub s]=11550 Hz, καθώς και οι αντίστοιχες αποσβέσεις. Παρατηρούμε ότι η απόκριση του φίλτρου στην ζώνη διόδου είναι 0.07 dB, ενώ στη ζώνη αποκοπής είναι 23.75 dB. Επομένως είναι φανερό ότι πληρείται ακριβώς η προδιαγραφή a#[sub min]=23.75 dB ενώ η προδιαγραφή a#[sub max]=0.35 dB υπερκαλύπτεται. + 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]=5500 Hz και η f#[sub s]=11550 Hz, καθώς και οι αντίστοιχες αποσβέσεις. Παρατηρούμε ότι η απόκριση του φίλτρου στην ζώνη διόδου είναι 0.07 dB, ενώ στη ζώνη αποκοπής είναι 23.75 dB. Επομένως είναι φανερό ότι πληρείτε ακριβώς η προδιαγραφή a#[sub min]=23.75 dB ενώ η προδιαγραφή a#[sub max]=0.35 dB υπερκαλύπτεται. p. - Πριν τη ρύθμιση κέρδους η συνάρτηση απόσβεσης δίνεται από το παρακάτω διάγραμμα: + Η συνάρτηση απόσβεσης, πριν τη ρύθμιση κέρδους, δίνεται από το παρακάτω διάγραμμα: -figure.block-center.width-19cm - img(src="1_low_pass/assets/diagrams/matlab_low_pass_inverse_chebyshev_original_gain_attenuation.svg").width-19cm +figure.block-center.width-15cm + img(src="1_low_pass/assets/diagrams/matlab_low_pass_inverse_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: (τυχαία) χαμηλή συχνότητα=10 Hz, f#[sub p]=5500 Hz, f#[sub hp]=8313.16 Hz και f#[sub s]=11550 Hz. \ No newline at end of file + Στο γράφημα σημειώνονται οι ίδιες κρίσιμες συχνότητες: (τυχαία) χαμηλή συχνότητα=10 Hz, f#[sub p]=5500 Hz, f#[sub hp]=8313.16 Hz και f#[sub s]=11550 Hz. diff --git a/report/1_low_pass/1_low_pass_transfer_function_multisim.pug b/report/1_low_pass/1_low_pass_transfer_function_multisim.pug index a9b160d..528c29b 100644 --- a/report/1_low_pass/1_low_pass_transfer_function_multisim.pug +++ b/report/1_low_pass/1_low_pass_transfer_function_multisim.pug @@ -1,7 +1,7 @@ h3 Υλοποίηση κυκλώματος στο Multisim p. Το κύκλωμα του φίλτρου που σχεδιάστηκε προηγουμένως, εισάγεται στο λογισμικό Multisim όπου θα ελεγχθεί η ορθότητα της σχεδίασης του μέσω διάφορων πειραμάτων και θα εξαχθούν χρήσιμα συμπεράσματα για τη λειτουργία του φίλτρου. - Το κύκλωμα, μαζί με τα διάφορα εργαλεία που χρησιμοποιούνται για τον έλεγχό του φαίνεται στο επόμενο σχηματικό: + Το κύκλωμα, μαζί με τα διάφορα εργαλεία που χρησιμοποιούνται για τον έλεγχό του, φαίνεται στο επόμενο σχηματικό: figure.block-center.width-19cm img(src="1_low_pass/assets/diagrams/multisim_low_pass_inverse_chebyshev_layout.svg").width-19cm @@ -13,10 +13,10 @@ figure.block-center.width-19cm Εκτός από το κύκλωμα του φίλτρου, το σχηματικό περιλαμβάνει ένα bode plotter (XBP1), δύο spectrum analyzers (XSA1 και XSA2) και ένα oscilloscope (XSC1) για την καταγραφή των εισόδων και εξόδων του φίλτρου. Επίσης έχουν τοποθετηθεί μία πηγή στοιχειώδους περιοδικού σήματος (V1), μία πηγή τετραγωνικών παλμών (V2) και ένας διακόπτης (S1) για την επιλογή του σήματος εισόδου. p. - Ο διακόπτης S1 τοποθετείται στην αριστερή επαφή ώστε να επιλεγχθεί ως σήμα εισόδου του φίλτρου το στοιχειώδες ημιτονοειδές σήμα της πηγής V1 με χαρακτηριστικά Vpp=1 V, f=1 kHz. Χρησιμοποιώντας το εργαλείο bode plotter, εξάγεται η απόκριση συχνότητας του κυκλώματος. Το διάγραμμα και οι επιλεγμένες τιμές του εργαλείου φαίνονται παρακάτω: + Ο διακόπτης S1 τοποθετείται στην αριστερή επαφή ώστε να επιλεχθεί ως σήμα εισόδου του φίλτρου το στοιχειώδες ημιτονοειδές σήμα της πηγής V1 με χαρακτηριστικά Vpp=1 V, f=1 kHz. Χρησιμοποιώντας το εργαλείο bode plotter (XBP1), εξάγεται η απόκριση συχνότητας του κυκλώματος. Το διάγραμμα και οι επιλεγμένες τιμές του εργαλείου φαίνονται παρακάτω: -figure.block-center.width-19cm - img(src="1_low_pass/assets/diagrams/multisim_low_pass_inversed_chebyshev_bode_plotter.svg").width-19cm +figure.block-center.width-15cm + img(src="1_low_pass/assets/diagrams/multisim_low_pass_inversed_chebyshev_bode_plotter.svg").width-15cm figcaption .reference #[span.plot-count] .caption.title. @@ -28,5 +28,169 @@ figure.block-center.width-19cm #[br/]#[strong Vertical:] Log με #[strong F:] 0 dB και #[strong I:] -200 dB #[br/]#[strong Set...] με #[strong Resolution points:] 1000 +p. + Το παρακάτω διάγραμμα είναι ίδιο με το προηγούμενο, σημειώνονται όμως οι αποκρίσεις στις κρίσιμες συχνότητες: + +figure.block-center.width-15cm + img(src="1_low_pass/assets/diagrams/multisim_low_pass_inversed_chebyshev_bode_plotter_with_values.svg").width-15cm + figcaption + .reference #[span.plot-count] + .caption.title. + Έξοδος bode plotter-XBP1 κατωδιαβατού αντίστροφου Chebyshev φίλτρου από το Multisim με σημειωμένες τις αποκρίσεις στις κρίσιμες συχνότητες. + .caption. + Οι επιλογές του bode plotter που χρησιμοποιήθηκαν: + #[br/]#[strong Mode:] Magnitude + #[br/]#[strong Horizontal:] Log με #[strong F:] 1 MHz και #[strong I:] 10 Hz + #[br/]#[strong Vertical:] Log με #[strong F:] 0 dB και #[strong I:] -200 dB + #[br/]#[strong Set...] με #[strong Resolution points:] 1000 + #[br/]Οι συχνότητες που σημειώνονται είναι f#[sub p]=5500 Hz, f#[sub hp]=8313.16 Hz και f#[sub s]=11550 Hz. + +p. + Από το διάγραμμα 2.3.3 γίνεται φανερό ότι η ανάλυση του κυκλώματος στο Multisim συμφωνεί με τη θεωρητική ανάλυση που προηγήθηκε κάθως και την ανάλυση που έγινε χρησιμοποιώντας το Matlab. Παρατηρούνται ωστόσο μικρές αποκλίσεις, της τάξης 10#[sup -3], οι οποίες αποδίδονται στο γεγονός ότι οι τιμές των στοιχείων που χρησιμοποιήθηκαν στο Multisim έχουν μικρότερη ακρίβεια από ότι οι αντίστοιχες τιμές στην ανάλυση στο Matlab. + +p. + Ο διακόπτης S1 τοποθετείται τώρα στην δεξιά επαφή ώστε να επιλεχθεί ως σήμα εισόδου του φίλτρου ο τετραγωνικός παλμός της πηγής V2 με χαρακτηριστικά V#[sub 0]=0 V, Vp=1 V, f=2 kHz, duty cycle ίσο με 40%. Χρησιμοποιώντας το εργαλείο oscilloscope (XSC1), εξάγεται η κυματομορφή του σήματος εισόδου. Το διάγραμμα και οι επιλεγμένες τιμές του εργαλείου φαίνονται παρακάτω: + +figure.block-center.width-17cm + img(src="1_low_pass/assets/diagrams/multisim_low_pass_inversed_chebyshev_oscilloscope_input_sig.svg").width-17cm + figcaption + .reference #[span.plot-count] + .caption.title. + Έξοδος oscilloscope-XSC1 (μόνο channel A) κατωδιαβατού αντίστροφου Chebyshev φίλτρου από το Multisim. + .caption. + Οι επιλογές του oscilloscope που χρησιμοποιήθηκαν: + #[br/]#[strong Timebase:] #[strong Scale:] 500 us/Div, #[strong X pos.:] 0 και #[strong mode:] Y/T + #[br/]#[strong Channel:] #[strong Scale:] 500 mV/Div, #[strong Y pos.:] 0 και #[strong mode:] DC + +p. + Χρησιμοποιώντας το ίδιο εργαλείο (XSC1), εξάγεται η κυματομορφή της εξόδου. Το διάγραμμα και οι επιλεγμένες τιμές του εργαλείου φαίνονται παρακάτω: + +figure.block-center.width-17cm + img(src="1_low_pass/assets/diagrams/multisim_low_pass_inversed_chebyshev_oscilloscope_output_sig.svg").width-17cm + figcaption + .reference #[span.plot-count] + .caption.title. + Έξοδος oscilloscope-XSC1 (μόνο channel B) κατωδιαβατού αντίστροφου Chebyshev φίλτρου από το Multisim. + .caption. + Οι επιλογές του oscilloscope που χρησιμοποιήθηκαν: + #[br/]#[strong Timebase:] #[strong Scale:] 500 us/Div, #[strong X pos.:] 0 και #[strong mode:] Y/T + #[br/]#[strong Channel:] #[strong Scale:] 500 mV/Div, #[strong Y pos.:] 0 και #[strong mode:] DC & - + +p. + Χρησιμοποιώντας και τα δύο κανάλια του εργαλείου (XSC1), εξάγεται η κυματομορφή της εισόδου και της εξόδου στο ίδιο διάγραμμα. Το διάγραμμα και οι επιλεγμένες τιμές του εργαλείου φαίνονται παρακάτω: + +figure.block-center.width-17cm + img(src="1_low_pass/assets/diagrams/multisim_low_pass_inversed_chebyshev_oscilloscope_combined_input_output_sig.svg").width-17cm + figcaption + .reference #[span.plot-count] + .caption.title. + Έξοδος oscilloscope-XSC1 κατωδιαβατού αντίστροφου Chebyshev φίλτρου από το Multisim. + .caption. + Οι επιλογές του oscilloscope που χρησιμοποιήθηκαν: + #[br/]#[strong Timebase:] #[strong Scale:] 500 us/Div, #[strong X pos.:] 0 και #[strong mode:] Y/T + #[br/]#[strong Channel A:] (input signal) #[strong Scale:] 500 mV/Div, #[strong Y pos.:] 0 και #[strong mode:] DC + #[br/]#[strong Channel B:] (output signal) #[strong Scale:] 500 mV/Div, #[strong Y pos.:] 0 και #[strong mode:] DC & - + +p. + Στα παραπάνω διαγράμματα μπορούμε να δούμε αναλυτικά τα σήματα εισόδου και εξόδου στο χρόνο. Στις περιγραφές των διαγραμμάτων φαίνονται οι επιλογές που έγιναν στον παλμογράφο για να προκύψουν οι αντίστοιχες παραστάσεις. + +p. + Η συνολική απόκριση του φίλτρου στο σήμα εισόδου (τετραγωνικός παλμός) που καθόρισε η εκφώνηση, ελέγχθηκε στο λογισμικό Matlab. Η είσοδος και η έξοδος του φίλτρου στο χρόνο, όπως προέκυψαν στο Matlab, φαίνονται στο παρακάτω διάγραμμα: + +figure.block-center.width-17cm + img(src="1_low_pass/assets/diagrams/matlab_low_pass_inversed_chebyshev_combined_input_output_sig.svg").width-17cm + figcaption + .reference #[span.plot-count] + .caption.title. + Σήματα εισόδου και εξόδου στο χρόνο, διάγραμμα από Matlab. + .caption. + Παρατηρείται ότι τα σήματα συμφωνούν με αυτά του Multisim. + +p. + Χρησιμοποιήθηκαν οι εντολές fft και lsim που παρέχονται από το λογισμικό για να εξαχθεί η απόκριση και στη συνέχεια το φάσμα της απόκρισης τόσο για την είσοδο όπως και για την έξοδο. Το φάσμα του σήματος εισόδου φαίνεται στο παρακάτω διάγραμμα: + +figure.block-center.width-17cm + img(src="1_low_pass/assets/diagrams/matlab_low_pass_inversed_chebyshev_input_spectrum.svg").width-17cm + figcaption + .reference #[span.plot-count] + .caption.title. + Φάσμα σήματος εισόδου, διάγραμμα από Matlab. + +p. + Στο επόμενο διάγραμμα φαίνεται και πάλι το φάσμα του σήματος εισόδου με μεγέθυνση στη περιοχή ενδιαφέροντος: + +figure.block-center.width-17cm + img(src="1_low_pass/assets/diagrams/matlab_low_pass_inversed_chebyshev_input_spectrum_zoom.svg").width-17cm + figcaption + .reference #[span.plot-count] + .caption.title. + Φάσμα σήματος εισόδου, διάγραμμα από Matlab. +div(style="page-break-before:always") +p. + Το φάσμα του σήματος εξόδου φαίνεται στο παρακάτω διάγραμμα: +figure.block-center.width-17cm + img(src="1_low_pass/assets/diagrams/matlab_low_pass_inversed_chebyshev_output_spectrum.svg").width-17cm + figcaption + .reference #[span.plot-count] + .caption.title. + Φάσμα σήματος εξόδου, διάγραμμα από Matlab. + +p. + Στο επόμενο διάγραμμα φαίνεται και πάλι το φάσμα του σήματος εξόδου με μεγέθυνση στη περιοχή ενδιαφέροντος: + +figure.block-center.width-17cm + img(src="1_low_pass/assets/diagrams/matlab_low_pass_inversed_chebyshev_output_spectrum_zoom.svg").width-17cm + figcaption + .reference #[span.plot-count] + .caption.title. + Φάσμα σήματος εξόδου, διάγραμμα από Matlab. + +p. + Η ίδια απόκριση ελέγχθηκε και στο Multisim. Διατηρώντας τον διακόπτη S1 στη δεξιά επαφή, χρησιμοποιείται το εργαλείο spectrum analyzer (XSA1) για να εξαχθεί το φάσμα εισόδου. Το διάγραμμα και οι επιλεγμένες τιμές του εργαλείου φαίνονται παρακάτω: + +figure.block-center.width-17cm + img(src="1_low_pass/assets/diagrams/multisim_low_pass_inversed_chebyshev_spectrum_analyzer_input.svg").width-17cm + figcaption + .reference #[span.plot-count] + .caption.title. + Φάσμα σήματος εισόδου, έξοδος spectrum analyzer-XSA1 από Multisim. + .caption. + Οι επιλογές του spectrum analyzer που χρησιμοποιήθηκαν: + #[br/]#[strong Frequency:] #[strong Span:] 20 kHz, #[strong Start:] 0 Hz, #[strong Center:] 10 kHz και #[strong End:] 20 kHz + #[br/]#[strong Amplitude:] #[strong lin] και #[strong Range:] 0.1 V/Div + #[br/]#[strong Resolution freq.:] 100 Hz + +p. + Με τον ίδιο τρόπο, χρησιμοποιείται το εργαλείο spectrum analyzer (XSA2) για να εξαχθεί το φάσμα εξόδου. Το διάγραμμα και οι επιλεγμένες τιμές του εργαλείου φαίνονται παρακάτω: + +figure.block-center.width-17cm + img(src="1_low_pass/assets/diagrams/multisim_low_pass_inversed_chebyshev_spectrum_analyzer_output.svg").width-17cm + figcaption + .reference #[span.plot-count] + .caption.title. + Φάσμα σήματος εξόδου, έξοδος spectrum analyzer-XSA2 από Multisim. + .caption. + Οι επιλογές του spectrum analyzer που χρησιμοποιήθηκαν: + #[br/]#[strong Frequency:] #[strong Span:] 20 kHz, #[strong Start:] 0 Hz, #[strong Center:] 10 kHz και #[strong End:] 20 kHz + #[br/]#[strong Amplitude:] #[strong lin] και #[strong Range:] 0.1 V/Div + #[br/]#[strong Resolution freq.:] 100 Hz + +div(style="page-break-before:always") +p. + Τα δύο παραπάνω διαγράμματα συνδυάστηκαν σε ένα για ευκολότερη εξαγωγή συμπερασμάτων: + +figure.block-center.width-17cm + img(src="1_low_pass/assets/diagrams/multisim_low_pass_inversed_chebyshev_spectrum_analyzer_combined_input_output.svg").width-17cm + figcaption + .reference #[span.plot-count] + .caption.title. + Φάσματα σημάτων εισόδου και εξόδου, εξόδου spectrum analyzers-XSA1 και XSA2 από Multisim. + +p. + Από τα παραπάνω διαγράμματα συμπεραίνουμε καταρχάς ότι η ανάλυση του φίλτρου που έγινε στο Matlab συμφωνεί με αυτή που έγινε στο Multisim. Το συμπέρασμα αυτό προέρχεται από το γεγονός ότι τα φάσματα εισόδου και εξόδου του σήματος εισόδου και εξόδου του φίλτρου είναι ίδια στα δύο πειράματα. +p. + Επίσης από τα φάσματα και κυρίως από το τελευταίο διάγραμμα (2.3.14) γίνεται εύκολα αντιληπτό ότι το κύκλωμα που σχεδιάστηκε υλοποιεί επιτυχώς το επιθυμητό κατωδιαβατό φίλτρο. +p. + Πιο συγκεκριμένα παρατηρείται ότι το φάσμα εξόδου είναι ίδιο με το φάσμα εισόδου στις χαμηλές συχνότητες, δηλαδή στη ζώνη διόδου μέχρι τα 5500 Hz. Ταυτόχρονα, οι συχνότητες της ζώνης αποκοπής, πάνω από 11550 Hz, υπέστησαν τόσο σημαντική απόσβεση, ώστε σχεδόν να μη φαίνονται στο φάσμα εξόδου, δείχνοντας ότι οι υψηλές συχνότητες κόβονται από το κύκλωμα. Τέλος σημειώνεται ότι η συχνότητα των 8000 Hz, η οποία βρίσκεται μέσα στη ζώνη μετάβασης του φίλτρου, έχει επίσης υποστεί κάποια απόσβεση, είναι όμως εμφανής και στο φάσμα εξόδου. diff --git a/report/1_low_pass/assets/diagrams/matlab_combined_transfer_functions_bode.svg b/report/1_low_pass/assets/diagrams/matlab_combined_transfer_functions_bode.svg index bcd2a08..62b3503 100644 --- a/report/1_low_pass/assets/diagrams/matlab_combined_transfer_functions_bode.svg +++ b/report/1_low_pass/assets/diagrams/matlab_combined_transfer_functions_bode.svg @@ -1,264 +1,288 @@ - - -Bode DiagramFrequency (rad/s)103104105106107-350-300-250-200-150-100-50050Magnitude (dB) + + + + + + + Bode Diagram + + + Frequency (rad/s) + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + 10 + + + 3 + + + 10 + + + 4 + + + 10 + + + 5 + + + 10 + + + 6 + + + 10 + + + 7 + + + + + + + + + + + + + + + + + + + + + + + + + -350 + + + -300 + + + -250 + + + -200 + + + -150 + + + -100 + + + -50 + + + 0 + + + 50 + + + + + + + + Magnitude (dB) + + + + + + Unit 1 + + + + + + Unit 2 + + + + + + Total filter + + + + + + + diff --git a/report/1_low_pass/assets/diagrams/matlab_low_pass_inversed_chebyshev_combined_input_output_sig.svg b/report/1_low_pass/assets/diagrams/matlab_low_pass_inversed_chebyshev_combined_input_output_sig.svg new file mode 100644 index 0000000..9f93f5b --- /dev/null +++ b/report/1_low_pass/assets/diagrams/matlab_low_pass_inversed_chebyshev_combined_input_output_sig.svg @@ -0,0 +1,227 @@ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + 0 + + + 0.5 + + + 1 + + + 1.5 + + + 2 + + + 2.5 + + + 3 + + + 3.5 + + + 4 + + + 4.5 + + + 5 + + + Time (s) + + + # 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