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Minor fixes

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Apostolos Fanakis 6 years ago
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5 changed files with 189 additions and 165 deletions
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  1. 24
      Band Elimination Chebyshev/band_elimination_design.m
  2. 22
      Band Pass Chebyshev/band_pass_design.m
  3. 10
      High Pass Butterworth/high_pass_design.m
  4. 18
      report/2_band_pass/2_band_pass_design.pug
  5. 280
      report/2_band_pass/assets/diagrams/matlab_band_pass_chebyshev_zero_pole.svg

24
Band Elimination Chebyshev/band_elimination_design.m
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@ -536,22 +536,22 @@ for i=1:2
(1/normalized_transfer_function_zero^2);
% Calculates R2 using the eq. 7-138
high_pass_notch_units_R2(1,i) = band_elimination_poles_Q(1,unit_index)^2* ...
(high_pass_notch_units_k1(1,i)+2)^2;
(high_pass_notch_units_k1(1,i)+2)^2; % Ohm
% Assumes that R3 is 1 Ohm and the radial frequency is 1 rad/s
high_pass_notch_units_R3(1,i) = 1;
high_pass_notch_units_R3(1,i) = 1; % Ohm
% Calculates R4 using the eq. 7-139
high_pass_notch_units_R4(1,i) = (high_pass_notch_units_k1(1,i)+2)* ...
band_elimination_poles_Q(1,unit_index)^2;
band_elimination_poles_Q(1,unit_index)^2; % Ohm
% Calculates C using the eq. 7-140
high_pass_notch_units_C(1,i) = 1/ ...
(band_elimination_poles_Q(1,unit_index)* ...
(high_pass_notch_units_k1(1,i)+2));
(high_pass_notch_units_k1(1,i)+2)); % Farad
% Initial axioms of the design were:
% C1 = k1 * C
high_pass_notch_units_C1(1,i) = high_pass_notch_units_k1(1,i)* ...
high_pass_notch_units_C(1,i);
high_pass_notch_units_C(1,i); % Farad
% R1 = 1 Ohm
high_pass_notch_units_R1(1,i) = 1;
high_pass_notch_units_R1(1,i) = 1; % Ohm
% Selects the appropriate frequency scale factor to transfer the
% normalized radial frequency back to the original
@ -565,19 +565,19 @@ for i=1:2
% Performs scaling
high_pass_notch_units_R1(1,i) = high_pass_notch_units_R1(1,i)* ...
high_pass_notch_units_amplitude_scale_factors(1,i);
high_pass_notch_units_amplitude_scale_factors(1,i); % Ohm
high_pass_notch_units_R2(1,i) = high_pass_notch_units_R2(1,i)* ...
high_pass_notch_units_amplitude_scale_factors(1,i);
high_pass_notch_units_amplitude_scale_factors(1,i); % Ohm
high_pass_notch_units_R3(1,i) = high_pass_notch_units_R3(1,i)* ...
high_pass_notch_units_amplitude_scale_factors(1,i);
high_pass_notch_units_amplitude_scale_factors(1,i); % Ohm
high_pass_notch_units_R4(1,i) = high_pass_notch_units_R4(1,i)* ...
high_pass_notch_units_amplitude_scale_factors(1,i);
high_pass_notch_units_amplitude_scale_factors(1,i); % Ohm
high_pass_notch_units_C(1,i) = high_pass_notch_units_C(1,i)/ ...
(high_pass_notch_units_frequency_scale_factors(1,i)* ...
high_pass_notch_units_amplitude_scale_factors(1,i));
high_pass_notch_units_amplitude_scale_factors(1,i)); % Farad
high_pass_notch_units_C1(1,i) = high_pass_notch_units_C1(1,i)/ ...
(high_pass_notch_units_frequency_scale_factors(1,i)* ...
high_pass_notch_units_amplitude_scale_factors(1,i));
high_pass_notch_units_amplitude_scale_factors(1,i)); % Farad
% Builds unit's transfer function using the eq. 7-129, 7-130, 7-131
high_pass_notch_unit_numerator = [1 ...

22
Band Pass Chebyshev/band_pass_design.m
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@ -394,12 +394,12 @@ for i=1:band_pass_number_of_poles
units_BW(1,i) = band_pass_poles_radial_frequencies(1,i)/ ...
band_pass_poles_Q(1,i);
% Calculates C21 (=C22=C) using the eq. 7-87
units_C21(1,i) = 1/(2*band_pass_poles_Q(1,i));
units_C22(1,i) = units_C21(1,i);
units_C21(1,i) = 1/(2*band_pass_poles_Q(1,i)); % Farad
units_C22(1,i) = units_C21(1,i); % Farad
% Using the eq. 7-86
units_R1(1,i) = 1;
units_R1(1,i) = 1; % Ohm
% Calculates R12 using the eq. 7-87
units_R2(1,i) = 4*band_pass_poles_Q(1,i)^2;
units_R2(1,i) = 4*band_pass_poles_Q(1,i)^2; % Ohm
% Selects the appropriate frequency scale factor to transfer the
% normalized radial frequency back to the original
@ -411,10 +411,10 @@ for i=1:band_pass_number_of_poles
(units_frequency_scale_factors(1,i)*0.1*10^(-6));
% Scales the circuit elements
units_C21(1,i) = 0.1*10^(-6);
units_C22(1,i) = 0.1*10^(-6);
units_R1(1,i) = units_amplitude_scale_factors(1,i);
units_R2(1,i) = units_R2(1,i)*units_amplitude_scale_factors(1,i);
units_C21(1,i) = 0.1*10^(-6); % Farad
units_C22(1,i) = 0.1*10^(-6); % Farad
units_R1(1,i) = units_amplitude_scale_factors(1,i); % Ohm
units_R2(1,i) = units_R2(1,i)*units_amplitude_scale_factors(1,i); % Ohm
% Calculates the gain at the central radial frequency and the alpha
% parameter using the eq. 7-89
@ -434,9 +434,9 @@ for i=1:band_pass_number_of_poles
% Calculates the values of the resistors used to diminish the entry
% using the eq. 7-90 (to include the scaling already done the equations
% are used in the form presented at example 7.2)
units_Z2(1,i) = units_R1(1,i)/units_alpha(1,i);
units_Z3(1,i) = units_R1(1,i)/(1-units_alpha(1,i));
unit_Z_parallel = (units_Z2(1,i)*units_Z3(1,i))/(units_Z2(1,i)+units_Z3(1,i));
units_Z2(1,i) = units_R1(1,i)/units_alpha(1,i); % Ohm
units_Z3(1,i) = units_R1(1,i)/(1-units_alpha(1,i)); % Ohm
unit_Z_parallel = (units_Z2(1,i)*units_Z3(1,i))/(units_Z2(1,i)+units_Z3(1,i)); % Ohm
%
unit_numerator = [-1/(units_Z2(1,i)*units_C21(1,i)) ...

10
High Pass Butterworth/high_pass_design.m
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@ -314,7 +314,7 @@ units_transfer_functions = [tf(1) tf(1)];
for i=1:high_pass_number_of_poles
% Calculates k and r2 using the eq. 6-75
units_r2(1,i) = 2-1/high_pass_poles_Q(1,i);
units_r2(1,i) = 2-1/high_pass_poles_Q(1,i); % Ohm
units_k(1,i) = 3-1/high_pass_poles_Q(1,i);
% Selects the appropriate frequency scale factor to transfer the
@ -329,12 +329,12 @@ for i=1:high_pass_number_of_poles
% Performs scaling
units_R(1,i) = units_R(1,i)* ...
units_amplitude_scale_factors(1,i);
units_C(1,i) = 0.1*10^(-6);
units_amplitude_scale_factors(1,i); % Ohm
units_C(1,i) = 0.1*10^(-6); % Farad
units_r1(1,i) = units_r1(1,i)* ...
units_amplitude_scale_factors(1,i);
units_amplitude_scale_factors(1,i); % Ohm
units_r2(1,i) = units_r2(1,i)* ...
units_amplitude_scale_factors(1,i);
units_amplitude_scale_factors(1,i); % Ohm
% Builds unit's transfer function
% Builds numerator and denominator of the transfer function using the

18
report/2_band_pass/2_band_pass_design.pug
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@ -21,7 +21,7 @@ h4 Υπολογισμός συνάρτησης μεταφοράς
p Αρχικά υπολογίζεται η κεντρική συχνότητα χρησιμοποιώντας την εξίσωση #[span.course-notes-equation 11-2]:
p.latex-equation.
$$\omega_0 = \sqrt{\omega_1\omega_2}=\sqrt{5026.548*6361.725}=5654.867$$
$$\omega_0 = \sqrt{\omega_1\omega_2}=\sqrt{5026.548*6361.725}=5654.867\frac{\text{rad}}{\text{s}}$$
p.
Η κεντρική συχνότητα που υπολογίστηκε προκύπτει ίση με αυτή που δίνεται στην εκφώνηση, επιβεβαιώνεται έτσι ότι οι συχνότητες ω#[sub 1] - ω#[sub 4] υπολογίστηκαν σωστά.
@ -30,7 +30,7 @@ p.
Υπολογίζεται το εύρος ζώνης διόδου χρησιμοποιώντας την εξίσωση #[span.course-notes-equation 11-52]:
p.latex-equation.
$$bw = \omega_2-\omega_1=6361.725-5026.548=1335.177$$
$$bw = \omega_2-\omega_1=6361.725-5026.548=1335.177\text{ rad}$$
p.
Σχεδιάζεται ένα πρότυπο κατωδιαβατό Chebyshev φίλτρο, το οποίο αργότερα θα μετατραπεί στο επιθυμητό ζωνοδιαβατό Chebyshev.
@ -46,7 +46,7 @@ p Οι προδιαγραφές απόσβεσης παραμένουν ίδιε
p Υπολογίζεται η τάξη του φίλτρου χρησιμοποιώντας την εξίσωση #[span.course-notes-equation 9-83]:
p.latex-equation.
$$n = \left \lceil \frac{cos^{-1}\bigg(\sqrt{\frac{10^{\frac{a_{min}}{10}}-1}{10^{\frac{a_{max}}{10}}-1}}\bigg)}{cosh^{-1}\Omega_S} \right \rceil = \left \lceil \frac{cos^{-1}\bigg(\sqrt{\frac{10^{2.8556}-1}{10^{0.0667}-1}}\bigg)}{cosh^{-1}(2.2)} \right \rceil = \left \lceil \frac{4.87789}{1.42542} \right \rceil = \left \lceil 3.422 \right \rceil = 4$$
$$n = \left \lceil \frac{\cosh^{-1}\bigg(\sqrt{\frac{10^{\frac{a_{min}}{10}}-1}{10^{\frac{a_{max}}{10}}-1}}\bigg)}{\cosh^{-1}\Omega_S} \right \rceil = \left \lceil \frac{\cosh^{-1}\bigg(\sqrt{\frac{10^{2.8556}-1}{10^{0.0667}-1}}\bigg)}{\cosh^{-1}(2.2)} \right \rceil = \left \lceil \frac{4.87789}{1.42542} \right \rceil = \left \lceil 3.422 \right \rceil = 4$$
p.
Από τον παραπάνω τύπο φαίνεται ότι κατά τον υπολογισμό της τάξης του φίλτρου γίνεται στρογγυλοποίηση της τάξης προς τον επόμενο #[strong μεγαλύτερο] ακέραιο. Αυτό γίνεται επειδή δεν είναι δυνατή η υλοποίηση ενός φίλτρου ρητής τάξεως, έτσι είναι απαραίτητο η τάξη να στρογγυλοποιηθεί. Η στρογγυλοποίηση είναι σημαντικό να γίνει προς τα επάνω (ceiling) ώστε να επιτευχθούν οι προδιαγραφές του φίλτρου. Μία πιθανή στρογγυλοποίηση προς τα κάτω θα είχε ως αποτέλεσμα την αποτυχία στη σχεδίαση.
@ -224,6 +224,9 @@ figure.block-center.width-15cm
tr
td Q
td 10.9546
tr
td ω#[sub z]
td 0+0j
tr
td Angle
td ±87.38°
@ -352,6 +355,9 @@ figure.block-center.width-15cm
tr
td Q
td 10.9546
tr
td ω#[sub z]
td 0+0j
tr
td Angle
td ±87.38°
@ -480,6 +486,9 @@ figure.block-center.width-15cm
tr
td Q
td 26.599
tr
td ω#[sub z]
td 0+0j
tr
td Angle
td ±88.92°
@ -608,6 +617,9 @@ figure.block-center.width-15cm
tr
td Q
td 26.599
tr
td ω#[sub z]
td 0+0j
tr
td Angle
td ±88.92°

280
report/2_band_pass/assets/diagrams/matlab_band_pass_chebyshev_zero_pole.svg
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@ -1,7 +1,7 @@
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