5 changed files with 349 additions and 397 deletions
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% AUTHOR : Apostolos Fanakis |
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% $DATE : 02-May-2018 17:21:18 $ |
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% $Revision : 1.00 $ |
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% DEVELOPED : 9.0.0.341360 (R2016a) |
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% FILENAME : low_pass_design_single.m |
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% AEM : 8261 |
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%% ========== DESIGN SPECIFICATIONS START ========== |
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% Figures out design specifications according to my AEM number |
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AEM = [8 2 6 1]; |
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if AEM(3)<3 |
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design_param_m = 1; |
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elseif AEM(3)<7 |
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design_param_m = 2; |
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else |
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design_param_m = 3; |
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end |
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specification_pass_frequency = (1.1*(3+design_param_m))*1000; % Hz |
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specification_pass_radial_frequency = ... |
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specification_pass_frequency*(2*pi); % rad/s |
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specification_stop_frequency = 2.1*specification_pass_frequency; % Hz |
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specification_stop_radial_frequency = ... |
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specification_stop_frequency*(2*pi); % rad/s |
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specification_min_stop_attenuation = 23+(max(1,AEM(3))-5)*(3/4); % dB |
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specification_max_pass_attenuation = 0.6+((max(1,AEM(4))-5)/16); % dB |
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clear design_param_m |
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% ========== DESIGN SPECIFICATIONS END ========== |
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%% ========== NORMALIZED DESIGN START ========== |
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% Calculates normalized design specifications and designs a normalized |
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% filter using them |
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normalized_pass_radial_frequency = specification_pass_radial_frequency/ ... |
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specification_stop_radial_frequency; % rad/s |
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% normalized_stop_radial_frequency = 1; % Hz (stop_frequency/stop_frequency) |
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% Calculates the filter's order using the eq. 9-137 |
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design_filter_order = ceil( ... |
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acosh(((10^(specification_min_stop_attenuation/10)-1)/ ... |
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(10^(specification_max_pass_attenuation/10)-1))^(1/2)) ... |
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/acosh(1/normalized_pass_radial_frequency)); |
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% Calculates epsilon parameter using the eq. 9-123 |
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epsilon_parameter = 1/(10^(specification_min_stop_attenuation/10)-1)^(1/2); |
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% Calculates alpha using the eq. ?? wtf is this? =========^^^^^^^^^^^^^^^^^^&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&========== |
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alpha_parameter = asinh(1/epsilon_parameter)/design_filter_order; |
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% Calculates the frequency at which half power occurs using the eq. 9-139 |
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design_half_power_radial_frequency = specification_stop_radial_frequency/ ... |
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(cosh(acosh(1/epsilon_parameter)/design_filter_order)); % rad/s |
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% ----- |
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% Calculates stable poles, zeros, angles and other characteristic sizes |
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% using the Guillemin algorithm |
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% ----- |
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% Initializes necessary variables |
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design_number_of_poles = idivide(design_filter_order,int32(2),'ceil'); |
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% Creates five vector arrays of dimensions [1 * number_of_poles] filled |
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% with zeros to store: |
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% - the Butterworth angles with reference to the negative horizontal axes, |
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% - the real parts of the poles, |
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% - the imaginary parts of the poles, |
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% - the radial frequencies (Omega0) of the poles and |
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% - the Q's of the poles (both the Chebyshev and Inverse Chebyshev poles |
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% have the same Q's) |
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design_butterworth_angles = zeros([1 design_number_of_poles]); |
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chebyshev_poles_real_parts = zeros([1 design_number_of_poles]); |
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chebyshev_poles_imaginary_parts = zeros([1 design_number_of_poles]); |
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chebyshev_poles_radial_frequencies = zeros([1 design_number_of_poles]); |
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inverse_chebyshev_poles_Q = zeros([1 design_number_of_poles]); |
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% Calculates the Butterworth angles using the method suggested in chapter |
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% 9 (page 10) of the course notes and then uses them to calculate the |
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% inverse Chebyshev poles |
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if mod(design_filter_order,2)~=0 % Odd number of poles |
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% First pole has a zero angle |
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design_butterworth_angles(1,1)=0; |
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% The rest of the poles are scattered in the left half pane with |
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% equal angles |
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% Theta is a helper parameter |
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theta=180/design_filter_order; |
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% Calculates the first pole's real part using the eq. 9-102 |
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chebyshev_poles_real_parts(1,1) = -sinh(alpha_parameter)* ... |
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cosd(design_butterworth_angles(1,1)); |
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% Calculates the first pole's imaginary part using the eq. 9-103 |
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chebyshev_poles_imaginary_parts(1,1) = cosh(alpha_parameter)* ... |
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sind(design_butterworth_angles(1,1)); |
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% Calculates the first pole's radial frequency using the eq. 9-150 |
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chebyshev_poles_radial_frequencies(1,1) = ... |
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(chebyshev_poles_real_parts(1,1)^2+ ... |
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chebyshev_poles_imaginary_parts(1,1)^2)^(1/2); |
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% Calculates the first pole's Q using the eq. 9-151 |
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inverse_chebyshev_poles_Q(1,1) = 1/ ... |
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(2*cos(atan(chebyshev_poles_imaginary_parts(1,1)/ ... |
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chebyshev_poles_real_parts(1,1)))); |
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% Calculates the rest of the poles in the same way |
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for i=2:design_number_of_poles |
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design_butterworth_angles(1,i)=double((i-1)*theta); |
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% Pole's real part, eq. 9-102 |
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chebyshev_poles_real_parts(1,i) = -sinh(alpha_parameter)* ... |
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cosd(design_butterworth_angles(1,i)); |
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% Pole's imaginary part, eq. 9-103 |
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chebyshev_poles_imaginary_parts(1,i) = cosh(alpha_parameter)* ... |
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sind(design_butterworth_angles(1,i)); |
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% Pole's radial frequency, eq. 9-150 |
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chebyshev_poles_radial_frequencies(1,i) = ... |
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(chebyshev_poles_real_parts(1,i)^2+ ... |
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chebyshev_poles_imaginary_parts(1,i)^2)^(1/2); |
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% Pole's Q, eq. 9-151 |
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inverse_chebyshev_poles_Q(1,i) = 1/ ... |
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(2*cos(atan(chebyshev_poles_imaginary_parts(1,i)/ ... |
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chebyshev_poles_real_parts(1,i)))); |
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end |
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else % Even number of poles |
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% Theta is a helper parameter |
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theta=90/design_number_of_poles; |
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for i=1:design_number_of_poles |
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design_butterworth_angles(1,i)=double(90)/ ... |
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double(design_filter_order)+double((i-1)*theta); |
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% Pole's real part, eq. 9-102 |
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chebyshev_poles_real_parts(1,i) = -sinh(alpha_parameter)* ... |
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cosd(design_butterworth_angles(1,i)); |
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% Pole's imaginary part, eq. 9-103 |
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chebyshev_poles_imaginary_parts(1,i) = cosh(alpha_parameter)* ... |
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sind(design_butterworth_angles(1,i)); |
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% Pole's radial frequency, eq. 9-150 |
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chebyshev_poles_radial_frequencies(1,i) = ... |
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(chebyshev_poles_real_parts(1,i)^2+ ... |
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chebyshev_poles_imaginary_parts(1,i)^2)^(1/2); |
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% Pole's Q, eq. 9-151 |
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inverse_chebyshev_poles_Q(1,i) = 1/ ... |
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(2*cos(atan(chebyshev_poles_imaginary_parts(1,i)/ ... |
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chebyshev_poles_real_parts(1,i)))); |
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end |
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end |
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% Initializes array to hold the inversed poles |
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inverse_chebyshev_poles_radial_frequencies = ... |
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zeros([1 design_number_of_poles]); |
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% Calculates inverse Chebyshev poles by inversing the Chebyshev poles |
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% using the eq. 9-146 |
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for i=1:design_number_of_poles |
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inverse_chebyshev_poles_radial_frequencies(1,i) = 1/ ... |
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chebyshev_poles_radial_frequencies(1,i); |
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end |
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% Initializes array to hold the transfer function zeros and a temporary |
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% helper variable |
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inverse_chebyshev_transfer_function_zeros = ... |
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zeros([1 length(design_butterworth_angles)]); |
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temp_index = 1; |
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% Calculates the transfer function's zeros using the eq. 9-143 |
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for i=1:2:design_filter_order |
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inverse_chebyshev_transfer_function_zeros(1,temp_index) = ... |
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sec((i*pi)/(2*design_filter_order)); |
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temp_index = temp_index + 1; |
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end |
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% Clears unneeded variable from workspace |
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clearVars = {'theta', 'i', 'temp_index', 'alpha_parameter' ... |
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'epsilon_parameter', 'normalized_pass_radial_frequency'}; |
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clear(clearVars{:}) |
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clear clearVars |
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clear -regexp ^chebyshev_ |
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% ========== NORMALIZED DESIGN END ========== |
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%% ========== ZEROS-POLES GROUPING START ========== |
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% ------------------------------------------------------------------------- |
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% Unit 1 has a pole pair with Q equal to 0.5822, radial frequency equal to |
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% 0.9631 rad/s and is grouped with a zero at 1.0824, resulting in a low |
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% pass notch. |
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% ------------------------------------------------------------------------- |
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% Unit 1 has a pole pair with Q equal to 1.8086, radial frequency equal to |
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% 0.7484 rad/s and is grouped with a zero at 2.6131, resulting in a low |
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% pass notch. |
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% ------------------------------------------------------------------------- |
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% Two low pass notch units are required to implement the desired low pass |
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% filter. |
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% ========== ZEROS-POLES GROUPING END ========== |
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%% ========== UNITS IMPLEMENTATION START ========== |
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% AEM(3) = 6, so the circuit shown in 7.23 is going to be used for the low |
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% pass notch units. |
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% Initializes necessary arrays, each array is 1X2, the first element (1,1) |
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% corresponds to the first unit and the second element (1,2) to second unit. |
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unit_low_pass_notch_resistors_1 = zeros([1 2]); |
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unit_low_pass_notch_resistors_2 = zeros([1 2]); |
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unit_low_pass_notch_resistors_3 = zeros([1 2]); |
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unit_low_pass_notch_resistors_4 = zeros([1 2]); |
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unit_low_pass_notch_resistors_5 = zeros([1 2]); |
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unit_low_pass_notch_capacitors = zeros([1 2]); |
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unit_low_pass_notch_gains_high = zeros([1 2]); |
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unit_low_pass_notch_gains_low = zeros([1 2]); |
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unit_frequency_scale_factors = zeros([1 2]); |
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unit_amplitude_scale_factors = zeros([1 2]); |
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unit_transfer_function = [tf(1) tf(1)]; |
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for i=1:design_number_of_poles |
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% normalized_inverse_pole_radial_frequency = 1; |
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normalized_transfer_function_zero = ... |
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inverse_chebyshev_transfer_function_zeros(1,i)/ ... |
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inverse_chebyshev_poles_radial_frequencies(1,i); |
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% According to the design method outlined in 7.6-B, at page 35 |
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unit_low_pass_notch_resistors_1(1,i) = 1; % Ohm |
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% Calculates the capacity of the normalized circuit capacitors using |
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% the eq. 7-150 |
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unit_low_pass_notch_capacitors(1,i) = 1/ ... |
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(2*inverse_chebyshev_poles_Q(1,i)); % Farad |
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% Calculates the resistance of R2 using the same equations (7-150) |
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unit_low_pass_notch_resistors_2(1,i) = 4* ... |
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inverse_chebyshev_poles_Q(1,i)^2; % Ohm |
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% Calculates the resistance of R5 using the eq. 7-152 |
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unit_low_pass_notch_resistors_5(1,i) = ... |
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(4*inverse_chebyshev_poles_Q(1,i)^2)/ ... |
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(normalized_transfer_function_zero^2-1); % Ohm |
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unit_low_pass_notch_resistors_4(1,i) = 1; % Ohm |
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% Calculates the resistance of R3 using the eq. 7-155 |
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unit_low_pass_notch_resistors_3(1,i) = ... |
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(normalized_transfer_function_zero^2)/ ... |
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(2*inverse_chebyshev_poles_Q(1,i)^2); % Ohm |
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% Calculates the gain of this unit in high frequencies using the eq. 7-143 |
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unit_low_pass_notch_gains_high(1,i) = ... |
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(unit_low_pass_notch_resistors_4(1,i))/ ... |
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(unit_low_pass_notch_resistors_3(1,i)+ ... |
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unit_low_pass_notch_resistors_4(1,i)); |
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% Calculates the gain of this unit in low frequencies using the |
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% eq. 7-146, 7-147, 7-148, setting s = 0 |
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unit_low_pass_notch_gains_low(1,i) = ... |
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unit_low_pass_notch_gains_high(1,i)* ... |
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normalized_transfer_function_zero^2; |
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% Performs scaling |
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unit_frequency_scale_factors(1,i) = ... |
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specification_stop_radial_frequency* ... |
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inverse_chebyshev_poles_radial_frequencies(1,i); |
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% AEM(4) = 1, so the scaling will be performed to achieve a capacitor |
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% value of 0.1uF using the eq. 6-33 |
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unit_amplitude_scale_factors(1,i) = ... |
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unit_low_pass_notch_capacitors(1,i)/ ... |
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(unit_frequency_scale_factors(1,i)*0.1*10^(-6)); |
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unit_low_pass_notch_resistors_1(1,i) = ... |
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unit_low_pass_notch_resistors_1(1,i)* ... |
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unit_amplitude_scale_factors(1,i); % Ohm |
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unit_low_pass_notch_resistors_2(1,i) = ... |
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unit_low_pass_notch_resistors_2(1,i)* ... |
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unit_amplitude_scale_factors(1,i); % Ohm |
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unit_low_pass_notch_resistors_3(1,i) = ... |
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unit_low_pass_notch_resistors_3(1,i)* ... |
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unit_amplitude_scale_factors(1,i); % Ohm |
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unit_low_pass_notch_resistors_4(1,i) = ... |
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unit_low_pass_notch_resistors_4(1,i)* ... |
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unit_amplitude_scale_factors(1,i); % Ohm |
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unit_low_pass_notch_resistors_5(1,i) = ... |
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unit_low_pass_notch_resistors_5(1,i)* ... |
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unit_amplitude_scale_factors(1,i); % Ohm |
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unit_low_pass_notch_capacitors(1,i) = 0.1*10^(-6); % Farad |
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% Builds unit's transfer function |
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% Builds numerator and denominator of the transfer function using the |
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% eq. 7-146, 7-147 & 7-148 |
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unit_numerator = [1 ... |
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(((unit_low_pass_notch_gains_high(1,i)-1)/ ... |
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(unit_low_pass_notch_gains_high(1,i)* ... |
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unit_low_pass_notch_resistors_1(1,i)* ... |
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unit_low_pass_notch_capacitors(1,i)))+ ... |
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(2/(unit_low_pass_notch_resistors_2(1,i)* ... |
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unit_low_pass_notch_capacitors(1,i)))+ ... |
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(2/(unit_low_pass_notch_resistors_5(1,i)* ... |
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unit_low_pass_notch_capacitors(1,i)))) ... |
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(1/(unit_low_pass_notch_resistors_1(1,i)* ... |
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unit_low_pass_notch_resistors_5(1,i)* ... |
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unit_low_pass_notch_capacitors(1,i)^2)+ ... |
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1/(unit_low_pass_notch_resistors_1(1,i)* ... |
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unit_low_pass_notch_resistors_2(1,i)* ... |
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unit_low_pass_notch_capacitors(1,i)^2))]; |
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unit_denominator = [1 ... |
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2/(unit_low_pass_notch_resistors_2(1,i)* ... |
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unit_low_pass_notch_capacitors(1,i)) ... |
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1/(unit_low_pass_notch_resistors_1(1,i)* ... |
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unit_low_pass_notch_resistors_2(1,i)* ... |
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unit_low_pass_notch_capacitors(1,i)^2)]; |
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unit_transfer_function(1,i) = tf(unit_numerator, unit_denominator); |
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unit_transfer_function(1,i) = unit_transfer_function(1,i)* ... |
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unit_low_pass_notch_gains_high(1,i); |
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end |
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% Clears unneeded variable from workspace |
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clearVars = {'normalized_transfer_function_zero', 'i'}; |
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clear(clearVars{:}) |
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clear clearVars |
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% ========== UNITS IMPLEMENTATION END ========== |
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%% ========== GAIN ADJUSTMENT START ========== |
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total_fried_units_attenuation = unit_low_pass_notch_gains_low(1,1)* ... |
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unit_low_pass_notch_gains_low(1,2); |
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unit_adjustment_gain = 1/total_fried_units_attenuation; |
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% We arbitrarily choose to use a 10KOhm series resistor in the adjustment |
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% unit |
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unit_adjustment_feedback_resistor = 10*10^3*unit_adjustment_gain; |
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% ========== GAIN ADJUSTMENT END ========== |
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%% ========== TRANSFER FUNCTIONS START ========== |
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total_transfer_function = series(unit_transfer_function(1,1), ... |
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unit_transfer_function(1,2)); |
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total_transfer_function = total_transfer_function*unit_adjustment_gain; |
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%{ |
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plot_transfer_function(total_transfer_function, ... |
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[10 ... |
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specification_pass_frequency ... |
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design_half_power_radial_frequency/(2*pi) ... |
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specification_stop_frequency]); |
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%} |
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%ltiview(unit_transfer_function(1,1)); |
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%ltiview(unit_transfer_function(1,2)); |
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%ltiview(total_transfer_function); |
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ltiview(unit_transfer_function(1,1), unit_transfer_function(1,2), ... |
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total_transfer_function); |
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% Clears unneeded variable from workspace |
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clear -regexp _numerator$ |
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clear -regexp _denominator$ |
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clear -regexp _transfer_function$ |
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% ========== TRANSFER FUNCTIONS END ========== |
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@ -1,397 +0,0 @@ |
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% AUTHOR : Apostolos Fanakis |
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% $DATE : 02-May-2018 17:21:18 $ |
|
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% $Revision : 1.00 $ |
|
||||
% DEVELOPED : 9.0.0.341360 (R2016a) |
|
||||
% FILENAME : low_pass_design_single.m |
|
||||
% AEM : 8261 |
|
||||
|
|
||||
%% ========== DESIGN SPECIFICATIONS START ========== |
|
||||
% Figures out design specifications according to my AEM number |
|
||||
|
|
||||
AEM = [8 2 6 1]; |
|
||||
|
|
||||
if AEM(3)<3 |
|
||||
design_param_m = 1; |
|
||||
elseif AEM(3)<7 |
|
||||
design_param_m = 2; |
|
||||
else |
|
||||
design_param_m = 3; |
|
||||
end |
|
||||
|
|
||||
specification_pass_frequency = (1.1*(3+design_param_m))*1000; % Hz |
|
||||
specification_pass_radial_frequency = specification_pass_frequency*(2*pi); % rad/s |
|
||||
|
|
||||
specification_stop_frequency = 2.1*specification_pass_frequency; % Hz |
|
||||
specification_stop_radial_frequency = specification_stop_frequency*(2*pi); % rad/s |
|
||||
|
|
||||
specification_min_stop_attenuation = 23+(max(1,AEM(3))-5)*(3/4); % dB |
|
||||
specification_max_pass_attenuation = 0.6+((max(1,AEM(4))-5)/16); % dB |
|
||||
|
|
||||
clear design_param_m |
|
||||
|
|
||||
specification_pass_radial_frequency = 1000; % rad/s |
|
||||
specification_stop_radial_frequency = 1400; % rad/s |
|
||||
specification_min_stop_attenuation = 18; % dB |
|
||||
specification_max_pass_attenuation = 0.25; % dB |
|
||||
% ========== DESIGN SPECIFICATIONS END ========== |
|
||||
|
|
||||
%% ========== NORMALIZED DESIGN START ========== |
|
||||
% Calculates normalized design specifications and designs a normalized |
|
||||
% filter using them |
|
||||
|
|
||||
normalized_pass_radial_frequency = specification_pass_radial_frequency/ ... |
|
||||
specification_stop_radial_frequency; % rad/s |
|
||||
% normalized_stop_radial_frequency = 1; % Hz (stop_frequency/stop_frequency) |
|
||||
|
|
||||
% Calculates the filter's order using the eq. 9-137 |
|
||||
design_filter_order = ceil( ... |
|
||||
acosh(((10^(specification_min_stop_attenuation/10)-1)/ ... |
|
||||
(10^(specification_max_pass_attenuation/10)-1))^(1/2)) ... |
|
||||
/acosh(1/normalized_pass_radial_frequency)); |
|
||||
% Calculates epsilon parameter using the eq. 9-123 |
|
||||
epsilon_parameter = 1/(10^(specification_min_stop_attenuation/10)-1)^(1/2); |
|
||||
|
|
||||
% Calculates alpha using the eq. ?? wtf is this? =========^^^^^^^^^^^^^^^^^^&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&========== |
|
||||
alpha_parameter = asinh(1/epsilon_parameter)/design_filter_order; |
|
||||
|
|
||||
% Calculates the frequency at which half power occurs using the eq. 9-139 |
|
||||
design_half_power_radial_frequency = specification_stop_radial_frequency/ ... |
|
||||
(cosh(acosh(1/epsilon_parameter)/design_filter_order)); % rad/s |
|
||||
|
|
||||
% ----- |
|
||||
% Calculates stable poles, zeros, angles and other characteristic sizes |
|
||||
% using the Guillemin algorithm |
|
||||
% ----- |
|
||||
|
|
||||
% Initializes necessary variables |
|
||||
design_number_of_poles = idivide(design_filter_order,int32(2),'ceil'); |
|
||||
% Creates five vector arrays of dimensions [1 * number_of_poles] filled |
|
||||
% with zeros to store: |
|
||||
% - the Butterworth angles with reference to the negative horizontal axes, |
|
||||
% - the real parts of the poles, |
|
||||
% - the imaginary parts of the poles, |
|
||||
% - the radial frequencies (Omega0) of the poles and |
|
||||
% - the Q's of the poles |
|
||||
design_butterworth_angles = zeros([1 design_number_of_poles]); |
|
||||
poles_real_parts = zeros([1 design_number_of_poles]); |
|
||||
poles_imaginary_parts = zeros([1 design_number_of_poles]); |
|
||||
poles_radial_frequencies = zeros([1 design_number_of_poles]); |
|
||||
inverse_poles_Q = zeros([1 design_number_of_poles]); |
|
||||
|
|
||||
% Calculates the Butterworth angles using the method suggested in chapter |
|
||||
% 9 (page 10) of the course notes and then uses them to calculate the |
|
||||
% inverse Chebyshev poles |
|
||||
if mod(design_filter_order,2)~=0 % Odd number of poles |
|
||||
% First pole has a zero angle |
|
||||
design_butterworth_angles(1,1)=0; |
|
||||
% The rest of the poles are scattered in the left half pane with |
|
||||
% equal angles |
|
||||
% Theta is a helper parameter |
|
||||
theta=180/design_filter_order; |
|
||||
|
|
||||
% Calculates the first pole's real part using the eq. 9-102 |
|
||||
poles_real_parts(1,1) = -sinh(alpha_parameter)* ... |
|
||||
cosd(design_butterworth_angles(1,1)); |
|
||||
% Calculates the first pole's imaginary part using the eq. 9-103 |
|
||||
poles_imaginary_parts(1,1) = cosh(alpha_parameter)* ... |
|
||||
sind(design_butterworth_angles(1,1)); |
|
||||
% Calculates the first pole's radial frequency using the eq. 9-150 |
|
||||
poles_radial_frequencies(1,1) = (poles_real_parts(1,1)^2+ ... |
|
||||
poles_imaginary_parts(1,1)^2)^(1/2); |
|
||||
% Calculates the first pole's Q using the eq. 9-151 |
|
||||
inverse_poles_Q(1,1) = 1/ ... |
|
||||
(2*cos(atan(poles_imaginary_parts(1,1)/poles_real_parts(1,1)))); |
|
||||
|
|
||||
% Calculates the rest of the poles in the same way |
|
||||
for i=2:design_number_of_poles |
|
||||
design_butterworth_angles(1,i)=double((i-1)*theta); |
|
||||
% Pole's real part, eq. 9-102 |
|
||||
poles_real_parts(1,i) = -sinh(alpha_parameter)* ... |
|
||||
cosd(design_butterworth_angles(1,i)); |
|
||||
% Pole's imaginary part, eq. 9-103 |
|
||||
poles_imaginary_parts(1,i) = cosh(alpha_parameter)* ... |
|
||||
sind(design_butterworth_angles(1,i)); |
|
||||
% Pole's radial frequency, eq. 9-150 |
|
||||
poles_radial_frequencies(1,i) = (poles_real_parts(1,i)^2+ ... |
|
||||
poles_imaginary_parts(1,i)^2)^(1/2); |
|
||||
% Pole's Q, eq. 9-151 |
|
||||
inverse_poles_Q(1,i) = 1/ ... |
|
||||
(2*cos(atan(poles_imaginary_parts(1,i)/poles_real_parts(1,i)))); |
|
||||
end |
|
||||
else % Even number of poles |
|
||||
% Theta is a helper parameter |
|
||||
theta=90/design_number_of_poles; |
|
||||
|
|
||||
for i=1:design_number_of_poles |
|
||||
design_butterworth_angles(1,i)=double(90)/ ... |
|
||||
double(design_filter_order)+double((i-1)*theta); |
|
||||
% Pole's real part, eq. 9-102 |
|
||||
poles_real_parts(1,i) = -sinh(alpha_parameter)* ... |
|
||||
cosd(design_butterworth_angles(1,i)); |
|
||||
% Pole's imaginary part, eq. 9-103 |
|
||||
poles_imaginary_parts(1,i) = cosh(alpha_parameter)* ... |
|
||||
sind(design_butterworth_angles(1,i)); |
|
||||
% Pole's radial frequency, eq. 9-150 |
|
||||
poles_radial_frequencies(1,i) = (poles_real_parts(1,i)^2+ ... |
|
||||
poles_imaginary_parts(1,i)^2)^(1/2); |
|
||||
% Pole's Q, eq. 9-151 |
|
||||
inverse_poles_Q(1,i) = 1/ ... |
|
||||
(2*cos(atan(poles_imaginary_parts(1,i)/poles_real_parts(1,i)))); |
|
||||
end |
|
||||
end |
|
||||
|
|
||||
% Initializes array to hold the inversed poles |
|
||||
inverse_poles_radial_frequencies = zeros([1 design_number_of_poles]); |
|
||||
% Calculates inverse Chebyshev poles by inversing the Chebyshev poles |
|
||||
% using the eq. 9-146 |
|
||||
for i=1:design_number_of_poles |
|
||||
inverse_poles_radial_frequencies(1,i) = 1/poles_radial_frequencies(1,i); |
|
||||
end |
|
||||
|
|
||||
% Initializes array to hold the transfer function zeros and a temporary |
|
||||
% helper variable |
|
||||
inverse_transfer_function_zeros = zeros([1 length(design_butterworth_angles)]); |
|
||||
temp_index = 1; |
|
||||
% Calculates the transfer function's zeros using the eq. 9-143 |
|
||||
for i=1:2:design_filter_order |
|
||||
inverse_transfer_function_zeros(1,temp_index) = sec((i*pi)/ ... |
|
||||
(2*design_filter_order)); |
|
||||
temp_index = temp_index + 1; |
|
||||
end |
|
||||
|
|
||||
% Clears unneeded variable from workspace |
|
||||
clearVars = {'theta', 'i', 'temp_index', 'alpha_parameter' ... |
|
||||
'epsilon_parameter', 'normalized_pass_radial_frequency', ... |
|
||||
'poles_real_parts', 'poles_imaginary_parts', 'poles_radial_frequencies'}; |
|
||||
clear(clearVars{:}) |
|
||||
clear clearVars |
|
||||
|
|
||||
% ========== NORMALIZED DESIGN END ========== |
|
||||
|
|
||||
%% ========== ZEROS-POLES GROUPING START ========== |
|
||||
|
|
||||
% Grouping is done "by hand". The first pole, that has a radial frequency |
|
||||
% equal to 0.9631, is grouped with the first zero (1.0824) and the second |
|
||||
% pole, that has a radial frequency equal to 0.7484, is grouped with the |
|
||||
% second zero (2.6131). |
|
||||
% Two low pass notch units are required to implement the desired low pass filter. |
|
||||
|
|
||||
% ========== ZEROS-POLES GROUPING END ========== |
|
||||
|
|
||||
%% ========== UNITS IMPLEMENTATION START ========== |
|
||||
% AEM(3) = 6, so the circuit shown in 7.23 is going to be used for the low |
|
||||
% pass notch units. |
|
||||
|
|
||||
% Initializes necessary arrays, each array is 1X2, the first element (1,1) |
|
||||
% corresponds to the first unit and the second element (1,2) to second unit. |
|
||||
unit_low_pass_notch_resistors_1 = zeros([1 2]); |
|
||||
unit_low_pass_notch_resistors_2 = zeros([1 2]); |
|
||||
unit_low_pass_notch_resistors_3 = zeros([1 2]); |
|
||||
unit_low_pass_notch_resistors_4 = zeros([1 2]); |
|
||||
unit_low_pass_notch_resistors_5 = zeros([1 2]); |
|
||||
unit_low_pass_notch_capacitors = zeros([1 2]); |
|
||||
unit_low_pass_notch_gains_high = zeros([1 2]); |
|
||||
unit_low_pass_notch_gains_low = zeros([1 2]); |
|
||||
|
|
||||
% The specifications for the first unit are: |
|
||||
% - inverse pole radial frequency = 0.9631 |
|
||||
% - zero at 1.0824 (zero > inverse pole radial frequency) |
|
||||
% - pole angle = 0.5822 |
|
||||
|
|
||||
% normalized_inverse_pole_radial_frequency = 1; |
|
||||
normalized_transfer_function_zero = inverse_transfer_function_zeros(1,1)/ ... |
|
||||
inverse_poles_radial_frequencies(1,3); |
|
||||
|
|
||||
% According to the design method outlined in 7.6-B, at page 35 |
|
||||
unit_low_pass_notch_resistors_1(1,1) = 1; % Ohm |
|
||||
% Calculates the capacity of the normalized circuit capacitors using the |
|
||||
% eq. 7-150 |
|
||||
unit_low_pass_notch_capacitors(1,1) = 1/(2*inverse_poles_Q(1,3)); % Farad |
|
||||
% Calculates the resistance of R2 using the same equations (7-150) |
|
||||
unit_low_pass_notch_resistors_2(1,1) = 4*inverse_poles_Q(1,3)^2; % Ohm |
|
||||
% Calculates the resistance of R5 using the eq. 7-152 |
|
||||
unit_low_pass_notch_resistors_5(1,1) = (4*inverse_poles_Q(1,3)^2)/ ... |
|
||||
(normalized_transfer_function_zero^2-1); % Ohm |
|
||||
unit_low_pass_notch_resistors_4(1,1) = 1; % Ohm |
|
||||
% Calculates the resistance of R3 using the eq. 7-155 |
|
||||
unit_low_pass_notch_resistors_3(1,1) = (normalized_transfer_function_zero^2)/ ... |
|
||||
(2*inverse_poles_Q(1,3)^2); % Ohm |
|
||||
% Calculates the gain of this unit in high frequencies using the eq. 7-143 |
|
||||
unit_low_pass_notch_gains_high(1,1) = (unit_low_pass_notch_resistors_4(1,1))/ ... |
|
||||
(unit_low_pass_notch_resistors_3(1,1)+unit_low_pass_notch_resistors_4(1,1)); |
|
||||
% Calculates the gain of this unit in low frequencies using the |
|
||||
% eq. 7-146, 7-147, 7-148, setting s = 0 |
|
||||
unit_low_pass_notch_gains_low(1,1) = unit_low_pass_notch_gains_high(1,1)* ... |
|
||||
normalized_transfer_function_zero^2; |
|
||||
|
|
||||
% The specifications for the first unit are: |
|
||||
% - inverse pole radial frequency = $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ |
|
||||
% - zero at $$$$$$$$$$$$$$$$$$$$ (zero > inverse pole radial frequency) |
|
||||
% - pole angle = $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ |
|
||||
|
|
||||
normalized_transfer_function_zero = inverse_transfer_function_zeros(1,2)/ ... |
|
||||
inverse_poles_radial_frequencies(1,2); |
|
||||
|
|
||||
% According to the design method outlined in 7.6-B, at page 35 |
|
||||
unit_low_pass_notch_resistors_1(1,2) = 1; % Ohm |
|
||||
% Calculates the capacity of the normalized circuit capacitors using the |
|
||||
% eq. 7-150 |
|
||||
unit_low_pass_notch_capacitors(1,2) = 1/(2*inverse_poles_Q(1,2)); % Farad |
|
||||
% Calculates the resistance of R2 using the same equations (7-150) |
|
||||
unit_low_pass_notch_resistors_2(1,2) = 4*inverse_poles_Q(1,2)^2; % Ohm |
|
||||
% Calculates the resistance of R5 using the eq. 7-152 |
|
||||
unit_low_pass_notch_resistors_5(1,2) = (4*inverse_poles_Q(1,2)^2)/ ... |
|
||||
(normalized_transfer_function_zero^2-1); % Ohm |
|
||||
unit_low_pass_notch_resistors_4(1,2) = 1; % Ohm |
|
||||
% Calculates the resistance of R3 using the eq. 7-155 |
|
||||
unit_low_pass_notch_resistors_3(1,2) = (normalized_transfer_function_zero^2)/ ... |
|
||||
(2*inverse_poles_Q(1,2)^2); % Ohm |
|
||||
% Calculates the gain of this unit in high frequencies using the eq. 7-143 |
|
||||
unit_low_pass_notch_gains_high(1,2) = (unit_low_pass_notch_resistors_4(1,2))/ ... |
|
||||
(unit_low_pass_notch_resistors_3(1,2)+unit_low_pass_notch_resistors_4(1,2)); |
|
||||
% Calculates the gain of this unit in low frequencies using the |
|
||||
% eq. 7-146, 7-147, 7-148, setting s = 0 |
|
||||
unit_low_pass_notch_gains_low(1,2) = unit_low_pass_notch_gains_high(1,2)* ... |
|
||||
normalized_transfer_function_zero^2; |
|
||||
|
|
||||
% Clears unneeded variable from workspace |
|
||||
clear normalized_transfer_function_zero |
|
||||
|
|
||||
% ========== UNITS IMPLEMENTATION END ========== |
|
||||
|
|
||||
%% ========== DENORMALIZATION START ========== |
|
||||
|
|
||||
% Unit sizes rescale |
|
||||
unit_frequency_scale_factors = zeros([1 2]); |
|
||||
unit_amplitude_scale_factors = zeros([1 2]); |
|
||||
|
|
||||
% For unit 1 |
|
||||
unit_frequency_scale_factors(1,1) = specification_stop_radial_frequency* ... |
|
||||
inverse_poles_radial_frequencies(1,3); |
|
||||
% AEM(4) = 1, so the scaling will be performed to achieve a capacitor value |
|
||||
% of 0.1uF using the eq. 6-33 |
|
||||
unit_amplitude_scale_factors(1,1) = unit_low_pass_notch_capacitors(1,1)/ ... |
|
||||
(unit_frequency_scale_factors(1,1)*0.1*10^(-6)); |
|
||||
|
|
||||
unit_low_pass_notch_resistors_1(1,1) = unit_low_pass_notch_resistors_1(1,1)* ... |
|
||||
unit_amplitude_scale_factors(1,1); % Ohm |
|
||||
unit_low_pass_notch_resistors_2(1,1) = unit_low_pass_notch_resistors_2(1,1)* ... |
|
||||
unit_amplitude_scale_factors(1,1); % Ohm |
|
||||
unit_low_pass_notch_resistors_3(1,1) = unit_low_pass_notch_resistors_3(1,1)* ... |
|
||||
unit_amplitude_scale_factors(1,1); % Ohm |
|
||||
unit_low_pass_notch_resistors_4(1,1) = unit_low_pass_notch_resistors_4(1,1)* ... |
|
||||
unit_amplitude_scale_factors(1,1); % Ohm |
|
||||
unit_low_pass_notch_resistors_5(1,1) = unit_low_pass_notch_resistors_5(1,1)* ... |
|
||||
unit_amplitude_scale_factors(1,1); % Ohm |
|
||||
unit_low_pass_notch_capacitors(1,1) = 0.1*10^(-6); % Farad |
|
||||
|
|
||||
% For unit 2 |
|
||||
unit_frequency_scale_factors(1,2) = specification_stop_radial_frequency* ... |
|
||||
inverse_poles_radial_frequencies(1,2); |
|
||||
% AEM(4) = 1, so the scaling will be performed to achieve a capacitor value |
|
||||
% of 0.1uF using the eq. 6-33 |
|
||||
unit_amplitude_scale_factors(1,2) = unit_low_pass_notch_capacitors(1,2)/ ... |
|
||||
(unit_frequency_scale_factors(1,2)*0.1*10^(-6)); |
|
||||
|
|
||||
unit_low_pass_notch_resistors_1(1,2) = unit_low_pass_notch_resistors_1(1,2)* ... |
|
||||
unit_amplitude_scale_factors(1,2); % Ohm |
|
||||
unit_low_pass_notch_resistors_2(1,2) = unit_low_pass_notch_resistors_2(1,2)* ... |
|
||||
unit_amplitude_scale_factors(1,2); % Ohm |
|
||||
unit_low_pass_notch_resistors_3(1,2) = unit_low_pass_notch_resistors_3(1,2)* ... |
|
||||
unit_amplitude_scale_factors(1,2); % Ohm |
|
||||
unit_low_pass_notch_resistors_4(1,2) = unit_low_pass_notch_resistors_4(1,2)* ... |
|
||||
unit_amplitude_scale_factors(1,2); % Ohm |
|
||||
unit_low_pass_notch_resistors_5(1,2) = unit_low_pass_notch_resistors_5(1,2)* ... |
|
||||
unit_amplitude_scale_factors(1,2); % Ohm |
|
||||
unit_low_pass_notch_capacitors(1,2) = 0.1*10^(-6); % Farad |
|
||||
|
|
||||
% ========== DENORMALIZATION END ========== |
|
||||
|
|
||||
%% ========== GAIN ADJUSTMENT START ========== |
|
||||
|
|
||||
total_fried_units_attenuation = unit_low_pass_notch_gains_low(1,1)*unit_low_pass_notch_gains_low(1,2); |
|
||||
unit_adjustment_gain = 1/total_fried_units_attenuation; |
|
||||
% We arbitrarily choose to use a 10KOhm series resistor in the adjustment |
|
||||
% unit |
|
||||
unit_adjustment_feedback_resistor = 10*10^3*unit_adjustment_gain; |
|
||||
|
|
||||
% ========== GAIN ADJUSTMENT END ========== |
|
||||
|
|
||||
%% ========== TRANSFER FUNCTIONS START ========== |
|
||||
|
|
||||
% Builds numerator and denominator of the transfer function of each unit |
|
||||
% using the eq. 7-146, 7-147 & 7-148 |
|
||||
unit_1_numerator = [1 ... |
|
||||
(((unit_low_pass_notch_gains_high(1,1)-1)/ ... |
|
||||
(unit_low_pass_notch_gains_high(1,1)*unit_low_pass_notch_resistors_1(1,1)* ... |
|
||||
unit_low_pass_notch_capacitors(1,1)))+ ... |
|
||||
(2/(unit_low_pass_notch_resistors_2(1,1)* ... |
|
||||
unit_low_pass_notch_capacitors(1,1)))+ ... |
|
||||
(2/(unit_low_pass_notch_resistors_5(1,1)* ... |
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unit_low_pass_notch_capacitors(1,1)))) ... |
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(1/(unit_low_pass_notch_resistors_1(1,1)* ... |
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unit_low_pass_notch_resistors_5(1,1)*unit_low_pass_notch_capacitors(1,1)^2)+ ... |
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1/(unit_low_pass_notch_resistors_1(1,1)* ... |
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unit_low_pass_notch_resistors_2(1,1)*unit_low_pass_notch_capacitors(1,1)^2))]; |
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unit_1_denominator = [1 ... |
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2/(unit_low_pass_notch_resistors_2(1,1)* ... |
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unit_low_pass_notch_capacitors(1,1)) ... |
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1/(unit_low_pass_notch_resistors_1(1,1)* ... |
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unit_low_pass_notch_resistors_2(1,1)*unit_low_pass_notch_capacitors(1,1)^2)]; |
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unit_1_transfer_function = tf(unit_1_numerator, unit_1_denominator); |
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unit_1_transfer_function = unit_1_transfer_function*unit_low_pass_notch_gains_high(1,1); |
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unit_2_numerator = [1 ... |
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((unit_low_pass_notch_gains_high(1,2)-1)/ ... |
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(unit_low_pass_notch_gains_high(1,2)*unit_low_pass_notch_resistors_1(1,2)* ... |
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unit_low_pass_notch_capacitors(1,2))+ ... |
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2/(unit_low_pass_notch_resistors_2(1,2)* ... |
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unit_low_pass_notch_capacitors(1,2))+ ... |
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2/(unit_low_pass_notch_resistors_5(1,2)* ... |
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unit_low_pass_notch_capacitors(1,2))) ... |
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(1/(unit_low_pass_notch_resistors_1(1,2)* ... |
|
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unit_low_pass_notch_resistors_5(1,2)*unit_low_pass_notch_capacitors(1,2)^2)+ ... |
|
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1/(unit_low_pass_notch_resistors_1(1,2)* ... |
|
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unit_low_pass_notch_resistors_2(1,2)*unit_low_pass_notch_capacitors(1,2)^2))]; |
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unit_2_denominator = [1 ... |
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2/(unit_low_pass_notch_resistors_2(1,2)* ... |
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unit_low_pass_notch_capacitors(1,2)) ... |
|
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1/(unit_low_pass_notch_resistors_1(1,2)* ... |
|
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unit_low_pass_notch_resistors_2(1,2)*unit_low_pass_notch_capacitors(1,2)^2)]; |
|
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|
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unit_2_transfer_function = tf(unit_2_numerator, unit_2_denominator); |
|
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unit_2_transfer_function = unit_2_transfer_function*unit_low_pass_notch_gains_high(1,2); |
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|
|
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tmpHpRC = double(1)/double(0.1*10^(-6)*4.14*10^3); |
|
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unit_3_transfer_function = tf([0 tmpHpRC], [1 tmpHpRC]); |
|
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|
|
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total_transfer_function = series(series(unit_1_transfer_function,unit_2_transfer_function), unit_3_transfer_function); |
|
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total_transfer_function = total_transfer_function*unit_adjustment_gain; |
|
||||
%plot_transfer_function(unit_1_transfer_function, [1 10]); |
|
||||
%plot_transfer_function(unit_2_transfer_function, [1 192.82 222.817 234 238.73]); |
|
||||
%plot_transfer_function(0.656*series(unit_1_transfer_function,unit_2_transfer_function), ... |
|
||||
% [1 159.155 192.82 222.817 234 238.73]); |
|
||||
%{ |
|
||||
plot_transfer_function(total_transfer_function, ... |
|
||||
[1 ... |
|
||||
specification_pass_radial_frequency/(2*pi) ... |
|
||||
design_half_power_radial_frequency/(2*pi) ... |
|
||||
specification_stop_radial_frequency/(2*pi)]); |
|
||||
%} |
|
||||
|
|
||||
%ltiview(unit_1_transfer_function); |
|
||||
%ltiview(unit_2_transfer_function); |
|
||||
%ltiview(unit_3_transfer_function); |
|
||||
%ltiview(total_transfer_function); |
|
||||
%ltiview(unit_1_transfer_function, unit_2_transfer_function, ... |
|
||||
% unit_3_transfer_function, total_transfer_function); |
|
||||
|
|
||||
% Clears unneeded variable from workspace |
|
||||
clear tmpHpRC |
|
||||
clear -regexp _numerator$ |
|
||||
clear -regexp _denominator$ |
|
||||
clear -regexp _transfer_function$ |
|
||||
|
|
||||
% ========== TRANSFER FUNCTIONS END ========== |
|
||||
Loading…
Reference in new issue