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@ -29,16 +29,19 @@ specification_stop_radial_frequency = ... |
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specification_min_stop_attenuation = 24+AEM(4)*(6/9); % dB |
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specification_max_pass_attenuation = 0.5+AEM(3)/36; % dB |
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clear design_param_m |
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% Outputs results |
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fprintf(['\n' '===== DESIGN SPECIFICATIONS =====' '\n' ... |
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'Filter design specifications:\n' ... |
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'Pass frequency = %.3fHz = %.3frad/s\n' ... |
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'Stop frequency = %.3fHz = %.3frad/s\n' ... |
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'Min stop attenuation = %.3fdB\n' ... |
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'Max pass attenuation = %.3fdB\n'], ... |
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specification_pass_frequency, specification_pass_radial_frequency, ... |
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specification_stop_frequency, specification_stop_radial_frequency, ... |
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specification_min_stop_attenuation, specification_max_pass_attenuation); |
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%{ |
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specification_pass_radial_frequency = 15707.96; % rad/s |
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specification_stop_radial_frequency = 6283.2; % rad/s |
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clear design_param_m |
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specification_min_stop_attenuation = 25; % dB |
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specification_max_pass_attenuation = 0.5; % dB |
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%} |
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% ========== DESIGN SPECIFICATIONS END ========== |
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%% ========== PROTOTYPE LOW PASS DESIGN SPECIFICATIONS START ========== |
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@ -53,16 +56,25 @@ prototype_normalized_stop_radial_frequency = ... |
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% Min and max attenuations remain the same |
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% Outputs results |
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fprintf(['\n' '===== PROTOTYPE LOW PASS DESIGN SPECIFICATIONS =====' '\n' ... |
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'The prototype low pass filter will be designed with the\n' ... |
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'normalized stop radial frequency %.3frad/s, the normalized\n' ... |
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'pass radial frequency is equal to 1rad/s.\n' ... |
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'Min and max attenuation specifications remain the same.\n'], ... |
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prototype_normalized_stop_radial_frequency); |
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% ========== PROTOTYPE LOW PASS DESIGN SPECIFICATIONS END ========== |
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%% ========== PROTOTYPE LOW PASS DESIGN START ========== |
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% Designs the prototype normalized filter. |
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% Calculates the filter's order using the eq. 9-52 |
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design_filter_order = ceil(log10(((10^ ... |
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temp_filter_order = log10(((10^ ... |
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(specification_min_stop_attenuation/10)-1)/(10^ ... |
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(specification_max_pass_attenuation/10)-1)))/ ... |
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(2*log10(prototype_normalized_stop_radial_frequency))); |
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(2*log10(prototype_normalized_stop_radial_frequency)); |
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design_filter_order = ceil(temp_filter_order); |
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% Calculates the frequency at which half power of the low pass prototype |
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% occurs using the eq. 9-48 |
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@ -162,13 +174,34 @@ else % Even number of poles |
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end |
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end |
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% Outputs results |
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fprintf(['\n' '===== PROTOTYPE LOW PASS DESIGN =====' '\n' ... |
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'A prototype low pass Butterworth filter is designed with the\n' ... |
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'specifications previously calculated.\n\n' ... |
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'Filter order = %.3f\n' ... |
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'Filter order ceiling = %d\n' ... |
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'Radial frequency at which half power occurs = %.3frad/s\n' ... |
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'Butterworth angles are ' char(177) '%.2f' char(176) ' and ' ... |
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char(177) '%.2f' char(176) '\n'], ... |
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temp_filter_order, design_filter_order, ... |
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design_half_power_radial_frequency, design_butterworth_angles(1,1), ... |
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design_butterworth_angles(1,2)); |
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fprintf('\nLow pass Butterworth poles found:\n'); |
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for i=1:low_pass_prototype_number_of_poles |
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fprintf(['Pole %d:\t' '%.3f' char(177) ... |
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'%.3fi, radial frequency = %.3f, Q = %.3f\n'], ... |
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i, low_pass_prototype_poles_real_parts(1,i), ... |
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low_pass_prototype_poles_imaginary_parts(1,i), ... |
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low_pass_prototype_poles_radial_frequencies(1,i), ... |
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low_pass_prototype_poles_Q(1,i)); |
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end |
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% Clears unneeded variables from workspace |
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% |
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clearVars = {'i', 'prototype_normalized_stop_radial_frequency', ... |
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'low_pass_prototype_half_power_radial_frequency', 'theta'}; |
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clear(clearVars{:}) |
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clear clearVars |
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% |
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% ========== PROTOTYPE LOW PASS DESIGN END ========== |
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@ -192,6 +225,27 @@ high_pass_poles_Q = low_pass_prototype_poles_Q; |
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% filter order |
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high_pass_transfer_function_zeros = zeros([1 design_filter_order]); |
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% Outputs results |
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fprintf(['\n' '===== LOW PASS TO HIGH PASS TRANSFORMATION =====' '\n' ... |
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'The prototype low pass Butterworth filter is transformed into\n' ... |
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'a high pass Butterworth using the transformation S = 1/s.\n']); |
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fprintf('\nHigh pass Butterworth normalized poles found:\n'); |
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for i=1:high_pass_number_of_poles |
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fprintf(['Pole %d:\t' '%.3f' char(177) ... |
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'%.3fi, radial frequency = %.3f, Q = %.3f\n'], ... |
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i, high_pass_poles_real_parts(1,i), ... |
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high_pass_poles_imaginary_parts(1,i), ... |
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high_pass_poles_radial_frequencies(1,i), ... |
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high_pass_poles_Q(1,i)); |
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end |
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fprintf('\nTransfer function zeros:\n'); |
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for i=1:length(high_pass_transfer_function_zeros) |
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fprintf(['Zero %d:\t' '0%+.3fi\n'], ... |
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i, high_pass_transfer_function_zeros(1,i)); |
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end |
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% Clears unneeded variables from workspace |
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clear low_pass_prototype_number_of_poles |
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clear -regexp ^low_pass_prototype_ |
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@ -213,6 +267,21 @@ for i=1:high_pass_number_of_poles |
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design_half_power_radial_frequency; |
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end |
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% Outputs results |
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fprintf(['\n' '===== POLES DE-NORMALIZATION =====' '\n' ... |
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'The high pass filter designed is normalized.\n' ... |
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'The poles are de-normalized.\n']); |
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fprintf('\nHigh pass Butterworth poles found:\n'); |
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for i=1:high_pass_number_of_poles |
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fprintf(['Pole %d:\t' '%.3f' char(177) ... |
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'%.3fi, radial frequency = %.3f, Q = %.3f\n'], ... |
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i, high_pass_poles_real_parts(1,i), ... |
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high_pass_poles_imaginary_parts(1,i), ... |
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high_pass_poles_radial_frequencies(1,i), ... |
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high_pass_poles_Q(1,i)); |
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end |
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% Clears unneeded variables from workspace |
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clear i |
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clear -regexp ^geffe_ |
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@ -283,10 +352,30 @@ for i=1:high_pass_number_of_poles |
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tf(unit_numerator, unit_denominator); |
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end |
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% Outputs results |
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fprintf(['\n' '===== UNITS IMPLEMENTATION =====' '\n' ... |
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'Units implementation details:\n']); |
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for i=1:high_pass_number_of_poles |
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fprintf(['Unit %d:\n' ... |
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'\tPole radial frequency = %.3f\n'... |
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'\tPole Q = %.3f\n' ... |
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'\tTransfer function zero = 0%+.3fi (double)\n' ... |
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'\tCircuit elements:\n' ... |
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'\t\tR1 = %.3fOhm\n' ... |
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'\t\tR2 = %.3fOhm\n' ... |
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'\t\tr1 = %.3fOhm\n' ... |
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'\t\tr2 = %.3fOhm\n' ... |
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'\t\tC1 = %.7fF\n' ... |
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'\t\tC2 = %.7fF\n'], ... |
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i, high_pass_poles_radial_frequencies(1,i), ... |
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high_pass_poles_Q(1,i), ... |
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high_pass_transfer_function_zeros(1,i), ... |
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units_R(1,i), units_R(1,i), units_r1(1,i), units_r2(1,i), ... |
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units_C(1,i), units_C(1,i)); |
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end |
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% Clears unneeded variables from workspace |
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clearVars = {''}; |
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clearVars = {'i'}; |
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clear(clearVars{:}) |
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clear clearVars |
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clear -regexp _transfer_function$ |
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@ -320,13 +409,13 @@ ltiview(units_transfer_functions(1,1), ... |
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%ltiview(total_transfer_function); |
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% |
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%{ |
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plot_transfer_function(total_transfer_function, ... |
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[design_half_power_radial_frequency/(2*pi) ... |
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specification_stop_frequency ... |
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specification_pass_frequency ... |
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15000]); |
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% |
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%} |
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% Clears unneeded variable from workspace |
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clearVars = {'total_transfer_function'}; |
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