Band elimination output init

Band Elimination Chebyshev/band_elimination_design.m

@@ -2,7 +2,7 @@
 %% $DATE     : 14-Aug-2018 15:32:12 $
 %% $Revision : 1.00 $
 %% DEVELOPED : 9.0.0.341360 (R2016a)
-%% FILENAME  : band_pass_design.m
+%% FILENAME  : band_elimination_design.m
 %% AEM       : 8261
 %%
 %% ========== DESIGN SPECIFICATIONS START ==========
@@ -46,6 +46,27 @@ specification_high_stop_radial_frequency = 2*pi* ...
 specification_min_stop_attenuation = 26+AEM(3)*5/9; % dB
 specification_max_pass_attenuation = 0.5+AEM(4)/18; % dB
 
+% Outputs results
+fprintf(['\n' '===== DESIGN SPECIFICATIONS =====' '\n' ...
+    'Filter design specifications:\n' ...
+    'Central frequency = %.3fHz = %.3frad/s\n' ...
+    'Low pass frequency = %.3fHz = %.3frad/s\n' ...
+    'High pass frequency = %.3fHz = %.3frad/s\n' ...
+    'Low stop frequency = %.3fHz = %.3frad/s\n' ...
+    'High stop frequency = %.3fHz = %.3frad/s\n' ...
+    'Min stop attenuation = %.3fdB\n' ...
+    'Max pass attenuation = %.3fdB\n'], ...
+    specification_central_frequency, specification_central_radial_frequency, ...
+    specification_low_pass_frequency, ...
+    specification_low_pass_radial_frequency, ...
+    specification_high_pass_frequency, ...
+    specification_high_pass_radial_frequency, ...
+    specification_low_stop_frequency, ...
+    specification_low_stop_radial_frequency, ...
+    specification_high_stop_frequency, ...
+    specification_high_stop_radial_frequency, ...
+    specification_min_stop_attenuation, specification_max_pass_attenuation);
+
 clear design_param_D
 
 % ========== DESIGN SPECIFICATIONS END ==========
@@ -73,19 +94,38 @@ design_geometric_central_radial_frequency = ...
 design_filter_bandwidth = specification_high_pass_radial_frequency- ...
     specification_low_pass_radial_frequency; % rad/s
 
+% Outputs results
+fprintf(['\n' '===== PROTOTYPE LOW PASS DESIGN SPECIFICATIONS =====' '\n' ...
+    'The prototype low pass filter will be designed with the\n' ...
+    'normalized stop radial frequency %.3frad/s, the normalized\n' ...
+    'pass radial frequency is equal to 1rad/s.\n' ...
+    'Min and max attenuation specifications remain the same.\n' ...
+    '\nThe filter bandwidth and geometric central frequency are also\n' ...
+    'calculated for later usage:\n' ...
+    'Filter bandwidth = %.3fHz = %.3frad/s\n' ...
+    'Geometric central frequency = %.3fHz = %.3frad/s\n' ...
+    '\nThe central frequency calculated is equal to the one given\n' ...
+    'in the specifications part, confirming the specifications\n' ...
+    'where calculated correctly.\n'], ...
+    prototype_normalized_stop_radial_frequency, ...
+    design_filter_bandwidth/(2*pi), design_filter_bandwidth, ...
+    design_geometric_central_radial_frequency/(2*pi), ...
+    design_geometric_central_radial_frequency);
+
 % ========== PROTOTYPE LOW PASS DESIGN SPECIFICATIONS END ==========
 
 %% ========== PROTOTYPE LOW PASS DESIGN START ==========
 % The calculated low pass design specifications have a form fit for a low
 % pass Chebyshev filter design (the pass radial frequency is normalized to
-% one).
+% unity).
 % Designs the prototype normalized filter.
 
 % Calculates the filter's order using the eq. 9-83
-design_filter_order = ceil(acosh(((10^ ...
+temp_filter_order = acosh(((10^ ...
     (specification_min_stop_attenuation/10)-1)/(10^ ...
     (specification_max_pass_attenuation/10)-1))^(1/2))/ ...
-    acosh(prototype_normalized_stop_radial_frequency));
+    acosh(prototype_normalized_stop_radial_frequency);
+design_filter_order = ceil(temp_filter_order);
 
 % Calculates epsilon parameter using the eq. 9-76
 epsilon_parameter = sqrt(10^(specification_max_pass_attenuation/10)-1);
@@ -190,11 +230,38 @@ else % Even number of poles
     end
 end
 
+% Outputs results
+fprintf(['\n' '===== PROTOTYPE LOW PASS DESIGN =====' '\n' ...
+    'A prototype low pass Chebyshev filter is designed with the\n' ...
+    'specifications previously calculated.\n\n' ...
+    'Filter order = %.3f\n' ...
+    'Filter order ceiling = %d\n' ...
+    'Epsilon parameter = %.3f\n' ...
+    'Alpha parameter = %.3f\n' ...
+    'Radial frequency at which half power occurs = %.3frad/s\n' ...
+    'Butterworth angles are ' char(177) '%.2f' char(176) ' and ' ...
+    char(177) '%.2f' char(176) '\n'], ...
+    temp_filter_order, design_filter_order, ...
+    epsilon_parameter, alpha_parameter, ...
+    design_half_power_radial_frequency, design_butterworth_angles(1,1), ...
+    design_butterworth_angles(1,2));
+
+fprintf('\nLow pass Chebyshev poles found:\n');
+for i=1:low_pass_prototype_number_of_poles
+    fprintf(['Pole %d:\t' '%.3f' char(177) ...
+        '%.3fi, radial frequency = %.3f, Q = %.3f\n'], ...
+        i, low_pass_prototype_poles_real_parts(1,i), ...
+        low_pass_prototype_poles_imaginary_parts(1,i), ...
+        low_pass_prototype_poles_radial_frequencies(1,i), ...
+        low_pass_prototype_poles_Q(1,i));
+end
+
 % Clears unneeded variables from workspace
 clearVars = {'prototype_normalized_stop_radial_frequency', ...
-    'epsilon_parameter', 'alpha_parameter', 'theta'};
+    'epsilon_parameter', 'alpha_parameter', 'theta', 'temp_filter_order'};
 clear(clearVars{:})
 clear clearVars
+
 % ========== PROTOTYPE LOW PASS DESIGN END ==========
 
 %% ========== LOW PASS TO HIGH PASS TRANSFORMATION START ==========
@@ -240,13 +307,28 @@ for i=1:high_pass_prototype_number_of_poles
         sind(high_pass_prototype_poles_angles(1,i));
 end
 
+% Outputs results
+fprintf(['\n' '===== LOW PASS TO HIGH PASS TRANSFORMATION =====' '\n' ...
+    'The prototype low pass Chebyshev filter is transformed into\n' ...
+    'a high pass Chebyshev using the transformation S = 1/s.\n']);
+
+fprintf('\nHigh pass Chebyshev poles found:\n');
+for i=1:low_pass_prototype_number_of_poles
+    fprintf(['Pole %d:\t' '%.3f' char(177) ...
+        '%.3fi, radial frequency = %.3f, Q = %.3f, angle = ' ...
+        char(177) '%.2f' char(176) '\n'], ...
+        i, high_pass_prototype_poles_real_parts(1,i), ...
+        high_pass_prototype_poles_imaginary_parts(1,i), ...
+        high_pass_prototype_poles_radial_frequencies(1,i), ...
+        high_pass_prototype_poles_Q(1,i), ...
+        high_pass_prototype_poles_angles(1,i));
+end
+
 % Clears unneeded variables from workspace
-%
 clearVars = {'i', 'high_pass_prototype_poles_radial_frequencies', ...
     'high_pass_prototype_poles_Q', 'high_pass_prototype_poles_angles'};
 clear(clearVars{:})
 clear clearVars
-%
 clear -regexp ^low_pass_prototype_
 
 % ========== LOW PASS TO HIGH PASS TRANSFORMATION END ==========
@@ -348,6 +430,26 @@ for i=1:high_pass_prototype_number_of_poles
     end
 end
 
+% Outputs results
+fprintf(['\n' '===== HIGH PASS TO BAND ELIMINATION TRANSFORMATION =====' '\n' ...
+    'The high pass Chebyshev filter is transformed into a band elimination\n' ...
+    'Chebyshev using the Geffe algorithm to transform the poles.\n']);
+
+fprintf('\nBand elimination Chebyshev poles found:\n');
+for i=1:band_elimination_number_of_poles
+    fprintf(['Pole %d:\t' 'radial frequency = %.3f, Q = %.3f, angle = ' ...
+        char(177) '%.2f' char(176) '\n'], ...
+        i, band_elimination_poles_radial_frequencies(1,i), ...
+        band_elimination_poles_Q(1,i), ...
+        band_elimination_poles_angle(1,i));
+end
+
+fprintf('\nTransfer function zeros:\n');
+for i=1:length(band_elimination_transfer_function_zeros)
+    fprintf(['Zero %d:\t' '0%+.3fi\n'], ...
+        i, imag(band_elimination_transfer_function_zeros(1,i)));
+end
+
 % Clears unneeded variables from workspace
 clearVars = {'i', 'temp_index'};
 clear(clearVars{:})
@@ -355,6 +457,7 @@ clear clearVars
 clear -regexp ^high_pass_prototype_
 clear -regexp ^geffe_
 clear -regexp ^transformation_
+
 % ========== POLES TRANSFORMATION END ==========
 
 %% ========== ZEROS-POLES GROUPING START ==========
@@ -386,7 +489,7 @@ clear -regexp ^transformation_
 
 %% ========== UNITS IMPLEMENTATION START ==========
 % AEM(3) = 6, so the circuits shown in 7.21 and 7.23 are going to be used
-% for the low pass notch units.
+% for the notch units.
 
 % High pass notch units 1 and 3
 % Initializes necessary arrays, each array is 1X2, the first element (1,1)
@@ -594,6 +697,63 @@ for i=1:2
         low_pass_notch_units_gains_high(1,i);
 end
 
+% Outputs results
+fprintf(['\n' '===== UNITS IMPLEMENTATION =====' '\n' ...
+    'Pole-zero pairing results in the implementation of two high\n' ...
+    'pass notch (HPN) units and two low pass notch (LPN) units.\n' ...
+    '\nUnits implementation details:\n']);
+for i=1:band_elimination_number_of_poles
+    if i==1 || i==3
+        fprintf(['Unit %d (HPN):\n' ...
+        '\tPole radial frequency = %.3f\n'...
+        '\tPole Q = %.3f\n' ...
+        '\tTransfer function zero = 0' char(177) '%.3fi\n' ...
+        '\tCircuit elements:\n' ...
+        '\t\tR1 = %.3fOhm\n' ...
+        '\t\tR2 = %.3fOhm\n' ...
+        '\t\tR3 = %.3fOhm\n' ...
+        '\t\tR4 = %.3fOhm\n' ...
+        '\t\tC = %.7fF\n' ...
+        '\t\tC1 = %.9fF\n' ...
+        '\tUnit gain at high frequencies = %.3f\n'], ...
+        i, band_elimination_poles_radial_frequencies(1,i), ...
+        band_elimination_poles_Q(1,i), ...
+        abs(imag(band_elimination_transfer_function_zeros(1,i))), ...
+        high_pass_notch_units_R1(1,(i+1)/2), ...
+        high_pass_notch_units_R2(1,(i+1)/2), ...
+        high_pass_notch_units_R3(1,(i+1)/2), ...
+        high_pass_notch_units_R4(1,(i+1)/2), ...
+        high_pass_notch_units_C(1,(i+1)/2), ...
+        high_pass_notch_units_C1(1,(i+1)/2), ...
+        high_pass_notch_units_gain_high(1,(i+1)/2));
+    else
+        fprintf(['Unit %d (LPN):\n' ...
+        '\tPole radial frequency = %.3f\n'...
+        '\tPole Q = %.3f\n' ...
+        '\tTransfer function zero = 0' char(177) '%.3fi\n' ...
+        '\tCircuit elements:\n' ...
+        '\t\tR1 = %.3fOhm\n' ...
+        '\t\tR2 = %.3fOhm\n' ...
+        '\t\tR3 = %.3fOhm\n' ...
+        '\t\tR4 = %.3fOhm\n' ...
+        '\t\tR5 = %.3fOhm\n' ...
+        '\t\tC = %.7fF\n' ...
+        '\tUnit gain at low frequencies = %.3f\n' ...
+        '\tUnit gain at high frequencies = %.3f\n'], ...
+        i, band_elimination_poles_radial_frequencies(1,i), ...
+        band_elimination_poles_Q(1,i), ...
+        abs(imag(band_elimination_transfer_function_zeros(1,i))), ...
+        low_pass_notch_units_resistors_1(1,i/2), ...
+        low_pass_notch_units_resistors_2(1,i/2), ...
+        low_pass_notch_units_resistors_3(1,i/2), ...
+        low_pass_notch_units_resistors_4(1,i/2), ...
+        low_pass_notch_units_resistors_5(1,i/2), ...
+        low_pass_notch_units_capacitors(1,i/2), ...
+        low_pass_notch_units_gains_low(1,i/2), ...
+        low_pass_notch_units_gains_high(1,i/2));
+    end
+end
+
 % Clears unneeded variable from workspace
 clearVars = {'i', 'temp', 'unit_index', 'normalized_transfer_function_zero'};
 clear(clearVars{:})
@@ -622,6 +782,17 @@ total_transfer_function = series(series(series( ...
 
 total_transfer_function = total_transfer_function*unit_adjustment_gain;
 
+fprintf(['\n' '===== GAIN ADJUSTMENT =====' '\n' ...
+    'A gain adjustment unit is needed to achieve 0dB attenuation at ' ...
+    'pass band.\n' ...
+    'We arbitrarily choose to use a 10KOhm series resistor.\n' ...
+    'The feedback resistor is %.3fOhm to get a gain equal to %.3fdB\n'], ...
+    unit_adjustment_feedback_resistor, unit_adjustment_gain);
+
+% ========== GAIN ADJUSTMENT END ==========
+
+%% ========== TRANSFER FUNCTIONS START ==========
+
 %{
 ltiview(high_pass_notch_units_transfer_functions(1,1), ...
     high_pass_notch_units_transfer_functions(1,2));
@@ -649,16 +820,14 @@ ltiview(high_pass_notch_units_transfer_functions(1,1), ...
 
 %ltiview(total_transfer_function);
 
-%
+%{
 plot_transfer_function(total_transfer_function, ...
-    [specification_central_frequency ...
+    [specification_low_stop_frequency ...
-    band_elimination_poles_radial_frequencies(1,1)/(2*pi) ...
-    design_half_power_radial_frequency*specification_low_pass_radial_frequency/(2*pi) ...
-    specification_low_stop_frequency ...
     specification_low_pass_frequency ...
+    specification_central_frequency ...
     specification_high_pass_frequency ...
     specification_high_stop_frequency]);
-%
+%}
  
 % Clears unneeded variable from workspace
 clearVars = {'total_transfer_function'};
@@ -666,4 +835,4 @@ clear(clearVars{:})
 clear clearVars
 clear -regexp _transfer_functions$
 
-% ========== GAIN ADJUSTMENT END ==========
+% ========== TRANSFER FUNCTIONS END ==========