Complete band elimination units and transfer functions

Band Elimination Chebyshev/band_elimination_design.m

@@ -390,8 +390,8 @@ clear -regexp ^transformation_
 % grouped with a zero at 0.0 + 15707.96 i, resulting in a low pass notch.
 % -------------------------------------------------------------------------
 
-% Two low pass notch units are required to implement the desired band
+% Two low pass notch units and two high pass notch units are required to
-% elimination filter.
+% implement the desired band elimination filter.
 
 % ========== ZEROS-POLES GROUPING END ==========
 
@@ -418,18 +418,20 @@ high_pass_notch_units_transfer_functions = [tf(1) tf(1)];
 
 for i=1:2
     unit_index = i*2-1;
+    
+    % normalized_pole_radial_frequency = 1;
+    normalized_transfer_function_zero = ...
+        abs(band_elimination_transfer_function_zeros(1,i))/ ...
+        band_elimination_poles_radial_frequencies(1,unit_index);
     % Calculates k1 design parameter using the eq. 7-135
-    high_pass_notch_units_k1(1,i) = ...
+    high_pass_notch_units_k1(1,i) = 1/normalized_transfer_function_zero^2-1;
-        band_elimination_poles_radial_frequencies(1,unit_index)^2/ ...
-        abs(band_elimination_transfer_function_zeros(1,i))^2-1;
     % Calculates k2 design parameter using the eq. 7-136
     temp = (2+high_pass_notch_units_k1(1,i))* ...
         band_elimination_poles_Q(1,unit_index)^2;
     high_pass_notch_units_k2(1,i) = temp/(temp+1);
     % Calculates k (unit's gain at high frequencies) using the eq. 7-137
     high_pass_notch_units_gain_high(1,i) = high_pass_notch_units_k2(1,i)* ...
-        (band_elimination_poles_radial_frequencies(1,unit_index)^2/ ...
+        (1/normalized_transfer_function_zero^2);
-        abs(band_elimination_transfer_function_zeros(1,i))^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;
@@ -475,15 +477,15 @@ for i=1:2
         (high_pass_notch_units_frequency_scale_factors(1,i)* ...
         high_pass_notch_units_amplitude_scale_factors(1,i));
     
-    % Builds unit's transfer function
+    % Builds unit's transfer function using the eq. 7-129, 7-130, 7-131
     high_pass_notch_unit_numerator = [1 ...
         0 ...
-        1/(high_pass_notch_units_R2(1,i)*high_pass_notch_units_C(1,i)^2* ...
+        1/(high_pass_notch_units_R1(1,i)*high_pass_notch_units_R2(1,i)*high_pass_notch_units_C(1,i)^2* ...
         (high_pass_notch_units_k1(1,i)+1))];
     high_pass_notch_unit_denominator = [1 ...
         (2+high_pass_notch_units_k1(1,i))/ ...
         (high_pass_notch_units_R2(1,i)*high_pass_notch_units_C(1,i)) ...
-        1/(high_pass_notch_units_R2(1,i)*high_pass_notch_units_C(1,i)^2)];
+        1/(high_pass_notch_units_R1(1,i)*high_pass_notch_units_R2(1,i)*high_pass_notch_units_C(1,i)^2)];
     
     high_pass_notch_units_transfer_functions(1,i) = tf( ...
         high_pass_notch_unit_numerator, high_pass_notch_unit_denominator);
@@ -492,18 +494,186 @@ for i=1:2
         high_pass_notch_units_gain_high(1,i);
 end
 
-plot_transfer_function(high_pass_notch_units_transfer_functions(1,1));
+% Low pass notch units 2 and 4
-%ltiview(high_pass_notch_units_transfer_functions(1,1));
+% Initializes necessary arrays, each array is 1X2, the first element (1,1)
+% corresponds to the first unit (unit 2) and the second element (1,2) to
+% second unit (unit 4).
+low_pass_notch_units_resistors_1 = zeros([1 2]);
+low_pass_notch_units_resistors_2 = zeros([1 2]);
+low_pass_notch_units_resistors_3 = zeros([1 2]);
+low_pass_notch_units_resistors_4 = zeros([1 2]);
+low_pass_notch_units_resistors_5 = zeros([1 2]);
+low_pass_notch_units_capacitors = zeros([1 2]);
+low_pass_notch_units_gains_high = zeros([1 2]);
+low_pass_notch_units_gains_low = zeros([1 2]);
+low_pass_notch_units_frequency_scale_factors = zeros([1 2]);
+low_pass_notch_units_amplitude_scale_factors = zeros([1 2]);
+low_pass_notch_units_transfer_functions = [tf(1) tf(1)];
+
+for i=1:2
+    unit_index = i*2;
+    
+    % normalized_inverse_pole_radial_frequency = 1;
+    normalized_transfer_function_zero = ...
+        abs(band_elimination_transfer_function_zeros(1,unit_index))/ ...
+        band_elimination_poles_radial_frequencies(1,unit_index);
+
+    % According to the design method outlined in 7.6-B, at page 35
+    low_pass_notch_units_resistors_1(1,i) = 1; % Ohm
+    % Calculates the capacity of the normalized circuit capacitors using
+    % the eq. 7-150
+    low_pass_notch_units_capacitors(1,i) = 1/ ...
+        (2*band_elimination_poles_Q(1,unit_index)); % Farad
+    % Calculates the resistance of R2 using the same equations (7-150)
+    low_pass_notch_units_resistors_2(1,i) = 4* ...
+        band_elimination_poles_Q(1,unit_index)^2; % Ohm
+    % Calculates the resistance of R5 using the eq. 7-152
+    low_pass_notch_units_resistors_5(1,i) = ...
+        (4*band_elimination_poles_Q(1,unit_index)^2)/ ...
+        (normalized_transfer_function_zero^2-1); % Ohm
+    low_pass_notch_units_resistors_4(1,i) = 1; % Ohm
+    % Calculates the resistance of R3 using the eq. 7-155
+    low_pass_notch_units_resistors_3(1,i) = ...
+        (normalized_transfer_function_zero^2)/ ...
+        (2*band_elimination_poles_Q(1,unit_index)^2); % Ohm
+    % Calculates the gain of this unit in high frequencies using the eq. 7-143
+    low_pass_notch_units_gains_high(1,i) = ...
+        (low_pass_notch_units_resistors_4(1,i))/ ...
+        (low_pass_notch_units_resistors_3(1,i)+ ...
+        low_pass_notch_units_resistors_4(1,i));
+    % Calculates the gain of this unit in low frequencies using the
+    % eq. 7-146, 7-147, 7-148, setting s = 0
+    low_pass_notch_units_gains_low(1,i) = ...
+        low_pass_notch_units_gains_high(1,i)* ...
+        normalized_transfer_function_zero^2;
+    
+    % Performs scaling
+    low_pass_notch_units_frequency_scale_factors(1,i) = ...
+        band_elimination_poles_radial_frequencies(1,unit_index);
+    % AEM(4) = 1, so the scaling will be performed to achieve a capacitor
+    % value of 0.1uF using the eq. 6-33
+    low_pass_notch_units_amplitude_scale_factors(1,i) = ...
+        low_pass_notch_units_capacitors(1,i)/ ...
+        (low_pass_notch_units_frequency_scale_factors(1,i)*0.1*10^(-6));
+    
+    low_pass_notch_units_resistors_1(1,i) = ...
+        low_pass_notch_units_resistors_1(1,i)* ...
+        low_pass_notch_units_amplitude_scale_factors(1,i); % Ohm
+    low_pass_notch_units_resistors_2(1,i) = ...
+        low_pass_notch_units_resistors_2(1,i)* ...
+        low_pass_notch_units_amplitude_scale_factors(1,i); % Ohm
+    low_pass_notch_units_resistors_3(1,i) = ...
+        low_pass_notch_units_resistors_3(1,i)* ...
+        low_pass_notch_units_amplitude_scale_factors(1,i); % Ohm
+    low_pass_notch_units_resistors_4(1,i) = ...
+        low_pass_notch_units_resistors_4(1,i)* ...
+        low_pass_notch_units_amplitude_scale_factors(1,i); % Ohm
+    low_pass_notch_units_resistors_5(1,i) = ...
+        low_pass_notch_units_resistors_5(1,i)* ...
+        low_pass_notch_units_amplitude_scale_factors(1,i); % Ohm
+    low_pass_notch_units_capacitors(1,i) = 0.1*10^(-6); % Farad
+    
+    % Builds unit's transfer function
+    % Builds numerator and denominator of the transfer function using the
+    % eq. 7-146, 7-147 & 7-148
+    unit_numerator = [1 ...
+        (((low_pass_notch_units_gains_high(1,i)-1)/ ...
+        (low_pass_notch_units_gains_high(1,i)* ...
+        low_pass_notch_units_resistors_1(1,i)* ...
+        low_pass_notch_units_capacitors(1,i)))+ ...
+        (2/(low_pass_notch_units_resistors_2(1,i)* ...
+        low_pass_notch_units_capacitors(1,i)))+ ...
+        (2/(low_pass_notch_units_resistors_5(1,i)* ...
+        low_pass_notch_units_capacitors(1,i)))) ...
+        (1/(low_pass_notch_units_resistors_1(1,i)* ...
+        low_pass_notch_units_resistors_5(1,i)* ...
+        low_pass_notch_units_capacitors(1,i)^2)+ ...
+        1/(low_pass_notch_units_resistors_1(1,i)* ...
+        low_pass_notch_units_resistors_2(1,i)* ...
+        low_pass_notch_units_capacitors(1,i)^2))];
+    unit_denominator = [1 ...
+        2/(low_pass_notch_units_resistors_2(1,i)* ...
+        low_pass_notch_units_capacitors(1,i)) ...
+        1/(low_pass_notch_units_resistors_1(1,i)* ...
+        low_pass_notch_units_resistors_2(1,i)* ...
+        low_pass_notch_units_capacitors(1,i)^2)];
+
+    low_pass_notch_units_transfer_functions(1,i) = ...
+        tf(unit_numerator, unit_denominator);
+    low_pass_notch_units_transfer_functions(1,i) = ...
+        low_pass_notch_units_transfer_functions(1,i)* ...
+        low_pass_notch_units_gains_high(1,i);
+end
+
+% Clears unneeded variable from workspace
+clearVars = {'i', 'temp', 'unit_index', 'normalized_transfer_function_zero'};
+clear(clearVars{:})
+clear clearVars
+clear -regexp _numerator$
+clear -regexp _denominator$
+
+% ========== UNITS IMPLEMENTATION END ==========
+
+%% ========== GAIN ADJUSTMENT START ==========
+
+total_gain_high = high_pass_notch_units_gain_high(1,1)* ...
+    high_pass_notch_units_gain_high(1,2)* ...
+    low_pass_notch_units_gains_high(1,1)* ...
+    low_pass_notch_units_gains_high(1,2);
+unit_adjustment_gain = 1/total_gain_high;
+% We arbitrarily choose to use a 10KOhm series resistor in the adjustment
+% unit
+unit_adjustment_feedback_resistor = 10*10^3*unit_adjustment_gain;
+
+total_transfer_function = series(series(series( ...
+    high_pass_notch_units_transfer_functions(1,1), ...
+    high_pass_notch_units_transfer_functions(1,2)), ...
+    low_pass_notch_units_transfer_functions(1,1)), ...
+    low_pass_notch_units_transfer_functions(1,2));
+
+total_transfer_function = total_transfer_function*unit_adjustment_gain;
 
 %{
 ltiview(high_pass_notch_units_transfer_functions(1,1), ...
-    high_pass_notch_units_transfer_functions(1,2), ...
+    high_pass_notch_units_transfer_functions(1,2));
-    series(high_pass_notch_units_transfer_functions(1,1), ...
-    high_pass_notch_units_transfer_functions(1,2)));
 %}
 
-% ========== UNITS IMPLEMENTATION END ==========
+%{
+ltiview(low_pass_notch_units_transfer_functions(1,1), ...
+    low_pass_notch_units_transfer_functions(1,2));
+%}
 
+%{
+ltiview(high_pass_notch_units_transfer_functions(1,1), ...
+    high_pass_notch_units_transfer_functions(1,2), ...
+    low_pass_notch_units_transfer_functions(1,1), ...
+    low_pass_notch_units_transfer_functions(1,2));
+%}
+
+%{
+ltiview(high_pass_notch_units_transfer_functions(1,1), ...
+    high_pass_notch_units_transfer_functions(1,2), ...
+    low_pass_notch_units_transfer_functions(1,1), ...
+    low_pass_notch_units_transfer_functions(1,2), ...
+    total_transfer_function);
+%}
 
+%ltiview(total_transfer_function);
 
+%
+plot_transfer_function(total_transfer_function, ...
+    [specification_central_frequency ...
+    design_half_power_radial_frequency/(2*pi) ...
+    specification_low_stop_frequency ...
+    specification_low_pass_frequency ...
+    specification_high_pass_frequency ...
+    specification_high_stop_frequency]);
+%
+ 
+% Clears unneeded variable from workspace
+clearVars = {'total_transfer_function'};
+clear(clearVars{:})
+clear clearVars
+clear -regexp _transfer_functions$
 
+% ========== GAIN ADJUSTMENT END ==========