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@ -390,8 +390,8 @@ clear -regexp ^transformation_ |
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% grouped with a zero at 0.0 + 15707.96 i, resulting in a low pass notch. |
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% ------------------------------------------------------------------------- |
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% Two low pass notch units are required to implement the desired band |
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% elimination filter. |
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% Two low pass notch units and two high pass notch units are required to |
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% implement the desired band elimination filter. |
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% ========== ZEROS-POLES GROUPING END ========== |
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@ -418,18 +418,20 @@ high_pass_notch_units_transfer_functions = [tf(1) tf(1)]; |
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for i=1:2 |
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unit_index = i*2-1; |
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% normalized_pole_radial_frequency = 1; |
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normalized_transfer_function_zero = ... |
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abs(band_elimination_transfer_function_zeros(1,i))/ ... |
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band_elimination_poles_radial_frequencies(1,unit_index); |
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% Calculates k1 design parameter using the eq. 7-135 |
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high_pass_notch_units_k1(1,i) = ... |
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band_elimination_poles_radial_frequencies(1,unit_index)^2/ ... |
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abs(band_elimination_transfer_function_zeros(1,i))^2-1; |
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high_pass_notch_units_k1(1,i) = 1/normalized_transfer_function_zero^2-1; |
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% Calculates k2 design parameter using the eq. 7-136 |
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temp = (2+high_pass_notch_units_k1(1,i))* ... |
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band_elimination_poles_Q(1,unit_index)^2; |
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high_pass_notch_units_k2(1,i) = temp/(temp+1); |
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% Calculates k (unit's gain at high frequencies) using the eq. 7-137 |
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high_pass_notch_units_gain_high(1,i) = high_pass_notch_units_k2(1,i)* ... |
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(band_elimination_poles_radial_frequencies(1,unit_index)^2/ ... |
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abs(band_elimination_transfer_function_zeros(1,i))^2); |
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(1/normalized_transfer_function_zero^2); |
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% Calculates R2 using the eq. 7-138 |
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high_pass_notch_units_R2(1,i) = band_elimination_poles_Q(1,unit_index)^2* ... |
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(high_pass_notch_units_k1(1,i)+2)^2; |
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@ -475,15 +477,15 @@ for i=1:2 |
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(high_pass_notch_units_frequency_scale_factors(1,i)* ... |
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high_pass_notch_units_amplitude_scale_factors(1,i)); |
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% Builds unit's transfer function |
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% Builds unit's transfer function using the eq. 7-129, 7-130, 7-131 |
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high_pass_notch_unit_numerator = [1 ... |
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0 ... |
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1/(high_pass_notch_units_R2(1,i)*high_pass_notch_units_C(1,i)^2* ... |
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1/(high_pass_notch_units_R1(1,i)*high_pass_notch_units_R2(1,i)*high_pass_notch_units_C(1,i)^2* ... |
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(high_pass_notch_units_k1(1,i)+1))]; |
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high_pass_notch_unit_denominator = [1 ... |
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(2+high_pass_notch_units_k1(1,i))/ ... |
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(high_pass_notch_units_R2(1,i)*high_pass_notch_units_C(1,i)) ... |
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1/(high_pass_notch_units_R2(1,i)*high_pass_notch_units_C(1,i)^2)]; |
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1/(high_pass_notch_units_R1(1,i)*high_pass_notch_units_R2(1,i)*high_pass_notch_units_C(1,i)^2)]; |
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high_pass_notch_units_transfer_functions(1,i) = tf( ... |
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high_pass_notch_unit_numerator, high_pass_notch_unit_denominator); |
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@ -492,18 +494,186 @@ for i=1:2 |
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high_pass_notch_units_gain_high(1,i); |
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end |
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plot_transfer_function(high_pass_notch_units_transfer_functions(1,1)); |
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%ltiview(high_pass_notch_units_transfer_functions(1,1)); |
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% Low pass notch units 2 and 4 |
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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 (unit 2) and the second element (1,2) to |
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% second unit (unit 4). |
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low_pass_notch_units_resistors_1 = zeros([1 2]); |
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low_pass_notch_units_resistors_2 = zeros([1 2]); |
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low_pass_notch_units_resistors_3 = zeros([1 2]); |
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low_pass_notch_units_resistors_4 = zeros([1 2]); |
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low_pass_notch_units_resistors_5 = zeros([1 2]); |
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low_pass_notch_units_capacitors = zeros([1 2]); |
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low_pass_notch_units_gains_high = zeros([1 2]); |
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low_pass_notch_units_gains_low = zeros([1 2]); |
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low_pass_notch_units_frequency_scale_factors = zeros([1 2]); |
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low_pass_notch_units_amplitude_scale_factors = zeros([1 2]); |
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low_pass_notch_units_transfer_functions = [tf(1) tf(1)]; |
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for i=1:2 |
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unit_index = i*2; |
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% normalized_inverse_pole_radial_frequency = 1; |
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normalized_transfer_function_zero = ... |
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abs(band_elimination_transfer_function_zeros(1,unit_index))/ ... |
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band_elimination_poles_radial_frequencies(1,unit_index); |
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% According to the design method outlined in 7.6-B, at page 35 |
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low_pass_notch_units_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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low_pass_notch_units_capacitors(1,i) = 1/ ... |
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(2*band_elimination_poles_Q(1,unit_index)); % Farad |
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% Calculates the resistance of R2 using the same equations (7-150) |
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low_pass_notch_units_resistors_2(1,i) = 4* ... |
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band_elimination_poles_Q(1,unit_index)^2; % Ohm |
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% Calculates the resistance of R5 using the eq. 7-152 |
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low_pass_notch_units_resistors_5(1,i) = ... |
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(4*band_elimination_poles_Q(1,unit_index)^2)/ ... |
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(normalized_transfer_function_zero^2-1); % Ohm |
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low_pass_notch_units_resistors_4(1,i) = 1; % Ohm |
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% Calculates the resistance of R3 using the eq. 7-155 |
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low_pass_notch_units_resistors_3(1,i) = ... |
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(normalized_transfer_function_zero^2)/ ... |
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(2*band_elimination_poles_Q(1,unit_index)^2); % Ohm |
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% Calculates the gain of this unit in high frequencies using the eq. 7-143 |
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low_pass_notch_units_gains_high(1,i) = ... |
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(low_pass_notch_units_resistors_4(1,i))/ ... |
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(low_pass_notch_units_resistors_3(1,i)+ ... |
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low_pass_notch_units_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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low_pass_notch_units_gains_low(1,i) = ... |
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low_pass_notch_units_gains_high(1,i)* ... |
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normalized_transfer_function_zero^2; |
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% Performs scaling |
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low_pass_notch_units_frequency_scale_factors(1,i) = ... |
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band_elimination_poles_radial_frequencies(1,unit_index); |
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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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low_pass_notch_units_amplitude_scale_factors(1,i) = ... |
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low_pass_notch_units_capacitors(1,i)/ ... |
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(low_pass_notch_units_frequency_scale_factors(1,i)*0.1*10^(-6)); |
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low_pass_notch_units_resistors_1(1,i) = ... |
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low_pass_notch_units_resistors_1(1,i)* ... |
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low_pass_notch_units_amplitude_scale_factors(1,i); % Ohm |
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low_pass_notch_units_resistors_2(1,i) = ... |
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low_pass_notch_units_resistors_2(1,i)* ... |
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low_pass_notch_units_amplitude_scale_factors(1,i); % Ohm |
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low_pass_notch_units_resistors_3(1,i) = ... |
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low_pass_notch_units_resistors_3(1,i)* ... |
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low_pass_notch_units_amplitude_scale_factors(1,i); % Ohm |
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low_pass_notch_units_resistors_4(1,i) = ... |
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low_pass_notch_units_resistors_4(1,i)* ... |
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low_pass_notch_units_amplitude_scale_factors(1,i); % Ohm |
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low_pass_notch_units_resistors_5(1,i) = ... |
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low_pass_notch_units_resistors_5(1,i)* ... |
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low_pass_notch_units_amplitude_scale_factors(1,i); % Ohm |
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low_pass_notch_units_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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(((low_pass_notch_units_gains_high(1,i)-1)/ ... |
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(low_pass_notch_units_gains_high(1,i)* ... |
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low_pass_notch_units_resistors_1(1,i)* ... |
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low_pass_notch_units_capacitors(1,i)))+ ... |
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(2/(low_pass_notch_units_resistors_2(1,i)* ... |
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low_pass_notch_units_capacitors(1,i)))+ ... |
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(2/(low_pass_notch_units_resistors_5(1,i)* ... |
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low_pass_notch_units_capacitors(1,i)))) ... |
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(1/(low_pass_notch_units_resistors_1(1,i)* ... |
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low_pass_notch_units_resistors_5(1,i)* ... |
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low_pass_notch_units_capacitors(1,i)^2)+ ... |
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1/(low_pass_notch_units_resistors_1(1,i)* ... |
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low_pass_notch_units_resistors_2(1,i)* ... |
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low_pass_notch_units_capacitors(1,i)^2))]; |
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unit_denominator = [1 ... |
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2/(low_pass_notch_units_resistors_2(1,i)* ... |
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low_pass_notch_units_capacitors(1,i)) ... |
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1/(low_pass_notch_units_resistors_1(1,i)* ... |
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low_pass_notch_units_resistors_2(1,i)* ... |
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low_pass_notch_units_capacitors(1,i)^2)]; |
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low_pass_notch_units_transfer_functions(1,i) = ... |
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tf(unit_numerator, unit_denominator); |
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low_pass_notch_units_transfer_functions(1,i) = ... |
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low_pass_notch_units_transfer_functions(1,i)* ... |
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low_pass_notch_units_gains_high(1,i); |
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end |
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% Clears unneeded variable from workspace |
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clearVars = {'i', 'temp', 'unit_index', 'normalized_transfer_function_zero'}; |
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clear(clearVars{:}) |
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clear clearVars |
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clear -regexp _numerator$ |
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clear -regexp _denominator$ |
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% ========== UNITS IMPLEMENTATION END ========== |
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%% ========== GAIN ADJUSTMENT START ========== |
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total_gain_high = high_pass_notch_units_gain_high(1,1)* ... |
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high_pass_notch_units_gain_high(1,2)* ... |
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low_pass_notch_units_gains_high(1,1)* ... |
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low_pass_notch_units_gains_high(1,2); |
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unit_adjustment_gain = 1/total_gain_high; |
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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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total_transfer_function = series(series(series( ... |
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high_pass_notch_units_transfer_functions(1,1), ... |
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high_pass_notch_units_transfer_functions(1,2)), ... |
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low_pass_notch_units_transfer_functions(1,1)), ... |
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low_pass_notch_units_transfer_functions(1,2)); |
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total_transfer_function = total_transfer_function*unit_adjustment_gain; |
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%{ |
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ltiview(high_pass_notch_units_transfer_functions(1,1), ... |
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high_pass_notch_units_transfer_functions(1,2), ... |
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series(high_pass_notch_units_transfer_functions(1,1), ... |
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high_pass_notch_units_transfer_functions(1,2))); |
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high_pass_notch_units_transfer_functions(1,2)); |
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%} |
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% ========== UNITS IMPLEMENTATION END ========== |
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%{ |
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ltiview(low_pass_notch_units_transfer_functions(1,1), ... |
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low_pass_notch_units_transfer_functions(1,2)); |
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%} |
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%{ |
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ltiview(high_pass_notch_units_transfer_functions(1,1), ... |
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high_pass_notch_units_transfer_functions(1,2), ... |
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low_pass_notch_units_transfer_functions(1,1), ... |
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low_pass_notch_units_transfer_functions(1,2)); |
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%} |
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%{ |
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ltiview(high_pass_notch_units_transfer_functions(1,1), ... |
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high_pass_notch_units_transfer_functions(1,2), ... |
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low_pass_notch_units_transfer_functions(1,1), ... |
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low_pass_notch_units_transfer_functions(1,2), ... |
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total_transfer_function); |
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%} |
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%ltiview(total_transfer_function); |
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% |
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plot_transfer_function(total_transfer_function, ... |
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[specification_central_frequency ... |
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design_half_power_radial_frequency/(2*pi) ... |
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specification_low_stop_frequency ... |
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specification_low_pass_frequency ... |
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specification_high_pass_frequency ... |
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specification_high_stop_frequency]); |
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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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clear(clearVars{:}) |
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clear clearVars |
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clear -regexp _transfer_functions$ |
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% ========== GAIN ADJUSTMENT END ========== |
