commit
b68a326754
2 changed files with 441 additions and 0 deletions
@ -0,0 +1,397 @@ |
|||||
|
% AUTHOR : Apostolos Fanakis |
||||
|
% $DATE : 02-May-2018 17:21:18 $ |
||||
|
% $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)* ... |
||||
|
unit_low_pass_notch_capacitors(1,1)))) ... |
||||
|
(1/(unit_low_pass_notch_resistors_1(1,1)* ... |
||||
|
unit_low_pass_notch_resistors_5(1,1)*unit_low_pass_notch_capacitors(1,1)^2)+ ... |
||||
|
1/(unit_low_pass_notch_resistors_1(1,1)* ... |
||||
|
unit_low_pass_notch_resistors_2(1,1)*unit_low_pass_notch_capacitors(1,1)^2))]; |
||||
|
unit_1_denominator = [1 ... |
||||
|
2/(unit_low_pass_notch_resistors_2(1,1)* ... |
||||
|
unit_low_pass_notch_capacitors(1,1)) ... |
||||
|
1/(unit_low_pass_notch_resistors_1(1,1)* ... |
||||
|
unit_low_pass_notch_resistors_2(1,1)*unit_low_pass_notch_capacitors(1,1)^2)]; |
||||
|
|
||||
|
|
||||
|
unit_1_transfer_function = tf(unit_1_numerator, unit_1_denominator); |
||||
|
unit_1_transfer_function = unit_1_transfer_function*unit_low_pass_notch_gains_high(1,1); |
||||
|
|
||||
|
unit_2_numerator = [1 ... |
||||
|
((unit_low_pass_notch_gains_high(1,2)-1)/ ... |
||||
|
(unit_low_pass_notch_gains_high(1,2)*unit_low_pass_notch_resistors_1(1,2)* ... |
||||
|
unit_low_pass_notch_capacitors(1,2))+ ... |
||||
|
2/(unit_low_pass_notch_resistors_2(1,2)* ... |
||||
|
unit_low_pass_notch_capacitors(1,2))+ ... |
||||
|
2/(unit_low_pass_notch_resistors_5(1,2)* ... |
||||
|
unit_low_pass_notch_capacitors(1,2))) ... |
||||
|
(1/(unit_low_pass_notch_resistors_1(1,2)* ... |
||||
|
unit_low_pass_notch_resistors_5(1,2)*unit_low_pass_notch_capacitors(1,2)^2)+ ... |
||||
|
1/(unit_low_pass_notch_resistors_1(1,2)* ... |
||||
|
unit_low_pass_notch_resistors_2(1,2)*unit_low_pass_notch_capacitors(1,2)^2))]; |
||||
|
unit_2_denominator = [1 ... |
||||
|
2/(unit_low_pass_notch_resistors_2(1,2)* ... |
||||
|
unit_low_pass_notch_capacitors(1,2)) ... |
||||
|
1/(unit_low_pass_notch_resistors_1(1,2)* ... |
||||
|
unit_low_pass_notch_resistors_2(1,2)*unit_low_pass_notch_capacitors(1,2)^2)]; |
||||
|
|
||||
|
unit_2_transfer_function = tf(unit_2_numerator, unit_2_denominator); |
||||
|
unit_2_transfer_function = unit_2_transfer_function*unit_low_pass_notch_gains_high(1,2); |
||||
|
|
||||
|
tmpHpRC = double(1)/double(0.1*10^(-6)*4.14*10^3); |
||||
|
unit_3_transfer_function = tf([0 tmpHpRC], [1 tmpHpRC]); |
||||
|
|
||||
|
total_transfer_function = series(series(unit_1_transfer_function,unit_2_transfer_function), unit_3_transfer_function); |
||||
|
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 ========== |
||||
@ -0,0 +1,44 @@ |
|||||
|
function plot_transfer_function( tf, frequency_markers ) |
||||
|
%PLOT_TRANSFER_FUNCTION Plots bode of a transfer function with markers |
||||
|
% |
||||
|
% tf - The transfer function (created using tf) |
||||
|
% frequency_markers - A matrix of frequencies in Hz |
||||
|
% |
||||
|
% Example: |
||||
|
% plot_transfer_function( tf([1000], [1 1000]), [10 1000 10000] ); |
||||
|
|
||||
|
figure; |
||||
|
x_space = logspace(1,5,1000); % 1000 points between 10^1 and 10^5 |
||||
|
x_space = 2 * pi * x_space; % to rad / sec |
||||
|
[mag,~,wout] = bode(tf,x_space); |
||||
|
mag = squeeze(mag); |
||||
|
wout = squeeze(wout); |
||||
|
mag = 20*log10(mag); |
||||
|
wout = wout/2/pi; |
||||
|
semilogx(wout,mag,'-b'); |
||||
|
axis([min(wout) max(wout) min(mag)-10 max(mag)+10]); |
||||
|
[num,den] = tfdata(tf); |
||||
|
syms s; |
||||
|
d1 = digits(5); |
||||
|
ltx = latex(vpa(poly2sym(cell2mat(num),s)/poly2sym(cell2mat(den),s))); |
||||
|
digits(d1); |
||||
|
title(strcat('$',ltx,'$'), 'Interpreter','latex', 'FontSize', 24); |
||||
|
xlabel('Frequency (Hz)', 'FontSize', 18); |
||||
|
ylabel('Magnitude (dB)', 'FontSize', 18); |
||||
|
grid on; |
||||
|
hold on; |
||||
|
[dbMarks,~,frequency_markers] = bode(tf,2 * pi * frequency_markers); |
||||
|
dbMarks = squeeze(dbMarks); |
||||
|
frequency_markers = squeeze(frequency_markers); |
||||
|
dbMarks = 20*log10(dbMarks); |
||||
|
frequency_markers = frequency_markers/2/pi; |
||||
|
Aw = cell(size(frequency_markers, 1) + 1, 1); |
||||
|
Aw{1} = 'Transfer function'; |
||||
|
for i = 1 : size(frequency_markers, 1) |
||||
|
semilogx(frequency_markers(i),dbMarks(i),'o'); |
||||
|
Aw{i+1} = sprintf('Attenuation at %.2f Hz is %.2f dB', ... |
||||
|
frequency_markers(i), dbMarks(i)); |
||||
|
end |
||||
|
legend(Aw,'Location','best','FontSize',12); |
||||
|
set(gca,'FontSize',14); |
||||
|
end |
||||
Loading…
Reference in new issue