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Band elimination unit implementation init

master
Apostolos Fanakis 6 years ago
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db79e41b30
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28b91dd8b2
2 changed files with 148 additions and 8 deletions
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  1. 142
      Band Elimination Chebyshev/band_elimination_design.m
  2. 14
      Low Pass Inverse Chebyshev/low_pass_design_single.m

142
Band Elimination Chebyshev/band_elimination_design.m
View File

@ -366,4 +366,144 @@ clear clearVars
clear -regexp ^high_pass_prototype_ clear -regexp ^high_pass_prototype_
clear -regexp ^geffe_ clear -regexp ^geffe_
clear -regexp ^transformation_ clear -regexp ^transformation_
% ========== POLES TRANSFORMATION END ========== % ========== POLES TRANSFORMATION END ==========
%% ========== ZEROS-POLES GROUPING START ==========
% Grouping is done "by hand".
% -------------------------------------------------------------------------
% Unit 1 has a pole pair with ±73.41 degrees of angle, Q equal to 1.751,
% the pole pair lies on a circle with a radius equal to 21505.94 and is
% grouped with a zero at 0.0 + 15707.96 i, resulting in a high pass notch.
% -------------------------------------------------------------------------
% Unit 2 has a pole pair with ±73.41 degrees of angle, Q equal to 1.751,
% the pole pair lies on a circle with a radius equal to 11473.11 and is
% grouped with a zero at 0.0 + 15707.96 i, resulting in a low pass notch.
% -------------------------------------------------------------------------
% Unit 3 has a pole pair with ±87.73 degrees of angle, Q equal to 12.67,
% the pole pair lies on a circle with a radius equal to 19957.29 and is
% grouped with a zero at 0.0 + 15707.96 i, resulting in a high pass notch.
% -------------------------------------------------------------------------
% Unit 4 has a pole pair with ±87.73 degrees of angle, Q equal to 12.67,
% the pole pair lies on a circle with a radius equal to 12363.40 and is
% 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
% elimination filter.
% ========== ZEROS-POLES GROUPING END ==========
%% ========== 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.
% High pass notch units 1 and 3
% Initializes necessary arrays, each array is 1X2, the first element (1,1)
% corresponds to the first unit (unit 1) and the second element (1,2) to
% second unit (unit 3).
high_pass_notch_units_k1 = zeros([1 2]);
high_pass_notch_units_k2 = zeros([1 2]);
high_pass_notch_units_gain_high = zeros([1 2]);
high_pass_notch_units_C = zeros([1 2]);
high_pass_notch_units_C1 = zeros([1 2]);
high_pass_notch_units_R1 = zeros([1 2]);
high_pass_notch_units_R2 = zeros([1 2]);
high_pass_notch_units_R3 = zeros([1 2]);
high_pass_notch_units_R4 = zeros([1 2]);
high_pass_notch_units_frequency_scale_factors = zeros([1 2]);
high_pass_notch_units_amplitude_scale_factors = zeros([1 2]);
high_pass_notch_units_transfer_functions = [tf(1) tf(1)];
for i=1:2
unit_index = i*2-1;
% Calculates k1 design parameter using the eq. 7-135
high_pass_notch_units_k1(1,i) = ...
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/ ...
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;
% Assumes that R3 is 1 Ohm and the radial frequency is 1 rad/s
high_pass_notch_units_R3(1,i) = 1;
% Calculates R4 using the eq. 7-139
high_pass_notch_units_R4(1,i) = (high_pass_notch_units_k1(1,i)+2)* ...
band_elimination_poles_Q(1,unit_index)^2;
% Calculates C using the eq. 7-140
high_pass_notch_units_C(1,i) = 1/ ...
(band_elimination_poles_Q(1,unit_index)* ...
(high_pass_notch_units_k1(1,i)+2));
% Initial axioms of the design were:
% C1 = k1 * C
high_pass_notch_units_C1(1,i) = high_pass_notch_units_k1(1,i)* ...
high_pass_notch_units_C(1,i);
% R1 = 1 Ohm
high_pass_notch_units_R1(1,i) = 1;
% Selects the appropriate frequency scale factor to transfer the
% normalized radial frequency back to the original
high_pass_notch_units_frequency_scale_factors(1,i) = ...
band_elimination_poles_radial_frequencies(1,unit_index);
% AEM(3) = 6, so the magnitude scaling will be performed to achieve a
% capacitor value of 0.1uF using the eq. 6-33
high_pass_notch_units_amplitude_scale_factors(1,i) = ...
high_pass_notch_units_C(1,i)/ ...
(high_pass_notch_units_frequency_scale_factors(1,i)*0.1*10^(-6));
% Performs scaling
high_pass_notch_units_R1(1,i) = high_pass_notch_units_R1(1,i)* ...
high_pass_notch_units_amplitude_scale_factors(1,i);
high_pass_notch_units_R2(1,i) = high_pass_notch_units_R2(1,i)* ...
high_pass_notch_units_amplitude_scale_factors(1,i);
high_pass_notch_units_R3(1,i) = high_pass_notch_units_R3(1,i)* ...
high_pass_notch_units_amplitude_scale_factors(1,i);
high_pass_notch_units_R4(1,i) = high_pass_notch_units_R4(1,i)* ...
high_pass_notch_units_amplitude_scale_factors(1,i);
high_pass_notch_units_C(1,i) = high_pass_notch_units_C(1,i)/ ...
(high_pass_notch_units_frequency_scale_factors(1,i)* ...
high_pass_notch_units_amplitude_scale_factors(1,i));
high_pass_notch_units_C1(1,i) = high_pass_notch_units_C1(1,i)/ ...
(high_pass_notch_units_frequency_scale_factors(1,i)* ...
high_pass_notch_units_amplitude_scale_factors(1,i));
% Builds unit's transfer function
high_pass_notch_unit_numerator = [1 ...
0 ...
1/(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)];
high_pass_notch_units_transfer_functions(1,i) = tf( ...
high_pass_notch_unit_numerator, high_pass_notch_unit_denominator);
high_pass_notch_units_transfer_functions(1,i) = ...
high_pass_notch_units_transfer_functions(1,i)* ...
high_pass_notch_units_gain_high(1,i);
end
plot_transfer_function(high_pass_notch_units_transfer_functions(1,1));
%ltiview(high_pass_notch_units_transfer_functions(1,1));
%{
ltiview(high_pass_notch_units_transfer_functions(1,1), ...
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 ==========

14
Low Pass Inverse Chebyshev/low_pass_design_single.m
View File

@ -5,7 +5,7 @@
% FILENAME : low_pass_design_single.m % FILENAME : low_pass_design_single.m
% AEM : 8261 % AEM : 8261
% ========== DESIGN SPECIFICATIONS START ========== %% ========== DESIGN SPECIFICATIONS START ==========
% Figures out design specifications according to my AEM number % Figures out design specifications according to my AEM number
AEM = [8 2 6 1]; AEM = [8 2 6 1];
@ -35,7 +35,7 @@ specification_min_stop_attenuation = 18; % dB
specification_max_pass_attenuation = 0.25; % dB specification_max_pass_attenuation = 0.25; % dB
% ========== DESIGN SPECIFICATIONS END ========== % ========== DESIGN SPECIFICATIONS END ==========
% ========== NORMALIZED DESIGN START ========== %% ========== NORMALIZED DESIGN START ==========
% Calculates normalized design specifications and designs a normalized % Calculates normalized design specifications and designs a normalized
% filter using them % filter using them
@ -168,7 +168,7 @@ clear clearVars
% ========== NORMALIZED DESIGN END ========== % ========== NORMALIZED DESIGN END ==========
% ========== ZEROS-POLES GROUPING START ========== %% ========== ZEROS-POLES GROUPING START ==========
% Grouping is done "by hand". The first pole, that has a radial frequency % 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 % equal to 0.9631, is grouped with the first zero (1.0824) and the second
@ -178,7 +178,7 @@ clear clearVars
% ========== ZEROS-POLES GROUPING END ========== % ========== ZEROS-POLES GROUPING END ==========
% ========== UNITS IMPLEMENTATION START ========== %% ========== UNITS IMPLEMENTATION START ==========
% AEM(3) = 6, so the circuit shown in 7.23 is going to be used for the low % AEM(3) = 6, so the circuit shown in 7.23 is going to be used for the low
% pass notch units. % pass notch units.
@ -259,7 +259,7 @@ clear normalized_transfer_function_zero
% ========== UNITS IMPLEMENTATION END ========== % ========== UNITS IMPLEMENTATION END ==========
% ========== DENORMALIZATION START ========== %% ========== DENORMALIZATION START ==========
% Unit sizes rescale % Unit sizes rescale
unit_frequency_scale_factors = zeros([1 2]); unit_frequency_scale_factors = zeros([1 2]);
@ -307,7 +307,7 @@ unit_low_pass_notch_capacitors(1,2) = 0.1*10^(-6); % Farad
% ========== DENORMALIZATION END ========== % ========== DENORMALIZATION END ==========
% ========== GAIN ADJUSTMENT START ========== %% ========== GAIN ADJUSTMENT START ==========
total_fried_units_attenuation = unit_low_pass_notch_gains_low(1,1)*unit_low_pass_notch_gains_low(1,2); 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; unit_adjustment_gain = 1/total_fried_units_attenuation;
@ -317,7 +317,7 @@ unit_adjustment_feedback_resistor = 10*10^3*unit_adjustment_gain;
% ========== GAIN ADJUSTMENT END ========== % ========== GAIN ADJUSTMENT END ==========
% ========== TRANSFER FUNCTIONS START ========== %% ========== TRANSFER FUNCTIONS START ==========
% Builds numerator and denominator of the transfer function of each unit % Builds numerator and denominator of the transfer function of each unit
% using the eq. 7-146, 7-147 & 7-148 % using the eq. 7-146, 7-147 & 7-148

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