From 17eae2dbbe089b546215852c6189224533d390df Mon Sep 17 00:00:00 2001 From: Apostolof Date: Mon, 20 Aug 2018 17:10:01 +0300 Subject: [PATCH] Low pass and band pass response to input signal Matlab and Multisim --- .../Multisim/band_pass_chebyshev.ms14 | Bin 486022 -> 507722 bytes Band Pass Chebyshev/band_pass_design.m | 107 +++++++++++++++--- .../Multisim/low_pass_inversed_chebyshev.ms14 | Bin 445186 -> 486835 bytes Low Pass Inverse Chebyshev/low_pass_design.m | 88 ++++++++------ 4 files changed, 145 insertions(+), 50 deletions(-) diff --git a/Band Pass Chebyshev/Multisim/band_pass_chebyshev.ms14 b/Band Pass Chebyshev/Multisim/band_pass_chebyshev.ms14 index 6c70b321356dbad1b5b28314b38d58741409a6fd..9e70922467102efeb01831db463e0500ff58953a 100644 GIT binary patch literal 507722 zcmd42cT`hf_wE}Y^xi}7y%<0s^j<q2Mzz6Q<^6;UHvxc{elfT~s zUk|5;<`4Y599?{!++q59q;<-G+eg_eQb33y761#69cyQ6tUBJ_tGg0+Kzb6rMGEsz>`e& z_i4bC($E9PGBxf#mIOn7>XIJP7+<#^R0PW`Kw}Nn!-DlP9Su>kBpPB|*)AFuQ(#!T 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a/Band Pass Chebyshev/band_pass_design.m +++ b/Band Pass Chebyshev/band_pass_design.m @@ -480,28 +480,20 @@ clear clearVars % ========== UNITS IMPLEMENTATION END ========== -%% ========== TRANSFER FUNCTIONS START ========== - -%{ -total_gain = units_filter_central_frequency_gain(1,1)* ... - units_filter_central_frequency_gain(1,2)* ... - units_filter_central_frequency_gain(1,3)* ... - units_filter_central_frequency_gain(1,4); -%} +%% ========== TRANSFER FUNCTIONS STUDY START ========== total_transfer_function = series(series(series( ... unit_transfer_function(1), unit_transfer_function(2)), ... unit_transfer_function(3)), unit_transfer_function(4)); -%total_transfer_function = total_transfer_function*(1/total_gain); - -%plot_transfer_function(unit_transfer_function(2), [1 10]); -%ltiview(unit_transfer_function(1), unit_transfer_function(2), ... -% unit_transfer_function(3), unit_transfer_function(4), total_transfer_function); - -%ltiview(total_transfer_function); - %{ +% Plots each unit's frequency response +for i=1:band_pass_number_of_poles + plot_transfer_function(unit_transfer_function(1,i), ... + design_geometric_central_radial_frequency); +end + +% Plots the total filter frequency response plot_transfer_function(total_transfer_function, ... [specification_low_stop_frequency ... specification_low_pass_frequency ... @@ -509,9 +501,90 @@ plot_transfer_function(total_transfer_function, ... 941.83 ... specification_high_pass_frequency ... specification_high_stop_frequency]); + +% Plots the total filter attenuation function +plot_transfer_function(inv(total_transfer_function), ... + [specification_low_stop_frequency ... + specification_low_pass_frequency ... + specification_central_frequency ... + 941.83 ... + specification_high_pass_frequency ... + specification_high_stop_frequency]); %} +%{ +ltiview(unit_transfer_function(1,1)); +ltiview(unit_transfer_function(1,2)); +ltiview(unit_transfer_function(1,3)); +ltiview(unit_transfer_function(1,4)); +ltiview(total_transfer_function); +ltiview(unit_transfer_function(1,1), unit_transfer_function(1,2), ... + unit_transfer_function(1,3), unit_transfer_function(1,4), ... + total_transfer_function); +%} + +hold off + +sampling_time_seconds = 60; % s +sampling_frequency_Fs = 80000; % Hz +sampling_period_T = 1/sampling_frequency_Fs; % s +sampling_time_vector = 0:sampling_period_T: ... + sampling_time_seconds-sampling_period_T; +sampling_length_L = length(sampling_time_vector); +frequency_vector = sampling_frequency_Fs/sampling_length_L* ... + (0:(sampling_length_L/2)); + +input_cos_signal_frequency_1 = specification_central_radial_frequency- ... + (specification_central_radial_frequency- ... + specification_low_pass_radial_frequency)/2; +input_cos_signal_frequency_2 = specification_central_radial_frequency+ ... + (specification_central_radial_frequency+ ... + specification_low_pass_radial_frequency)/3; +input_cos_signal_frequency_3 = 0.4*specification_low_stop_radial_frequency; +input_cos_signal_frequency_4 = 2.5*specification_high_stop_radial_frequency; +input_cos_signal_frequency_5 = 3*specification_high_stop_radial_frequency; + +input_signal = cos(input_cos_signal_frequency_1*sampling_time_vector)+ ... + 0.8*cos(input_cos_signal_frequency_2*sampling_time_vector)+ ... + 0.8*cos(input_cos_signal_frequency_3*sampling_time_vector)+ ... + 0.6*cos(input_cos_signal_frequency_4*sampling_time_vector)+ ... + 0.5*cos(input_cos_signal_frequency_5*sampling_time_vector); + +[gain,phase] = ... + bode(total_transfer_function, ... + 850*2*pi); + +system_output = lsim(total_transfer_function, input_signal, ... + sampling_time_vector); + +% Plots only the first 2000 samples +figure(1) +plot(sampling_time_vector(1:2000), input_signal(1:2000), ... + sampling_time_vector(1:2000), system_output(1:2000)); +grid on + + +% Plots the power spectrum of the input signal +input_square_wave_fft = fft(input_signal); +Pyy = input_square_wave_fft.*conj(input_square_wave_fft)/sampling_length_L; +figure(2) +semilogx(frequency_vector,Pyy(1:sampling_length_L/2+1)) +grid on + + +% Plots the power spectrum of the output signal +system_output_fft = fft(system_output, length(sampling_time_vector)); +Pyy = system_output_fft.*conj(system_output_fft)/sampling_length_L; +figure(3) +semilogx(frequency_vector,Pyy(1:sampling_length_L/2+1)) +grid on % Clears unneeded variables from workspace +clearVars = {'temp', 'Pyy', 'frequency_vector', ... + 'system_output', 'system_output_fft'}; +clear(clearVars{:}) +clear clearVars clear -regexp _transfer_function$ +clear -regexp ^sampling_ +%clear -regexp ^input_ -% ========== TRANSFER FUNCTIONS END ========== \ No newline at end of file +% ========== TRANSFER FUNCTIONS STUDY END ========== \ No newline at end of file diff --git a/Low Pass Inverse Chebyshev/Multisim/low_pass_inversed_chebyshev.ms14 b/Low Pass Inverse Chebyshev/Multisim/low_pass_inversed_chebyshev.ms14 index 23da8d5db3b2f70333b7df7f4ab2f38d6e23379e..d31ca13934cd819ac6b0c39decce06cc27e5beba 100644 GIT binary patch literal 486835 zcmdqIXINA3w)Pt!l+Zf?LhptWdT7#H=)ITFLBLQ&K&1EH1nC_GkxoQGdPjN(r3;7( zN>fo!_?NZUUVH6*?f1IQdp?|edLHJ?Gv{QEIqu)M$Bd4Vj`CeEl&`a&pR<#yr?aEK z?_FzIPm)y&c`mb+p|WB>^{|(w8IvF$5L>3y&3Rdvmlp&i>BRDn>UHXAm0o z$_wV->8vjabx8tZ!&ymbg*8}PGHm8tcvm|uh-sP|*kG?UPmdoI9M@A36T@Funm=t; 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-59,7 +59,7 @@ design_filter_order = ceil(temp_filter_order); % 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? =========^^^^^^^^^^^^^^^^^^&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&========== +% Calculates alpha using the eq. 9-92 alpha_parameter = asinh(1/epsilon_parameter)/design_filter_order; % Calculates the frequency at which half power occurs using the eq. 9-139 @@ -91,12 +91,12 @@ inverse_chebyshev_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 +% 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 + % The rest of the poles are scattered in the left half pane in equal + % angle arcs % Theta is a helper parameter theta=180/design_filter_order; @@ -281,6 +281,7 @@ for i=1:design_number_of_poles unit_low_pass_notch_resistors_5(1,i) = ... (4*inverse_chebyshev_poles_Q(1,i)^2)/ ... (normalized_transfer_function_zero^2-1); % Ohm + unit_low_pass_notch_resistors_4(1,i) = 1; % Ohm % Calculates the resistance of R3 using the eq. 7-155 unit_low_pass_notch_resistors_3(1,i) = ... @@ -449,51 +450,72 @@ ltiview(unit_transfer_function(1,1), unit_transfer_function(1,2), ... hold off -Fs = 1000; % Sampling frequency -T = 1/Fs; % Sampling period -L = 1500; % Length of signal -t = (0:L-1)*T; % Time vector - input_signal_frequency = 2000; % Hz -input_signal_number_of_periods = 100000; -input_signal_T = input_signal_number_of_periods*(1/input_signal_frequency); input_signal_duty_cycle = 20; -input_signal_Fs = 80000; -input_signal_dt = 1/input_signal_Fs; -input_signal_t = 0:input_signal_dt:input_signal_T-input_signal_dt; -input_square_wave = (1+square(2*pi*input_signal_frequency*input_signal_t, ... +number_of_periods_sampled = 120000; +sampling_time_seconds = number_of_periods_sampled* ... + (1/input_signal_frequency); % s + +sampling_frequency_Fs = 80000; % Hz +sampling_period_T = 1/sampling_frequency_Fs; % s +sampling_time_vector = 0:sampling_period_T: ... + sampling_time_seconds-sampling_period_T; +sampling_length_L = length(sampling_time_vector); +frequency_vector = sampling_frequency_Fs/sampling_length_L* ... + (0:(sampling_length_L/2)); + +input_square_wave = (1+ ... + square(2*pi*input_signal_frequency*sampling_time_vector, ... input_signal_duty_cycle))/2; -system_output = lsim(total_transfer_function, input_square_wave, input_signal_t); +system_output = lsim(total_transfer_function, input_square_wave, ... + sampling_time_vector); + % Plots only the first 10 periods -temp = 10*input_signal_Fs/input_signal_frequency; +temp = 10*sampling_frequency_Fs/input_signal_frequency; figure(1) -plot(input_signal_t(1:temp), input_square_wave(1:temp), ... - input_signal_t(1:temp), system_output(1:temp)); +plot(sampling_time_vector(1:temp), input_square_wave(1:temp), ... + sampling_time_vector(1:temp), system_output(1:temp)); grid on +% Plots the power spectrum of the input signal input_square_wave_fft = fft(input_square_wave); -L = length(input_signal_t); -P2 = abs(input_square_wave_fft/L); -P1 = P2(1:L/2+1); -P1(2:end-1) = 2*P1(2:end-1); -f = input_signal_Fs*(0:(L/2))/L; +Pyy = input_square_wave_fft.*conj(input_square_wave_fft)/sampling_length_L; figure(2) -%plot(f,P1) -semilogx(f,P1) +semilogx(frequency_vector,Pyy(1:sampling_length_L/2+1)) grid on -system_output_fft = fft(system_output, length(input_signal_t)); -P2 = abs(system_output_fft/L); -P1 = P2(1:L/2+1); -P1(2:end-1) = 2*P1(2:end-1); +% Plots the power spectrum of the output signal +system_output_fft = fft(system_output, length(sampling_time_vector)); +Pyy = system_output_fft.*conj(system_output_fft)/sampling_length_L; figure(3) -%plot(f, P11) -semilogx(f,P1) +semilogx(frequency_vector,Pyy(1:sampling_length_L/2+1)) grid on -%filter_fft = fft(total_transfer_function); +%{ +asdf = 1:length(frequency_vector); +for i=1:length(frequency_vector) + if i<175000 + asdf(i) = 1; + elseif mod(i,200)==0 + [asdf(i),phase] = ... + bode(total_transfer_function, ... + frequency_vector(i)*2*pi); + else + asdf(i) = 0; + end + %{ + if mod(i,10000)==0 + disp(i) + end + %} +end + +figure(4) +semilogx(frequency_vector,asdf,'.',frequency_vector,P1,'-') +grid on +%} % Clears unneeded variable from workspace clear low_frequency