  Forum Pages: 1 Noise: Track & Hold: Theory <=> Sim.: Fits for f3dB >> fs but do (Read 289 times)
 bernd2700 Junior Member  Offline Posts: 28 Noise: Track & Hold: Theory <=> Sim.: Fits for f3dB >> fs but do Apr 8th, 2021, 8:05am   Noise: Track & Hold: Theory <=> Sim.: Fits for "f3dB >> fs" but doesn't fit for "f3dB << fs"With big interest I have read the paper from Ken Kundert: �Simulating Switched-Capacitor Filters with Cadence SpectreRF� and I have written an according Matlab script for it, which then I compare with a PNOISE Cadence simulation of a Track And Hold circuit.Case #1: MatchingIn this paper, an example with values is presented (R = 2.3k, C=10pF, m=0.4, fs=400kHz) which I compared against the values calculated from the Matlab script and they fit, so the script looks for me to be correct.Case #2: Matching as wellWith other values (R = 1k, C=1uF, m=0.5, fs=1), the script also matches the Cadence simulation.We see the Root-Spectral-Density RSD noise result at low frequencies of just the RC filter �Vo1� gives 4.07 nV/sqrt(Hz), the PNoise result of �Vo� gives 45 nV/sqrt(Hz) and after the S&H gives �90 nV/sqrt(Hz)�:The Matlab RSD gives everywhere matching results: At low frequencies, these are 4.07 nV for just the RC filter, 45 nV/sqrt(Hz) for the Track and Hold (m=0.5), and after the S&H (m=0) it gives �90 nV/sqrt(Hz)�:Case #3: Does NOT match!If I just change the capacitor from 1uF to 1F, the script does NOT match anymore with the Cadence simulation. The integrated result with 64pVrms matches again, but the Root-Spectral Density RSD = �sqrt(PSD)� plot looks _different_ ! At low frequencies I have (2 times) sqrt(2) noise difference from the Cadence simulation (5.76 nVrms/sqrt(Hz)) compared to the Matlab script (4.07nVrms/sqrt(Hz) or 2.88nVrms/sqrt(Hz)).In this �Case #3�, as in contrast to the others, the -3dB bandwidth of the RC filter is 159 uHz which is much less than the sampling frequency fs with 1 Hz and for me it seems clear that there is no aliasing.Question:Are then the equations for �f-3dB << fs� maybe not valid anymore and if so, what do I have to modify where in the script in order that I get a closed form result ( = not with �if� �else� statements) for ALL cases matching?Ken Kundert writes about the �time average noise� so maybe I do the PNoise sim. not correct? For me it�s hard to say now if the Cadence sim is wrong due to a maybe wrong setup / use (�time-average� vs. �sampled� etc. *1)) or the theory / equations are just not true anymore for Case #3.Does anyone hopefully please have an idea or a hint for me? That would be great!Thanks very much,bernd 2700*1) For the PAC analysis I got completely (!) wrong results when I used the simulator option �time-average�, so I had to use the �PAC sampled� analysis to show the correct result for required data-read out at phase 1 or 2 active in a switched-capacitor integrator. Maybe here with noise it is the same thing? Back to top « Last Edit: Apr 09th, 2021, 5:19am by bernd2700 » IP Logged
 bernd2700 Junior Member  Offline Posts: 28 Re: Noise: Track & Hold: Theory <=> Sim.: Fits for f3dB >> fs but doesn't vice versa Reply #1 - Apr 8th, 2021, 8:16am   Matlab code: Relevant code lines:% Define ...    k = 1.3806488E-23;    T = 300;    Ron = 1E3   % [Ohms]    C = 1E-6    % [Farad]    m = 0.5     % []    % Duty-cycle: Switch operated: Closed for "m * Ts" and opened for "(1 - m) * Ts"    m_SH = 0;   % The less the duty-cycle "m", the less components from the track mode and thus it resembles more and more a S&H instead of a T&H    fs = 1      % [Hz]  % Sampling frequency    Ts=1/fs;    bw_ll = 1E-3 % [Hz]  % Lower BandWidth Limit    bw_ul = 10E3 % [Hz]  % Upper BandWidth Limit% Generate frequency vector    Nr_freq_points_per_dec = 100    Nr_freq_points = round( log10(bw_ul / bw_ll) * Nr_freq_points_per_dec );    f_vec = logspace( log10(bw_ll) , log10(bw_ul) , Nr_freq_points );% During tracking mode   % ( , ) ,     %% Switch permanently closed : Of course same results as just RC assumed that Ron = R.        Vn_PermClsd_RSD_rms_vec = sqrt(     4 * k * T * Ron ./ ( 1 + (2*pi.*f_vec.*Ron*C).^2) );                % [Vrms/sqrt(Hz)]        Vn_PermClsd_Vrms = sqrt( trapz(f_vec , Vn_PermClsd_RSD_rms_vec .^2 ) );                                 % [Vrms]        Vn_PermClsd_Vrms_check = sqrt(     k * T / C )                                                          % [Vrms]    %% Switch operated: Closed for "m * Ts" and opened for "(1 - m) * Ts"        Vn_TrckMode_TimeAvg_RSD_rms_vec = sqrt( m * 4 * k * T * Ron ./ ( 1 + (2*pi.*f_vec.*Ron*C).^2) );        % [Vrms/sqrt(Hz)]        Vn_TrckMode_operated_Vrms = sqrt( trapz(f_vec , Vn_TrckMode_TimeAvg_RSD_rms_vec .^2 ) );                % [Vrms]        Vn_TrckMode_operated_Vrms_check = sqrt( m * k * T / C )% Hold mode    Vn_HoldMode_TimeAvg_RSD_rms_vec = sqrt( ((1-m)*sinc(f_vec.*(1-m)*Ts)).^2*2*k*T/(C*fs) );                    % [Vrms/sqrt(Hz)]    Vn_HoldMode_operated_Vrms = sqrt( trapz(f_vec , Vn_HoldMode_TimeAvg_RSD_rms_vec .^2 ) );                    % [Vrms]% Total     % sqrt( PSD_track + PSD_hold )    Vn_tot_RSD_vec = sqrt( Vn_TrckMode_TimeAvg_RSD_rms_vec .^2 + Vn_HoldMode_TimeAvg_RSD_rms_vec.^2 );          % [Vrms/sqrt(Hz)]    Vn_tot_Vrms = sqrt( trapz(f_vec , Vn_tot_RSD_vec .^2 ) );                                                   % [Vrms]%% Only a S&H ("m = 0")    Vn_TrckMode_TimeAvg_RSD_SH_rms_vec = sqrt( m_SH * 4 * k * T * Ron ./ ( 1 + (2*pi.*f_vec.*Ron*C).^2) );      % [Vrms/sqrt(Hz)]    Vn_HoldMode_TimeAvg_RSD_SH_rms_vec = sqrt( ((1-m_SH)*sinc(f_vec.*(1-m_SH)*Ts)).^2*2*k*T/(C*fs) );           % [Vrms/sqrt(Hz)]    Vn_tot_RSD_SH_vec = sqrt( Vn_TrckMode_TimeAvg_RSD_SH_rms_vec .^2 + Vn_HoldMode_TimeAvg_RSD_SH_rms_vec.^2 ); % [Vrms/sqrt(Hz)]    Vn_tot_SH_Vrms = sqrt( trapz(f_vec , Vn_tot_RSD_SH_vec .^2 ) );                                             % [Vrms]%% Plot    figure();    semilogx( f_vec , Vn_PermClsd_RSD_rms_vec , 'c-.' );    hold on;    semilogx( f_vec , Vn_TrckMode_TimeAvg_RSD_rms_vec , 'g-.' );    semilogx( f_vec , Vn_HoldMode_TimeAvg_RSD_rms_vec , 'm-.' );    semilogx( f_vec , Vn_tot_RSD_vec , 'b' );    semilogx( f_vec , Vn_tot_RSD_SH_vec , 'r' ); Back to top IP Logged
 bernd2700 Junior Member  Offline Posts: 28 Re: Noise: Track & Hold: Theory <=> Sim.: Fits for f3dB >> fs but doesn't vice versa Reply #2 - Apr 8th, 2021, 8:18am   Case2_Schematic.png Back to top  IP Logged
 bernd2700 Junior Member  Offline Posts: 28 Re: Noise: Track & Hold: Theory <=> Sim.: Fits for f3dB >> fs but doesn't vice versa Reply #3 - Apr 8th, 2021, 8:19am   Case2_Result_Cadence.png Back to top  IP Logged
 bernd2700 Junior Member  Offline Posts: 28 Re: Noise: Track & Hold: Theory <=> Sim.: Fits for f3dB >> fs but doesn't vice versa Reply #4 - Apr 8th, 2021, 8:19am   Case2_Result_Matlab.png Back to top  IP Logged
 bernd2700 Junior Member  Offline Posts: 28 Re: Noise: Track & Hold: Theory <=> Sim.: Fits for f3dB >> fs but doesn't vice versa Reply #5 - Apr 8th, 2021, 8:20am   Case3_Result_Cadence.png Back to top  IP Logged
 bernd2700 Junior Member  Offline Posts: 28 Re: Noise: Track & Hold: Theory <=> Sim.: Fits for f3dB >> fs but doesn't vice versa Reply #6 - Apr 8th, 2021, 8:20am   Case3_Result_Matlab.png Back to top  IP Logged Pages: 1