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https://designers-guide.org/forum/YaBB.pl Modeling >> Behavioral Models >> Noise: Track & Hold: Theory <=> Sim.: Fits for f3dB >> fs but do https://designers-guide.org/forum/YaBB.pl?num=1617894310 Message started by bernd2700 on Apr 8^{th}, 2021, 8:05am |
Title: Noise: Track & Hold: Theory <=> Sim.: Fits for f3dB >> fs but do Post by bernd2700 on Apr 8^{th}, 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: Matching In 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 well With 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? |
Title: Re: Noise: Track & Hold: Theory <=> Sim.: Fits for f3dB >> fs but doesn't vice versa Post by bernd2700 on Apr 8^{th}, 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 % ([1] , [2]) , [3] %% 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' ); |
Title: Re: Noise: Track & Hold: Theory <=> Sim.: Fits for f3dB >> fs but doesn't vice versa Post by bernd2700 on Apr 8^{th}, 2021, 8:18am Case2_Schematic.png |
Title: Re: Noise: Track & Hold: Theory <=> Sim.: Fits for f3dB >> fs but doesn't vice versa Post by bernd2700 on Apr 8^{th}, 2021, 8:19am Case2_Result_Cadence.png |
Title: Re: Noise: Track & Hold: Theory <=> Sim.: Fits for f3dB >> fs but doesn't vice versa Post by bernd2700 on Apr 8^{th}, 2021, 8:19am Case2_Result_Matlab.png |
Title: Re: Noise: Track & Hold: Theory <=> Sim.: Fits for f3dB >> fs but doesn't vice versa Post by bernd2700 on Apr 8^{th}, 2021, 8:20am Case3_Result_Cadence.png |
Title: Re: Noise: Track & Hold: Theory <=> Sim.: Fits for f3dB >> fs but doesn't vice versa Post by bernd2700 on Apr 8^{th}, 2021, 8:20am Case3_Result_Matlab.png |
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