======================NOISE_OFFSET========================================== Rules of thumb 1K is 4nV/sqrt(Hz) 100R is 10 time noise Noise_figure Total_noise/noise_R pink noise equal noise per octave red noise 1/f^2 Excess_Noise 1/f called noise current, flicker noise Due to microarc between carbon granules for dc current. Noise_Index_dB 20*log( Excess_noise_uV/Vdc ) 0 dB = 1uV of noise per 1volt DC current. Noise_Index_dB carbon composition -20 to +10 carbon granular mixed with binder carbon comp_molded -20 to -8 deposited carbon -25 to -8 C film on ceramic rod,cut spiral grooves metal film -35 to -20 M film on ceramic rod,cut spiral grooves wirewound -40 to -10 Zeners have shot noise (7V or less ) below 3V .. very little noise 3V = 30uV_per_rt_Hz at 250uA 30V = 40uV_per_rt_Hz at 250uA Battery quiet until almost dead. Caps quiet because they low pass filter. ------------------------------------------------------------- Pop Corn Noise pops msec to sec ------------------------------------------------------------- 1/F_Noise about three times value at 1Hz 2.7 times 1Hz over 1 second 4 times 1Hz over 1 hour 4.4 times 1Hz over 1 day ------------------------------------------------------------- transient Noise Bandwidth = 1/2 sample period RMS=stand_dev=Flat_nV_per_sqrtHz*sqrt(Bandwidth) 6 sd about 1ppm 6 time constants in a cycle (2pi) __ / \ each section a RC \__/ ------------------------------------------------------------- Q number of cycles to settle ratio of real resistance to X ------------------------------------------------------------- noise/offset You can treat the same Shot noise statical, not physcial Thermal noise physical, not stasitical negative feedback one pole must dominate for stabilty Write down all assumptions, calculations Tolerance Think in terms of signal to noise/interferrence Know errors that can be cancelled out If Linear Use the SuperPosition Theory... offset/noise drops as the square root.. how averaging works ------------------------------------------------------------- Popcorn /Burst Noise discrete levels of channel current modulation due to trapping and release of a single carrier +20nA_ _ ______ __ __________ | | | | | | | | | -20nA |__| |______| |___| |_| |_____ 0 20msec ------------------------------------------------------------- Input Noise V LM394 100nV _______________________________ | . . . | |Rs=100 . . . | | . . . | | . . . | | . . . | |## . . 1uA . | | #############################| 10nV|...............................| | . . . | | . . . | | . . 10uA . | |###############################| |# . . 100uA. | | ##############################| |# . . 1mA . | 1nV | ##############################| 10Hz 100Hz 1kHz 10kHz 100kHz ------------------------------------------------------------- Input Noise Current LM394 _______________________________ 100pA| . . . | |# . . . | | . . . | | # . . . | 10pA|.......#.......................| |# . . 10mA . | | # . # . . | | # # # # # #| |# . # . . | 1pA|...#...........#...1mA.........| | # . # # # | | . # . 100uA | |# . # # # # | | # . . . | 100fA|.......#...#.......10uA........| | . # # # # | | # . . 1uA | | # # # # # # | | . . . | 10fA|_______________________________| 10Hz 100Hz 1kHz 10kHz 100kHz ------------------------------------------------------------- typical noise IDS =20uA @3V Hz nV/rt_Hz nV/rt_Hz freq NMOS 40/.8 PMOS 40/.8 10 800 150 100 400 60 1000 150 30 10000 50 20 100000 10 15 ------------------------------------------------------------- 1/F_noise 40/.8 1000nV........................................ NMOS . . . . | . . . . | . . . . | . . . . | NMOS . . . 300nV|........................................ | . . . . | . . . . | . NMOS . . PMOS . . . . | . . . . 100nV|........................................ | . . . . | PMOS . NMOS . | . . . . | . . . . 30nV |..................PMOS.................. | . . PMOS . | . . . NMOS | . . . PMOS | . . . . | . . . . 10nV |________________________________________ 10Hz 100Hz 1000Hz 10KHz 100K ======================SILICON_MATCH==================== Resistor\sigma in With Without % matching dummy Rs dummy Rs P+ 23x1100 0.02 0.13 P+ 11x 550 0.05 0.26 P+ 5x 275 0.19 0.48 N+ Poly 11x 550 0.25 0.45 ------------------------------------------------------------- Cap matching 0.025% best layout .5pF cap hysteresis less than 16bit PolyR match 0.1% Vt_Nch_sd_mV 15/sqrt(W_u*L*_u) Larry data Vt_Pch_sd_mV 18/sqrt(W_u*L*_u) Vt_Nch_Beta_sd_% 2.3/sqrt(W_u*L*_u) Vt_Nch_Beta_sd_% 3.2/sqrt(W_u*L*_u) Vt_Pch_match 12mV min geo Nch 20% better min input stage sd Beta_Pch_match 2% min geo Nch 40% better min input stage sd match_I_% Beta% +Vt_mV/Vod match_V_mV Vt_mV +Vod*Beta% su_Vt_I match 50% to 100% I mismatch sd I_mirror match 20% to 2% match for .001 to 100 I offset 5mV to 20mV at 100 I Matching of vth half the thickness has 1/2 vth mismatch Vth_sd should_equal 11mV/sqrt(W*L) starting offset untrimed 1mV sd in assemble shift 25-50uV theram hysterise 75-150uVo both plastic/ceranmic lifetest good 1000 hours to 50uV Package plastic 100micron particle cmos is piezo generate a randon 2mV sd offset in cmos.. have seen drift up to 20mV drift ------------------------------------------------------------- drift activated 156degree burn in for 22 to 24 hours will try to settle back to 20% of orignal value at room temp youcan see drift at room, wer before it was stabile. can see drift at 5mins at 200degreees. adc16061 550pf inside wish list high linear 15ppm/volt poly to poly Caps parasitc 5-10% Bsim charge conservation, impact ionization smooth strong to weak inversion transition noise model valid Match of vth half the thickness has 1/2 vth mismatch Vth_sd should_equal 11mV/sqrt(W*L) Cap matching 0.025% best layout .5pF cap hysteresis less than 16bit Poly resistor match 0.1% Low Vt Low thresshold increase subthrehold current. Noise dominated by Cap size which set RC ------------------------------------------------------------- Vdd max 120Angstrom? typical noise IDS =20uA @3V Hz nV/rt_Hz nV/rt_Hz freq NMOS 40/.8 PMOS 40/.8 10 800 150 100 400 60 1000 150 30 10000 50 20 100000 10 15 ------------------------------------------------------------- 1/F_noise 1000nV........................................ NMOS . . . . | . . . . | . . . . | . . . . | NMOS . . . 300nV|........................................ | . . . . | . . . . | . NMOS . . PMOS . . . . | . . . . 100nV|........................................ | . . . . | PMOS . NMOS . | . . . . | . . . . 30nV |..................PMOS.................. | . . PMOS . | . . . NMOS | . . . PMOS | . . . . | . . . . 10nV |________________________________________ 10Hz 100Hz 1000Hz 10KHz 100K ------------------------------------------------------------- Noise levels_dB relative to room noise temp 70dB ................................................ | . .___________________ . 60dB|........................|A Atmosphere |....3e8_K | U . .|U Urban | . 50dB|......U.................|G Galactic |....3e7_K | . .|S Solar | . 40dB|A..........U............|T Typical receiver|....3e6_K | A . .|__________________| . 30dBG.................U..............................3e5_K | A . . . . 20dB|....G..................U........................3e4_K | A . . . T. 10dB|..........G............T....U...................3e3_K | A T . . . 0dBST..............G................U...............300_K | S . . . . -10dB|______A____S________G___________________________30_k 10MHz 100MHz 1GHz 10GHz Frequencies Noise levels_dB relative to room noise temp +20dB ........S+....................................... | . . . . +10dB|..............S+................................. S+ Disturbed sun | . . . . S- Quiet sun 0dB|.......C.......G...S+............................ | . . . . G Galactic plane -10dB|...........S-.....G.....S+....................... C Cassiopia | . S- . . -20dB|...........C..........GS-....................... | . . S- . . -30dB|............................G......S-............ | . C . . . -40dB|...................................G............ | . . . . -50dB|.......................C........................ | . . . . -60dB|................................................ | . . . . -70dB|______________________________C_________________ 10MHz 100MHz 1GHz 10GHz Fig. 4ÑGalactic noise levels for a half-wave-dipole receiving antenna. Man-Made Noise -------------------------------------------------------------------------------------- Noise_Floor_FFT_dB Theoretical FFT Points 12Bits 14Bits 16Bits 1024 101 113 125 2048 104 116 128 4096 107 119 131 8192 110 122 134 16384 113 125 137 32768 116 128 140 SNR_dB 74.0 86.0 98.1 -------------------------------------------------------------------------------------- FFT _ _ _ _ _ _ _ _ _ _ _ _ OdB Spurious | ^ Free Dyn | | Fundamental | SNR Range | | at_max_signal v |__\ |--|---------------------------RMS_Noise_Level / | | | 3rd Harmonic | _| | __| 5rd Harmonic |/ \/\__|/\/ |_/\/ -------Average Noise Level |______________________________\ (Noise Floor) ^ ^ ^ ^ ^ ^ / Bin_width = Sample_rate/Number_Points_FFT F_max =Sample_rate/2 RMS Signal A/SQRT(2) = (FSR/2)/SQRT(2) = 2^(n-1)*q/SQRT(2) RMS Noise = Qn = q/SQRT(12) SNR= RMS_Signal/RMS_Noise = 2^(n-1)*SQRT(6) SNR_pos_dB = 20*log(2^(n-1)*SQRT(6)) = 6.02*n + 1.76 NOISE_FLOOR_neg_dB = 6.02*n + 1.76 + 10*log(N/2) NOISE_FLOOR_neg_dB = 6.02*n +10*log(3*N/(PI*ENBW)) THD_neg_dB= 20*log(SQRT(sum_of_Harm_squared) ) Note: HAR (-dB) SINAD_pos_dB = -20*log( SQRT( SNR^2+THD^2 ) ) SINAD = Singal to noise ratio and distortion ENOB (SNR+Distortion-1.76+20*log(Amp_FS/Amp_Actual))/6.02 ENOB= Effective number of bits fs = Sampling Rate (Hz) fin = Input Signal Frequency (Hz) FSR = Full Scale (Input) Range of Sampling A/D Converter FS = FSRi2 = Full Scale input of Sampling A/D Converter A = Input Signal Amplitude = FS = FSR/2= OdB n = Numberof Bitsof Resolution q = LSB Size LSB = Least Significant Bit N = Numberof FFT Points N/2 = Numberof Frequency Bins (real component) ENBW = Equivalent noise bandwidth of the window function. (For a four-term Blackman-Harris window, ENBW= 2.) --------------------FFT_COS------------------------------ ^ /|\ Signal = SIN(2*P()*Num/8) S--__ __-- | \S_ __S | \_ _/ | \S S/ | \_ _/ | \__ __/ | S__ ___S |_ _ _ _ _ _ _ _ _ _--S-- _ _ _ _ _ \ | / Num Samp FFt 0 2 8 1 1.71 4 2 1 0 3 .29 0 4 0 0 5 .29 0 6 1 0 7 1.71 4 REAL MAGNITUDE ^ /|\ | \ | \ ^ 8 at @bin0 \ /|\ \ ^ | Nyq\_ /|\| \ | | \ | | \| | ^ 4 at @bin1 \ |/|\ \|_|_________________\ \ | / \| IMAGINARY MAGNITUDE \ \ ^ Nyq\_ /|\ 4 at @bin7 \ | \ | \| \ _V J_OMEGA