; File: SpecLab/html/eve_calc.txt ; Author: Wolfgang Buescher ; Purpose: ; Calculator for some theoretic values for the EVE experiment . ; Details in earth_venus_earth.htm . ; Use DL4YHF's CalcEd to calculate all formulas in this document ; ( press F9 to update all ) . ; Assumed SNR values, estimated by Karl Meinzer: ; On 10 GHz: SNR = -21.6dB ; RBW = 40 Hz ; on 2.4 GHz: SNR = -8 dB ; RBW = 10 Hz ; (! - so much better ?! ) ; Input: Expected Signal-to-Noise ratio SNR := -8dB ; Input: FFT-bin-width, or Receiver Bandwidth RBW := 10Hz ; Theoretic Sigma values versus number of integrations ; (greek Sigma for standard deviation) ; Sigma := 4.32 / sqrt(N_Averages) @format("%5.2lg dB") : REM format with two decimal places for output 4.32 / sqrt(1) =: 4.3 dB 4.32 / sqrt(2) =: 3.1 dB 4.32 / sqrt(10) =: 1.4 dB 4.32 / sqrt(100) =: 0.43 dB 4.32 / sqrt(1000) =: 0.14 dB 4.32 / sqrt(5000) =: 0.061 dB 4.32 / sqrt(10000) =: 0.043 dB 4.32 / sqrt(50000) =: 0.019 dB 4.32 / sqrt(100000) =: 0.014 dB 4.32 / sqrt(500000) =: 0.0061 dB ; Theoretic ratio of Signal-Plus-Noise to Noise ; Assuming the input is dominated by white gaussian noise, ; with a weak narrow-band signal added . ; Input: SNR = Signal-to-Noise-Ratio (in dB, using the RX bandwidth) ; Ouput: SNNR = Signal+Noise to Noise Ratio (which is what we CAN MEASURE) @format("%4.2lg dB") : REM format with two decimal places for output SNNR := 10 * log10( ( 1 + 10^( SNR / 10) ) ) SNNR =: 0.64 dB ; How many integrations are required to reach a given Sigma ? @format("%4.2lf") Sigma := SNNR / 4 N_Averages := (4.32/Sigma)^2 SNNR =: 0.64 Sigma =: 0.16 N_Averages =: 731.47 731*1024/8138 =: 91.98 ; How long does it take to acquire enough samples for this number of averages ? ; Depends on FFT size and sampling rate, or -easier- the FFT_bin_width in Hz ; ( an FFT with 40 Hz bin width requires 1/40 second of time domain samples, ; the optional overlap doesn't affect this ) T_Avrg := N_Averages / RBW =: 73.15 ; Integration time in minutes: T_Avrg / 60 =: 1.22 ; Integration time in hours: T_Avrg / 3600 =: 0.02