; 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