1. SOFIE Signal Gain Analysis Mark Hervig GATS

2. SOFIE Analog Signal Path V in is the signal into the balance attenuator, after synchronous rectification: V in = V A/Dmax * margin set margin to 1.2, so V in = 3V * 1.2 = 3.6V we’ll get V w and V s below 3V using the BA’s for example to get V exo = 2.95V requires BA = 0.82 The difference signal:  V = (V in,w * BA w – V in,s * BA s ) * G  V Weak Channel Balance Attenuator attenuation = BA w V in,w Strong Channel Balance Attenuator attenuation = BA s V in,s Differential Amp gain = G  V A/D 14 bits -3V to 3V -2 13 to 2 13 counts 1 count = 366  V

3. Balance attenuator setting vs.  V balance voltages We can balance at various voltages to increase dynamic range in  V Little impact on V w These curves apply to all channels Difference signal balance voltage,  V bal :  V bal = (V in,w * BA w – V in,s * BA s ) * G  V Solve for BA w

4.  V precision vs.  V gain and balance attenuator settings count precision, CP  V = (2 14 BA s G  V ) -1 These curves apply to all channels

5. V precision vs. balance attenuator setting Count precision, CP V = (2 14 BA) -1 Lowering BA reduces precision These curves apply to all channels

6. Recommended  V Gain Settings Channel, Target  V Gain Required  V Gain Recommended  V precision Required / CBE 1-count Altitude Range (km) 1. O 3 13.3 1.0  10 -4 / 2.2  10 -5 60 - 99 2. PMC74300 1.0  10 -6 / 2.5  10 -7 Cloud 3. H 2 O296 4.0  10 -5 / 7.7  10 -7 50 - 98 4. CO 2 2227 3.3  10 -6 / 2.8  10 -6 55 - 114 5. PMC7120 1.0  10 -5 / 6.1  10 -7 Cloud 6. CH 4 30202 2.5  10 -6 / 3.7  10 -7 40 - 95 7. CO 2 3036 2.5  10 -6 / 2.1  10 -6 64 - 121 8. NO22300 3.3  10 -6 / 2.5  10 -7 80 - 127 Assumes 14 bit A/D, -3 to 3V.  V balance voltage was –2.5V for all channels. Upper altitude is where the 1 st 10 count change occurs. Lower altitude is where  V reaches 0.8  2 14 counts. Note that the CBE 1-count precisions are not CBE system noise. Required  V precisions are taken as the strong band requirements. Signals were based on atmospheric transmissions calculated using a climatology for summer at 60°N. The analyses that lead to the above results are shown on the following pages.

7. SOFIE spectral band specifications and channel S/N requirements BandS/N*# Bits for S/N RangeRequired Physical Gain On Diff Channel (Above 2 14 counts) O 3 strong 1.0  10 4 2 14 (1.64  10 4 ) 2 O 3 weak 1.0  10 4 2 14 (1.64  10 4 ) 2 particle strong 1.0  10 6 2 20 (1.05  10 6 ) 128 particle weak 1.0  10 6 2 20 (1.05  10 6 ) 128 H 2 O weak 2.5  10 4 2 14 (1.64  10 4 ) 2 H 2 O strong 2.5  10 4 2 14 (1.64  10 4 ) 2 CO 2 strong 3.0  10 5 2 19 (5.24  10 5 ) 64 CO 2 weak 3.0  10 5 2 19 (5.24  10 5 ) 64 particle strong 1.0  10 5 2 17 (1.31  10 5 ) 16 particle weak 1.0  10 5 2 17 (1.31  10 5 ) 16 CH 4 strong 4.0  10 5 2 19 (5.24  10 5 ) 64 CH 4 weak 4.0  10 5 2 19 (5.24  10 5 ) 64 CO 2 strong 4.0  10 5 2 19 (5.24  10 5 ) 64 CO 2 weak 4.0  10 5 2 19 (5.24  10 5 ) 64 NO weak 3.0  10 5 2 19 (5.24  10 5 ) 64 NO strong 3.0  10 5 2 19 (5.24  10 5 ) 64 (Chad) SOFIE Radiometric Measurement End-to-End Required SNRs

8. SOFIE PC Radiometric Electronics Overview –Carrier Frequency = 1kHz, Modulation = 2 Hz, Effective Sync Rect Q = 500 –Nominal Equal System-wide Phasing: Butterworth and Bessel Filters

9. 1) O 3 channel profiles Balance  V at –2.5V BA s = 0.819 BA w = 0.613 G  V = 3.3  V saturates at 60 km, or 0.8*2 14 counts

10. 1) O 3 Channel useful altitude Useful altitude of  V signals is determined by the  V gain and balance attenuator settings. Baseline altitude range will be determined by G  V Adjusting the BA settings changes the altitude range very little in this case

11. 2) SW particle channel profiles Balance  V at –2.5V BA s = 0.819 BA w = 0.814 G  V = 300  V useable through typical PMC

12. 3) H 2 O channel profiles Balance  V at –2.5V BA s = 0.819 BA w = 0.812 G  V = 96  V saturates at 50 km, or 0.8*2 14 counts

13. 3) H 2 O Channel useful altitude Useful altitude of  V signals is determined by the  V gain and balance attenuator settings. Baseline altitude range will be determined by G  V We can adjust the BA settings to change our altitude range

14. 3) H 2 O channel useful altitude The  V gain to saturate at 50 km altitude changes with  V balance voltage Decreasing the  V balance voltage increases the dynamic range With increased dynamic range, we can tolerate an increase in the  V gain The figure shows the  V gain that saturates  V at 50 km vs.  V bal Decreasing  V bal allows us to get more precision and dynamic range

15. 4) 2.8  m CO 2 channel profiles

16. 4) 2.8  m CO 2 channel useful altitude Useful altitude of  V signals is determined by the  V gain and balance attenuator settings. Baseline altitude range will be determined by G  V Adjusting the BA settings changes the altitude range

17. 5) IR particle channel profiles Balance  V at –2.5V BA s = 0.819 BA w = 0.814 G  V = 120  V useable through typical PMC

18. 6) CH 4 channel profiles Balance  V at –2.5V BA s = 0.819 BA w = 0.816 G  V = 202  V saturates at 40 km, or 0.8*2 14 counts

19. 6) CH 4 Channel useful altitude Useful altitude of  V signals is determined by the  V gain and balance attenuator settings. Baseline altitude range will be determined by G  V Adjusting the BA settings changes the altitude range

20. 7) 4.3  m CO 2 channel profiles

21. 7) 4.3  m CO 2 channel useful altitude Useful altitude of  V signals is determined by the  V gain and balance attenuator settings. Baseline altitude range will be determined by G  V Adjusting the BA settings changes the altitude range

22. 8) NO channel profiles Balance  V at –2.5V BA s = 0.819 BA w = 0.817 G  V = 300  V never saturates, but the signal is dominated by atmospheric interference below 80 km.