Difference between revisions of "HFI time response model"

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(LFER4 model)
(Parameters of LFER4 model)
Line 64: Line 64:
 
The details of determining the model parameters are given in (reference P03c paper) and the best-fit parameters listed below.
 
The details of determining the model parameters are given in (reference P03c paper) and the best-fit parameters listed below.
  
{| class="wikitable" style="text-align: left; align: center; border-collapse: collapse; border-width: 1px; border-style: solid; border-color: #000"
+
<center>
|+ LFER4 model parameters.
+
{| class="wikitable"  align="center" style="text-align:center" border="1" cellpadding="5" cellspacing="0"  width=500px
 +
|+ '''LFER4 model parameters'''
 +
|- bgcolor="ffdead"
 +
! Bolometer ||  <math>A_1</math> ||  <math>\tau_1</math> (s) || <math>A_2</math> || <math>\tau_2</math> (s) || <math>A_3</math> || <math>\tau_3</math> (s) || <math>A_4</math> || <math>\tau_4</math> (s) || <math>\tau_{stray}</math> (s) || <math>S_{phase}</math> (s)
 
|-
 
|-
|style="border-style: solid; border-width: 1px"|Bolometer
+
| 100-1a|| 0.392|| 0.01|| 0.534|| 0.0209|| 0.0656|| 0.0513|| 0.00833|| 0.572|| 0.00159|| 0.00139
|style="border-style: solid; border-width: 1px"|<math>A_1</math>
 
|style="border-style: solid; border-width: 1px"|<math>\tau_1</math> (s)
 
|style="border-style: solid; border-width: 1px"|<math>A_2</math>
 
|style="border-style: solid; border-width: 1px"|<math>\tau_2</math> (s)
 
|style="border-style: solid; border-width: 1px"|<math>A_3</math>
 
|style="border-style: solid; border-width: 1px"|<math>\tau_3</math> (s)
 
|style="border-style: solid; border-width: 1px"|<math>A_4</math>
 
|style="border-style: solid; border-width: 1px"|<math>\tau_4</math> (s)
 
|style="border-style: solid; border-width: 1px"|<math>\tau_{stray}</math> (s)
 
|style="border-style: solid; border-width: 1px"|<math>S_{phase}</math> (s)
 
 
|-
 
|-
|style="border-style: solid; border-width: 1px"|100-1a
+
| 100-1b|| 0.484|| 0.0103|| 0.463|| 0.0192|| 0.0451|| 0.0714|| 0.00808|| 0.594|| 0.00149|| 0.00139
|style="border-style: solid; border-width: 1px"|0.392
 
|style="border-style: solid; border-width: 1px"|0.01
 
|style="border-style: solid; border-width: 1px"|0.534
 
|style="border-style: solid; border-width: 1px"|0.0209
 
|style="border-style: solid; border-width: 1px"|0.0656
 
|style="border-style: solid; border-width: 1px"|0.0513
 
|style="border-style: solid; border-width: 1px"|0.00833
 
|style="border-style: solid; border-width: 1px"|0.572
 
|style="border-style: solid; border-width: 1px"|0.00159
 
|style="border-style: solid; border-width: 1px"|0.00139
 
 
|-
 
|-
|style="border-style: solid; border-width: 1px"|100-1b
+
| 100-2a|| 0.474|| 0.00684|| 0.421|| 0.0136|| 0.0942|| 0.0376|| 0.0106|| 0.346|| 0.00132|| 0.00125
|style="border-style: solid; border-width: 1px"|0.484
 
|style="border-style: solid; border-width: 1px"|0.0103
 
|style="border-style: solid; border-width: 1px"|0.463
 
|style="border-style: solid; border-width: 1px"|0.0192
 
|style="border-style: solid; border-width: 1px"|0.0451
 
|style="border-style: solid; border-width: 1px"|0.0714
 
|style="border-style: solid; border-width: 1px"|0.00808
 
|style="border-style: solid; border-width: 1px"|0.594
 
|style="border-style: solid; border-width: 1px"|0.00149
 
|style="border-style: solid; border-width: 1px"|0.00139
 
 
|-
 
|-
|style="border-style: solid; border-width: 1px"|100-2a
+
| 100-2b|| 0.126|| 0.00584|| 0.717|| 0.0151|| 0.142|| 0.0351|| 0.0145|| 0.293|| 0.00138|| 0.00125
|style="border-style: solid; border-width: 1px"|0.474
 
|style="border-style: solid; border-width: 1px"|0.00684
 
|style="border-style: solid; border-width: 1px"|0.421
 
|style="border-style: solid; border-width: 1px"|0.0136
 
|style="border-style: solid; border-width: 1px"|0.0942
 
|style="border-style: solid; border-width: 1px"|0.0376
 
|style="border-style: solid; border-width: 1px"|0.0106
 
|style="border-style: solid; border-width: 1px"|0.346
 
|style="border-style: solid; border-width: 1px"|0.00132
 
|style="border-style: solid; border-width: 1px"|0.00125
 
 
|-
 
|-
|style="border-style: solid; border-width: 1px"|100-2b
+
| 100-3a|| 0.744|| 0.00539|| 0.223|| 0.0147|| 0.0262|| 0.0586|| 0.00636|| 0.907|| 0.00142|| 0.00125
|style="border-style: solid; border-width: 1px"|0.126
 
|style="border-style: solid; border-width: 1px"|0.00584
 
|style="border-style: solid; border-width: 1px"|0.717
 
|style="border-style: solid; border-width: 1px"|0.0151
 
|style="border-style: solid; border-width: 1px"|0.142
 
|style="border-style: solid; border-width: 1px"|0.0351
 
|style="border-style: solid; border-width: 1px"|0.0145
 
|style="border-style: solid; border-width: 1px"|0.293
 
|style="border-style: solid; border-width: 1px"|0.00138
 
|style="border-style: solid; border-width: 1px"|0.00125
 
 
|-
 
|-
|style="border-style: solid; border-width: 1px"|100-3a
+
| 100-3b|| 0.608|| 0.00548|| 0.352|| 0.0155|| 0.0321|| 0.0636|| 0.00821|| 0.504|| 0.00166|| 0.00125
|style="border-style: solid; border-width: 1px"|0.744
 
|style="border-style: solid; border-width: 1px"|0.00539
 
|style="border-style: solid; border-width: 1px"|0.223
 
|style="border-style: solid; border-width: 1px"|0.0147
 
|style="border-style: solid; border-width: 1px"|0.0262
 
|style="border-style: solid; border-width: 1px"|0.0586
 
|style="border-style: solid; border-width: 1px"|0.00636
 
|style="border-style: solid; border-width: 1px"|0.907
 
|style="border-style: solid; border-width: 1px"|0.00142
 
|style="border-style: solid; border-width: 1px"|0.00125
 
 
|-
 
|-
|style="border-style: solid; border-width: 1px"|100-3b
+
| 100-4a|| 0.411|| 0.0082|| 0.514|| 0.0178|| 0.0581|| 0.0579|| 0.0168|| 0.37|| 0.00125|| 0.00125
|style="border-style: solid; border-width: 1px"|0.608
 
|style="border-style: solid; border-width: 1px"|0.00548
 
|style="border-style: solid; border-width: 1px"|0.352
 
|style="border-style: solid; border-width: 1px"|0.0155
 
|style="border-style: solid; border-width: 1px"|0.0321
 
|style="border-style: solid; border-width: 1px"|0.0636
 
|style="border-style: solid; border-width: 1px"|0.00821
 
|style="border-style: solid; border-width: 1px"|0.504
 
|style="border-style: solid; border-width: 1px"|0.00166
 
|style="border-style: solid; border-width: 1px"|0.00125
 
 
|-
 
|-
|style="border-style: solid; border-width: 1px"|100-4a
+
| 100-4b|| 0.687|| 0.0113|| 0.282|| 0.0243|| 0.0218|| 0.062|| 0.00875|| 0.431|| 0.00138|| 0.00139
|style="border-style: solid; border-width: 1px"|0.411
 
|style="border-style: solid; border-width: 1px"|0.0082
 
|style="border-style: solid; border-width: 1px"|0.514
 
|style="border-style: solid; border-width: 1px"|0.0178
 
|style="border-style: solid; border-width: 1px"|0.0581
 
|style="border-style: solid; border-width: 1px"|0.0579
 
|style="border-style: solid; border-width: 1px"|0.0168
 
|style="border-style: solid; border-width: 1px"|0.37
 
|style="border-style: solid; border-width: 1px"|0.00125
 
|style="border-style: solid; border-width: 1px"|0.00125
 
 
|-
 
|-
|style="border-style: solid; border-width: 1px"|100-4b
+
| 143-1a|| 0.817|| 0.00447|| 0.144|| 0.0121|| 0.0293|| 0.0387|| 0.0101|| 0.472|| 0.00142|| 0.00125
|style="border-style: solid; border-width: 1px"|0.687
 
|style="border-style: solid; border-width: 1px"|0.0113
 
|style="border-style: solid; border-width: 1px"|0.282
 
|style="border-style: solid; border-width: 1px"|0.0243
 
|style="border-style: solid; border-width: 1px"|0.0218
 
|style="border-style: solid; border-width: 1px"|0.062
 
|style="border-style: solid; border-width: 1px"|0.00875
 
|style="border-style: solid; border-width: 1px"|0.431
 
|style="border-style: solid; border-width: 1px"|0.00138
 
|style="border-style: solid; border-width: 1px"|0.00139
 
 
|-
 
|-
|style="border-style: solid; border-width: 1px"|143-1a
+
| 143-1b|| 0.49|| 0.00472|| 0.333|| 0.0156|| 0.134|| 0.0481|| 0.0435|| 0.27|| 0.00149|| 0.00125
|style="border-style: solid; border-width: 1px"|0.817
 
|style="border-style: solid; border-width: 1px"|0.00447
 
|style="border-style: solid; border-width: 1px"|0.144
 
|style="border-style: solid; border-width: 1px"|0.0121
 
|style="border-style: solid; border-width: 1px"|0.0293
 
|style="border-style: solid; border-width: 1px"|0.0387
 
|style="border-style: solid; border-width: 1px"|0.0101
 
|style="border-style: solid; border-width: 1px"|0.472
 
|style="border-style: solid; border-width: 1px"|0.00142
 
|style="border-style: solid; border-width: 1px"|0.00125
 
 
|-
 
|-
|style="border-style: solid; border-width: 1px"|143-1b
+
| 143-2a|| 0.909|| 0.0047|| 0.0763|| 0.017|| 0.00634|| 0.1|| 0.00871|| 0.363|| 0.00148|| 0.00125
|style="border-style: solid; border-width: 1px"|0.49
 
|style="border-style: solid; border-width: 1px"|0.00472
 
|style="border-style: solid; border-width: 1px"|0.333
 
|style="border-style: solid; border-width: 1px"|0.0156
 
|style="border-style: solid; border-width: 1px"|0.134
 
|style="border-style: solid; border-width: 1px"|0.0481
 
|style="border-style: solid; border-width: 1px"|0.0435
 
|style="border-style: solid; border-width: 1px"|0.27
 
|style="border-style: solid; border-width: 1px"|0.00149
 
|style="border-style: solid; border-width: 1px"|0.00125
 
 
|-
 
|-
|style="border-style: solid; border-width: 1px"|143-2a
+
| 143-2b|| 0.912|| 0.00524|| 0.0509|| 0.0167|| 0.0244|| 0.0265|| 0.0123|| 0.295|| 0.00146|| 0.00125
|style="border-style: solid; border-width: 1px"|0.909
 
|style="border-style: solid; border-width: 1px"|0.0047
 
|style="border-style: solid; border-width: 1px"|0.0763
 
|style="border-style: solid; border-width: 1px"|0.017
 
|style="border-style: solid; border-width: 1px"|0.00634
 
|style="border-style: solid; border-width: 1px"| 0.1
 
|style="border-style: solid; border-width: 1px"|0.00871
 
|style="border-style: solid; border-width: 1px"|0.363
 
|style="border-style: solid; border-width: 1px"|0.00148
 
|style="border-style: solid; border-width: 1px"|0.00125
 
 
|-
 
|-
|style="border-style: solid; border-width: 1px"|143-2b
+
| 143-3a|| 0.681|| 0.00419|| 0.273|| 0.00956|| 0.0345|| 0.0348|| 0.0115|| 0.317|| 0.00145|| 0.00125
|style="border-style: solid; border-width: 1px"|0.912
 
|style="border-style: solid; border-width: 1px"|0.00524
 
|style="border-style: solid; border-width: 1px"|0.0509
 
|style="border-style: solid; border-width: 1px"|0.0167
 
|style="border-style: solid; border-width: 1px"|0.0244
 
|style="border-style: solid; border-width: 1px"|0.0265
 
|style="border-style: solid; border-width: 1px"|0.0123
 
|style="border-style: solid; border-width: 1px"|0.295
 
|style="border-style: solid; border-width: 1px"|0.00146
 
|style="border-style: solid; border-width: 1px"|0.00125
 
 
|-
 
|-
|style="border-style: solid; border-width: 1px"|143-3a
+
| 143-3b|| 0.82|| 0.00448|| 0.131|| 0.0132|| 0.0354|| 0.0351|| 0.0133|| 0.283|| 0.00161|| 0.000832
|style="border-style: solid; border-width: 1px"|0.681
 
|style="border-style: solid; border-width: 1px"|0.00419
 
|style="border-style: solid; border-width: 1px"|0.273
 
|style="border-style: solid; border-width: 1px"|0.00956
 
|style="border-style: solid; border-width: 1px"|0.0345
 
|style="border-style: solid; border-width: 1px"|0.0348
 
|style="border-style: solid; border-width: 1px"|0.0115
 
|style="border-style: solid; border-width: 1px"|0.317
 
|style="border-style: solid; border-width: 1px"|0.00145
 
|style="border-style: solid; border-width: 1px"|0.00125
 
 
|-
 
|-
|style="border-style: solid; border-width: 1px"|143-3b
+
| 143-4a|| 0.914|| 0.00569|| 0.072|| 0.0189|| 0.00602|| 0.0482|| 0.00756|| 0.225|| 0.00159|| 0.00125
|style="border-style: solid; border-width: 1px"|0.82
 
|style="border-style: solid; border-width: 1px"|0.00448
 
|style="border-style: solid; border-width: 1px"|0.131
 
|style="border-style: solid; border-width: 1px"|0.0132
 
|style="border-style: solid; border-width: 1px"|0.0354
 
|style="border-style: solid; border-width: 1px"|0.0351
 
|style="border-style: solid; border-width: 1px"|0.0133
 
|style="border-style: solid; border-width: 1px"|0.283
 
|style="border-style: solid; border-width: 1px"|0.00161
 
|style="border-style: solid; border-width: 1px"|0.000832
 
 
|-
 
|-
|style="border-style: solid; border-width: 1px"|143-4a
+
| 143-4b|| 0.428|| 0.00606|| 0.508|| 0.00606|| 0.0554|| 0.0227|| 0.00882|| 0.084|| 0.00182|| 0.00125
|style="border-style: solid; border-width: 1px"|0.914
 
|style="border-style: solid; border-width: 1px"|0.00569
 
|style="border-style: solid; border-width: 1px"|0.072
 
|style="border-style: solid; border-width: 1px"|0.0189
 
|style="border-style: solid; border-width: 1px"|0.00602
 
|style="border-style: solid; border-width: 1px"|0.0482
 
|style="border-style: solid; border-width: 1px"|0.00756
 
|style="border-style: solid; border-width: 1px"|0.225
 
|style="border-style: solid; border-width: 1px"|0.00159
 
|style="border-style: solid; border-width: 1px"|0.00125
 
 
|-
 
|-
|style="border-style: solid; border-width: 1px"|143-4b
+
| 143-5|| 0.491|| 0.00664|| 0.397|| 0.00664|| 0.0962|| 0.0264|| 0.0156|| 0.336|| 0.00202|| 0.00139
|style="border-style: solid; border-width: 1px"|0.428
 
|style="border-style: solid; border-width: 1px"|0.00606
 
|style="border-style: solid; border-width: 1px"|0.508
 
|style="border-style: solid; border-width: 1px"|0.00606
 
|style="border-style: solid; border-width: 1px"|0.0554
 
|style="border-style: solid; border-width: 1px"|0.0227
 
|style="border-style: solid; border-width: 1px"|0.00882
 
|style="border-style: solid; border-width: 1px"|0.084
 
|style="border-style: solid; border-width: 1px"|0.00182
 
|style="border-style: solid; border-width: 1px"|0.00125
 
 
|-
 
|-
|style="border-style: solid; border-width: 1px"|143-5
+
| 143-6|| 0.518|| 0.00551|| 0.409|| 0.00551|| 0.0614|| 0.0266|| 0.0116|| 0.314|| 0.00153|| 0.00111
|style="border-style: solid; border-width: 1px"|0.491
 
|style="border-style: solid; border-width: 1px"|0.00664
 
|style="border-style: solid; border-width: 1px"|0.397
 
|style="border-style: solid; border-width: 1px"|0.00664
 
|style="border-style: solid; border-width: 1px"|0.0962
 
|style="border-style: solid; border-width: 1px"|0.0264
 
|style="border-style: solid; border-width: 1px"|0.0156
 
|style="border-style: solid; border-width: 1px"|0.336
 
|style="border-style: solid; border-width: 1px"|0.00202
 
|style="border-style: solid; border-width: 1px"|0.00139
 
 
|-
 
|-
|style="border-style: solid; border-width: 1px"|143-6
+
| 143-7|| 0.414|| 0.00543|| 0.562|| 0.00543|| 0.0185|| 0.0449|| 0.00545|| 0.314|| 0.00186|| 0.00139
|style="border-style: solid; border-width: 1px"|0.518
 
|style="border-style: solid; border-width: 1px"|0.00551
 
|style="border-style: solid; border-width: 1px"|0.409
 
|style="border-style: solid; border-width: 1px"|0.00551
 
|style="border-style: solid; border-width: 1px"|0.0614
 
|style="border-style: solid; border-width: 1px"|0.0266
 
|style="border-style: solid; border-width: 1px"|0.0116
 
|style="border-style: solid; border-width: 1px"|0.314
 
|style="border-style: solid; border-width: 1px"|0.00153
 
|style="border-style: solid; border-width: 1px"|0.00111
 
 
|-
 
|-
|style="border-style: solid; border-width: 1px"|143-7
+
| 217-5a|| 0.905|| 0.00669|| 0.0797|| 0.0216|| 0.00585|| 0.0658|| 0.00986|| 0.342|| 0.00157|| 0.00111
|style="border-style: solid; border-width: 1px"|0.414
 
|style="border-style: solid; border-width: 1px"|0.00543
 
|style="border-style: solid; border-width: 1px"|0.562
 
|style="border-style: solid; border-width: 1px"|0.00543
 
|style="border-style: solid; border-width: 1px"|0.0185
 
|style="border-style: solid; border-width: 1px"|0.0449
 
|style="border-style: solid; border-width: 1px"|0.00545
 
|style="border-style: solid; border-width: 1px"|0.314
 
|style="border-style: solid; border-width: 1px"|0.00186
 
|style="border-style: solid; border-width: 1px"|0.00139
 
 
|-
 
|-
|style="border-style: solid; border-width: 1px"|217-5a
+
| 217-5b|| 0.925|| 0.00576|| 0.061|| 0.018|| 0.00513|| 0.0656|| 0.0094|| 0.287|| 0.00187|| 0.00125
|style="border-style: solid; border-width: 1px"|0.905
 
|style="border-style: solid; border-width: 1px"|0.00669
 
|style="border-style: solid; border-width: 1px"|0.0797
 
|style="border-style: solid; border-width: 1px"|0.0216
 
|style="border-style: solid; border-width: 1px"|0.00585
 
|style="border-style: solid; border-width: 1px"|0.0658
 
|style="border-style: solid; border-width: 1px"|0.00986
 
|style="border-style: solid; border-width: 1px"|0.342
 
|style="border-style: solid; border-width: 1px"|0.00157
 
|style="border-style: solid; border-width: 1px"|0.00111
 
 
|-
 
|-
|style="border-style: solid; border-width: 1px"|217-5b
+
| 217-6a|| 0.844|| 0.00645|| 0.0675|| 0.0197|| 0.0737|| 0.0316|| 0.0147|| 0.297|| 0.00154|| 0.00125
|style="border-style: solid; border-width: 1px"|0.925
 
|style="border-style: solid; border-width: 1px"|0.00576
 
|style="border-style: solid; border-width: 1px"|0.061
 
|style="border-style: solid; border-width: 1px"|0.018
 
|style="border-style: solid; border-width: 1px"|0.00513
 
|style="border-style: solid; border-width: 1px"|0.0656
 
|style="border-style: solid; border-width: 1px"|0.0094
 
|style="border-style: solid; border-width: 1px"|0.287
 
|style="border-style: solid; border-width: 1px"|0.00187
 
|style="border-style: solid; border-width: 1px"|0.00125
 
 
|-
 
|-
|style="border-style: solid; border-width: 1px"|217-6a
+
| 217-6b|| 0.284|| 0.00623|| 0.666|| 0.00623|| 0.0384|| 0.024|| 0.0117|| 0.15|| 0.00146|| 0.00111
|style="border-style: solid; border-width: 1px"|0.844
 
|style="border-style: solid; border-width: 1px"|0.00645
 
|style="border-style: solid; border-width: 1px"|0.0675
 
|style="border-style: solid; border-width: 1px"|0.0197
 
|style="border-style: solid; border-width: 1px"|0.0737
 
|style="border-style: solid; border-width: 1px"|0.0316
 
|style="border-style: solid; border-width: 1px"|0.0147
 
|style="border-style: solid; border-width: 1px"|0.297
 
|style="border-style: solid; border-width: 1px"|0.00154
 
|style="border-style: solid; border-width: 1px"|0.00125
 
 
|-
 
|-
|style="border-style: solid; border-width: 1px"|217-6b
+
| 217-7a|| 0.343|| 0.00548|| 0.574|| 0.00548|| 0.0717|| 0.023|| 0.0107|| 0.32|| 0.00152|| 0.00139
|style="border-style: solid; border-width: 1px"|0.284
 
|style="border-style: solid; border-width: 1px"|0.00623
 
|style="border-style: solid; border-width: 1px"|0.666
 
|style="border-style: solid; border-width: 1px"|0.00623
 
|style="border-style: solid; border-width: 1px"|0.0384
 
|style="border-style: solid; border-width: 1px"|0.024
 
|style="border-style: solid; border-width: 1px"|0.0117
 
|style="border-style: solid; border-width: 1px"|0.15
 
|style="border-style: solid; border-width: 1px"|0.00146
 
|style="border-style: solid; border-width: 1px"|0.00111
 
 
|-
 
|-
|style="border-style: solid; border-width: 1px"|217-7a
+
| 217-7b|| 0.846|| 0.00507|| 0.127|| 0.0144|| 0.0131|| 0.0479|| 0.0133|| 0.311|| 0.00151|| 0.00139
|style="border-style: solid; border-width: 1px"|0.343
 
|style="border-style: solid; border-width: 1px"|0.00548
 
|style="border-style: solid; border-width: 1px"|0.574
 
|style="border-style: solid; border-width: 1px"|0.00548
 
|style="border-style: solid; border-width: 1px"|0.0717
 
|style="border-style: solid; border-width: 1px"|0.023
 
|style="border-style: solid; border-width: 1px"|0.0107
 
|style="border-style: solid; border-width: 1px"|0.32
 
|style="border-style: solid; border-width: 1px"|0.00152
 
|style="border-style: solid; border-width: 1px"|0.00139
 
 
|-
 
|-
|style="border-style: solid; border-width: 1px"|217-7b
+
| 217-8a|| 0.496|| 0.00722|| 0.439|| 0.00722|| 0.0521|| 0.0325|| 0.0128|| 0.382|| 0.00179|| 0.00111
|style="border-style: solid; border-width: 1px"|0.846
 
|style="border-style: solid; border-width: 1px"|0.00507
 
|style="border-style: solid; border-width: 1px"|0.127
 
|style="border-style: solid; border-width: 1px"|0.0144
 
|style="border-style: solid; border-width: 1px"|0.0131
 
|style="border-style: solid; border-width: 1px"|0.0479
 
|style="border-style: solid; border-width: 1px"|0.0133
 
|style="border-style: solid; border-width: 1px"|0.311
 
|style="border-style: solid; border-width: 1px"|0.00151
 
|style="border-style: solid; border-width: 1px"|0.00139
 
 
|-
 
|-
|style="border-style: solid; border-width: 1px"|217-8a
+
| 217-8b|| 0.512|| 0.00703|| 0.41|| 0.00703|| 0.0639|| 0.0272|| 0.0139|| 0.232|| 0.00173|| 0.00125
|style="border-style: solid; border-width: 1px"|0.496
 
|style="border-style: solid; border-width: 1px"|0.00722
 
|style="border-style: solid; border-width: 1px"|0.439
 
|style="border-style: solid; border-width: 1px"|0.00722
 
|style="border-style: solid; border-width: 1px"|0.0521
 
|style="border-style: solid; border-width: 1px"|0.0325
 
|style="border-style: solid; border-width: 1px"|0.0128
 
|style="border-style: solid; border-width: 1px"|0.382
 
|style="border-style: solid; border-width: 1px"|0.00179
 
|style="border-style: solid; border-width: 1px"|0.00111
 
 
|-
 
|-
|style="border-style: solid; border-width: 1px"|217-8b
+
| 217-1|| 0.0136|| 0.00346|| 0.956|| 0.00346|| 0.0271|| 0.0233|| 0.00359|| 1.98|| 0.00159|| 0.00111
|style="border-style: solid; border-width: 1px"|0.512
 
|style="border-style: solid; border-width: 1px"|0.00703
 
|style="border-style: solid; border-width: 1px"|0.41
 
|style="border-style: solid; border-width: 1px"|0.00703
 
|style="border-style: solid; border-width: 1px"|0.0639
 
|style="border-style: solid; border-width: 1px"|0.0272
 
|style="border-style: solid; border-width: 1px"|0.0139
 
|style="border-style: solid; border-width: 1px"|0.232
 
|style="border-style: solid; border-width: 1px"|0.00173
 
|style="border-style: solid; border-width: 1px"|0.00125
 
 
|-
 
|-
|style="border-style: solid; border-width: 1px"|217-1
+
| 217-2|| 0.978|| 0.00352|| 0.014|| 0.0261|| 0.00614|| 0.042|| 0.00194|| 0.686|| 0.0016|| 0.00125
|style="border-style: solid; border-width: 1px"|0.0136
 
|style="border-style: solid; border-width: 1px"|0.00346
 
|style="border-style: solid; border-width: 1px"|0.956
 
|style="border-style: solid; border-width: 1px"|0.00346
 
|style="border-style: solid; border-width: 1px"|0.0271
 
|style="border-style: solid; border-width: 1px"|0.0233
 
|style="border-style: solid; border-width: 1px"|0.00359
 
|style="border-style: solid; border-width: 1px"|1.98
 
|style="border-style: solid; border-width: 1px"|0.00159
 
|style="border-style: solid; border-width: 1px"|0.00111
 
 
|-
 
|-
|style="border-style: solid; border-width: 1px"|217-2
+
| 217-3|| 0.932|| 0.00355|| 0.0336|| 0.00355|| 0.0292|| 0.0324|| 0.00491|| 0.279|| 0.00174|| 0.00125
|style="border-style: solid; border-width: 1px"|0.978
 
|style="border-style: solid; border-width: 1px"|0.00352
 
|style="border-style: solid; border-width: 1px"|0.014
 
|style="border-style: solid; border-width: 1px"|0.0261
 
|style="border-style: solid; border-width: 1px"|0.00614
 
|style="border-style: solid; border-width: 1px"|0.042
 
|style="border-style: solid; border-width: 1px"|0.00194
 
|style="border-style: solid; border-width: 1px"|0.686
 
|style="border-style: solid; border-width: 1px"|0.0016
 
|style="border-style: solid; border-width: 1px"|0.00125
 
 
|-
 
|-
|style="border-style: solid; border-width: 1px"|217-3
+
| 217-4|| 0.658|| 0.00135|| 0.32|| 0.00555|| 0.0174|| 0.0268|| 0.00424|| 0.473|| 0.00171|| 0.00111
|style="border-style: solid; border-width: 1px"|0.932
 
|style="border-style: solid; border-width: 1px"|0.00355
 
|style="border-style: solid; border-width: 1px"|0.0336
 
|style="border-style: solid; border-width: 1px"|0.00355
 
|style="border-style: solid; border-width: 1px"|0.0292
 
|style="border-style: solid; border-width: 1px"|0.0324
 
|style="border-style: solid; border-width: 1px"|0.00491
 
|style="border-style: solid; border-width: 1px"|0.279
 
|style="border-style: solid; border-width: 1px"|0.00174
 
|style="border-style: solid; border-width: 1px"|0.00125
 
 
|-
 
|-
|style="border-style: solid; border-width: 1px"|217-4
+
| 353-3a|| 0.554|| 0.00704|| 0.36|| 0.00704|| 0.0699|| 0.0305|| 0.0163|| 0.344|| 0.0017|| 0.00125
|style="border-style: solid; border-width: 1px"|0.658
 
|style="border-style: solid; border-width: 1px"|0.00135
 
|style="border-style: solid; border-width: 1px"|0.32
 
|style="border-style: solid; border-width: 1px"|0.00555
 
|style="border-style: solid; border-width: 1px"|0.0174
 
|style="border-style: solid; border-width: 1px"|0.0268
 
|style="border-style: solid; border-width: 1px"|0.00424
 
|style="border-style: solid; border-width: 1px"|0.473
 
|style="border-style: solid; border-width: 1px"|0.00171
 
|style="border-style: solid; border-width: 1px"|0.00111
 
 
|-
 
|-
|style="border-style: solid; border-width: 1px"|353-3a
+
| 353-3b|| 0.219|| 0.00268|| 0.671|| 0.00695|| 0.0977|| 0.0238|| 0.0119|| 0.289|| 0.00157|| 0.00111
|style="border-style: solid; border-width: 1px"|0.554
 
|style="border-style: solid; border-width: 1px"|0.00704
 
|style="border-style: solid; border-width: 1px"|0.36
 
|style="border-style: solid; border-width: 1px"|0.00704
 
|style="border-style: solid; border-width: 1px"|0.0699
 
|style="border-style: solid; border-width: 1px"|0.0305
 
|style="border-style: solid; border-width: 1px"|0.0163
 
|style="border-style: solid; border-width: 1px"|0.344
 
|style="border-style: solid; border-width: 1px"|0.0017
 
|style="border-style: solid; border-width: 1px"|0.00125
 
 
|-
 
|-
|style="border-style: solid; border-width: 1px"|353-3b
+
| 353-4a|| 0.768|| 0.00473|| 0.198|| 0.00993|| 0.0283|| 0.0505|| 0.00628|| 0.536|| 0.00181|| 0.00125
|style="border-style: solid; border-width: 1px"|0.219
 
|style="border-style: solid; border-width: 1px"|0.00268
 
|style="border-style: solid; border-width: 1px"|0.671
 
|style="border-style: solid; border-width: 1px"|0.00695
 
|style="border-style: solid; border-width: 1px"|0.0977
 
|style="border-style: solid; border-width: 1px"|0.0238
 
|style="border-style: solid; border-width: 1px"|0.0119
 
|style="border-style: solid; border-width: 1px"|0.289
 
|style="border-style: solid; border-width: 1px"|0.00157
 
|style="border-style: solid; border-width: 1px"|0.00111
 
 
|-
 
|-
|style="border-style: solid; border-width: 1px"|353-4a
+
| 353-4b|| 0.684|| 0.00454|| 0.224|| 0.0108|| 0.0774|| 0.08|| 0.0149|| 0.267|| 0.00166|| 0.00111
|style="border-style: solid; border-width: 1px"|0.768
 
|style="border-style: solid; border-width: 1px"|0.00473
 
|style="border-style: solid; border-width: 1px"|0.198
 
|style="border-style: solid; border-width: 1px"|0.00993
 
|style="border-style: solid; border-width: 1px"|0.0283
 
|style="border-style: solid; border-width: 1px"|0.0505
 
|style="border-style: solid; border-width: 1px"|0.00628
 
|style="border-style: solid; border-width: 1px"|0.536
 
|style="border-style: solid; border-width: 1px"|0.00181
 
|style="border-style: solid; border-width: 1px"|0.00125
 
 
|-
 
|-
|style="border-style: solid; border-width: 1px"|353-4b
+
| 353-5a|| 0.767|| 0.00596|| 0.159|| 0.0124|| 0.0628|| 0.0303|| 0.0109|| 0.357|| 0.00156|| 0.00111
|style="border-style: solid; border-width: 1px"|0.684
 
|style="border-style: solid; border-width: 1px"|0.00454
 
|style="border-style: solid; border-width: 1px"|0.224
 
|style="border-style: solid; border-width: 1px"|0.0108
 
|style="border-style: solid; border-width: 1px"|0.0774
 
|style="border-style: solid; border-width: 1px"|0.08
 
|style="border-style: solid; border-width: 1px"|0.0149
 
|style="border-style: solid; border-width: 1px"|0.267
 
|style="border-style: solid; border-width: 1px"|0.00166
 
|style="border-style: solid; border-width: 1px"|0.00111
 
 
|-
 
|-
|style="border-style: solid; border-width: 1px"|353-5a
+
| 353-5b|| 0.832|| 0.00619|| 0.126|| 0.0111|| 0.0324|| 0.035|| 0.0096|| 0.397|| 0.00166|| 0.00111
|style="border-style: solid; border-width: 1px"|0.767
 
|style="border-style: solid; border-width: 1px"|0.00596
 
|style="border-style: solid; border-width: 1px"|0.159
 
|style="border-style: solid; border-width: 1px"|0.0124
 
|style="border-style: solid; border-width: 1px"|0.0628
 
|style="border-style: solid; border-width: 1px"|0.0303
 
|style="border-style: solid; border-width: 1px"|0.0109
 
|style="border-style: solid; border-width: 1px"|0.357
 
|style="border-style: solid; border-width: 1px"|0.00156
 
|style="border-style: solid; border-width: 1px"|0.00111
 
 
|-
 
|-
|style="border-style: solid; border-width: 1px"|353-5b
+
| 353-6a|| 0.0487|| 0.00176|| 0.855|| 0.006|| 0.0856|| 0.0216|| 0.0105|| 0.222|| 0.00199|| 0.00125
|style="border-style: solid; border-width: 1px"|0.832
 
|style="border-style: solid; border-width: 1px"|0.00619
 
|style="border-style: solid; border-width: 1px"|0.126
 
|style="border-style: solid; border-width: 1px"|0.0111
 
|style="border-style: solid; border-width: 1px"|0.0324
 
|style="border-style: solid; border-width: 1px"|0.035
 
|style="border-style: solid; border-width: 1px"|0.0096
 
|style="border-style: solid; border-width: 1px"|0.397
 
|style="border-style: solid; border-width: 1px"|0.00166
 
|style="border-style: solid; border-width: 1px"|0.00111
 
 
|-
 
|-
|style="border-style: solid; border-width: 1px"|353-6a
+
| 353-6b|| 0.829|| 0.00561|| 0.127|| 0.00561|| 0.0373|| 0.0252|| 0.00696|| 0.36|| 0.00228|| 0.00111
|style="border-style: solid; border-width: 1px"|0.0487
 
|style="border-style: solid; border-width: 1px"|0.00176
 
|style="border-style: solid; border-width: 1px"|0.855
 
|style="border-style: solid; border-width: 1px"|0.006
 
|style="border-style: solid; border-width: 1px"|0.0856
 
|style="border-style: solid; border-width: 1px"|0.0216
 
|style="border-style: solid; border-width: 1px"|0.0105
 
|style="border-style: solid; border-width: 1px"|0.222
 
|style="border-style: solid; border-width: 1px"|0.00199
 
|style="border-style: solid; border-width: 1px"|0.00125
 
 
|-
 
|-
|style="border-style: solid; border-width: 1px"|353-6b
+
| 353-1|| 0.41|| 0.000743|| 0.502|| 0.00422|| 0.0811|| 0.0177|| 0.0063|| 0.329|| 0.00132|| 0.00097
|style="border-style: solid; border-width: 1px"|0.829
 
|style="border-style: solid; border-width: 1px"|0.00561
 
|style="border-style: solid; border-width: 1px"|0.127
 
|style="border-style: solid; border-width: 1px"|0.00561
 
|style="border-style: solid; border-width: 1px"|0.0373
 
|style="border-style: solid; border-width: 1px"|0.0252
 
|style="border-style: solid; border-width: 1px"|0.00696
 
|style="border-style: solid; border-width: 1px"|0.36
 
|style="border-style: solid; border-width: 1px"|0.00228
 
|style="border-style: solid; border-width: 1px"|0.00111
 
 
|-
 
|-
|style="border-style: solid; border-width: 1px"|353-1
+
| 353-2|| 0.747|| 0.00309|| 0.225|| 0.00726|| 0.0252|| 0.0447|| 0.00267|| 0.513|| 0.00154|| 0.00097
|style="border-style: solid; border-width: 1px"|0.41
 
|style="border-style: solid; border-width: 1px"|0.000743
 
|style="border-style: solid; border-width: 1px"|0.502
 
|style="border-style: solid; border-width: 1px"|0.00422
 
|style="border-style: solid; border-width: 1px"|0.0811
 
|style="border-style: solid; border-width: 1px"|0.0177
 
|style="border-style: solid; border-width: 1px"|0.0063
 
|style="border-style: solid; border-width: 1px"|0.329
 
|style="border-style: solid; border-width: 1px"|0.00132
 
|style="border-style: solid; border-width: 1px"|0.00097
 
 
|-
 
|-
|style="border-style: solid; border-width: 1px"|353-2
+
| 353-7|| 0.448|| 0.0009|| 0.537|| 0.0041|| 0.0122|| 0.0273|| 0.00346|| 0.433|| 0.00178|| 0.00125
|style="border-style: solid; border-width: 1px"|0.747
 
|style="border-style: solid; border-width: 1px"|0.00309
 
|style="border-style: solid; border-width: 1px"|0.225
 
|style="border-style: solid; border-width: 1px"|0.00726
 
|style="border-style: solid; border-width: 1px"|0.0252
 
|style="border-style: solid; border-width: 1px"|0.0447
 
|style="border-style: solid; border-width: 1px"|0.00267
 
|style="border-style: solid; border-width: 1px"|0.513
 
|style="border-style: solid; border-width: 1px"|0.00154
 
|style="border-style: solid; border-width: 1px"|0.00097
 
 
|-
 
|-
|style="border-style: solid; border-width: 1px"|353-7
+
| 353-8|| 0.718|| 0.00223|| 0.261|| 0.00608|| 0.0165|| 0.038|| 0.00408|| 0.268|| 0.00177|| 0.00111
|style="border-style: solid; border-width: 1px"|0.448
 
|style="border-style: solid; border-width: 1px"|0.0009
 
|style="border-style: solid; border-width: 1px"|0.537
 
|style="border-style: solid; border-width: 1px"|0.0041
 
|style="border-style: solid; border-width: 1px"|0.0122
 
|style="border-style: solid; border-width: 1px"|0.0273
 
|style="border-style: solid; border-width: 1px"|0.00346
 
|style="border-style: solid; border-width: 1px"|0.433
 
|style="border-style: solid; border-width: 1px"|0.00178
 
|style="border-style: solid; border-width: 1px"|0.00125
 
 
|-
 
|-
|style="border-style: solid; border-width: 1px"|353-8
+
| 545-1|| 0.991|| 0.00293|| 0.00743|| 0.026|| 0.00139|| 2.6||   0||   0|| 0.00216|| 0.00111
|style="border-style: solid; border-width: 1px"|0.718
 
|style="border-style: solid; border-width: 1px"|0.00223
 
|style="border-style: solid; border-width: 1px"|0.261
 
|style="border-style: solid; border-width: 1px"|0.00608
 
|style="border-style: solid; border-width: 1px"|0.0165
 
|style="border-style: solid; border-width: 1px"|0.038
 
|style="border-style: solid; border-width: 1px"|0.00408
 
|style="border-style: solid; border-width: 1px"|0.268
 
|style="border-style: solid; border-width: 1px"|0.00177
 
|style="border-style: solid; border-width: 1px"|0.00111
 
 
|-
 
|-
|style="border-style: solid; border-width: 1px"|545-1
+
| 545-2|| 0.985|| 0.00277|| 0.0128|| 0.024|| 0.00246|| 2.8||   0||   0|| 0.00187|| 0.00097
|style="border-style: solid; border-width: 1px"|0.991
 
|style="border-style: solid; border-width: 1px"|0.00293
 
|style="border-style: solid; border-width: 1px"|0.00743
 
|style="border-style: solid; border-width: 1px"|0.026
 
|style="border-style: solid; border-width: 1px"|0.00139
 
|style="border-style: solid; border-width: 1px"| 2.6
 
|style="border-style: solid; border-width: 1px"|   0
 
|style="border-style: solid; border-width: 1px"|   0
 
|style="border-style: solid; border-width: 1px"|0.00216
 
|style="border-style: solid; border-width: 1px"|0.00111
 
 
|-
 
|-
|style="border-style: solid; border-width: 1px"|545-2
+
| 545-4|| 0.972|| 0.003|| 0.0277|| 0.025|| 0.000777|| 2.5||   0||   0|| 0.00222|| 0.00111
|style="border-style: solid; border-width: 1px"|0.985
 
|style="border-style: solid; border-width: 1px"|0.00277
 
|style="border-style: solid; border-width: 1px"|0.0128
 
|style="border-style: solid; border-width: 1px"|0.024
 
|style="border-style: solid; border-width: 1px"|0.00246
 
|style="border-style: solid; border-width: 1px"| 2.8
 
|style="border-style: solid; border-width: 1px"|   0
 
|style="border-style: solid; border-width: 1px"|   0
 
|style="border-style: solid; border-width: 1px"|0.00187
 
|style="border-style: solid; border-width: 1px"|0.00097
 
 
|-
 
|-
|style="border-style: solid; border-width: 1px"|545-4
+
| 857-1|| 0.974|| 0.00338|| 0.0229|| 0.025|| 0.00349|| 2.2||   0||   0|| 0.00176|| 0.00111
|style="border-style: solid; border-width: 1px"|0.972
 
|style="border-style: solid; border-width: 1px"|0.003
 
|style="border-style: solid; border-width: 1px"|0.0277
 
|style="border-style: solid; border-width: 1px"|0.025
 
|style="border-style: solid; border-width: 1px"|0.000777
 
|style="border-style: solid; border-width: 1px"| 2.5
 
|style="border-style: solid; border-width: 1px"|   0
 
|style="border-style: solid; border-width: 1px"|   0
 
|style="border-style: solid; border-width: 1px"|0.00222
 
|style="border-style: solid; border-width: 1px"|0.00111
 
 
|-
 
|-
|style="border-style: solid; border-width: 1px"|857-1
+
| 857-2|| 0.84|| 0.00148|| 0.158|| 0.00656|| 0.00249|| 3.2||   0||   0|| 0.0022|| 0.00125
|style="border-style: solid; border-width: 1px"|0.974
 
|style="border-style: solid; border-width: 1px"|0.00338
 
|style="border-style: solid; border-width: 1px"|0.0229
 
|style="border-style: solid; border-width: 1px"|0.025
 
|style="border-style: solid; border-width: 1px"|0.00349
 
|style="border-style: solid; border-width: 1px"| 2.2
 
|style="border-style: solid; border-width: 1px"|   0
 
|style="border-style: solid; border-width: 1px"|   0
 
|style="border-style: solid; border-width: 1px"|0.00176
 
|style="border-style: solid; border-width: 1px"|0.00111
 
 
|-
 
|-
|style="border-style: solid; border-width: 1px"|857-2
+
| 857-3|| 0.36|| 4.22e-05|| 0.627|| 0.0024|| 0.0111|| 0.017|| 0.002|| 1.9|| 0.00152|| 0.00126
|style="border-style: solid; border-width: 1px"|0.84
 
|style="border-style: solid; border-width: 1px"|0.00148
 
|style="border-style: solid; border-width: 1px"|0.158
 
|style="border-style: solid; border-width: 1px"|0.00656
 
|style="border-style: solid; border-width: 1px"|0.00249
 
|style="border-style: solid; border-width: 1px"| 3.2
 
|style="border-style: solid; border-width: 1px"|   0
 
|style="border-style: solid; border-width: 1px"|   0
 
|style="border-style: solid; border-width: 1px"|0.0022
 
|style="border-style: solid; border-width: 1px"|0.00125
 
 
|-
 
|-
|style="border-style: solid; border-width: 1px"|857-3
+
| 857-4|| 0.278|| 0.0004|| 0.719|| 0.00392|| 0.00162|| 0.09|| 0.00152|| 0.8|| 0.00149|| 0.000558
|style="border-style: solid; border-width: 1px"|0.36
 
|style="border-style: solid; border-width: 1px"|4.22e-05
 
|style="border-style: solid; border-width: 1px"|0.627
 
|style="border-style: solid; border-width: 1px"|0.0024
 
|style="border-style: solid; border-width: 1px"|0.0111
 
|style="border-style: solid; border-width: 1px"|0.017
 
|style="border-style: solid; border-width: 1px"|0.002
 
|style="border-style: solid; border-width: 1px"| 1.9
 
|style="border-style: solid; border-width: 1px"|0.00152
 
|style="border-style: solid; border-width: 1px"|0.00126
 
|-
 
|style="border-style: solid; border-width: 1px"|857-4
 
|style="border-style: solid; border-width: 1px"|0.278
 
|style="border-style: solid; border-width: 1px"|0.0004
 
|style="border-style: solid; border-width: 1px"|0.719
 
|style="border-style: solid; border-width: 1px"|0.00392
 
|style="border-style: solid; border-width: 1px"|0.00162
 
|style="border-style: solid; border-width: 1px"|0.09
 
|style="border-style: solid; border-width: 1px"|0.00152
 
|style="border-style: solid; border-width: 1px"| 0.8
 
|style="border-style: solid; border-width: 1px"|0.00149
 
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[[Category:HFI design, qualification and performance|0093]]
 
[[Category:HFI design, qualification and performance|0093]]

Revision as of 14:26, 17 June 2013

LFER4 model[edit]

If we write the input signal (power) on a bolometer as [math]\label{bol_in} s_0(t)=e^{i\omega t} [/math] the bolometer physical impedance can be written as: [math]\label{bol_out} s(t)=e^{i\omega t}F(\omega) [/math] where [math]\omega[/math] is the angular frequency of the signal and [math]F(\omega)[/math] is the complex intrinsic bolometer transfer function. For HFI the bolometer transfer function is modelled as the sum of 4 single pole low pass filters: [math]\label{bol_tf} F(\omega) = \sum_{i=0,4} \frac{a_i}{1 + i\omega\tau_i} [/math] The modulation of the signal is done with a square wave, written here as a composition of sine waves of decreasing amplitude: [math]\label{sigmod} s'(t)=e^{i\omega t}F(\omega)\sum_{k=0}^{\infty} \frac{e^{i\omega_r(2k+1)t}-e^{-i\omega_r(2k+1)t}}{2i(2k+1)} [/math] where we have used the Euler relation [math]\sin x=(e^{ix}-e^{-ix})/2i[/math] and [math]\omega_r[/math] is the angular frequency of the square wave. The modulation frequency is [math]f_{mod} = \omega_r/2\pi[/math] and was set to [math]f_{mod} = 90.18759 [/math]Hz in flight. This signal is then filtered by the complex electronic transfer function [math]H(\omega)[/math]. Setting: [math]\omega_k^+=\omega+(2k+1)\omega_r[/math] [math]\omega_k^-=\omega-(2k+1)\omega_r[/math] we have: [math]\label{sigele} \Sigma(t)=\sum_{k=0}^\infty\frac{F(\omega)}{2i(2k+1)}\left[H(\omega_k^+)e^{i\omega_k^+t}-H(\omega_k^-)e^{i\omega_k^-t}\right] [/math] This signal is then sampled at high frequency ([math]2 f_{mod} NS[/math]). [math]NS[/math] is one of the parameters of the HFI electronics and corresponds to the number of high frequency samples in each modulation semi-period. In order to obtain an output signal sampled every [math]\pi/\omega_r[/math] seconds, we must integrate on a semiperiod, as done in the HFI readout. To also include a time shift [math]\Delta t[/math], the integral is calculated between [math]n\pi/\omega_r+\Delta t[/math] and [math](n+1)\pi/\omega_r+\Delta t[/math] (with [math]T=2 \pi/\omega_r[/math] period of the modulation). The time shift [math]\Delta t[/math] is encoded in the HFI electronics by the parameter [math]S_{phase}[/math], with the relation [math]\Delta t = S_{phase}/NS/f_{mod} [/math].

After integration, the [math]n[/math]-sample of a bolometer can be written as [math]\label{eqn:output} Y(t_n) = (-1)^n F(\omega) H'(\omega) e^{i t_n \omega} [/math] where [math]\label{tfele} H'(\omega) = \frac 12 \sum_{k=0}^\infty e^{-i(\frac{\pi\omega}{2\omega_r}+\omega\Delta t)} \Bigg[ \frac{H(\omega_k^+)e^{i\omega_k^+ \Delta t}}{(2k+1)\omega_k^+} \left(1-e^{\frac{i\omega_k^+\pi}{\omega_r}}\right) \\ - \frac{H(\omega_k^-)e^{i\omega_k^- \Delta t}}{(2k+1)\omega_k^-} \left(1-e^{\frac{i\omega_k^-\pi}{\omega_r}}\right) \Bigg] [/math]

The output signal in equation eqn:output can be demodulated (thus removing the [math](-1)^n[/math]) and compared to the input signal in equation bol_in. The overall transfer function is composed of the bolometer transfer function and the effective electronics transfer function, [math]H'(\omega)[/math]: [math]TF(\omega) = F(\omega) H'(\omega) [/math]

The shape of [math]H(\omega)[/math] is obtained combining low and high-pass filters with Sallen Key topologies (with their respective time constants) and accounting also for the stray capacitance low pass filter given by the bolometer impedance combined with the stray capacitance of the cables. The sequence of filters that define the electronic band-pass function [math]H(\omega) = h_0*h_1*h_2*h_3*h_4*h_{5}[/math] are listed in the following table.

HFI electronics filter sequence. We define $s = i \omega$
Filter Parameters Function
0. Stray capacitance low pass filter [math]\tau_{stray}= R_{bolo} C_{stray}[/math] [math]h_0 = \frac{1}{1.0+\tau_{stray}*s}[/math]
1. Low pass filter [math]R_1=1[/math]k[math]\Omega[/math]
[math]C_1=100[/math]nF
[math]h_1 = \frac{2.0+R_1*C_1*s}{2.0*(1.0+R_1*C_1*s)}[/math]
2. Sallen Key high pass filter [math]R_2=51[/math]k[math]\Omega[/math]
[math]C_2=1\mu[/math]
[math]h_2= \frac{(R_2*C_2*s)^2}{(1.0+R_2*C_2*s)^2}[/math]3
3. Sign reverse with gain [math]h_3=-5.1[/math]
4. Single pole low pass filter with gain [math]R_4=10[/math]k[math]\Omega[/math]
[math]C_4=10[/math]nF
[math]h_4= \frac{1.5}{1.0+R_4*C_4*s}[/math]
5. Single pole high pass filter coupled to a Sallen Key low pass filter [math]R_9=18.7[/math]k[math]\Omega[/math]
[math]R_{12}=37.4[/math]k[math]\Omega[/math]
[math]C=10.0[/math]nF
[math]R_{78}=510[/math]k[math]\Omega[/math]
[math]C_{18}=1.0\mu[/math]F
[math]K_3 = R_9^2*R_{78}*R_{12}^2*C^2*C_{18}[/math]
[math]K_2 = R_9*R_{12}^2*R_{78}*C^2+R_{9}^2*R_{12}^2*C^2+R_9*R_{12}^2*R_{78}*C_{18}*C[/math]
[math]K_1 =R_9*R_{12}^2*C+R_{12}*R_{78}*R_9*C_{18}[/math]
[math]h_{5} = \frac{2.0*R_{12}*R_9*R_{78}*C_{18}*s}{s^3*K_3 + s^2*K_2+ s*K_1 + R_{12}*R_9 } [/math]

Parameters of LFER4 model[edit]

The LFER4 model has are a total of 10 parameters([math]A_1[/math],[math]A_2[/math],[math]A_3[/math],[math]A_4[/math],[math]\tau_1[/math],[math]\tau_2[/math],[math]\tau_3[/math],[math]\tau_4[/math],[math]S_{phase}[/math],[math]\tau_{stray}[/math]) 9 of which are independent, for each bolometer. The free parameters of the LFER4 model are determined using in-flight data in the following ways:

  • [math]S_{phase}[/math] is fixed at the value of the REU setting.
  • [math]\tau_{stray}[/math] is measured during the QEC test during CPV.
  • [math]A_1[/math], [math]\tau_1[/math], [math]A_2[/math], [math]\tau_2[/math] are fit forcing the compactness of the scanning beam.
  • [math]A_3[/math], [math]\tau_3[/math], [math]A_{4}[/math] [math]\tau_4[/math] are fit by forcing agreement of survey 2 and survey 1 maps.
  • The overall normalization of the LFER4 model is forced to be 1.0 at the signal frequency of the dipole.

The details of determining the model parameters are given in (reference P03c paper) and the best-fit parameters listed below.

LFER4 model parameters
Bolometer [math]A_1[/math] [math]\tau_1[/math] (s) [math]A_2[/math] [math]\tau_2[/math] (s) [math]A_3[/math] [math]\tau_3[/math] (s) [math]A_4[/math] [math]\tau_4[/math] (s) [math]\tau_{stray}[/math] (s) [math]S_{phase}[/math] (s)
100-1a 0.392 0.01 0.534 0.0209 0.0656 0.0513 0.00833 0.572 0.00159 0.00139
100-1b 0.484 0.0103 0.463 0.0192 0.0451 0.0714 0.00808 0.594 0.00149 0.00139
100-2a 0.474 0.00684 0.421 0.0136 0.0942 0.0376 0.0106 0.346 0.00132 0.00125
100-2b 0.126 0.00584 0.717 0.0151 0.142 0.0351 0.0145 0.293 0.00138 0.00125
100-3a 0.744 0.00539 0.223 0.0147 0.0262 0.0586 0.00636 0.907 0.00142 0.00125
100-3b 0.608 0.00548 0.352 0.0155 0.0321 0.0636 0.00821 0.504 0.00166 0.00125
100-4a 0.411 0.0082 0.514 0.0178 0.0581 0.0579 0.0168 0.37 0.00125 0.00125
100-4b 0.687 0.0113 0.282 0.0243 0.0218 0.062 0.00875 0.431 0.00138 0.00139
143-1a 0.817 0.00447 0.144 0.0121 0.0293 0.0387 0.0101 0.472 0.00142 0.00125
143-1b 0.49 0.00472 0.333 0.0156 0.134 0.0481 0.0435 0.27 0.00149 0.00125
143-2a 0.909 0.0047 0.0763 0.017 0.00634 0.1 0.00871 0.363 0.00148 0.00125
143-2b 0.912 0.00524 0.0509 0.0167 0.0244 0.0265 0.0123 0.295 0.00146 0.00125
143-3a 0.681 0.00419 0.273 0.00956 0.0345 0.0348 0.0115 0.317 0.00145 0.00125
143-3b 0.82 0.00448 0.131 0.0132 0.0354 0.0351 0.0133 0.283 0.00161 0.000832
143-4a 0.914 0.00569 0.072 0.0189 0.00602 0.0482 0.00756 0.225 0.00159 0.00125
143-4b 0.428 0.00606 0.508 0.00606 0.0554 0.0227 0.00882 0.084 0.00182 0.00125
143-5 0.491 0.00664 0.397 0.00664 0.0962 0.0264 0.0156 0.336 0.00202 0.00139
143-6 0.518 0.00551 0.409 0.00551 0.0614 0.0266 0.0116 0.314 0.00153 0.00111
143-7 0.414 0.00543 0.562 0.00543 0.0185 0.0449 0.00545 0.314 0.00186 0.00139
217-5a 0.905 0.00669 0.0797 0.0216 0.00585 0.0658 0.00986 0.342 0.00157 0.00111
217-5b 0.925 0.00576 0.061 0.018 0.00513 0.0656 0.0094 0.287 0.00187 0.00125
217-6a 0.844 0.00645 0.0675 0.0197 0.0737 0.0316 0.0147 0.297 0.00154 0.00125
217-6b 0.284 0.00623 0.666 0.00623 0.0384 0.024 0.0117 0.15 0.00146 0.00111
217-7a 0.343 0.00548 0.574 0.00548 0.0717 0.023 0.0107 0.32 0.00152 0.00139
217-7b 0.846 0.00507 0.127 0.0144 0.0131 0.0479 0.0133 0.311 0.00151 0.00139
217-8a 0.496 0.00722 0.439 0.00722 0.0521 0.0325 0.0128 0.382 0.00179 0.00111
217-8b 0.512 0.00703 0.41 0.00703 0.0639 0.0272 0.0139 0.232 0.00173 0.00125
217-1 0.0136 0.00346 0.956 0.00346 0.0271 0.0233 0.00359 1.98 0.00159 0.00111
217-2 0.978 0.00352 0.014 0.0261 0.00614 0.042 0.00194 0.686 0.0016 0.00125
217-3 0.932 0.00355 0.0336 0.00355 0.0292 0.0324 0.00491 0.279 0.00174 0.00125
217-4 0.658 0.00135 0.32 0.00555 0.0174 0.0268 0.00424 0.473 0.00171 0.00111
353-3a 0.554 0.00704 0.36 0.00704 0.0699 0.0305 0.0163 0.344 0.0017 0.00125
353-3b 0.219 0.00268 0.671 0.00695 0.0977 0.0238 0.0119 0.289 0.00157 0.00111
353-4a 0.768 0.00473 0.198 0.00993 0.0283 0.0505 0.00628 0.536 0.00181 0.00125
353-4b 0.684 0.00454 0.224 0.0108 0.0774 0.08 0.0149 0.267 0.00166 0.00111
353-5a 0.767 0.00596 0.159 0.0124 0.0628 0.0303 0.0109 0.357 0.00156 0.00111
353-5b 0.832 0.00619 0.126 0.0111 0.0324 0.035 0.0096 0.397 0.00166 0.00111
353-6a 0.0487 0.00176 0.855 0.006 0.0856 0.0216 0.0105 0.222 0.00199 0.00125
353-6b 0.829 0.00561 0.127 0.00561 0.0373 0.0252 0.00696 0.36 0.00228 0.00111
353-1 0.41 0.000743 0.502 0.00422 0.0811 0.0177 0.0063 0.329 0.00132 0.00097
353-2 0.747 0.00309 0.225 0.00726 0.0252 0.0447 0.00267 0.513 0.00154 0.00097
353-7 0.448 0.0009 0.537 0.0041 0.0122 0.0273 0.00346 0.433 0.00178 0.00125
353-8 0.718 0.00223 0.261 0.00608 0.0165 0.038 0.00408 0.268 0.00177 0.00111
545-1 0.991 0.00293 0.00743 0.026 0.00139 2.6 0 0 0.00216 0.00111
545-2 0.985 0.00277 0.0128 0.024 0.00246 2.8 0 0 0.00187 0.00097
545-4 0.972 0.003 0.0277 0.025 0.000777 2.5 0 0 0.00222 0.00111
857-1 0.974 0.00338 0.0229 0.025 0.00349 2.2 0 0 0.00176 0.00111
857-2 0.84 0.00148 0.158 0.00656 0.00249 3.2 0 0 0.0022 0.00125
857-3 0.36 4.22e-05 0.627 0.0024 0.0111 0.017 0.002 1.9 0.00152 0.00126
857-4 0.278 0.0004 0.719 0.00392 0.00162 0.09 0.00152 0.8 0.00149 0.000558

(Planck) High Frequency Instrument

Readout Electronic Unit

Calibration and Performance Verification