Progress Toward a Full UncertaintyPropagation Machinery for EDGES: II

Raul Monsalve

SESE, Arizona State University

February 19, 2015

DescriptionThis report describes the progress toward a full uncertainty propagation procedure forEDGES. It explores aspects not described in the previous report, available at:http://loco.lab.asu.edu/memos/edges_reports/report_20150212.pdfFor a general description of the pipeline, please read that document.

The main purpose of this document is to explore the effect of the phase of the antennaS11. Three cases are compared. In all cases, the magnitude is -15 dB, completely flatin frequency in the range 100 to 200 MHz. The phases are different, and shown inFigure 1. The black trace corresponds to the steepest phase, the blue trace is theintermediate case, and the red trace is the extreme case of zero phase across thefrequency range.

Figure 2 shows the scale, offset, and noise wave parameters obtained duringcalibration of the receiver. The scale and offset are modeled with 6th degreepolynomials, and the noise wave parameters are modeled with 3rd degree polynomials.

Figures 3 through 30 show the isolated effect of each source uncertainty, for the threecases of antenna phase. The color of the traces correspond to those in Figure 1. The1σ bounds are obtained after removing a 4-term Log-Poly model from 2000 MCrealizations of calibrated antenna temperature.

Figures 29 and 30 show the impact of systematic uncertainty in the magnitude andphase of the antenna S11 itself.

Finally, the combined effect of all the uncertainties is presented in Figure 31, andFigure 32 shows the effect of only the systematic uncertainty (S11, and physicaltemperature of the ambient load, hot load, and open cable).2

Results

The plots from Figure 3 onward show a clear dependence of the uncertainty level andshape, on the phase of the antenna S11. The steeper the phase in the 100-200 MHzrange, the more ripples that appear. The cases of highest sensitivity to the antennaphase are:

I Physical Temp. of Open CableI Spectrum of Open CableI S11 of LNAI S11 of Open CableI S11 of Antenna

The uncertainty due to the sources listed above can be significantly reduced byreducing the antenna delay.

Even for zero antenna delay, there is residual ripples in the shape of the uncertaintiesdue to the modeling of the other quantities, and the covariance between theirparameters. Understanding this structure at a deeper level requires more investigation.

3

100 120 140 160 180 200−16

−15.5

−15

−14.5

−14

Ma

g S

11

[d

B]

100 120 140 160 180 200−1000

−500

0

Ph

ase

S1

1 [

de

g]

frequency [MHz]

Figure : (1)4

100 150 2001

1.2

1.4S

ca

le [

no

un

its]

100 150 200−100

−50

0

Off

se

t [K

]

100 150 20068

69

70

71

TU

[K

]

frequency [MHz]100 150 2008

10

12

14

TC

[K

]

frequency [MHz]100 150 200

−20

−10

0

TS

[K

]

frequency [MHz]

Figure : (2)

5

100 120 140 160 180 200−20

−15

−10

−5

0

5

10

15

201

σ [

mK

]

frequency [MHz]

SOURCE UNCERTAINTY: Physical Temp. of Ambient Load

Figure : (3)

6

100 120 140 160 180 200−20

−15

−10

−5

0

5

10

15

201

σ [

mK

]

frequency [MHz]

SOURCE UNCERTAINTY: Physical Temp. of Hot Load

Figure : (4)

7

100 120 140 160 180 200−0.4

−0.3

−0.2

−0.1

0

0.1

0.2

0.3

0.41

σ [m

K]

frequency [MHz]

SOURCE UNCERTAINTY: Physical Temp. of Open Cable

Figure : (5)

8

100 120 140 160 180 200−4

−3

−2

−1

0

1

2

3

41

σ [

mK

]

frequency [MHz]

SOURCE UNCERTAINTY: Spectrum of Ambient Load

Figure : (6)

9

100 120 140 160 180 200−4

−3

−2

−1

0

1

2

3

41

σ [

mK

]

frequency [MHz]

SOURCE UNCERTAINTY: Spectrum of Hot Load

Figure : (7)

10

100 120 140 160 180 200−20

−15

−10

−5

0

5

10

15

201

σ [

mK

]

frequency [MHz]

SOURCE UNCERTAINTY: Spectrum of Open Cable

Figure : (8)

11

100 120 140 160 180 200−1

−0.5

0

0.5

11

σ [m

K]

frequency [MHz]

SOURCE UNCERTAINTY: Mag S11 of LNA (STAT)

Figure : (9)

12

100 120 140 160 180 200−1

−0.5

0

0.5

11

σ [m

K]

frequency [MHz]

SOURCE UNCERTAINTY: Phase S11 of LNA (STAT)

Figure : (10)

13

100 120 140 160 180 200−0.01

−0.005

0

0.005

0.011

σ [m

K]

frequency [MHz]

SOURCE UNCERTAINTY: Mag S11 of Ambient Load (STAT)

Figure : (11)

14

100 120 140 160 180 200−0.02

−0.015

−0.01

−0.005

0

0.005

0.01

0.015

0.021

σ [m

K]

frequency [MHz]

SOURCE UNCERTAINTY: Phase S11 of Ambient Load (STAT)

Figure : (12)

15

100 120 140 160 180 200−0.04

−0.03

−0.02

−0.01

0

0.01

0.02

0.03

0.041

σ [m

K]

frequency [MHz]

SOURCE UNCERTAINTY: Mag S11 of Hot Load (STAT)

Figure : (13)

16

100 120 140 160 180 200−0.2

−0.15

−0.1

−0.05

0

0.05

0.1

0.15

0.21

σ [m

K]

frequency [MHz]

SOURCE UNCERTAINTY: Phase S11 of Hot Load (STAT)

Figure : (14)

17

100 120 140 160 180 200−0.2

−0.15

−0.1

−0.05

0

0.05

0.1

0.15

0.21

σ [m

K]

frequency [MHz]

SOURCE UNCERTAINTY: Mag S11 of Open Cable (STAT)

Figure : (15)

18

100 120 140 160 180 200−10

−5

0

5

101

σ [

mK

]

frequency [MHz]

SOURCE UNCERTAINTY: Phase S11 of Open Cable (STAT)

Figure : (16)

19

100 120 140 160 180 200−0.4

−0.3

−0.2

−0.1

0

0.1

0.2

0.3

0.41

σ [m

K]

frequency [MHz]

SOURCE UNCERTAINTY: Mag S12S21 of SR Cable (STAT)

Figure : (17)

20

100 120 140 160 180 200−1

−0.5

0

0.5

1x 10

−3

1σ

[m

K]

frequency [MHz]

SOURCE UNCERTAINTY: Phase S12S21 of SR Cable (STAT)

Figure : (18)

21

100 120 140 160 180 200−40

−30

−20

−10

0

10

20

30

401

σ [

mK

]

frequency [MHz]

SOURCE UNCERTAINTY: Mag S11 of LNA (SYST)

Figure : (19)

22

100 120 140 160 180 200−20

−15

−10

−5

0

5

10

15

201

σ [

mK

]

frequency [MHz]

SOURCE UNCERTAINTY: Phase S11 of LNA (SYST)

Figure : (20)

23

100 120 140 160 180 200−20

−15

−10

−5

0

5

10

15

201

σ [

mK

]

frequency [MHz]

SOURCE UNCERTAINTY: Mag S11 of Ambient Load (SYST)

Figure : (21)

24

100 120 140 160 180 200−2

−1.5

−1

−0.5

0

0.5

1

1.5

21

σ [m

K]

frequency [MHz]

SOURCE UNCERTAINTY: Phase S11 of Ambient Load (SYST)

Figure : (22)

25

100 120 140 160 180 200−20

−15

−10

−5

0

5

10

15

201

σ [

mK

]

frequency [MHz]

SOURCE UNCERTAINTY: Mag S11 of Hot Load (SYST)

Figure : (23)

26

100 120 140 160 180 200−2

−1.5

−1

−0.5

0

0.5

1

1.5

21

σ [m

K]

frequency [MHz]

SOURCE UNCERTAINTY: Phase S11 of Hot Load (SYST)

Figure : (24)

27

100 120 140 160 180 200−40

−30

−20

−10

0

10

20

30

401

σ [

mK

]

frequency [MHz]

SOURCE UNCERTAINTY: Mag S11 of Open Cable (SYST)

Figure : (25)

28

100 120 140 160 180 200−10

−5

0

5

101

σ [

mK

]

frequency [MHz]

SOURCE UNCERTAINTY: Phase S11 of Open Cable (SYST)

Figure : (26)

29

100 120 140 160 180 200−20

−15

−10

−5

0

5

10

15

201

σ [

mK

]

frequency [MHz]

SOURCE UNCERTAINTY: Mag S12S21 of SR Cable (SYST)

Figure : (27)

30

100 120 140 160 180 200−1

−0.5

0

0.5

1x 10

−3

1σ

[m

K]

frequency [MHz]

SOURCE UNCERTAINTY: Phase S12S21 of SR Cable (SYST)

Figure : (28)

31

100 120 140 160 180 200−20

−15

−10

−5

0

5

10

15

201

σ [

mK

]

frequency [MHz]

SOURCE UNCERTAINTY: Mag S11 of Antenna (SYST)

Figure : (29)

32

100 120 140 160 180 200−20

−15

−10

−5

0

5

10

15

201

σ [

mK

]

frequency [MHz]

SOURCE UNCERTAINTY: Phase S11 of Antenna (SYST)

Figure : (30)

33

100 120 140 160 180 200−100

−50

0

50

1001

σ [m

K]

frequency [MHz]

SOURCE UNCERTAINTY: All

Figure : (31)

34

100 120 140 160 180 200−100

−50

0

50

1001

σ [m

K]

frequency [MHz]

SOURCE UNCERTAINTY: Only Systematic

Figure : (32)

35