Performance of Antenna Measurement Setup

Raul Monsalve

SESE, Arizona State University

November 27, 2013

Description

This report is divided into two parts:

I PART 1: Check of recovered instrumental S-parameters

I PART 2: Analysis of changes in measurement setup with temperature

2

PART 1: S-parametersThe S-parameters of the measurement setup used in Boolardy tomeasure the antenna are obtained every minute, by computing: S11

S12S21 − S11S22S22

=

1 Γ1 Γ1 · Γ′11 Γ2 Γ2 · Γ′21 Γ3 Γ3 · Γ′3

−1 Γ′1Γ′2Γ′3

. (1)

where Γ and Γ′ correspond to the true and measured reflectioncoefficients of the standards: 1=open, 2=short , and 3=match.

The test presented here has the purpose of confirming that theS-parameters have been calculated properly. The method simplyconsists of computing the true reflection coefficients, Γ, using thepreviously obtained S-parameters and the measured standards Γ′:

Γ =Γ′ − S11

S12S21 + S22(Γ′ − S11). (2)

If the S-parameters are correct, the recovered reflection coefficients Γ

should be identical to the expectations for the three standards.

3

PART 1: S-parameters

For the correction process to be performed accurately, it is necessary to have a goodestimation of the temperature of the match at all moments. This temperature isobtained from a thermistor located 1 cm away from the match, which measures airtemperature. The expected DC resistance of the match is assigned based on thistemperature, and the model coefficients presented inhttp://loco.lab.asu.edu/memos/edges_reports/report_20131002.pdf.

This thermistor is inside the switch box, where also the standards are located. The boxis of the same size as the thermal enclosure for the LNA, and has limited air circulation,allowed only by small holes on the sides.

In the following plots, two temperatures are presented: 1) the exterior temperature (inblack) obtained from a thermistor located at the weather station, which measures airtemperature and is also sensitive to direct sun light, and 2) the match temperature (inred), obtained from the thermistor described above, located 1 cm away from the match.In general, the match temperature is a couple of degrees higher than the exteriortemperature due to being fairly isolated from wind.

4

PART 1: S11

0 5 10 15 20

20

30

40

tem

pera

ture

[oC

]

temp. of exterior

temp. of match

time [hours]

frequency [M

Hz]

S11

[dB]

0 5 10 15 20

0

100

200

300 −60

−40

−20

0

Figure: (1) Magnitude of S11 (BOTTOM) corresponding to the instrumental setup used for measuring theantenna, along with temperature measured in parallel (TOP).

5

PART 1: S12S21

0 5 10 15 20

20

30

40

tem

pe

ratu

re [

oC

]

temp. of exterior

temp. of match

time [hours]

fre

qu

en

cy [

MH

z]

S12

⋅ S21

[dB]

0 5 10 15 20

0

100

200

300 −1.2

−0.6

0

0.6

1.2

Figure: (2) Magnitude of S12 · S21 (BOTTOM) corresponding to the instrumental setup used for measuring theantenna, along with temperature measured in parallel (TOP).

6

PART 1: S22

0 5 10 15 20

20

30

40

tem

pera

ture

[oC

]

temp. of exterior

temp. of match

time [hours]

frequency [M

Hz]

S22

[dB]

0 5 10 15 20

0

100

200

300 −80

−60

−40

−20

Figure: (3) Magnitude of S22 (BOTTOM) corresponding to the instrumental setup used for measuring theantenna, along with temperature measured in parallel (TOP).

7

PART 1: Correction of OPEN

0 5 10 15 20

20

30

40

tem

pe

ratu

re [

oC

]

temp. of exterior

temp. of match

fre

qu

en

cy [

MH

z]

raw measurement of OPEN [dB]

0 5 10 15 20

0

100

200

300

−2

0

2

time [hours]

fre

qu

en

cy [

MH

z]

corrected measurement of OPEN [dB]

0 5 10 15 20

0

100

200

300 −0.01

−0.005

0

0.005

0.01

Figure: (4) The instrumental S-parameters (figures 1, 2, 3) are used for correcting the measurement of theopen (middle). The corrected data (bottom) are identical to the expectation, which validates the computedS-parameters and the method.

8

PART 1: Correction of OPEN

0 50 100 150 200 250 300

−2

0

2

frequency [MHz]

ma

g [

dB

]

0 50 100 150 200 250 300−0.01

0

0.01

frequency [MHz]

ma

g [

dB

]

measured

corrected

Figure: (5) Example of correction of an open trace taken ∼ 13.7 hours into the measurement. Same data arepresented in both plots; the vertical scale has been zoomed in in the plot at the bottom. The corrected trace (red) isconstant in time, and identical to the expectation.

9

PART 1: Correction of SHORT

0 5 10 15 20

20

30

40

tem

pe

ratu

re [

oC

]

temp. of exterior

temp. of match

fre

qu

en

cy [

MH

z]

raw measurement of SHORT [dB]

0 5 10 15 20

0

100

200

300

−2

0

2

time [hours]

fre

qu

en

cy [

MH

z]

corrected measurement of SHORT [dB]

0 5 10 15 20

0

100

200

300 −0.01

−0.005

0

0.005

0.01

Figure: (6) The instrumental S-parameters (figures 1, 2, 3) are used for correcting the measurement of theshort (middle). The corrected data (bottom) are identical to the expectation, which validates the computedS-parameters and the method.

10

PART 1: Correction of SHORT

0 50 100 150 200 250 300

−2

0

2m

ag

[d

B]

0 50 100 150 200 250 300−0.01

0

0.01

frequency [MHz]

ma

g [

dB

]

measured

corrected

Figure: (7) Example of correction of a short trace taken ∼ 13.7 hours into the measurement. Same data arepresented in both plots; the vertical scale has been zoomed in in the plot at the bottom. The corrected trace (red) isconstant in time, and identical to the expectation.

11

PART 1: Correction of MATCH

0 5 10 15 20

20

30

40

tem

pera

ture

[oC

]

temp. of exterior

temp. of match

frequency [M

Hz]

raw measurement of MATCHT [dB]

0 5 10 15 20

0

100

200

300−80

−60

−40

−20

time [hours]

frequency [M

Hz]

corrected measurement of MATCH [dB]

0 5 10 15 20

0

100

200

300 −66

−64

−62

−60

−58

Figure: (8) The instrumental S-parameters (figures 1, 2, 3) are used for correcting the measurement of thematch (middle). The corrected data (bottom) show the expected dependence of reflection coefficient on thetemperature of the match (red line in plot at the top). This temperature corresponds to air temperature measured 1cm from the match.

12

PART 1: Correction of MATCH

0 50 100 150 200 250 300−70

−60

−50

−40

−30

−20

−10

0

frequency [MHz]

ma

g [

dB

]

measured

corrected

Figure: (9) Example of correction of a match trace taken ∼ 13.7 hours into the measurement, at a temperatureof 19.46C. The corrected trace (red) corresponds to an impedance of 50.1336 Ω, which is equal to the expectationat that temperature.

13

PART 1: Conclusion

The correction procedure is self-consistent, in the sense that it returns the expectedvalues for the loads being measured, i.e., the open, short , and match standardsmeasured in Boolardy along with the antenna.

Therefore, the computed S-parameters (used also to correct the antennameasurements) are an adequate representation of the measurement setup at anymoment, assuming that the setup does not change within each cycle of measurement(open, short, match, and antenna) which lasts 1 minute. If, however, the setup changedwithin a cycle, an error would be introduced to the S-parameters, and propagated tothe antenna correction.

The following section (PART 2) looks into this non-ideal scenario.

14

PART 2: Change of Setup with Frequency

As presented in the report from 11/21/2013:

http://loco.lab.asu.edu/memos/edges_reports/report_20131121.pdf,

the scatter in the reflection coefficient of the antenna increases significantly with temperature (and wind, althoughthere are no data available). It is suspected for the primary cause of this to be rapid changes in the measurementsetup due to temperature fluctuations, rather than changes in the antenna itself.

To test this hypothesis it is necessary to analyze the changes in the measured reflection coefficient, for a load thatdoesn’t change with temperature or time. Therefore, this is carried out by looking at data for the open standard.

The figure of merit for comparison is the root-mean-square, in the frequency domain, of the difference between themagnitude of two consecutive traces. This quantity provides information about the sensitivity of the setup totemperature changes.

In order to have a reference, and before performing this operation for the antenna case, the figure of merit describedabove is computed for the data obtained when measuring the 6-dB and 10-dB attenuators, described in:

http://loco.lab.asu.edu/memos/edges_reports/report_20131023_12dB.pdfhttp://loco.lab.asu.edu/memos/edges_reports/report_20131023_20dB.pdf

15

PART 2: Change of Setup with Frequency

There are two main differences between the measurement of the attenuators inPhoenix, and the antenna in Boolardy. The first is that for the attenuators, the cablebetween the VNA and the switch box was 200-ft long, while for the antenna it wasapproximately 280-ft long.

The second is that for the attenuators, the equipment (coax cable, switch box,standards, and attenuator) was exposed to the environment and temperature changesbut NOT to direct sunlight (the equipment was always in the shade), while for theantenna the switch box and an important part of the (longer) cable was exposed todirect sun.

In the following plots:

I All the data correspond to raw measurements of the open standard, in threedifferent contexts: while measuring the 6-dB attenuator, the 10-dB attenuator, orthe antenna.

I ∆mag = |Γt2 | − |Γt1 |, where t2 and t1 are 1 minute apart.I K = RMS(∆mag) is the figure of merit. It is the root-mean-square of ∆mag in

the frequency range 100-200 MHz. When plotting this quantity, the x-axiscorresponds to time in minutes. In particular, at a time t = 100 [min] the value ofK is RMS(|Γ100 [min]| − |Γ99 [min]|).

16

PART 2: Open Measured (6-dB attn)

0 500 1000 1500 2000 2500 3000 350010

20

30

tem

pera

ture

[oC

]

0 500 1000 1500 2000 2500 3000 35000

0.005

0.01

time [minutes]

K=

RM

S(∆

mag)

[dB

]

Figure: (10) Results for the raw open data obtained during measurements of the 6-dB attenuator. The figure ofmerit (BOTTOM) is constant throughout the measurement (2.5 days), and therefore independent of the outsidetemperature (TOP) or its derivative. In principle, the lowest possible value should be obtained for a flat slope intemperature (occurring at the highest and lowest peaks; for example, at 500 minutes). The fact that K doesn’t getworse (doesn’t increase) when the temperature changes suggests that the equipment remains constant within timescales of 1 minute (at least under these temperature gradients) and therefore the assumption used for thecomputation of the S-parameters is valid to a high degree. Estimated slopes for the sections of ascending anddescending temperature are 0.021 and -0.015 C min−1 respectively.

17

PART 2: Open Measured (6-dB attn)

100 110 120 130 140 150 160 170 180 190 200−0.01

−0.005

0

0.005

0.01

∆ m

ag [dB

]

∆ = 500 − 499

100 110 120 130 140 150 160 170 180 190 200−0.01

−0.005

0

0.005

0.01

∆ = 700 − 699

frequency [MHz]

∆ m

ag [dB

]

Figure: (11) Difference between two open traces corresponding to the previous data set (6-dB attn), measured1 minute apart. (TOP) At time 500 [min] with stable temperature, and (BOTTOM) 700 [min] with increasingtemperature. The noise level is comparable between the two cases.

18

PART 2: Open Measured (10-dB attn)

0 500 1000 1500 2000 2500 300010

20

30

tem

pera

ture

[oC

]

0 500 1000 1500 2000 2500 30000

0.005

0.01

time [minutes]

K=

RM

S(∆

mag)

[dB

]

Figure: (12) Results for the raw open data obtained during measurements of the 10-dB attenuator. The figureof merit (BOTTOM) is constant throughout the measurement (2 days), and therefore independent of the outsidetemperature (TOP) or its derivative. In principle, the lowest possible value should be obtained for a flat slope intemperature (occurring at the highest and lowest peaks; for example at 2700 minutes). The fact that the K doesn’tget worse (doesn’t increase) when the temperature changes suggests that the equipment remains constant withintime scales of 1 minute (at least under these temperature gradients) and therefore the assumption used for thecomputation of the S-parameters is valid to a high degree. Estimated slopes for the sections of ascending anddescending temperature are 0.020 and -0.013 C min−1 respectively. The value of K is almost the same as that forthe 6-dB case, figure 10, which is to be expected since the measurement equipment is the same, and theenvironmental conditions are very similar.

19

PART 2: Open Measured (10-dB attn)

100 110 120 130 140 150 160 170 180 190 200−0.01

−0.005

0

0.005

0.01

∆ m

ag [dB

]

∆ = 1000 − 999

100 110 120 130 140 150 160 170 180 190 200−0.01

−0.005

0

0.005

0.01

∆ = 2700 − 2699

frequency [MHz]

∆ m

ag [dB

]

Figure: (13) Difference between two open traces corresponding to the previous data set (10-dB attn),measured 1 minute apart. (TOP) At time 1000 [min] with increasing temperature, and (BOTTOM) 2700 [min] withstable temperature. The noise level is comparable between the two cases.

20

PART 2: Open Measured (antenna)

0 200 400 600 800 1000 1200 1400

20

30

40

tem

pe

ratu

re [

oC

]

0 200 400 600 800 1000 1200 14000

0.005

0.01

time [minutes]

K=

RM

S(∆

ma

g)

[dB

]

Figure: (14) Results for the raw open data obtained during measurements of the antenna. Unlike the previouscases corresponding to measurements of the attenuators, here there is a notorious sensitivity of the measurementsetup to changes in ambient temperature. The region enclosed by the green lines corresponds to a night period withtemperature descending from 30C to 20C. This section is the one with the lowest sensitivity to temperaturevariations, but this sensitivity is still higher than that for the attenuators (K ≈ 0.002 dB, compared to K ≤ 0.001 dBfor the attenuators). Considering that the temperature slope is -0.022 C min−1 (only ∼ 10% higher than those forthe attenuators), and that the rest of the equipment is the same, the most probable cause for the increasedsensitivity is the use of a cable ∼ 40% longer than that used in the previous cases. The sensitivity outside theselected region is clearly higher, most probably due to time-varying temperature gradients across the cable whichare driven by wind gusts and a continuously changing amount of direct sun light.

21

PART 2: Open Measured (antenna)

100 110 120 130 140 150 160 170 180 190 200−0.01

−0.005

0

0.005

0.01

∆ m

ag [dB

]∆ = 400 − 399

100 110 120 130 140 150 160 170 180 190 200−0.01

−0.005

0

0.005

0.01

∆ = 1100 − 1099

frequency [MHz]

∆ m

ag [dB

]

Figure: (15) Difference between two open traces corresponding to the previous data set (antenna), measured 1minute apart. (TOP) At time 400 [min] during night time with decreasing temperature, and (BOTTOM) at 1100 [min]during the day with increasing temperature. The residuals of the plot on top are larger than those of figures 11 and13, obtained under similar conditions except for the shorter cable. The plot at the bottom clearly illustrates thechanges that occurred in time scales of 1 minute, during the day.

22

PART 2: Conclusion

For the measurements of the attenuators (Phoenix) and antenna (Boolardy), thechanges in the setup has been quantified using the difference between two traces ofthe open standard measured 1 minute apart.

For the attenuators, the setup seems insensitive to variations in ambient temperature inthis time scale. For the antenna, the sensitivity during the night is low but not zero.Given that the measurement equipment is the same except for the cable, this elementis the most probable cause for the difference in performance. During the day, the setupfor measuring the antenna is significantly more sensitive to environmental factors, andthe cable is again most probably the largest contributor.

With all this in mind, the antenna data taken during the night is still useful as long as anuncertainty term (on top of the noise) is assigned to the measured traces. The cleanestapproach would be letting the uncertainty be the difference between traces measured1 minute apart; this for the open, short , match, and antenna. This uncertainty wouldthen be propagated to the computed S-parameters, and the corrected antenna traces.

23