Correction of Reflection Coefficient of 10-dBAttenuator Measured with a FieldFox VNA

(Revised)

Raul Monsalve

SESE, Arizona State University

October 23, 2013

Description

The Agilent FieldFox VNA has been used for measuring the reflection coefficient of anopen-ended 10-dB attenuator at the end of a 200-ft cable, using the RF switch in asetup that also measures the open, short , and match in a continuous loop. The VNAsettings are:

1. frequency range: 2 to 300 MHz

2. frequency resolution: 1 MHz

3. power level: +5 dBm

4. IF bandwidth: 300 Hz

5. trace averaging: no

The measurement of each trace takes 15 seconds to complete, and therefore the cycleopen-short-match-attenuator takes 1 minute. The standards belong to the Agilent85033E calibration kit, and have been modeled using half the loss reported by Agilent,after checking these values against those from the Maury and Anritsu kits.

2

Measurement correction

0 50 100 150 200 250 300−20.4

−20.3

−20.2

−20.1

−20

−19.9|S

11| [d

B]

measured

corrected

expected

0 50 100 150 200 250 300−50

−40

−30

−20

−10

0

an

gle

(S1

1)

[de

g]

frequency [MHz]

Figure: (1) Correction of a typical trace, along with the expectation at DC.

3

Corrected trace, zoomed in

0 50 100 150 200 250 300

−20.22

−20.17

−20.12

−20.07

|S1

1| [d

B]

frequency [MHz]

corrected

expected

Figure: (2) Typical corrected magnitude, zoomed in. The noise level increases withfrequency up to ∼ 0.04 dB peak-to-peak at 300 MHz.

4

Performance of trace correction in the time domain

0 5 10 15 20 25 30 35 40 45 50−20.18

−20.16

−20.14

−20.12

−20.1

−20.08

−20.06

−20.04

−20.02

−20

time [hours]

|S1

1| [d

B]

measured

corrected

expected: linear

expected: quadratic

Figure: (3) Comparison of time streams at 2 MHz for the raw measurement, corrected measurement, and twomodels from the DC resistance of the attenuator coming from the study available athttp://loco.lab.asu.edu/memos/edges_reports/report_20131002.pdf. Even though in that report itwas argued that a quadratic model was more adequate, in the plot above the linear model (black line) follows thecorrected trace (red) more closely, with a constant offset. The line corresponding to the quadratic model (green)evidences a lower temperature coefficient than the data. Within the temperature range of this measurement, thecorrected data at 2 MHz departs from both models by 0.01 dB or less (if smoothing were performed on the data).

5

Raw v/s corrected data: magnitude

tim

e [

ho

urs

]

Measured |S11

| [dB]

50 100 150 200 250 300

10

20

30

40

50 −20.3

−20.2

−20.1

−20

−19.9

−19.8

frequency [MHz]

tim

e [

ho

urs

]

Corrected |S11

| [dB]

50 100 150 200 250 300

10

20

30

40

50 −20.3

−20.2

−20.1

−20

−19.9

−19.8

Figure: (4) Using the same color scale, the raw and corrected magnitude are shown. Top: most structure andripples in the raw data come from drifts in the measurement setup. Variations of the attenuator with temperature donot stand out. Bottom: once corrected, the data allow to identify the effect of changes in air temperature on theattenuator.

6

Raw v/s corrected data: phase

tim

e [hours

]

Measured angle(S11

) [deg]

50 100 150 200 250 300

10

20

30

40

50 −40

−30

−20

−10

0

frequency [MHz]

tim

e [hours

]

Corrected angle(S11

) [deg]

50 100 150 200 250 300

10

20

30

40

50 −40

−30

−20

−10

0

Figure: (5) The effect of the data correction on the phase is smaller, but noticeablenonetheless. The ripples are removed and the scale is re-adjusted.

7

Corrected time streams

0 5 10 15 20 25 30 35 40 45 5015

20

25

30

tem

pera

ture

of

attenuato

r [C

]

0 5 10 15 20 25 30 35 40 45 50−20.25

−20.2

−20.15

−20.1

−20.05

Corr

ecte

d|S

11| [d

B]

0 5 10 15 20 25 30 35 40 45 50−0.5

0

0.5

Corr

ecte

dangle

(S1

1)

(mean s

ubtr

acte

d)

[deg]

time [hours]

2 MHz 50 MHz 100 MHz 150 MHz 200 MHz 250 MHz 300 MHz

Figure: (6) Top: air temperature at the attenuator. Middle: magnitude time streams.Bottom: phase time streams. Both plots evidence different rates of change at differentfrequencies. For the phase, the average value at each frequency has been removed.

8

Plots of temperature correlation

16 18 20 22 24 26−20.25

−20.2

−20.15

−20.1

−20.05

Co

rre

cte

d|S

11| [d

B]

16 18 20 22 24 26−0.5

0

0.5

Co

rre

cte

da

ng

le(S

11)

(me

an

su

btr

acte

d)

[de

g]

temperature [C]

2 MHz 50 MHz 100 MHz 150 MHz 200 MHz 250 MHz 300 MHz

Figure: (8) Magnitude and phase change with temperature in a relatively linear way,even in dB scale, at different rates and with different signs depending on the frequency.For the phase, the average of the streams has been removed.

9

Temperature coefficients

0 50 100 150 200 250 300

−6

−4

−2

0

2

x 10−3

magnitude [dB

/C]

0 50 100 150 200 250 300−0.01

0

0.01

0.02

0.03

0.04

frequency [MHz]

phase [deg/C

]

from corrected measurements

from linear expectation

Figure: (9) First-order polynomials were fit to the temperature correlation of the magnitude and phase, at eachfrequency. These two plots show the first-order coefficients, along with the expectations at DC for a linear model. Inparticular, the expected temperature coefficient for the magnitude at DC is 1.6 mdB/◦C, 15% less than the oneobtained at 2 MHz.10

Conclusion

The corrected trace at 2 MHz differs from the expectation at DC (using eithera linear or quadratic model) by ∼ 0.01 dB (Figure 4). This is in the context ofa reference level of -20.14 dB.

The temperature coefficient for the corrected magnitude and phase wascomputed for each frequency by fitting a first-order polynomial. They changesmoothly across the frequency band (Figure 10). For the magnitude, theexpectation at DC is 15% smaller than the value obtained for 2 MHz.

11