Performance of Antenna Measurement Setup

Transcription

1 Performance of Antenna Measurement Setup Raul Monsalve SESE, Arizona State University November 27, 213

2 2 Description This report is divided into two parts: PART 1: Check of recovered instrumental S-parameters PART 2: Analysis of changes in measurement setup with temperature

3 3 PART 1: S-parameters The S-parameters of the measurement setup used in Boolardy to measure the antenna are obtained every minute, by computing: S 11 S 12 S 21 S 11 S 22 = 1 Γ 1 Γ 1 Γ 1 1 Γ 2 Γ 2 Γ 2 S 22 1 Γ 3 Γ 3 Γ 3 1 Γ 1 Γ 2 Γ 3 where Γ and Γ correspond to the true and measured reflection coefficients of the standards: 1=open, 2=short, and 3=match.. (1) The test presented here has the purpose of confirming that the S-parameters have been calculated properly. The method simply consists of computing the true reflection coefficients, Γ, using the previously obtained S-parameters and the measured standards Γ : Γ = Γ S 11 S 12 S 21 + S 22 (Γ S 11 ). (2) If the S-parameters are correct, the recovered reflection coefficients Γ should be identical to the expectations for the three standards.

4 PART 1: S-parameters For the correction process to be performed accurately, it is necessary to have a good estimation of the temperature of the match at all moments. This temperature is obtained from a thermistor located 1 cm away from the match, which measures air temperature. The expected DC resistance of the match is assigned based on this temperature, and the model coefficients presented in This thermistor is inside the switch box, where also the standards are located. The box is 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 (in black) obtained from a thermistor located at the weather station, which measures air temperature and is also sensitive to direct sun light, and 2) the match temperature (in red), 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 exterior temperature due to being fairly isolated from wind.

5 5 PART 1: S 11 temperature [ o C] temp. of exterior temp. of match S 11 [db] time [hours] Figure: (1) Magnitude of S 11 (BOTTOM) corresponding to the instrumental setup used for measuring the antenna, along with temperature measured in parallel (TOP).

6 6 PART 1: S 12 S 21 temperature [ o C] temp. of exterior temp. of match S 12 S 21 [db] time [hours] Figure: (2) Magnitude of S 12 S 21 (BOTTOM) corresponding to the instrumental setup used for measuring the antenna, along with temperature measured in parallel (TOP).

7 7 PART 1: S 22 temperature [ o C] temp. of exterior temp. of match S 22 [db] time [hours] Figure: (3) Magnitude of S 22 (BOTTOM) corresponding to the instrumental setup used for measuring the antenna, along with temperature measured in parallel (TOP).

8 8 PART 1: Correction of OPEN temperature [ o C] temp. of exterior temp. of match raw measurement of OPEN [db] corrected measurement of OPEN [db] time [hours] Figure: (4) The instrumental S-parameters (figures 1, 2, 3) are used for correcting the measurement of the open (middle). The corrected data (bottom) are identical to the expectation, which validates the computed S-parameters and the method.

9 9 PART 1: Correction of OPEN mag [db] mag [db] measured corrected Figure: (5) Example of correction of an open trace taken 13.7 hours into the measurement. Same data are presented in both plots; the vertical scale has been zoomed in in the plot at the bottom. The corrected trace (red) is constant in time, and identical to the expectation.

10 1 PART 1: Correction of SHORT temperature [ o C] temp. of exterior temp. of match raw measurement of SHORT [db] corrected measurement of SHORT [db] time [hours] Figure: (6) The instrumental S-parameters (figures 1, 2, 3) are used for correcting the measurement of the short (middle). The corrected data (bottom) are identical to the expectation, which validates the computed S-parameters and the method.

11 PART 1: Correction of SHORT mag [db] mag [db].1 measured corrected Figure: (7) Example of correction of a short trace taken 13.7 hours into the measurement. Same data are presented in both plots; the vertical scale has been zoomed in in the plot at the bottom. The corrected trace (red) is constant in time, and identical to the expectation.

12 PART 1: Correction of MATCH temperature [ o C] temp. of exterior temp. of match raw measurement of MATCHT [db] corrected measurement of MATCH [db] time [hours] Figure: (8) The instrumental S-parameters (figures 1, 2, 3) are used for correcting the measurement of the match (middle). The corrected data (bottom) show the expected dependence of reflection coefficient on the temperature of the match (red line in plot at the top). This temperature corresponds to air temperature measured 1 cm from the match.

13 13 PART 1: Correction of MATCH 1 measured corrected 2 mag [db] Figure: (9) Example of correction of a match trace taken 13.7 hours into the measurement, at a temperature of C. The corrected trace (red) corresponds to an impedance of Ω, which is equal to the expectation at that temperature.

14 PART 1: Conclusion The correction procedure is self-consistent, in the sense that it returns the expected values for the loads being measured, i.e., the open, short, and match standards measured in Boolardy along with the antenna. Therefore, the computed S-parameters (used also to correct the antenna measurements) are an adequate representation of the measurement setup at any moment, 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 changed within a cycle, an error would be introduced to the S-parameters, and propagated to the antenna correction. The following section (PART 2) looks into this non-ideal scenario.

15 15 PART 2: Change of Setup with Frequency As presented in the report from 11/21/213: the scatter in the reflection coefficient of the antenna increases significantly with temperature (and wind, although there are no data available). It is suspected for the primary cause of this to be rapid changes in the measurement setup 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 that doesn 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 the magnitude of two consecutive traces. This quantity provides information about the sensitivity of the setup to temperature changes. In order to have a reference, and before performing this operation for the antenna case, the figure of merit described above is computed for the data obtained when measuring the 6-dB and 1-dB attenuators, described in:

16 16 PART 2: Change of Setup with Frequency There are two main differences between the measurement of the attenuators in Phoenix, and the antenna in Boolardy. The first is that for the attenuators, the cable between the VNA and the switch box was 2-ft long, while for the antenna it was approximately 28-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 changes but NOT to direct sunlight (the equipment was always in the shade), while for the antenna the switch box and an important part of the (longer) cable was exposed to direct sun. In the following plots: All the data correspond to raw measurements of the open standard, in three different contexts: while measuring the 6-dB attenuator, the 1-dB attenuator, or the antenna. mag = Γ t2 Γ t1, where t 2 and t 1 are 1 minute apart. K = RMS( mag) is the figure of merit. It is the root-mean-square of mag in the frequency range 1-2 MHz. When plotting this quantity, the x-axis corresponds to time in minutes. In particular, at a time t = 1 [min] the value of K is RMS( Γ 1 [min] Γ 99 [min] ).

17 PART 2: Open Measured (6-dB attn) temperature [ o C] K=RMS( mag) [db] time [minutes] Figure: (1) Results for the raw open data obtained during measurements of the 6-dB attenuator. The figure of merit (BOTTOM) is constant throughout the measurement (2.5 days), and therefore independent of the outside temperature (TOP) or its derivative. In principle, the lowest possible value should be obtained for a flat slope in temperature (occurring at the highest and lowest peaks; for example, at 5 minutes). The fact that K doesn t get worse (doesn t increase) when the temperature changes suggests that the equipment remains constant within time scales of 1 minute (at least under these temperature gradients) and therefore the assumption used for the computation of the S-parameters is valid to a high degree. Estimated slopes for the sections of ascending and descending temperature are.21 and -.15 C min 1 respectively.

18 18 PART 2: Open Measured (6-dB attn) mag [db] mag [db] = = Figure: (11) Difference between two open traces corresponding to the previous data set (6-dB attn), measured 1 minute apart. (TOP) At time 5 [min] with stable temperature, and (BOTTOM) 7 [min] with increasing temperature. The noise level is comparable between the two cases.

19 19 PART 2: Open Measured (1-dB attn) temperature [ o C] K=RMS( mag) [db] time [minutes] Figure: (12) Results for the raw open data obtained during measurements of the 1-dB attenuator. The figure of merit (BOTTOM) is constant throughout the measurement (2 days), and therefore independent of the outside temperature (TOP) or its derivative. In principle, the lowest possible value should be obtained for a flat slope in temperature (occurring at the highest and lowest peaks; for example at 27 minutes). The fact that the K doesn t get worse (doesn t increase) when the temperature changes suggests that the equipment remains constant within time scales of 1 minute (at least under these temperature gradients) and therefore the assumption used for the computation of the S-parameters is valid to a high degree. Estimated slopes for the sections of ascending and descending temperature are.2 and -.13 C min 1 respectively. The value of K is almost the same as that for the 6-dB case, figure 1, which is to be expected since the measurement equipment is the same, and the environmental conditions are very similar.

20 2 PART 2: Open Measured (1-dB attn) mag [db] mag [db] = = Figure: (13) Difference between two open traces corresponding to the previous data set (1-dB attn), measured 1 minute apart. (TOP) At time 1 [min] with increasing temperature, and (BOTTOM) 27 [min] with stable temperature. The noise level is comparable between the two cases.

21 21 PART 2: Open Measured (antenna) temperature [ o C] K=RMS( mag) [db] time [minutes] Figure: (14) Results for the raw open data obtained during measurements of the antenna. Unlike the previous cases corresponding to measurements of the attenuators, here there is a notorious sensitivity of the measurement setup to changes in ambient temperature. The region enclosed by the green lines corresponds to a night period with temperature descending from 3 C to 2 C. This section is the one with the lowest sensitivity to temperature variations, but this sensitivity is still higher than that for the attenuators (K.2 db, compared to K.1 db for the attenuators). Considering that the temperature slope is -.22 C min 1 (only 1% higher than those for the attenuators), and that the rest of the equipment is the same, the most probable cause for the increased sensitivity is the use of a cable 4% longer than that used in the previous cases. The sensitivity outside the selected region is clearly higher, most probably due to time-varying temperature gradients across the cable which are driven by wind gusts and a continuously changing amount of direct sun light.

22 22 PART 2: Open Measured (antenna) mag [db] mag [db] = = Figure: (15) Difference between two open traces corresponding to the previous data set (antenna), measured 1 minute apart. (TOP) At time 4 [min] during night time with decreasing temperature, and (BOTTOM) at 11 [min] during the day with increasing temperature. The residuals of the plot on top are larger than those of figures 11 and 13, obtained under similar conditions except for the shorter cable. The plot at the bottom clearly illustrates the changes that occurred in time scales of 1 minute, during the day.

23 23 PART 2: Conclusion For the measurements of the attenuators (Phoenix) and antenna (Boolardy), the changes in the setup has been quantified using the difference between two traces of the open standard measured 1 minute apart. For the attenuators, the setup seems insensitive to variations in ambient temperature in this 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 element is the most probable cause for the difference in performance. During the day, the setup for measuring the antenna is significantly more sensitive to environmental factors, and the 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 an uncertainty term (on top of the noise) is assigned to the measured traces. The cleanest approach would be letting the uncertainty be the difference between traces measured 1 minute apart; this for the open, short, match, and antenna. This uncertainty would then be propagated to the computed S-parameters, and the corrected antenna traces.