sssm system design considerationsece.vt.edu/swe/ratf/docs/astron_rp013_sssm... · doc.nr.:...

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Doc.nr.: ASTRON-RP-013 Rev.: 3.0 SSSM

SSSM System Design Considerations Organization Date Author(s):

R.P. Millenaar ASTRON 26 aug. 2005

Checked:

Approval:

W. Baan ASTRON 30 aug. 2005

© ASTRON 2005 All rights are reserved. Reproduction in whole or in part is prohibited without written consent of the copyright owner.

Date: 21-02-2006 Class.: Public

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Distribution list: Group: Others:

SSSM @ ASTRON Albert-Jan Boonstra Sieds Damstra Klaas Dijkstra Jerome Dromer Sjouke Kuindersma Henri Meulman Rob Millenaar Paul Nijssen Paul Riemers Bou Schipper Harm-Jan Stiepel

W. Baan H. Butcher S. Ellingson P. Hall R.T. Schilizzi

Document history: Revision Date Chapter / Page Modification / Change

1.0 8-03-2005 - Creation

1.0 31-03-2005 - Final

2.0 26-08-2005

3.1.2 5.1.4 5.2

Expression (4) Factor 4π missing in expression (36), works through to exp. (42) Expression (58) was corrected twice for dBm.

3.0 21-02-2006 5.2 Approximations and exact expressions for TR and GR written more explicit.


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Table of contents:

1 Introduction........................................................................................................................................... 4 2 System Overview.................................................................................................................................. 5 3 Using the Spectrum Analyzer ............................................................................................................... 7

3.1 Scan speed................................................................................................................................... 7 3.1.1 IF filters ................................................................................................................................. 7 3.1.2 Detector: Dwell- vs. Integration time..................................................................................... 9 3.1.3 Video filter........................................................................................................................... 10 3.1.4 Scan speed in practice ....................................................................................................... 11

3.2 Sensitivity.................................................................................................................................... 11 3.3 Noise Figure ............................................................................................................................... 12 3.4 High speed sampling .................................................................................................................. 13

4 System Noise ..................................................................................................................................... 16 5 System Calibration ............................................................................................................................. 18

5.1 Theoretical calibration ................................................................................................................ 18 5.1.1 Units.................................................................................................................................... 18 5.1.2 Antenna .............................................................................................................................. 18 5.1.3 Receiver.............................................................................................................................. 20 5.1.4 Instrumentation sensitivity .................................................................................................. 20

5.2 Noise source calibration ............................................................................................................. 22 6 References ......................................................................................................................................... 25


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1 Introduction Within the framework of the international SKA Site Spectrum Monitoring programme ASTRON designs, constructs and operates portable instrumentation consisting of a suite of antennas, low noise amplifiers, a spectrum analyzer and computing hard and software. The foundation for the specifications for the instrumentation is laid down in [1], ‘the protocol document’. The proposal document [2] translated this into a set of components and gave an estimate of cost and effort for the realization of such a portable system. This document is intended to present a number of design principles and parameters, a collection of notes, that are of importance to the system’s properties. It doesn’t aim to give a step-by-step account of how and why the system was designed the way it turned out to be.


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2 System Overview

1D16-24

2D8-16

80.1-26.5

5B0.1-8

90.1-4

70.04-2

SA

SSSM Schematic

RPM V1.4 19-11-04

M

HL050.85-26.5 GHz

VULP9118G.04-1.5 GHz

HK014.08-1.6 GHz

HF9021-3 GHz

NSNS

HV

1 2 3

1 2 3

1 2 3 4 5 6

31 2

1 2 3

1 2 3 4 5 6

1 2 3 4 5

1 2

1 2

Mast 1 Mast 2

S01

S02

S03

S04

S05

S11

S12

S13

S20

HSS IF outIF out

RF in

Fig. 1


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The system block diagram is shown in Fig. 1. It consists of a spectrum analyzer (SA), connected to signals from two frontends in separate masts. The masts carry a total of four antennas that are grouped such that the directional ones share a dual axis rotor (azimuth and polarization). The antennas are listed in Table 1. Model Type Pol. Dir. Gain (dBi) Freq. range (GHz)

VULP 9118G (Schwarzbeck) logper H/V dir. 0.04 – 1.5

HK014 (R&S) coaxial dipole V omni 2 0.08 – 1.6

HF902 (R&S) pod w. patch H+V omni 0 1 – 3

HL050 (R&S) logper H/V dir. 0.85 – 26.5

Table 1

The lna’s are intended to make sure that the system noise temperatures meet the requirements, set down in [1] and [2], of better than 30000K for mode 1 and 300K for mode 2. Mode 1 is the quick scan for finding the strongest signals and mode 2 is the sensitive survey. The lna’s carry a historically evolved number and are summarized in Table 2. The ‘1 dB’ columns denote the 1 dB compression point. Nr. Type Freq.

range GHz

Gain listed

Gain meas.

NF listed

NF meas.

1 dB listed

1 dB meas.

1D AMF-5F-160240-17-8P 16-24 GHz 36 dB (min)

39.0-41.5 dB

1.70 dB (max)

1.10-1.52 dB

8.0 dBm (min)

11.4-12.0 dB

2D AFS3-08001600-15-8P-4 8-16 GHz 28 dB (min)

32.05-33.14 dB

1.5 dB (max)

1.13-1.32 dB

8.0 dBm (min)

14.8-16.07 dB

5B AFS3-00100800-14-S-4 0.1-8 GHz 28 dB (min)

30.78-33.15 dB

1.4 dB (max)

0.91-1.19 dB

10 dB (min) 10.35-13.75 dB

5C AFS2-00100800-15-S-2 0.1-8 GHz 22 dB (min)

21.12-23.60 dB

1.5 dB (max)

1.20-1.88 dB

10 dB (max)

11.1-16.8 dB

7 AFS1-00040200-12-10P-4 0.04-2 GHz

15 dB (min)

17.10-18.94 dB

1.2 dB (max)

0.72-1.78 dB

10 dB (min) 10.93-12.59 dB

8 AFS4-00102650-42-8P-4 .1-26.5 GHz

22 dB (min)

29.20-31.55 dB

4.2 dB (max)

3.01-5.73 dB

8 dB (min) 12.26-16.47 dB

9 AFS3-00100400-13-10P-4 0.1-4 GHz 28 dB (min)

31.0-32.3 dB

1.30 dB (max)

1.08-1.22 dB

10 dB (min) 11.7-12.9 dB

Table 2

Coaxial switches that were selected for minimum insertion loss provide the capability to change configuration automatically, without interfering manually. The same is true for the control of the noise sources. In the block diagram HSS stands for high speed sampling which is the implementation of a subset of the mode 1 measurements, where widely separated time windows (scans), but fast samples are taken to detect pulsed signals. This mode is rechristened as mode H within the SSSM project. The HSS system is implemented as a fast A/D board with fast on-board memory, enough to hold one complete scan. The board takes its input from the spectrum analyzer’s 20.4 MHz IF output. The HSS system resides within the data acquisition and system control pc.


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3 Using the Spectrum Analyzer The measurements are performed using a spectrum analyzer. Therefore some basic knowledge about how spectrum analyzers work in general, and about the Rohde&Schwarz model FSU-26 in particular, is required. The necessary background is presented here. Most is rather obvious, but some counter intuitive aspects need to be discussed. In broad terms a spectrum analyzer has a low noise RF input section, followed by conversion to IF. Here bandpass filtering takes place to define the resolution bandwidth. The resulting signal is detected, passes through a video filter and is further processed to be presented on a screen. The type of IF filter, the resolution bandwidth chosen, the type of detector and the video filter all play a role in the spectrum analyzer’s properties as far as speed in scanning is concerned. The part of the spectrum analyzer where these components come into play is shown in Fig. 2. The figure is taken from [3].

Fig. 2

3.1 Scan speed The factors determining the scan speed of the spectrum analyzer are summarized here. On the one hand the speed must be maximized to reduce the total time needed to perform the measurements and on the other hand must be lengthened to achieve the desired sensitivity. The spectrum analyzer’s components that affect the permissible speed of scanning are:

• IF band limiting filters; bandwidth and type of filter • envelope detector • video filtering; bandwidth

3.1.1 IF filters

The IF filter sets the resolution bandwidth RBW. The FSU series of spectrum analyzers have IF filters ranging from 10 Hz to 50 MHz. These are implemented as analog, digital or FFT filters. The transient response of the filter is inversely proportional to the bandwidth and to the type of filter involved. In the simplest approximation the filter passband should not be traversed in a time less than 1/∆f, the IF reciprocal bandwidth, and the representative impulse response duration. Sweeping a cw signal at any speed through the filter will in fact cause an error, but with suitable combinations of filter bandwidths and sweep speeds, the measurement error can be small. Within the industry a proportionality factor k (not Boltzmann’s constant) is used to describe the filter’s transient response. In [4] the following definition is given. The time a signal is present in the pass band of the filter is:


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in passbandsweep

RBWtf t

=∆

(1)

where ∆f is the frequency span. The transient response of a filter can be approximated by:

respkt

RBW= (2)

Taking as a requirement that the time spent in the pass band should be equal to the response time, it follows that :

2sweepft k

RBW∆

= (3)

The proportionality factor is k and is a measure of how much longer the time spent per unit bandwidth should be to keep the error below a certain fraction. In [3] an error of 0.15 dB is mentioned. In other words, the sweep time has to be a factor k longer than in the ideal case. Setting the spectrum analyzer sweep time to automatic, will cause the firmware to select the appropriate value, so for standard tasks all this is immaterial. In our case, however, we need to know and minimize the amount of time involved in performing all the required measurements.

Fig. 3

The factor k differs for the various filter implementations. In Fig. 3 the relationship between resolution bandwidth and minimum sweep time is shown for the relevant filters. The graph is taken from [3] and shows the theoretical relationship for RBW=1 MHz, for two values of k. The real example shown is for an


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FSU family spectrum analyzer; variations in actual figures are expected for individual models and firmware versions. Analog filters For the large resolution bandwidths analog filters are used. These are 4 or 5 section filters. In Fig. 2 the analog filters are indicated as a split implementation before and after the IF amplifier. The FSU-26 uses analog filters from 200 kHz upwards. The FSU manual does not specify the k factor for the FSU analog filters, but in [3] the analog filters are specified to have a k=2.5 value as indicated by the green line in Fig. 3. The applicability for the FSU-26 that us used for SSSM was confirmed by personal communication with the R&S representative. Digital filters From 100 kHz downwards the FSU-26 uses digital filters that are implemented such that k=1 (black line in Fig. 3). For these filters the IF’s I and Q signals are directly sampled. The analog filters are used for anti-aliasing in this case. FFT filters For lower bandwidths an FFT processor is used to do the filtering. The FSU-26 can do this for 30 kHz and lower. The advantage of the FFT filter is that it is potentially much faster than the digital filters mainly because parallel processing can be done over a large span at once. Therefore the sweep time is inversely proportional to RBW instead of to the square (the orange line in Fig. 3). Counteracting this is the time required for doing the calculations, which results in the red dots in the graph. It turns out that, even if the FFT filter works up to 30 kHz, the speed advantage over the digital filter is only achieved below 3 kHz for the spectrum analyzer in the graph. Note that the FFT results in the graph are valid for that particular frequency span (1 MHz). Increasing the span to much larger values, as is needed for SSSM, will lead to differing results, depending of the implementation inside the spectrum analyzer. Because of these uncertainties bench tests need to be done. Of importance further is that the FFT filter is not suitable for pulsed signals because it operates only on a limited window in the time series of the sampled signal. Since the RFI environment certainly will include pulsed signals the use of the FFT filters should be excluded. The RBW’s given in the protocol [1] for both mode 1 and 2 are summarized in Table 3, together with the fastest filter available on the spectrum analyzer. Note that these figures, especially the trade off point FFT or digital, depend on the model and firmware version and frequency span. This data could not be made available by the manufacturer: the advise was to test it. For results of the timing in practice, see RBW (kHz) fastest filter type K 1 FFT 0.2 3 FFT/digital 1 30 digital 1 100 digital 1 300 analog 2.5 1000 analog 2.5 10000 analog 2.5

Table 3

The conclusion is that (including the earlier finding that the FFT filter should not be used): for RBW≥300 kHz the analog filter must be used; for 1≤RBW≤100 KHz the digital filter. The choice can be left to the spectrum analyzer by default: it will select the appropriate filter. For this the Filter Type selection in the FSU should be ‘NORMAL’.

3.1.2 Detector: Dwell- vs. Integration time

Above, the filter’s influence on the maximum permissible sweep speed was investigated. It would seem that sweeping slower than this maximum would increase the time spent per unit bandwidth and that


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therefore some kind of integration would take place, thus lowering the noise. That this is not the case is explained below. Slower than maximum sweep speeds result only in smaller errors, see the previous section. The protocol document [1] describes the measurements that have to be done at the site and gives an estimate of the required time to do this. These are based on the concept of ‘dwell time’ which is taken to be equal to the integration time in the relation for the sensitivity of the measurement. This appears to be an intuitive approximation which turns out to be only partially correct however. For the spectrum analyzer the dwell time can be controlled by changing the sweep time and the number of frequency bins (take one bin per RBW):

sweepdwell

RBW tt

f=

∆ (4)

To think, however, that increasing the dwell time a factor larger than k/RBW (2) increases the integration time by the same factor, is a mistake. This would be true assuming that a purely integrating detector was used for measuring the power in the resolution bandwidth bin. The spectrum analyzer’s IF signal is detected using an envelope detector, see Fig. 2. The resulting signal passes the video filter (see 3.1.3) and is fed into a choice of statistical processors (‘detectors’) that affect the way a pixel is displayed on the screen. Several types of detectors are used in contemporary spectrum analyzers, but none behave as pure integrators. These post-video filter detectors serve a necessary step in modern analyzers, of only because the number of displayable pixels generally is less than the number of samples per trace (the FSU-26 has a display with 625x500 pixels, while the number of measurement points ranges from 155 to 10001). The FSU-26 has sample, max-hold, min-hold, RMS, average and channel filters. All combine a number measured points into one screen pixel, with the exception of the sample filter, which just takes one data point per pixel. The use of the sample filter is recommended for ‘raw’ data viewing. In practice increasing the dwell time only results in increasing the dead time between samples and is not used for increasing the integrating time per measurement point. So in conclusion, the actual integration time applied to the signal up to the envelope detector cannot be taken to be equal to the dwell time but is equal to the time spent in the resolution bandwidth (equal to the IF filter’s response time), see (2)

int respkt t

RBW= = (5)

The dwell times that are given in the protocol document [1] are used there for calculating the obtained sensitivity of a measurement. Because of the conclusion that the dwell time as calculated from (4) does not correspond to the effective integration time we must obtain the required sensitivity by doing the integration in a different way. So perform multiple sweeps with the k/RBW dwell times and calculate the averages per data point in linear units (convert from dBm to voltage first, average and convert back to dBm). Obviously, because of the overhead this takes, more time is needed to arrive at the intended integration time. This is discussed further in 3.2.

3.1.3 Video filter

The video filter can be seen as a first order smoothing network following the envelope detector. In the FSU the video filter is implemented digitally, see Fig. 2. In general, the video filter is used to average out noise to enhance the visibility of weak cw-like signals in the spectrum. The video filter however influences the maximum sweep speed in the same manner as the RBW does: the minimum sweep time increases with decreasing video bandwidth. The sweep time for cases where the video bandwidth VBW<RBW can be approximated by (see [4]):


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sweepft k

RBW VBW∆

≈⋅

(6)

The recommended setting of VBW in relation to RBW depends on the application. For sinusoidal signals with high S/N ratio the video bandwidth us usually set equal to or larger than the RBW. For pulsed signals VBW≥10RBW is taken. For low S/N the video bandwidth is made substantially less. Although setting the video filter such that VBW<RBW gives rise to smoothing the trace and thus reduction in the trace noise, it is not clear to what degree the integration time rises with lower VBW. Using the video filter for integration purposes therefore is not considered here, in favour of trace averaging, as discussed in 3.2. Therefore the spectrum analyzer’s video bandwidth setting can best be at default, ‘VIDEO BW AUTO’, where the VBW is coupled to the RBW, according to the ‘COUPLING RATIO’. The latter is set by default to the ‘SINE’ setting in which the VBW=3RBW. This setting needs to be modified to ‘MANUAL’ with a parameter that in 3.2 is taken to be ≥10.

3.1.4 Scan speed in practice

The relation of the scan speed to factors such as span, bandwidths and filter types, as discussed up to here is the result of considerations concerning arithmetic and physical aspects. As was already indicated, the spectrum analyzer’s manufacturer was not able to specify actual sweep times for the various circumstances that the analyzer is used in practice. Apparently the interplay of all relevant factors makes the prediction of the sweep time a difficult task. It was assumed that the tables that the internal firmware uses for setting the sweep time could be made available. Alas, such has not proved to be the case. Therefore tests were done to come up with actual sweep times for real life analyzer settings. The results have shown that the sweep time depends in sometimes unpredictable ways on combinations of:

• RBW (VBW was set to 10 times the RBW) • Span (affects the sweep time in more ways than just the relation in (3)) • Start- and stop frequency (below and above 3.6 GHz are separate domains) • Filter type • Averaging cycles • Number of data points per scan

The measured sweep times exceed the theoretical times by a factor ranging from 1 to as much as 20. The scheduling software that is used to assemble daily measurement sequences is able to make best effort calculations based on the theoretical model, supplemented with RBW dependent fudge factors that were derived from lab tests. But more importantly, it is able to use the actually measured times for given measurement jobs.

3.2 Sensitivity The sensitivity of the spectrum analyzer depends on the instrument’s noise figure on the one hand (see 3.3) and on the effective signal integration in the instrument that can be achieved. While discussing the scan speed in 3.1, the issue of integration time was already touched upon, with the conclusion that the overall signal integration is not equal to the dwell time per frequency point. The parts of the system that affect the integration of the signal are:

• IF filter bandwidth and type • video filter • post-video detector • trace averaging • post-readout integration

The last part obviously is not a feature of the spectrum analyzer but takes place in software.


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The contribution of the IF filter to the overall integration is the filter’s response time, see (5). The use of the video filter isn’t considered here as integrator of the signal. Trace averaging takes place inside the spectrum analyzer and should preferably be done in linear instead of log (dBm) values. The summation of logarithmic values of a noise like signal gives rise to results that are too low. For gaussian noise this amounts to results being about 2.5 dB too low. That could be accounted for by applying a correction. For steady signals the difference obviously is 0 dB, but for fluctuating, pulsed or intermittent signals the difference may be much higher, depending on the signal statistics. In [3] the recommendation is given to use linear level display and VBW≥10RBW to obtain true average when averaging over several measurements. However, setting the instrument to linear may imply a dynamic range penalty. This caveat is not explored at this time. Note that the number of traces that can be averaged in the FSU-26 is 3.104. For post-readout averaging the last mentioned dynamic range problem can be avoided by reading out logarithmic scan data to the computer and do the averaging on the values that are converted to linear first. After a final linear to logarithmic conversion the end results are available in dBm’s. The resulting data would be obtained involving much more overhead however, which can be prohibitively large: mode 2 measurements specified in the protocol which are done at 30 kHz RBW that need a total dwell

(integration) time tint of 10 seconds need to average a total N of int int1kt N N t RBW

RBW k= ⇒ = ⋅

traces. This is the maximum (where digital IF filtering is used, so k=1) and amounts to 3.105 traces. For this maximum number of traces to be averaged it turns out that even if internal averaging is used to the maximum number possible for this model spectrum analyzer, externally 10 of these pre-averaged scans will have to be combined in post-readout software. In conclusion, the general expression for the integration time achieved according to the strategy of trace plus post-readout averaging is:

intkt NM

RBW= (7)

where N is the number of traces averaged in the spectrum analyzer and M the number of the resulting averaged ‘scans’ averaged in software.

3.3 Noise Figure A specification for the noise figure of the FSU spectrum analyzer cannot be found in the specifications. However an other parameter can be used to derive the noise figure. This is the Displayed Average Noise Level (DANL or LDAN) which can be read off the screen easily. This is discussed in [3]. This level is equal to the spectrum analyzer’s noise figure NFSA over the thermal kTB noise plus an additional factor, expressed in dBm:

,310 log ( ) ( ) ( )

1 10N IF

DAN SA

kTBL dBm NF dB X dB

W−

⎛ ⎞= +⎜ ⎟⋅⎝ ⎠

− (8)

where BN,IF is the noise bandwidth of the IF filter. A popular expression for the normalized case for 1 Hz bandwidth at 290K is:


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,174 ( ) 10log ( ) ( ) ( )1

N IFDAN SA

BL dBm dB NF dB X dB

Hz⎛ ⎞

= − + + −⎜ ⎟⎝ ⎠

(9)

(The thermal noise power in 1 Hz at 290K is –174dBm) The additional correction term of X dB depends on whether averaging of logarithmic values takes place in the selected detector or in the use of trace averaging to stabilize the display. In [3] and [6] a correction of X=2.5 dB is given for gaussian noise. The specification of the DANL for the FSU-26, equipped with the FSU-B23 preamplifier is summarized in the table below, which is taken from the specifications insert in [6]:

Table 4

Note that these figures are normalized to 10Hz and that they were measured using trace averaging. It is not clear what type of detector is used, so there is some uncertainty about the X correction to be applied. Nevertheless, using the 2.5 dB is a safe, not optimistic bet. This (plus the data for the analyzer with the preamplifier off) then leads to the values of the (typical) noise figure NF and noise temperature TN, summarized in Table 5, where the conversion from NF to TN is done by:

10290 10 1NF

NT⎛ ⎞

= ⎜⎝ ⎠

− ⎟ (10)

Freq. range Preamp ON Preamp OFF DANL (typ. @1Hz) NF TN DANL (typ. @1Hz) NF TN.01-2 GHz -162 dBm 14.5 dB 7883 K -155 dBm 21.5 dB 40670 K2-3.6 GHz -160 dBm 16.5 dB 12664 K -152 dBm 24.5 dB 72550 K3.6-8 GHz -165 dBm 11.5 dB 3806 K -154 dBm 22.5 dB 51280 K8-13 GHz -162 dBm 14.5 dB 7883 K -150 dBm 26.5 dB 129250 K13-8 GHz -160 dBm 16.5 dB 12664 K -148 dBm 28.5 dB 202010 K18-22 GHz -159 dBm 17.5 dB 16018 K -147 dBm 29.5 dB 258170 K22-26.5 GHz -155 dBm 21.5 dB 40674 K -145 dBm 31.5 dB 409350 K

Table 5

The analyzer is equipped with pre-amplifiers options FSU-B25 (below 3.6 GHz) and FSU-B23 (above 3.6 GHz). These reduce the NF significantly. The table presents the noise figures with both pre-amplifiers on. These noise figures/temperatures can be used for calculating the system’s overall noise temperature.

3.4 High speed sampling In the specified series of measurements for Mode 1 (see [1]) the frequency range 960 to 1400 MHz is to be measured with high time resolution (2 µsec) with large RBW (1 MHz). The purpose of this is to obtain data in which the numerous strong pulsed signals (DME, radar) in this band have a high probability of


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detection. Getting this data using the spectrum analyzer in its normal mode of operation would be far too time consuming. A complete dedicated high speed data acquisition system has not been considered. Instead, the spectrum analyzer is used as high quality frontend and the data is read out from the analyzer’s IF output, see [8]. For this purpose a 12 bit ADC board with on-board memory for fast sample storage is used. The board is clocked at 80 MHz, more than sufficient to sample the 20.4 MHz IF output. The spectrum analyzer is set to zero span mode and RBW to 10MHz. The time series data in sample memory is dumped to file and off-line the data is processed to obtain the required frequency channels.

Fig. 4

The data processing involves an 128 point FFT, resulting in a channel distance of

80 0.625128

f MHz∆ = = . A number of these channels within the band around 20.4MHz are chosen. The

shape of the spectrum analyzer’s (analog) 10 MHz IF filter was investigated and a rather arbitrary specification for maximum allowed attenuation of each channel w.r.t. the center frequency of 1 dB was adopted to see how many channels fit within that band. In Fig. 4, copied from [8], the result is shown. The IF filter’s shape is such that the 3dB bandwidth of 10 MHz is confirmed, and that the 1 dB bandwidth of 7.5 MHz allows the simultaneous use of 13 frequency channels. The data processing is to be adjusted such that the 3 dB bandwidth per channel equals 0.625 MHz. The figure shows that the filter shape is slightly asymmetrical and the way the channels are chosen to make optimal use of the 1 dB bandwidth available: the 7th channel corresponds to 20.00 MHz. The spectrum analyzer’s IF frequency sense is reversed with respect to the input frequency; a higher input frequency results in a lower response at the 20.4 MHz output. The set of frequencies measured is therefore:

0.4 ( 7) ( )n cf f n f M= + + − ∆ Hz (11) where fc is the analyzer’s central frequency, n is the channel number (1≤n≤13). The measurement strategy is that the control software sets up the spectrum analyzer, starting with a center frequency tuned such that the lowest frequency channel is at fstart (960 MHz). N channels (N=13) are then measured with the Nth offset at ( 1)N f− ∆ MHz. Next, the spectrum analyzer is tuned


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N f∆ MHz higher. This is repeated for M measurements until the highest frequency is reached. The control software therefore has to tune the analyzer to the following series of center frequencies:

0.4 int ( 1)2Mc startNf f N⎛ ⎞⎛ ⎞= − + + − ∆⎜ ⎟⎜ ⎝ ⎠⎝ ⎠

M f⎟ (12)

The frequency range covered by one measurement is 8.125N f MHz∆ = and the number of measurements (spectrum analyzer settings) that need to be done is (1400-960)/8.125=55. In fact, the upper frequency will then be 1406.875 MHz.


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4 System Noise The system consists of a series of components, both active and passive, with the spectrum analyzer as the final element, see Fig. 1. The system noise temperature of a set of cascaded elements in general is ([5], 7-57):

321 1

1 1 2

1

... nn

ii

T TTT TG G G G

−

=

= + + + +

∏ (13)

where Tx and Gx are the noise temperatures and power gains of the xth element respectively. The noise temperature therefore is given by the sum of the contributions of all individual stages, adjusted by the amount of gain before each stage. In a practicable system the cascade also includes lossy elements, attenuators. The noise temperature of such an element is ([5], 7-55a):

( 1) aT L T= − (14) where L is the loss factor (∞ ≥ L ≥ 1) and Ta the physical, ambient temperature. Consider the generalized scheme of the measurement equipment in Fig. 5, consisting of both passive, attenuating and active components.

1 32 4 5 6 (SA)TR

TL

TL

TL

TG

TG

T

frontend

Fig. 5

The boxes represent the lossy elements and the Spectrum Analyzer on the right and the triangles the gain elements. Element 1 is the part between antenna and first lna and obviously has to have the lowest loss as possible. Element 3 is the interconnection loss between first and second lna and may also include a band limiting filter. Element 5 mainly represents the loss from the long cable between front-end and Spectrum Analyzer. From (13) and (14) it follows that the Receiver Noise Temperature TR for this system is given by:

1 3 1 3 1 3 5 1 3 51 1 2 1 3 4 5 6

2 2 2 4 2 4

( 1) ( 1)( 1)RL L L L L L L L LT T L T L T T T T

G G G G G G− −

= − + + + + +L

5

(15)

where in most, but certainly not in all cases (esp. where cryogenics are being used), the physical temperatures of the lossy elements are the same, at ambient temperature:

1 3aT T T T= = = (16)


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In [2] receiver noise temperatures were presented, as calculated with (15), based on noise figures, lna gains and losses in connectors and cables. The data were taken from available documentation or best estimates.


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5 System Calibration Calibration of the system can be done on two levels: 1) a theoretical calibration, based on the components properties as taken from their specifications or actually measured in the lab, and 2) an overall calibration of the system using a calibrated noise step, generated by a noise source. Both methods are anticipated to be used by the data reduction software.

5.1 Theoretical calibration An assessment of the theoretical relationship between measured output power from the spectrum analyzer and the signal flux at the antenna can be made. For this the properties of all components in the signal path need to be considered. Assuming linear behaviour throughout, these properties can be limited to noise figure and gain.

5.1.1 Units

The data read out from the spectrum analyzer is assumed to be in dBm, and the signal spectral flux density S at the antenna in Wm-2Hz-1 or Jy (Jansky’s), where:

26 2 11 10Jy Wm Hz− −= − (17) or

2 11 ( ) 260 ( )dB Jy dB Wm Hz− −= − (18)

5.1.2 Antenna

The parameters that describe the conversion of signal spectral flux density into signal power delivered to the electronics by the antenna are the antenna effective area, antenna gain and/or antenna factor. By definition the power available from the antenna PA equals the flux density in Wm-2 (is the spectral flux density S times the bandwidth B) captured by the effective area in m2:

( )A e sP A SB Wρ= (19) Note that this relation in its general form makes no mention of the factor ρ, that we introduce here to account for the fact that only one of two orthogonal polarizations are being measured. Assuming equal power in the two polarizations ρ=½. See also the appendices in [1]. The signal’s bandwidth Bs is used to go from spectral flux density to flux density. The antenna’s effective area is related to its isotropic gain Gi by (see [5]):

22(

4e iA G mλπ

= ) (20)

So, in power and antenna gain units the available power from the antenna is:

2 2

24 4A s i s icP SB G SB G

fλρ ρπ π

= = (21)


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In order to get an expression where the antenna factor can be used we need to use the unit of electrical field at the antenna. The definition of the (receiving) antenna factor is the ratio of incident electric field E in Vm-1 and the voltage VA delivered from the antenna to an impedance Z.

1(AA

EkV

−= )m (22)

Back to power units (2

AA

VPZ

= ), then gives the alternative definition of kA:

AA

EkP Z

= (23)

Rewriting this for PA while re-introducing the factor ρ to take care of the single polarization being measured, gives:

2

2 ( )AA

EPk Zρ

= W (24)

and replacing E with its relationship to the flux density, using

2

00

sESB E SB ZZ

= ⇒ = s (25)

(Z0 is the free space impedance and 0 120 377Z π= ≈ Ω ), gives for PA:

02s

AA

SB ZPk Zρ

= (26)

In conclusion, equation (21) gives PA in terms of the antenna gain and equation (26) in terms of the antenna factor. As a side benefit, equating the PA terms in (21) and (26) gives the relationship between kA and Gi:

02

4 4 30 4 30A

i i

Z fkiZG ZG c

π π πλ λ

= = =ZG

(27)

And in a practical form for Z=50Ω this becomes:

8 13.24 10Ai

kG

−= ⋅ f (28)

or in logarithmic (dB) units (since kA is defined in voltage units, take 20log):

( )20log 29.79dBA MHz dBik f G= − − (29)


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The antennas in use have either been individually calibrated by the manufacturer or a type calibration set is available, in the form of a table of kA or GdBi values over the frequency range.

5.1.3 Receiver

The input power PA undergoes amplification and attenuation before being presented to the spectrum analyzer. The analyzer provides the power level at its input, corrected for the internally used attenuator (should be explicitly set to 0 dB) and reference level. Therefore the incident spectral flux density relates to the measured power from the spectrum analyzer as (choosing equation (26) to use the antenna factor as these are well available for the entire frequency range):

2

0

SA A

s R

P k ZSB G Zρ

= (30)

where PSA is the measured power by the spectrum analyzer (in this generic equation in Watts) and GR is the net receiver gain: the product of gain or attenuation of all individual components. In practical form for a 50Ω system and with ρ=½, this comes down to:

22 10.265 ( )SA A

s R

P kS WmB G

− −= Hz

y

sB

(31)

or in logarithmic form, assuming the power is measured in dBm (subtract 30 dB):

( ) 2 110log 35.77 ( )dBm dB dBdB SA s R AS P B G k dBWm Hz− −= − − + − (32)

(kAdB is given in 20log values) According to (18) this becomes in dBJy:

10 log( ) 224.23 ( )dBm dB dBdBJy SA s R AS P B G k dBJ= − − + + (33)

The receiver noise temperature can be calculated from (15), entering the noise temperatures and theoretical gains/losses from all elements in the data path.

5.1.4 Instrumentation sensitivity

The protocol [1] requires that the sensitivity of the instrumentation is presented in a set of graphs as function of frequency. For this the properties of the antenna (gain, directivity or kA factor) and the receiver temperature TR are used. The system noise temperature Tsys, which includes the background noise contribution, should actually be used in these sensitivity calculations, but here this is not considered to be a limitation of the instrumentation. In Appendix A of [1] the sensitivity of the system is discussed and the sensitivity is defined there as the received flux in one polarization from the direction of the horizon where the signal power at the antenna terminals ( A eP A Sρ= , see (19)) equals the receiver noise power

( ) for a signal to noise ratio of 1. For noise signals both bandwidths Bn sysP kT B= m s (signal) and Bm (measurement) can be take to be equal, and that results in a sensitivity S0 of:

0R

e

kTSAρ

= (34)

which corresponds to equation 3 in [1]. As discussed before, in practice ρ=½ but we leave the ρ in the equations to avoid confusion in constants. Note that this sensitivity S0 is achieved in the natural


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integration time τ corresponding to the bandwidth B ( 1Bτ −= ). Using the radiometer relationship the sensitivity is more accurately written as:

2 10 (R

e

kTS WmA Bρ τ

− −= )Hz (35)

Now the effective area is replaced by the antenna factor, where we avoid confusing Boltzmann's constant with the antenna factor again by denoting the latter with kA. For this we combine equations (20) and (27) and solve for Ae , expressed in kA:

2

120 1e

A

AZ kπ

= ⋅ (36)

where Z is the characteristic impedance of the antenna’s output and the receiver’s input (thus assuming ideal matching). For a 50Ω system the relation is further simplified to:

2

2.4e

A

Akπ

= (37)

Plugging (36)into (35) gives the required relationship of the sensitivity and the antenna factor:

22 1

0 (120

R AkT kZS WBπρ τ

− −= )m Hz (38)

For 50Ω and equal polarization contributions (12

ρ = ):

2 2

2 10

0.133 0.265 ( )R A R AkT k kT kSB Bρ τ τ

− −Wm Hz (39)

where S0, TR and kA are all functions of frequency. In (39) S0 is in Wm-2Hz-1; so in Jy, MJy and dBJy this can be written respectively as:

2

0 366 ( )Jy

R AT kSBτ

Jy (40)

2

0 0.000366 ( )MJy

R AT kSBτ

MJy

dBJy

(41)

0 25.63 10 log( ) 5 log( ) ( )dBJy dBR AS T k Bτ+ ⋅ + − ⋅ (42)

where kAdB is the standard 20log value of the antenna factor.


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5.2 Noise source calibration A radio telescope generally uses noise injection into the astronomical signal, by means of a noise launcher in the antenna feed or using a directional coupler very early in the signal path. The first method cannot be applied here for the entire frequency range and the second method will introduce a substantial insertion loss if the coupler is inserted into the signal path at the obvious point, between antenna and first lna. The system noise temperature would therefore be increased to unacceptable levels. Mainly for this reason the noise injection method is not used, in favour of the alternative of replacing the antenna signal by the noise signal, as can be seen in the block diagram Fig. 1. A noise source generates a step in noise power applied to the input of the first lna when switching the bias voltage on and off. The idea is to perform a complete frequency scan with the noise source off and a scan with the source on and use the observed step in measured power to derive the total system’s gain and noise temperature per frequency point. The method works if the noise source’s noise power is known over the frequency range. The calibration data of the noise source is available for this purpose. The available noise power from sources of the type used here are expressed in ‘excess noise ratio’. The ENR is defined as the ratio between the difference of the noise temperatures on and off, divided by the reference temperature T0=290K, usually expressed in dB, see [7]:

0 0

10log on off on offdB

T T T TENR ENR

T T− −⎛ ⎞

= ⎜ ⎟⎝ ⎠

= (43)

In practice the off noise temperature is often taken to be equal to the reference temperature, so that the linear approximation becomes:

( )00

1 1onon

TENR T T ENRT

− + (44)

Two noise sources are available to be built into the two frontend boxes: Agilent 346C, with nominal ENR=15 dB (10 MHz to 26.5 GHz) Agilent 346B, with nominal ENR=15.2 dB (10 MHz to 18 GHz) Calibration data over the frequency range is available and applied. Noise figure measurements are carried out in what is known as the ‘Y-factor’ method, where Y is defined as the ratio in measured output power of the device under test when the noise source is on and off:

on

off

PYP

= (45)

This is a relative measure independent of the absolute output power of the device under test. The gain G of the device needs to be linear for the method to work. The noise factor (which is the linear expression of the noise figure) of a device is defined as the ratio of the total output noise power and the output noise power due to the input source:

0

0

aP kT BGFkT BG+

= (46)

where Pa is the device’s internal (added) noise power and is the thermal noise at the input modified by the device gain.

0kT BG


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Poff

Pon

Out

put P

ower

Pa

Toff Ton

Input Noise Temperature

Fig. 6

For the calibration of the system we need to find the receiver noise temperature TR and the system gain over the frequency range. Consider Fig. 6, which shows a linear system with the measured output noise powers resulting from the applied noise input. The slope of the line is and is equal to: kBG

on off

on off

P PkBG

T T−

=−

(47)

The noise factor can be written as (for the noise source off state):

off

off

PF

kT BG= (48)

Expressing F into the ENR and the Y factor:

1 11

off off on off on off off on off

off off on off off on off off

P P T T T T P T TF

T kBG T P P T P P T Y− − −

= = = =− − −

(49)

Inserting the ENR definition in (43):

0 0

0

11 1

on off

off off

T T T TENRFT T Y Y T

⎛ ⎞−= = ⎜⎜− − ⎝ ⎠

⎟⎟ (50)

In (50) the noise source off noise temperature can be different from the reference temperature of 290K, but in practice many times both are assumed to be equal, leading to this very simple approximation characterizing the Y-method:


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1ENRFY −

(51)

The noise figure approximation (in dB) then becomes:

(10log 1dbNF ENR Y− )−

)

(52) By definition a device’s effective noise temperature is:

(0 1RT T F= − (53) (see also (10)) and therefore the receiver noise temperature becomes:

0 11R

ENRT TY

⎛ ⎞−⎜ −⎝ ⎠⎟ (54)

where T0=290K. Expression (50) can be used to get values corrected for ambient temperature. An ambient temperature for the noise source of 40oC, however, comes down to an error in NF of 0.3 dB. Expression (54) is useful when the ENR and Y data are available (and when the approximation condition that is valid). 0offT T=Expressing TR in the actually measured powers and known noise temperatures, using (43) and (45) and going back to the exact expression of F in (50) yields:

0 0

1on off on off off on

Roff off on off

T YT T P T PT TTT Y T P P

− −= =

− − (55)

To get the system gain note that the measured output power is:

(on R on RP kBG T T= + ) (56) Solve for GR:

( )on

Ron R

PGkB T T

=+

(57)

Be aware that in (57) usually the measured power Pon is available in dBm units, while kT is in Watts; so divide by 1000 or subtract 30 dB to get the correct gain. In dB’s:

( )( ) 10log( ) 10log 10log( ) 30dBR on on RG P dBm T T B k= − + − − − (58)


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6 References [1] R. Ambrosini, R. Beresford, A.J. Boonstra, S. Ellingson, and K. Tapping, “RFI Measurement

Protocol for Candidate SKA Sites” May 23, 2003. [2] R.P. Millenaar, A.J. Boonstra – SKA Spectrum Monitoring Plan for Candidate Sites, ASTRON,

revision 1.1, 9-01-2004 [3] C. Rauscher, Fundamentals of Spectrum Analysis, Rohde&Schwarz, 2001. [4] Spectrum Analysis Basics, Application Note 150, Agilent [5] J.D. Kraus, Radio Astronomy [6] Operating Manual Spectrum Analyzer, FSU-26, Rohde&Schwarz [7] Fundamentals of RF and Microwave Noise Figure Measurements, Application Note 57-1, Agilent [8] J. Dromer: Digital processing for SKA Site Spectrum Monitoring, November 2004, ASTRON


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