Chandra X-ray Center

HRC Deadtime and Telemetry Saturation

M. Juda and A. Dobrzycki
1999 June 18

1  Introduction

There are two sources of electronic deadtime within the HRC. The first is due to the time the HRC takes to process the information from an event registered by the MCP. The second is telemetry saturation; the Chandra X-ray Observatory has a limited telemetry bandwidth that results in a maximum allowed number of telemetered events per major frame (32.8 s) for the focal plane science instruments. When the HRC has the observing mode telemetry allocation (24 kbps of serial digital data), the telemetry has 378 ``slots'' available for event information every 2.05 s, for a mean event rate maximum of ~ 184.39 events s-1. Observations of bright, diffuse sources could exceed this mean rate resulting in a deadtime as events cannot be put into the telemetry stream.

The following setion describes how the parts of the HRC hardware that perform event processing effect deadtime. Subsequent sections describe a computer simulation of the timing aspects of event processing and presents results from simulations for a range of input event rates which includes rates higher than the telemetry limit. Algorithms for determining the deadtime for rates both above and below the telemetry saturation limit are given. The final section compares the simulation results to measurements using ``flight-like'' electronics.

2  HRC Event Processing

When the HRC MCPs are triggered by an event, it is counted and a series of hardware checks are performed to decide whether it should be processed and telemetered to the ground; this takes ~ 19.5 µs. If the event passes these checks it is counted as a valid event and the hardware processing that generates the telemetered event information is usually started. The processing will not occur if the hardware is already processing an event. From the time of the trigger to the time that the event information for telemetry has been generated is 68.5 µs. The HRC hardware is effectively ``dead'' to event processing during the 19.5 µs interval for the rejected events or the 68.5 µs interval for the accepted events. In simple terms these two times are the deadtime per rejected and accepted events respectively.

The HRC contains a hardware buffer that queues events for output into the telemetry slots. This ``primary'' science FIFO is large enough to hold the event information for 128 events. If events arrive faster than they can be telemetered, the FIFO will fill. Once it is full the hardware will hold the last event it receives, stop processing, and wait until one event has been removed from the FIFO; at this point it moves the event information it is holding into the FIFO and resumes processing. It is the fact that the hardware stops processing when the FIFO fills that creates the possibility for telemetry saturating deadtime. Even though the ``valid'' events are not being processed, they are still being counted.

3  Simulation Description

In an effort to understand the HRC performance at sustained rates near telemetry saturation, we have written a set of software tools that simulates the process. The simulation operates in a series of steps.

The simulation starts with the generation of event times; a Poissonian process is simulated by generating a sequence of times with an exponential distribution of times between events. The mean event rate is controlled by the mean of the exponential distribution. These event times are piped to a tool that determines where the times occur relative to the telemetry major frames and minor frames. Additional information that can be used for other simulation purposes are also generated.

The event time information is then passed on to a tool that simulates how the HRC hardware processing works. All events are assumed to have passed the hardware tests, i.e. they are considered to be ``valid'' events. An event time is compared to the previous time to see if it arrived while the hardware was processing that event; if so it is counted as a piled-up event and not put into the FIFO storage space. If the event wasn't piled-up, the event time is compared to the current telemetry time to see if events should be taken from the FIFO.

If the time of the next telemetry slot occurs before the event time the event information is taken from the FIFO storage space and the major frame, minor frame, and event slot within the minor frame in which the event is telemetered is added to it. This process is repeated as many times as necessary, either the time of the slot is after the event time or there are no more events in the FIFO storage space.

If the time of the next telemetry slot is after the event time, the FIFO is checked to see if there is room for an event; if there is the event timing information is put into the FIFO storage space. If the FIFO is full, the event is not put into the FIFO storage space. The time from when the FIFO fills to when the next set of event information is transfered from the FIFO storage space to a telemetry slot is accumulated. At the end of the simulation the total time spent with the FIFO full is reported along with the total number of events input, the number of telemetered events, the number of piled-up events, and the number of events that occurred while the FIFO was full.

4  Simulation Results

Simulator runs where performed for a range of mean event rates up to 1050 events s-1. Each simulation was run for an exposure of 1000 s. Table 1 contains the summary results from several simulation runs. As expected, the time spent with the FIFO full is zero until the mean rate is higher than the telemetry saturation rate. For rates above the telemetry saturation rate the deadtime increases rapidly with event rate. The deadtime fraction is plotted as a function of mean input rate in Figure 1.

Table 1: Telemetry Saturation Simulations - 1000 s exposures
Number of Events Time
Mean Rate Total Valid Telemetered Piled-up FIFO-full FIFO-Full
10 10016 10007 9 0 0.000
100 100090 99422 668 0 0.000
150 150250 148721 1529 0 0.000
180 180233 177996 2237 0 0.000
185 185284 182857 2365 62 0.403
190 190312 184493 2501 3318 18.065
195 195317 184489 2636 8192 43.714
200 200346 184514 2788 13044 67.718
210 210412 184511 3090 22811 112.388
220 220362 184515 3385 32462 152.731
230 230257 184514 3694 42049 188.999
240 240361 184511 4030 51820 223.909
250 250327 184515 4354 61458 254.340
260 260596 184515 4679 71402 283.804
270 270627 184516 5062 81049 311.018
280 280634 184516 5413 90705 336.072
290 290517 184515 5795 100207 358.590
300 300579 184516 6195 109868 381.057
350 349832 184517 8333 156982 466.721997
400 399440 184516 10793 204131 535.607309
450 449640 184516 13551 251573 586.421435
505 504242 184517 16973 302752 632.676754
600 599854 184517 23961 391376 690.467608
740 739840 184517 36493 518830 748.298812
800 799881 184517 42688 572676 768.222602
1000 1000362 184517 66294 749551 815.157201
1050 1050192 184517 72955 792720 823.445800

In addition to the information from the events, the HRC telemeters the total event rate (total triggers of the MCP in 1 s intervals) and the valid event rate (those triggers that pass the hardware tests). We can use these to derive the instrument deadtime.

At rates below telemetry saturation, the deadtime td for a selected interval is given by:

td = t1 Ntotal (1 - Nvalid-Ntelem
) + t2Ntelem,
where t1 is the time for the hardware checks (19.5 µs), t2 is the time to complete the event information processing (49 µs), Ntotal is the number of events that triggered the MCPs, Nvalid is the number of events that passed the hardware tests, and Ntelem is the number of events that was telemetered.

At rates above telemetry saturation a simple approximation to the deadtime is given by

td = T Nvalid-Ntelem
where T is the duration of the interval. Note that this is just the fraction of the events that were acceptable for processing and inclusion in telemetry but which didn't make it. This approximation is plotted as a dashed line in figure 1; it provides a reasonably close match ( < 2% different) to the simulation result near the point of telemetry saturation.

5  Comparison to Measurements

In order to demonstrate the validity of the model, a set of data were taken in the HRC laboratory using ``flight-like'' HRC electronics, a remote command and telemetry unit (RCTU), a command and telemetry unit emulator (CTUE), and an HRC EGSE computer. A random pulse generator was used to stimulate the inputs to the MCP-trigger and a set of crossed-grid charge detector pre-amplifiers of the HRC electronics. These random pulses were also counted on a scaler. Data collection runs were performed for 100 s each, with the mean input event rate adjusted from run to run; mean rates from ~ 50 pulses s-1 to ~ 1000 pulses s-1 were used. For each run, the intervals of telemetry collection and scaler counting were started nearly simultaneously.

Table 2 gives the results of these data collections. The ``root name'' of each telemetry data set is given; these names give the date-time stamp of the start of the data collection. The average input event rate is determined from the total number of events counted by the scaler in the 100 s interval; the statistical uncertainty is given. The average total and valid event rates are the means of the values of the samples in the telemetry file for the given run; the uncertainty is the standard deviation of the samples. The average telemetered event rate is given by the total number of events in the telemetry file for the given run divided time duration of the telemetry. The time duration of the telemetry file is given by the number of minor frames that it contains times the duration of a minor frame (0.25625 s). The uncertainty on the telemetered event rate is solely statistical.

As expected, the telemetered event rate saturates at ~ 184.4 events s-1 as the input rate rises above this level. Figure 2 shows the deadtime fraction calculated from the data in table 2 using the algorithms given in section 4; the plotted curve is the deadtime fraction given by simulation runs. The deadtime corrected rates are in included in table 2. The deadtime corrected rates are in good agreement with the input rates below the telemetry saturation point (184.4 events s-1) and in reasonable agreement, systematically low by less than 2%, for input rates up to 5 times the telemetry saturating rate.

Table 2: Event Rate Comparisons - 100 s exposures
Average Event Rates (counts s-1)
Data Set Input Total Valid Telemetered DT Corrected
1999167.134447 51.57±0.72 51.34±3.98 51.34±3.98 51.40± 0.73 51.58
1999167.134819 107.72±1.04 107.56±4.74 107.56±4.74 107.17±1.05 108.00
1999167.135106 164.23±1.28 163.78±4.98 163.78±4.98 162.65±1.31 164.5
1999167.135417 177.08±1.33 176.28±4.69 176.28±4.69 175.31±1.34 177.4
1999167.135736 184.25±1.36 184.17±5.28 184.16±5.28 182.44±1.39 184.7
1999167.140029 200.09±1.41 199.15±4.61 199.15±4.61 184.38±1.38 199.2
1999167.140357 217.85±1.48 217.30±6.08 217.30±6.08 184.47±1.43 217.3
1999167.140648 250.02±1.58 249.48±5.46 249.48±5.46 184.42±1.38 249.5
1999167.140946 295.34±1.72 293.62±5.81 293.62±5.81 184.40±1.45 293.6
1999167.141241 505.38±2.25 501.89±6.09 501.88±6.07 184.38±1.41 501.9
1999167.141529 739.13±2.72 730.64±6.48 730.64±6.48 184.47±1.43 730.6
1999167.141824 1026.02±3.20 1008.76±7.68 1008.76±7.68 184.36±1.39 1009.00


Figure 1: Deadtime fraction as a function of mean input event rate. The solid line is the result of the simulations. The dashed line is an approximation given by the fraction of the total number input that were not telemetered.


Figure 2: Comparison of simulations to data. Boxes give the calculated deadtime fraction for the laboratory measurements at each of the input rates. The solid line is the deadtime fraction determined from simulations.

Dr. Michael Juda
Harvard-Smithsonian Center for Astrophysics
60 Garden Street, Mail Stop 70
Cambridge, MA 02138, USA
Ph.: (617) 495-7062
Fax: (617) 495-7356

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On 18 Jun 1999, 10:03.