Precision testing methods of Event Timer A032-ET

Precision testing methods of Event Timer A032-ET Event Timer A032-ET provides extreme precision. Therefore exact determination of its characteristics in commonly accepted way is impossible or, at least, very difficult. For example, the widely used comparison method needs a reference instrument with much higher certified precision than that of the A032-ET. There are only a few such instruments in the world and they are accessible only in exceptional cases. For this reason custom methods have been developed for reliable precision testing of each manufactured A032-ET device. Although in fact the A032-ET measures separate events, its precision is specified for the time interval between two measured events. The total measurement error Tj of time interval T j between any two measured input events can be expressed as follows: where: Tj = B(t)+E(T j )+ξ j, B(t) time-varying measurement offset; E(T j ) non-linearity error depending on the value of the measured time interval; ξ j unbiased random error. Specific values of these error components completely specify precision of the A032-ET device for most applications. As to the errors caused by instability of the reference frequency and trigger errors, they are beyond the scope of A032-ET specifications since the A032-ET usually uses an external reference frequency source and measures events presented by normalised pulses. Particular methods and means considered below are intended for the experimental evaluation and specification of each mentioned component of the measurement error and are presented in this document as follows: 1. Stability Test (evaluation of the offset drift) 2. Linearity Test (evaluation of non-linearity errors) 3. Resolution Test (evaluation of random errors) It should be noted that, although these methods are considered only in connection with testing of A032-ET devices, they also are used for testing of other devices from the family of event timers with similar architecture produced by the Institute of Electronics and Computer Science in Riga. Special notice. Taking into account the features of the presented test methods, developer assumes responsibility for their scientific reasonableness and practicability but not for completeness and legal validity.

1. STABILITY TEST 1.1. Introduction Event Timer A032-ET has a single-channel configuration i.e. all events provided by either input of the ET-device are measured sequentially in the same manner and by the same means. Owing to this there is no any noticeable offset in time intervals between the measured events if these events come from the same input. However when the events come from different inputs, some offset appears. It is caused by the difference between internal propagation delays of input signals before they reach the common measurement unit. These delays slightly vary with the change of ambient temperature, causing certain offset drift and corresponding long-term instability of time interval measurements. There are no other essential reasons for the offset drift. Hereby own long-term stability of the A032-ET for the event measurement using different inputs is almost fully defined by the temperature stability of the offset. Typically the temperature stability of the offset drift is in the range of 0.1-0.5 ps/ 0 C and depends on particularities of the chips used for specific ETdevice. However it should be pointed out that this parameter cannot be defined strictly as its value considerably depends on the test conditions which may differ substantially from the actual operating conditions. Test method presented below is used for the experimental evaluation of the offset temperature stability. The method is based on differential measurement providing insensitivity to the long-term instability of test signals. 1.2. Test Setup The test setup (Fig.1.1) contains a custom-made Test Signal Generator W06 (see Annex), which generates low-jittered periodic pulse sequence. The splitter symmetrically splits this signal and provides two inputs of the ET-device with almost identical test signals. Signal propagation delays from the splitter to the ET-device inputs are minimized and equalized as far as possible. As in the case of other tests considered in this paper, the ETdevice under test is housed in a closed rack corresponding to the operating conditions recommended for highest-precision measurements; temperature inside the rack is continuously measured and recorded during the test. A032-ET Generator W06 Splitter A B ET-device Measurement software 10 MHz timebase Test software PC Fig.1.1. Test setup for offset drift evaluation The A032-ET operates in the mode performing cyclical measurements of Start-Stop events (A032.2 option). The test software processes the measurement results according to the method considered below. In this case the measurement software and test software are integrated in the test program Offset&HW3. 2

1.3. Evaluation method During the test the A032-ET measures test signals cyclically so that in the beginning of each cycle it captures a single event coming at the input A, and only then - two events coming at the input B (Fig.1.2). Under these test conditions the time interval T AB is measured with some offset but the time interval T BB without any offset by definition. Correspondingly, the calculated difference between time intervals T AB and T BB is an estimate of offset value under current test conditions. Input A 1st event T AB T BB Input B 2nd event 3rd event Fig.1.2. Time diagram of events measured in a single test cycle Note that in this case long-term instability of test signals does not affect the precision of the estimate. However every single estimate of the offset is considerably distorted by both a test signal jitter and random errors of event measurement, resulting in certain evaluation error. Typically such errors dominate over offset drift. As the offset drift is a quite slow process, a number of sequential single estimates can be averaged to minimize the evaluation error. In our case the averaging of 10 000 single estimates provides RMS value of evaluation errors about 0.2 ps. Additionally, moving averaging of 50 such offset values is applied to detect the offset drift more distinctly. 1.4. Example of the test The test program operates according to the considered method and calculates a new offset value every 20 seconds to display the offset drift as a function of time. Fig.1.3 demonstrates a typical result of the stability test under naturally varying ambient temperature. Duration of the test was about 16.7 hours. Fig.1.3. Ambient temperature and offset vs. time As can be seen, the offset variation is directly related to temperature changes, indicating the offset temperature stability about 0.48 ps/ 0 C. Generally this parameter value is specific for every ET-device under test. 3

2. LINEARITY TEST 2.1. Introduction The single-channel configuration of the A032-ET provides many benefits but also brings about specific limitations in event measurement. The A032-ET needs about 60 ns for single event measurement. During this time (called dead time ) the next measurement is impossible. But even after the dead time interval there is some damping transient in electrical circuits responsible for event measurement. If this process is not completed before the next measurement, the latter will be performed with some error. This error depends on the time interval width between the previous event and event currently measured, causing so-called non-linearity of event measurement. The A032-ET provides a special correction of such non-linearity. However it cannot correct initial non-linearity completely, leaving slight, noise-like non-linearity in the time interval range up to 2000 ns (Fig.2.1). This residual non-linearity appears as bias errors, which are specific and constant for every 1 ns increment of the time interval. In the range exceeding 2000 ns non-linearity is negligible. Fig.2.1. Typical non-linearity of the A032-ET Typically the non-linearity of the A032-ET does not exceed few picoseconds and is most noticeable only in the very beginning of the range. Test method presented below concerns the experimental evaluation of this parameter for each specific ET-device. The method is based on differential measurement, providing insensitivity to long-term instability of test signals. 2.2. Test Setup The test setup (Fig.2.2) contains two stand-alone mutually unsynchronized sources of test signals. One of them is the Test Signal Generator W06 (the same as in the previous test), which generates periodic pulse sequence B. Period of this sequence is surely greater than the range of time intervals where the non-linearity is possible (in our case greater than 2000 ns). The generator A generates a pulse sequence A with much greater period than that for the generator W06, defining periodicity of test cycles. The test signals come at the different inputs of ET-device so that the sequences A and B overlap. The A032-ET measures the events and provides corresponding time-tags for further processing by the test software. In this case the measurement software and test software are integrated in the test program CorrectionTest. 4

A032-ET Generator A A B A B ET-device Measurement software Generator W06 10 MHz timebase Test software PC Fig.2.2. Test setup for linearity evaluation 2.3. Evaluation method In test conditions defined above there are series of four sequential events where the first event is randomly located within the period of the sequence B (Fig.2.3). In this case the incomplete transient may distort the measurement of the second event after the first event measurement while the next third and fourth events are measured without such distortions by definition. Correspondingly the calculated difference D j between time intervals T B1 and T B2 (see Fig.2.3) characterizes the non-linearity error for specific measurable value of time interval T AB. A T AB 1st event T B1 T B2 B 2nd event 3rd event 4th event Fig.2.3. Time diagram of events measured in a single test cycle Other similar series characterize similar non-linearity errors but for some other, naturally randomized values of time interval T AB. When a number of such series is large enough, a set of values {D j } corresponding to increasing time intervals T AB characterizes the linearity function. However this presentation provides the values of linearity function with evaluation errors caused by test signal jitter and random errors of event measurement. Typically the evaluation errors considerably dominate over non-linearity errors. That is why these function values are further averaged for each considered value of the time interval T AB chosen with a constant increment. The averaging procedure results in uniformly spaced values of linearity function where evaluation errors is reduced down to an acceptable level by a rational choice of the increment value and available volume of statistics. In our case the time increment is equal to 1 ns as the averaging over a greater step may mask possible bursts of non-linearity errors. The test program CorrectionTest operating according to the considered evaluation method displays the current view of evaluated linearity function so that the process of its creation could be monitored. The program is able to support the test continuously during practically unlimited time. 2.4. Example of the test Although the method is applicable for a wide range of time intervals (up to hundreds of ms) the A032-ET are normally tested in much smaller range where the non-linearity is really expected. Fig.2.4 demonstrates a typical result of the linearity test. Total number of measurements was about 500 million (more than 9000 initial estimates for each 1 ns increment). Such statistics has been collected during 9.1 hours of continuous test. 5

Fig.2.4. The result of non-linearity evaluation It can be simply concluded from the test result that the maximum non-linearity does not exceed ±1 ps. However such estimate may be considerably overstated due to the evaluation errors. More precise estimate can be obtained from this test result by simple calculation. As can be seen, there is some appreciable (but not so large as Fig.2.1 suggests) difference between variances of measured values in the first sub-range to 2000 ns and in the second sub-range exceeding 2000 ns (the calculated standard deviations: 244 fs vs. 146 fs). The reason is that the values in the second sub-range are practically only evaluation errors but the values in the first sub-range are sums of non-linearity errors and evaluation errors. Assuming that these errors are statistically independent, it can be simply calculated that the RMS of non-linearity errors is about 195 fs. This conforms to the maximum non-linearity about ±0.5 ps and is much closer to its true value. In the very beginning of range (up to 100-150 ns) the non-linearity is a little larger. 2.5. Additional notice The considered method of linearity testing is conventionally used for all Riga event timers, including the previous model A031-ET. Linearity of this instrument was independently tested in comparison with the high-performance Event Timing System at Graz SLR station. Basic results of such tests conform well to the results obtained earlier using the above method and hereby confirm its reliability. (Selke C., Koidl F., Kirchner G., Grunwaldt L. Tests of the Stability and Linearity of the A031- ET Event Timer at Graz Station, Proceedings of the 14th International Laser Ranging Workshop, San Fernando, Spain, 2004, pp.337-341) 6

3. RESOLUTION TEST 3.1. Introduction Like any instrument, the Event Timer A032-ET performs event measurement with some random error, resulting in random errors in estimated time intervals between the measured events. For characterizing practicable measurement precision, the smallest displayed increment in measurement (1 ps for the A032-ET) is not so important. Instead, standard deviation of measured time interval is of primary interest as it characterizes precision more adequately. It is a common practice to call this parameter single-shot RMS resolution, keeping in mind comparing readouts from the same instrument. The A032-ET provides the single-shot RMS resolution surely better than 10 ps under conditions when input signals conform to the specified requirements and long-term instability of an external frequency standard is negligibly small during measurement. It is also supposed that the A032-ET has been calibrated under actual operating conditions which are stable enough during measurement. 3.2. Evaluation method The simplest and demonstrative way how to specify the RMS resolution is to perform direct repetitive measurement of a test signal that has a jitter much smaller than expected random errors produced by the instrument. According to this approach evaluation of RMS resolution is based on measurement of periodic low-jittered pulse sequence and cyclical calculation of standard deviation for time intervals between measured events. In this case the test result represents an estimate of single-shot RMS resolution as a function of time. It must be noted that such estimates are slightly overstated due to an inevitable test signal jitter and the true RMS resolution is slightly better than these estimates suggest. The test setup (Fig.3.1) contains the Test Signal Generator W06 generating periodic pulse sequence. There are two distinctive features of this generator: low jitter (<2 ps RMS) and test signal period (14077.4 ns) which is not a multiple of the A032-ET master clock period (10 ns). The latter feature ensures providing measured events which are uniformly distributed within the interval of interpolation so that the evaluated resolution concerns all possible cases of event measurement. A032-ET Generator W06 A ET-device Measurement software B 10 MHz timebase Test software PC Fig.3.1. Test setup During the test the A032-ET measures the events and provides corresponding time-tags for further processing by the test software. In this case the measurement software and test software are integrated in the test program Test&HW3. Every 5 sec the test program displays a new estimate of standard deviation calculated from 10 000 sequential single-shot measurements. It is assumed that the deviation of external reference frequency during such measurements (140.77 ms) has not a noticeable impact on the test result. Additionally the moving averaging of 100 estimates is used to present the evaluation result more distinctly. 7

3.3. Example of the test Typically the A032-ET is being tested continuously (without re-calibrations) during 15-20 hours to define the RMS resolution under temperature-varying operating conditions. Fig.3.2 demonstrates typical result of the resolution test performed during 19.6 hours. Fig.3.2. Ambient-temperature and RMS resolution vs. time (12500 sequential cycles) As can be seen, directly after initial calibration the RMS resolution is about 7.8 ps and it gradually degrades to 8 ps when the ambient-temperature is changed for 2 0 C. In other words, the temperature stability of RMS resolution is about 0.1ps/1 0 C. Thus it can be stated that: the best RMS resolution of the device under test is about 7.8 ps; the RMS resolution is surely better than 10 ps without re-calibrations if the ambienttemperature variation does not exceed ±10 0 C approx. Note that generally the best resolution and its temperature stability are specific for every ETdevice under test. Institute of Electronics and Computer Science 2006 October 2006 Rev.2 8

Annex Test Signal Generator W06 The W06 is a custom-made stand-alone device to provide standard conditions for testing the Riga event timers in terms of their RMS resolution, linearity and offset drift. The W06 is tailored to the particular methods of evaluating the mentioned characteristics. The W06 generates periodic sequence of test pulses, using synchronous divider of clock pulses produced by the high-performance internal oscillator (VCXO). There are two distinctive features of the W06: extreme low jitter and test signal frequency non-synchronous with the master clock frequencies of the Riga event timers. Key specification: Output (BNC): NIM pulses Output current: 40 ma Pulses width: 80 ns Fall time: <2 ns RMS jitter: <2 ps Nominal frequency: 71,036 KHz (14077. xxx ns period) Temperature stability: 1.4 ppm/ 0 C (see Fig.A1) High immunity to the external interferences Fig.A1. W06 temperature stability (Upper graph: ambient temperature vs. time; lower graph: period vs. time) 9