Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Control system wikipedia , lookup
Immunity-aware programming wikipedia , lookup
Switched-mode power supply wikipedia , lookup
Chirp spectrum wikipedia , lookup
Ringing artifacts wikipedia , lookup
Pulse-width modulation wikipedia , lookup
Time-to-digital converter wikipedia , lookup
Oscilloscope history wikipedia , lookup
Chirp compression wikipedia , lookup
1 I II III IV V VI VII VIII IX Ch 17 GK Linear and Logical Pulse Instruments Standard Application Specific Integrated Circuits Summary of Pulse Processing Units Components common to many applications. Pulse Counting Systems Pulse Height Analysis Digital Pulse Processing A. Analog-to-Digital Converters B Digital Shaping or Filtering C. Pulse Shape Analysis D. Digital Baseline Restoration E. Deconvolution of Piled-Up Pulses System Involving Pulse Timing a) Time Pick off methods b) Measurements of Timing Properties c) Modular Instruments for Timing Measurements X Pulse shape discrimination 2 3 4 4 5 6 7 8 9 11 12 13 14 15 16 8-9: Figure 17.33a shows the architecture of a module that carries out one stage of the process described above. At each clock cycle, the input voltage is momentarily held by a track-hold (T /H) circuit. A flash ADC carries out a digitization to n bits (n = 3 in the example above), and that value serves as the digital output of the stage. That same value is supplied to a digital-to-analog converter (DAC) and subtracted from the input voltage. The analog difference is sent through an amplifier with gain of G corresponding to the magnification factor (G = 8 in the example above), and the amplified analog voltage is passed on to the next stage. A number of such modules can now be combined in a "multipass" or "pipelined" arrangement illustrated in Fig. 17.33b, with all stages synchronized by a common clock. The digital outputs of all the modules are combined in a logic block that typically includes functions of bit alignment, error correction, and selfcalibration to form the overall digital result. Because of the serial operation of the individual stages, the final result is produced a number of clock cycles following the appearance of the corresponding analog input. This "latency time" is the same for all samples and introduces some delay. between input and output, but it does not affect the frequency of the conversions. Examples of some representative commercially available multipass or 17 18 19 20 1. LINEAR TIME-INVARIANT FILTERS-8-10 The processes of shaping the signal pulse from a radiation detector can be thought of as a filtering operation. For example, we have seen that the CR differentiator is equivalent to a high-pass filter in the frequency domain. Most (If the puIs" shxping op.-!ra'ions involve what are known as "linear timeinvariant filters." Their definition incorporates the restriction that the properties of the filter are fixed and do not change with time. A "transversal filter“ or "finite impulse response" filter is, by definition, limited to using input data over the restricted time range L < t < 0, where L is the length of the filter. This time range reaches backward from the present time simply because only data that have already occurred can contribute. to the output at a specific instant. The mathematical expression of the filtering process then takes the form of the convolution integral Set) = It vet') H(t - t') dt' (17.26) t - L where H(t) is called the impulse response function of the system. This function reflects the operations carried out by the analog shaping networks in conventional linear amplifiers. The definitions given above apply to cases in which the input data appear as an analog or smoothly varying function. That would be the case if we were dealing with the standard analog voltage output produced by a radiation detector. However, the fast digital converters described in the previous section Can be applied to convert 21 voltage into a series of digital samples. Once this conversion to digital data it 8-11: For the digital case, we start by assuming that the input signal has been sampled series of values Veil that starts at i = O. The time period between each sequential i simply represents the sampling period of the ADC. For the filtering process, the lent of the impulse response function now becomes a discrete set of weighting H(O) ., . H(L). We will assume that this filter is of finite length L so that the values of are 0 for values of i < 0 or i > L. The convolution process equivalent to Eq. (17.26) then can be written i=j S(j) = 2: V(i)H(j - i) (17.21 i=j-L where S(j) now represents the discrete series of output values produced by the digital fiiltering process. To give a more graphic picture of this filtering process, let us choose an examaple,,‘ which the filter consists of four weighting factors, H(O) ... H(3), so the length of the filter' . is equal to 3. Values of H{i) are by definition 0 outside this range. The input consists of .'~.'.'.' digital samples Veil, where we assume that the data begin at i = O. Evaluating the sum giv ,. in Eq. (17.27) for this example then gives, starting with the first nonzerO 22 output value (j = tJ <04. The process continues producing output values for 8-12: This convolution process is illustrated graphically in Fig. 17.34. For the example shoWll the weighting factors are written along the upper line in sequence from right to left. []Qfl H(2) I H(I) I H(O) I I V(O) I V(I) I V(2) I V(3) I V(4) I V(S) I S(O) ., V(O)H(O) I H(3) I H(2) I H(I) I H(O) I I V(O) I V(I) I V(2) I V(3) I V(4) I V(S) I 5(1) ., V(O)H(l) + V(l)H(O) I H(3) I H(2) I H(I) I H(O) I I V(O) I V(l) I V(2) I V(3) I V(4) I V(S) I S(2) = V(O)H(2) + V(I)H(l) + V(2)H(0) Figure 17.34 An illustration of a digital transversal filter. The filter element are shown (right to left) along the top line of each step, with the digitized data along the lower line. The output is formed by multiplying factors that are aligned and summing. Directly below, the sampled input values are written starting at V(O). The output is then given by multiplying each of these input voltages by the weighting factor shown directly above it and summing over the length of the filter. The first nonzero value o 23 the output 2. ADAPTIVE FILTERING-8-13 Digital pulse-processing systems, since they are controlled through software, easily allow the filter weighting functions to be customized to suit the circumstances of the measurement. In our previous discussion of pulse shaping, it was illustrated that each particular shaping choice results in a somewhat different theoretical signal-to-noise ratio (see Fig. 17.15). The choice of the optimum shaping method depends on the magnitude and nature of the noise that is present with the signal. Systems have been designed48- 51 that sample the detailed character of the noise present with the signal and then choose a weighting function that is optimal for the measured results. This is one . . r xp . . adjust the shaping parameters. Another example of adaptive filtering is applied to systems in which the counting rate changes substantially during a measurement. In many cases, one would 24 like to use shaping I, Pulse Shape Analysis 8-14 Once the input waveform from the detector has been digitized, measurements of its detailed shape also become straightforward. We have seen many examples of detectors in which the detailed time profile of the current pulse reveals additional information about the nature of the event in the detector. Examples are in distinguishing one type of radiation from another, measuring the spatial position of an event, or distinguishing pulses that arise from multiple gamma-ray interactions from those that are due to a single interaction only. Sophisticated algorithms can be used to inspect the string of digital data representing each individual pulse so that rather subtle differences among them can be distinguished. As these operations become more complex, however, it is increasingly difficult to carry them out entirely in real time at high counting rates because of the limited time available between signal pulses. In such cases, the digital data can be sent to 25 D. Digital Baseline Restoration-8-15 In digital pUlse-processing systems, the baseline restoration process described on be accomplished by digitally sampling the baseline between pulses and then appropriate value from the measured pulse amplitude.52 Independent baseline can be obtained for each pulse that is processed or, alternatively, a common applied to a series of pulses between more widely spaced samples of the baseline. one would like multiple digital measurements of the baseline to be taken for a sample to enhance its accuracy, requiring a relatively long time interval between Long intervals occur less frequently than short ones, so there must be a trade-off the accuracy of the baseline measurement and the frequency with which they can be Digital filters that can be applied to these baseline samples to optimize the lllt:aSllrem accuracy are described in Ref. 53. 26 E. Deconvolution of Piled-Up Pulses 8-16: Figure 17.35 Demonstration of the deconvolution of piled-Up pulses from output of a scintillation counter. The sampled data from the ADC operating at 100 MHz are shown as the series of points in both plots. In the bottom plot, an analytic fit to these da using the assumption that a single pulse shape should suffice results in a poor fit. In the t plot, an iterative procedure was used to fit two pulse components that allow the separati of both from the piled-up recorded data. (From Komar and Mak.54) Chapter 17 Systems Involving Pulse TIming 659 carried by the two separated pulses can be obtained. Although the utility of this type of pile-up deconvolution has been demonstrated in off-line systems,54.55 the requi processing times are still sufficiently long that it is not yet routine in standard spectroscop systems in which the pulse analysis is carried out in real time. 27 28 29 30 31 32 33