Optimum time constant

With a new, or repaired, detector it may be worthwhile to check whether you agree with the manufacturer s suggestion. You may wish, in any case, to select a shorter time constant in order to cope with particularly high count rates, accepting a small resolution penalty in return. 

F nre 11,5 System resolution at high and low count rates as a function of amplifier time constant 

With each new detector, or after a detector repair, the user will receive a specification sheet which should be retained. A typical sheet (see Table 11.3) will contain, in addition to model number, serial number, type of Dewar, etc., the following information  

Such a specification would refer to a standard coaxial detector. Specification sheets for other types of detector will contain other infomiation and not all the parameters noted in Table 11.3 will be warranted. For example, for a well detector geometric details of the well and the active volume will be quoted. It is likely that only the detector resolution will be warranted. Peak-to-Compton ratio may be measured, but not warranted. For low-energy detectors, only the resolution wiU be warranted. 

The first parameter to check is the resolution of the detector. In addition, checking this will also immediately confirm that the electronic system has been set up correctly. Unless that is the case, there is little point in pressing on with efficiency and peak-to-Compton measurements. 

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The time constant and scan time are the last parameters to be set. The time constant is set to produce the desired signal-to-noise ratio. To record a spectrum that is not distorted, the spectrometer should take 8 10 times the time constant to scan the maximum-to-minimum peak of the sharpest line. For example, suppose that the optimum time constant is 0.1 s, the sharpest line has a peak-to-peak width of 1.0 G and the fiiU scan is 1000 G. The spectrometer should take 10 times the time constant to go LOG, or 1.0 s. Therefore, to record 1000 G the spectrometer has to take 1000 s or 16.6 min, which corresponds to the minimum scan time. Scan times significantly shorter than this will result in a distorted signal. 

Amplifier throughput is inversely proportional to the shaping time — the narrower the pulses, the more through the system per second. So, at any particular input rate there can be a trade-off between the throughput capability and resolution. If the optimum time constant is halved, then we expect twice as many counts to be processed before pile-up effects become a problem, at the cost of slight... 

The Ziegler and Nichols closed-loop method requires forcing the loop to cycle uniformly under proportional control. The natural period of the cycle—the proportional controller contributes no phase shift to alter it—is used to set the optimum integral and derivative time constants. The optimum proportional band is set relative to the undamped proportional band P , which produced the uniform oscillation. Table 8-4 lists the tuning rules for a lag-dominant process. A uniform cycle can also be forced using on/off control to cycle the manipulated variable between two limits. The period of the cycle will be close to if the cycle is symmetrical the peak-to-peak amphtude of the controlled variable divided by the difference between the output limits A, is a measure of process gain at that period and is therefore related to for the proportional cycle ... 

Finally, the speed of response of the detector sensor and the associated electronics once played an important part in optimum column design. The speed of response, or the overall time constant of the detector and associated electronics, would be particularly important in the analysis of simple mixtures where the analysis time can be extremely short and the elution of each peak extremely rapid. Fortunately, modern LC detector sensors have a very fast response and the associated electronic circuits very small time constants and, thus, the overall time constant of the detector system does not significantly influence column design in contemporary instruments. The instrument constraints are summarized in Table 2... 

In Figme 4 is shown the effect of initiator half-life for an initiation activation energy of 120 KJ/mol on the optimum temperature and optimum time. It can be seen that the optimum temperature is almost independent of the half-life. As expected, the optimum time increases with an increase in half-life. Closer study of the results reveals that an almost constant optimal temperature is due to high NL, Values. A much higher temperature would cause to be higher than the desired Mf. 

The choice of optimum compression parameters to maximize speech intelligibility or speech quality is still open to contention. Rapid attack time constants (less than 5 ms) are accepted in the industry and also by researchers to prevent transients from saturating the output power amplifier. Arguments for fast release times (less than 20 ms), also termed syllabic compression, are based on considerations of the syllabic variations in speech and the desire to amplify soft speech sounds on a nearly instantaneous basis... 

The high heat transfer rates achievable in micro heat exchangers and reactors avoid unfavorable reaction conditions resulting from hot spots or thermal runaway effects. An optimum temperature or temperature profile for the reaction can be chosen with respect to spatial distribution and time. Thus, a fast-flowing fluid element can be cooled down or heated up very rapidly, in fractions of a millisecond. Because of the small thermal mass of microdevices, a periodic change of temperature of the reactor can be realized, with a typical time constant of some seconds. All these examples offer possibilities to improve yield and selectivity. 

More typically, instead of setpoint changes, the regulatory problem of responding to a system disturbance is encountered in commercial reactors. For this reason, the optimum tuning constants for the PID controller were developed from the IAE ralations for load disturbances. First, however, it is necessary to obtain a process model of the system. Brantley (10) has developed a process identification technique which fits process data to the second order plus dead-time form ... 

Determination of the optimum time for which the SPME sorbent will be in direct contact with the sample is made by constructing an extraction-time profile of each analyte(s) of interest. The sorption and desorption times are greater for semi volatile compounds than for volatile compounds. To prepare the extraction-time profile, samples composed of a pure matrix spiked with the analyte(s) of interest are extracted for progressively longer times. Constant temperature and sample convection must be controlled. Stirring the... 

Results for an intermediate constant sample time of 10 seconds are shown in Figure 5. The control in this case and also for the 15 second sample time case, not shown, is improved compared with the constant 25 and 5 second sample times. This suggests that an optimal constant sample time exists for application of the variable sample time algorithm. The optimum constant sample time appears to be on the order of 2 to 3 thermocouple time constants plus the average fluid residence time. 

Clearly, both packed column GC and conventional capillary GC already put serious constraints on the maximum allowable time constants. Ironically, the easiest separations, requiring the lowest numbers of theoretical plates and hence requiring short columns, are the most difficult ones to perform in an optimum way. The generation of 106 plates (in about an hour) allows the highest value for r (180 ms) in the entire table ... 

In round numbers, the length L in the apparatus to be employed is 50 cm and the two diffusion constants are of order of magnitude 0.6 cm s for CO2—He and 0.15 cm s for CO2—Ar. Using these figures the optimum diffusion times can be estimated from Eq. (14). The actual time should approximate this optimum time but in any case should not differ from it by more than 30 percent. 

The thickness of the membrane should exceed the penetration depth of the IR radiation in order to suppress the absorption bands of water. The optimum thickness is about 10 to 20 pm. The stability of such a membrane is satisfactory and the resulting time constant for the enrichment process is not too large. 

Flowever, the transition time is quite long, as expected when the objective was set. From an initial guess of 6 hours, the optimum solution led to a transition time of about 24 hours. To determine the cause of this behaviour, a study of the system s time constant... 

Computer-controlled systems were originally developed by Ebel and his team in order to achieve the most optimum positioning of any spot on a sample track in the measuring slit. Furthermore scanning during a standstill of the plate was considered an advantage, since errors which result from the time constants of densitometers and integrators could be avoided 28,29). 

The peak width in seconds (equation 9) is influenced by the mobile phase flow rate, whilst the peak width in microlitres (the peak volume, equation 9a) is not, if we assume that the decrease in plate number by a flow rate other than the optimum one is negligible. Yet the peak width in seconds is an important parameter for the calculation of the detector time constant (equation 12) ... 

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