Curve tracer

Kurven-schar, /. group or system of curves, -schreiber, m. curve tracer, -zacke, /. iag (sharp change in direction) in a curve, -zeichnen, n. curve plotting. -zug, m. curve. 

A simple curve tracer circuit was created in each of the simulators. The IsSpice circuit is shown in Fig. 10.18. The diode on the left is the IsSpice model the one on the right is the model Kielkowski created... 

The output response curve for the tracer test is called C-curve. Tracer concentration at the inlet Q(0) = Q for all 0 > 0, as the tracer is added continuously starting from time 0 = 0. All the fluid elements entering the vessel at and after time 0 = 0 are marked uniformly with the tracer. At any time 0 > 0, qCg is the amount of fluid elements entering the vessel, which is the same as the amoimt of fluid elements leaving the vessel. Of this total amount of fluid elements qCg leaving the vessel at any time 0 > 0, only qC Q) fluid element is marked by the tracer. This qC Q) represents the fluid elements that have resided, in the vessel for a time span lesser than or equal to 0. As the RTD F(0) is defined as the fraction of the fluid elements whose residence time is less than or equal to 0, we have... 

Fig. 10.7 Voltage versus current "curve tracer" for an inductor.

As observed in the curve tracer experiment, the current lags the voltage, and the voltage is said to lead the current, when an ac sine wave goes through an inductor. (Doing the experiment requires two transformers, so it will not be performed here.) The relationship is shown in Fig. 10.8. Actually, the pendulum on page 98... 

Fig. 14.3 Curve tracer, to study diode (or other "DUT") behavior.

Another type of avalanche diode is the "diac." This also has a characteristic curve that is the same in both directions, because it is a symmetrical design with a PNP structure. It can be thought of as two PN diodes, back to back. Each one is designed to be able to avalanche at about 1 ma of current without being damaged. Breakdown can be as low as about 6 volts, and this goes lower after the avalanche has started, even more so than in the neon bulb. We will make use of this device in Chapter 21. As an optional experiment, it can be inserted into the curve tracer to give a curve like that in Fig. 14.4. 

NOTE The most reliable procedure would be to test the transistor with a transistor curve tracer. This instrument will tell you whether the transistor is still alive or definitely gone, but would also enable you to determine whether a deterioration in its characteristics has occurred. 

If a curve tracer is not available in your laboratory, you can construct the very simple transistor tester of Fig. 6.8. The tester accepts on two different sockets both NPN and PNP transistor. The two-position, two-pole switch selects either type. The tester is basically a B meter and is surely much more effective than a simple ohmmeter employed to determine whether either junction is open or not. With the tester of Fig. 6.8 you put the transistor under test on the relevant socket having previously correctly positioned the switch, and take note of the panel meter reading. If such a reading is between 0 and 3V, your transistor has to be replaced. 

Having the transistor disconnected, check It with a curve tracer, a se1f-construe ted tester or with a commercial transistor fixture and decide whether to replace It or not. 

Two different types of dynamic test have been devised to exploit this possibility. The first and more easily interpretable, used by Gibilaro et al [62] and by Dogu and Smith [63], employs a cell geometrically similar to the Wicke-Kallenbach apparatus, with a flow of carrier gas past each face of the porous septum. A sharp pulse of tracer is injected into the carrier stream on one side, and the response of the gas stream composition on the other side is then monitored as a function of time. Interpretation is based on the first two moments of the measured response curve, and Gibilaro et al refer explicitly to a model of the medium with a blmodal pore... 

An approximate, but sufficient, solution of dris equation for the thin tracer him experimental technique shows that the penetration curve has two components Ai, All and b being known constants. 

Total area under tracer concentration (or a quantity proportional to it) curve versus time as measured at the outlet... 

The distribution of tracer molecule residence times in the reactor is the result of molecular diffusion and turbulent mixing if tlie Reynolds number exceeds a critical value. Additionally, a non-uniform velocity profile causes different portions of the tracer to move at different rates, and this results in a spreading of the measured response at the reactor outlet. The dispersion coefficient D (m /sec) represents this result in the tracer cloud. Therefore, a large D indicates a rapid spreading of the tracer curve, a small D indicates slow spreading, and D = 0 means no spreading (hence, plug flow). 

For a large amount of dispersion or small value of Np, the pulse response is broad, and it passes the measurement point slowly enough for changes to occur in the shape of the tracer curve. This gives a non-symmetrical E-curve. 

If the ligand aliosterically affects the affinity of the receptor (antagonist binds to a site separate from that for the tracer ligand) to produce a change in receptor conformation to affect the affinity of the tracer (vide infra) for the tracer ligand (see Chapter 6 for more detail), the displacement curve is given by (see Section 4.6.3)... 

As noted previously, in all cases these various functions describe an inverse sigmoidal curve between the displacing ligand and the signal. Therefore, the mechanism of interaction cannot be determined from a single displacement curve. However, observation of a pattern of such curves obtained at different tracer ligand concentrations (range of [A ] values) may indicate whether the displacements are due to a competitive, noncompetitive, or allosteric mechanism. 

Schiesser and Lapidus (S3), in later studies, measured the liquid residencetime distribution for a column of 4-in. diameter and 4-ft height packed with spherical particles of varying porosity and nominal diameters of in. and in. The liquid medium was water, and as tracers sodium chloride or methyl orange were employed. The specific purposes of this study were to determine radial variations in liquid flow rate and to demonstrate how pore diffusivity and pore structure may be estimated and characterized on the basis of tracer experiments. Significant radial variations in flow rate were observed methods are discussed for separating the hydrodynamic and diffusional contributions to the residence-time curves. 

Ross (R2) measured liquid-phase holdup and residence-time distribution by a tracer-pulse technique. Experiments were carried out for cocurrent flow in model columns of 2- and 4-in. diameter with air and water as fluid media, as well as in pilot-scale and industrial-scale reactors of 2-in. and 6.5-ft diameters used for the catalytic hydrogenation of petroleum fractions. The columns were packed with commercial cylindrical catalyst pellets of -in. diameter and length. The liquid holdup was from 40 to 50% of total bed volume for nominal liquid velocities from 8 to 200 ft/hr in the model reactors, from 26 to 32% of volume for nominal liquid velocities from 6 to 10.5 ft/hr in the pilot unit, and from 20 to 27 % for nominal liquid velocities from 27.9 to 68.6 ft/hr in the industrial unit. In that work, a few sets of results of residence-time distribution experiments are reported in graphical form, as tracer-response curves. 

These can be solved by classical methods (i.e., eliminate Sout to obtain a second-order ODE in Cout), by Laplace transformation techniques, or by numerical integration. The initial conditions for the washout experiment are that the entire system is full of tracer at unit concentration, Cout = Sout = L Figure 15.7 shows the result of a numerical simulation. The difference between the model curve and that for a normal CSTR is subtle, and would not normally be detected by a washout experiment. The semilog plot in Figure 15.8 clearly shows the two time constants for the system, but the second one emerges at such low values of W t) that it would be missed using experiments of ordinary accuracy. 

Via a passive scalar method [6] where or, denotes the volume fraction of the i-th phase, while T, represents the diffusivity coefiBcient of the tracer in the i-th phase. The transient form of the scalar transport equation was utilized to track the pulse of tracer through the computational domain. The exit age distribution was evaluated from the normalized concentration curve obtained via measurements at the reactor outlet at 1 second intervals. This was subsequently used to determine the mean residence time, tm and Peclet number, Pe [7]. 

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