Plotting Transfer Curves

When you have a clipping circuit, as in the last example, a transfer curve may be desired. This can easily be done by changing the x-axis. A transfer curve usually plots VQ versus Vjn, so we need to change the x-axis from Time to VQ/IN). We must first delete the trace VflfINl from the plot above. Click the LEFT mouse button on the text V/VIN). The text will appear in red, indicating that it has been selected. Once the trace is selected, press the DELETE key to delete the trace. You can delete the other text items and lines on the screen using the same method. Click the LEFT mouse button on an item to select it and then press the DELETE key to delete it. You should have a screen with a single trace  

We will now change the x-axis. Select Plot and then Axis Settings from the Probe menus. By default, the dialog box displays the settings for the x-axis  

We see that the present x-axis variable is Time. We would like to change the x-axis variable to V(Vin) so click the LEFT mouse button on the text V/VIN). 

Click the OK button twice to plot the transfer curve  

EXERCISE B-7 Find the output voltage waveform and the transfer curve for the circuit below. Let the input be a 15 volt triangle wave. Use the source Vtri to create a 1 Hz triangle wave. 

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One of the more useful functions of the DC Sweep is to plot transfer curves. A transfer curve usually plots an input versus an output. A DC transfer curve plots an input versus an output, assuming all capacitors are open circuits and all inductors are short circuits. In a DC Sweep, all capacitors are replaced by open circuits and all inductors are replaced by short circuits. Thus the DC Sweep is ideal for DC transfer curves. The Transient Analysis can also be used for DC transfer curves, but you must run the analysis with low-frequency waveforms to eliminate the effects of capacitance and inductance. Usually a DC Sweep works better for a transfer curve. The one place where a transient analysis works better is plotting a hysteresis curve for a Schmitt Trigger. For a Schmitt Trigger, the input must go from positive to negative, and then from negative to positive to trace out the entire hysteresis loop. This is not possible with a DC Sweep. 

Schwartz has published some hypothetical data for the titration of a 1.02 X ICr" M solution of a monoprotic weak acid (pXa = 8.16) with 1.004 X ICr M NaOH. " A 50-mL pipet is used to transfer a portion of the weak acid solution to the titration vessel. Calibration of the pipet, however, shows that it delivers a volume of only 49.94 ml. Prepare normal, first-derivative, second-derivative, and Gran plot titration curves for these data, and determine the equivalence point for each. How do these equivalence points compare with the expected equivalence point Comment on the utility of each titration curve for the analysis of very dilute solutions of very weak acids. 

The lower Emit of applicability of the nucleate-boiling equations is from 0.1 to 0.2 of the maximum limit and depends upon the magnitude of natural-convection heat transfer for the liquid. The best method of determining the lower limit is to plot two curves one of h versus At for natural convection, the other ofh versus At for nucleate boiling. The intersection of these two cui ves may be considered the lower limit of apphcability of the equations. 

One plots the curve F(x) (Fig. 6-9) and the construction consists in tracing the direction field of lineal elements. We take, for instance x = xx to which corresponds the point on the curve F(x), and transfer... 

We would like to plot the transfer curve Vo versus Vln for the NMOS inverter below ... 

The goal functions are used in Probe. Follow the procedure of Section 4.D.3. When you obtain the Probe plot of the transfer curve V(Vo) versus V Vin below, continue with this section ... 

The wall of an insulated container can be modeled as a 5-cm wide vertical enclosure with an aspect ratio of 5. The enclosure is filled with a low grade insulating material that has a permeability of 10"8 m2 and an apparent thermal conductivity of 0.04 W/m-K. The inner wall of the enclosure is at 5°C. Plot a curve showing how the heat transfer rate across the enclosure varies with outer wall temperature. 

Fig. 7.21. Responses of NTCDI devices to DMMP. (a) semilog transfer curves before and after exposure, (b) linear plots of current vs. time, before, during, and after exposure... 

The technique most often used (i.e., for an atom transfer) is to hrst plot the energy curve due to stretching a bond that is to be broken (without the new bond present) and then plot the energy curve due to stretching a bond that is to be formed (without the old bond present). The transition structure is next dehned as the point at which these two curves cross. Since most molecular mechanics methods were not designed to describe bond breaking and other reaction mechanisms, these methods are most reliable when a class of reactions has been tested against experimental data to determine its applicability and perhaps a suitable correction factor. 

Fig. 18. Rate constant calculated with the use of (2.80a) plotted against (m/mH). The hydrogen transfer rate is assumed to be 10 s the effective symmetric vibration mass 125mH. The ratio of force constants corresponding to the intra (Kq) and intermolecular (K,) vibrations is (Ki/Ko) = 2.5 x 10 , 5 x 10 and l.Ox 10 for curves 1-3, respectively.

The curves represent a plot of log (h ) (reduced plate height) against log (v) (reduced velocity) for two very different columns. The lower the curve, the better the column is packed (the lower the minimum reduced plate height). At low velocities, the (B) term (longitudinal diffusion) dominates, and at high velocities the (C) term (resistance to mass transfer in the stationary phase) dominates, as in the Van Deemter equation. The best column efficiency is achieved when the minimum is about 2 particle diameters and thus, log (h ) is about 0.35. The optimum reduced velocity is in the range of 3 to 5 cm/sec., that is log (v) takes values between 0.3 and 0.5. The Knox... 

In Figure 7, the resistance to mass transfer term (the (C) term from the Van Deemter curve fit) is plotted against the reciprocal of the diffusivity for both solutes. It is seen that the expected linear curves are realized and there is a small, but significant, intercept for both solutes. This shows that there is a small but, nevertheless, significant contribution from the resistance to mass transfer in the stationary phase for these two particular solvent/stationary phase/solute systems. Overall, however, all the results in Figures 5, 6 and 7 support the Van Deemter equation extremely well. 

Over the years the original Evans diagrams have been modified by various workers who have replaced the linear E-I curves by curves that provide a more fundamental representation of the electrode kinetics of the anodic and cathodic processes constituting a corrosion reaction (see Fig. 1.26). This has been possible partly by the application of electrochemical theory and partly by the development of newer experimental techniques. Thus the cathodic curve is plotted so that it shows whether activation-controlled charge transfer (equation 1.70) or mass transfer (equation 1.74) is rate determining. In addition, the potentiostat (see Section 20.2) has provided... 

It should be noted that the weighed amount of KBr/KSCN is constant and that although the problem of non-quantitative transfer of powder from the ball-mill grinder still exists it affects both the carrier and the organic compound equally. When the infrared spectra for the six discs have been obtained the calibration curve is prepared by plotting the ratio of the intensity of the selected... 

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