Incremental resistance

This is the incremental resistance at the input. Let us call this Rin. So for a buck converter, its incremental resistance in ohms is... 

As seen in Figure 7.14, the resultant AC current will depend on the local slope of the DC current curve. The slope defines the incremental resistance ... 

The incremental resistance varies according to the DC (bias) level. Because the DC current curve is not linear, it is clear that with large amplitudes the current response will not be a sine wave even if the superimposed AC voltage is a pure sine wave. Because of the capacitive properties of the cell, the current will not be in phase with the applied sine voltage. 

From Figure 7.20 and file Butler—Volmer Eq. 7.15, it is clear that file DC resistance is strongly dependent on the DC current through the electrode. Wifli an AC superimposed on a DC, the resultant AC is dependent on the incremental resistance/conductance of the DC curve. If excitation is sinusoidal, and the measured AC voltage or current also is sinusoidal, then the system is linear with the amplitudes used. By increasing the amplitude, there will always be a level when nonlinearity is reached. 

Prior to the studies on the I Ce system, Sugawara (1%5) had found that Ce impurities dissolved in an Y host give rise to the resistance minimum phenomenon. Sugawara s original data are shown in fig. 11.1. From these and additional low temperature data, Sugawara and Yoshida (1968) extracted the temperature dependence of the incremental resistivity Ap contributed by the Ce impurity ions i.e., 4p(T) = pYCe(T)-py(r). These data are shown in fig. 11.2. The incremental resistivity was found to have the following characteristic form below 5 K -... 

Fig. 11.14. Temperature of the Kondo resistance minimum depth of the resistance minimum dpmin, and logarithmic slope of the solute incremental resistivity -d(4p)/d(log T) for (Ag, Au)Yb alloys vs Au composition of the Ag, Au matrix from resistivity data of Talmor and Sierro (1975).

This is another example of "negative incremental resistance" (pages 19 and 84). With extra resistors and also a capacitor, this circuit can be used to make a "gyrator" (page 125). 

But the two curves still do not exactly match, as Fig. 8.7 shows. The reason is a displacement of (for example) u = l f2 in tension and compression gives different strains) it represents a drawing out of the tensile specimen from 1q to 1.5 1q, but a squashing down of the compressive specimen from /q to 0.5/q. The material of the compressive specimen has thus undergone much more plastic deformation than the material in the tensile specimen, and can hardly be expected to be in the same state, or to show the same resistance to plastic deformation. The two conditions can be compared properly by taking small strain increments... 

For an increment of crack extension, A A is represented by a movement from B to D on the load versus deflection curve, the energy consumed may be represented by the area Attjj. Hence the crack growth resistance may be expressed as... 

Note that the total static pressure curve of Figure 12-145 is limited by the lowest output pressure of the multifan system. The limit curve is established using the fan curve (No. 1 in this example) having the smallest volume increment to the system resistance curve. In this situation fen No. 2 cannot add to the system until its pressure-volume relation reaches the peak point on its curve. 

The electrical resistance exerted by a separator on the ionic current is defined as the total resistance of the separator filled with electrolyte minus the resistance of a layer of electrolyte of equal thickness, but without the separator. The separator resistance has to be considered as an increment over the electrolyte resistance. 

For conductimetric incremental titrations, large rugged analogue conductivity meters have also become available, e.g., the Metrohm 518 conductometer (in connection with the Model 536 potentiograph its yields a rapid recording of the curve together with end-point indication) and the Philips PW 9505 analogue conductivity meter (in addition to a recorder output and an output for electrode re-platinization, there is a choice of manual or, by use of a Pt 100 resistance thermometer, automatic temperature compensation). 

It was shown by our investigations that such cell can be cycled with self-charging at least during 10-15 cycles. After that, the internal resistance of such cell is incremented considerably due to the accumulation of... 

The choice of cyclone modification, from an operating point of view, becomes a balance of incremental profit from increased conversion, versus catalyst makeup charges, and from a capital cost point of view, the price of either of the cyclone modifications, which must be depreciated. In many instances, there is an additional background time element, involving ongoing development of more attrition resistant and/or active catalyst. 

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