Family of transfer curves

EXEHCI5E 1-B For the circuit below, find the nested family of transfer curves if the breakdown voltage of the Zener is swept from 1 V to 6 V. 

A question we would like to ask is, how does the transfer curve of the circuit from the previous section change as we change the driver MOSFET width-to-length ratio We would like a family of curves that show the effect of changing the driver width. Families of transfer curves can be generated using the Parametric Sweep in conjunction with the DC Sweep or by using the Secondary Sweep. The Secondary Sweep was demonstrated in Section 4.D.2, so we will demonstrate the Parametric Sweep here. 

Although this model was initially developed for reactions occurring in an adiabatic potential energy surface, it can be extended to weak interaction systems under the assumptions mentioned above, because the reaction path is obtained in terms of independent stretches of the two reactants. This contrasts with the Agmon-Levine approach, which is restricted to atom or group transfer reactions, where reactant and product are connected via a family of parallel curves each defined by the same positive bond order, maintained constant through the compensation between the decrease in the reactant bond order and the increase in the product one. One caution must be observed in our analysis the extensions x are not directly related to the intersection of the reactants curves, although it is convenient to represent them that way. Therefore, we can use the transition state expression to estimate the rates of ET reactions... 

Returning now to proton transfers in methanol solution, we see that the family of curves in Fig. 44, calculated with S = 185.4 is very similar to those for aqueous solution. The curve for a = 0.0 passes through its maximum at the characteristic temperature 185.4°K. We now find that we can interpret the experimental results recorded in Table 16 for we see in Fig. 44 that curves drawn for values of a between —3 and —4 pass through zero near room temperature. The row of circles give values of... 

In the case of 0-pipettes, the collection efficiency also decreases markedly with increasing separation. The situation becomes more complicated when the transferred ion participates in a homogeneous chemical reaction. For the pseudo-first-order reaction a semiquantita-tive description is given by the family of dimensionless working curves calculated for two disks (Fig. 6) [23]. Clearly, at any separation distance the collection efficiency approaches zero when the dimensionless rate constant (a = 2kr /D, where k is the first-order rate constant of the homogeneous ionic reaction) becomes 1. 

This is a functional equation for the boundary position X and the unknown constant parameter n. Upon substituting Eq. (256) into Eq. (251) an ordinary differential equation is obtained for X(t, n), and a family of curves in the phase plane (X, X) can be obtained. For n sufficiently close to unity two functions in the phase plane can be determined which serve as upper and lower bounds for the trajectories. The choice is guided by reference to the exact solution for the limiting case of constant surface temperature. It is shown that the upper and lower bounds are quite close to the one-parameter phase plane solution, although no comparison is made with a direct numerical solution. The one-parameter solution also agrees well with experiments on the solidification of aluminum under conditions of low surface heat transfer coefficient (hi = 0.02 cm.-1). 

Figure 3.53 shows the increase in the mass transfer coefficient (K), as calculated from Equation 10, due to the centrifugal force. The family of curves are for different concentrations of casein. 

Also plotted on the psychrometric chart are a family of adiabatic saturation curves. The operation of adiabatic saturation is indicated schematically in Figure 1.5. The entering gas is contacted with a liquid and as a result of mass and heat transfer between the gas and liquid the gas leaves at conditions of humidity and temperature different from those at the entrance. The operation is adiabatic as no heat is gained or lost by the surroundings. Doing a mass balance on the vapor results in... 

Thus far we have looked at the Ids vs. Vqs curve only for the case of Vbs = 0. In Fig. 7.16 a family of curves of Ids vs. Vds for various constant values of Vbs is presented. This is called the drain characteristics, and is also known as the output characteristics, since the output side of the JFET is usually the drain side. In the active region where Fds is relatively independent of Vds > there is a simple approximate equation relating 7ds to Vgs- This is the square law trans-ferequationasgivenby/Ds = Fdss[1-(Vgs/Vp)]l In Fig. 7.17 a graph of the 7ds vs. Vgs transfer characteristics for the JFET is presented. When Vgs = 0,... 

Experimental data and models for the heat transfer coefficients in freeboards space are limited. Biyikli et al. (1983) measured heat transfer coefficients on horizontal tubes in freeboards of fluidized beds with particle mean diameters ranging from 275 to 850 pm. These investigators discovered that data for particles of different sizes and materials could be unified into a family of curves by plotting the normalized ratios of heat transfer coefficients against dimensionless velocity ... 

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