Cascaded Stages

The performance of cascaded stages may also be described analytically on the basis of material balances and phase equilibrium relations. Consider, for simplicity, a binary mixture of components 1 and 2 and again assume component 1 to be the lower boiling, or more volatile, component. The equilibrium equations at stage j are... 

Additionally, Equations 3.1 and 3.2 used for cascaded stages in Section 3.2.2 are... 

When we combine transfer functions, decibels add up. So for example, if we take the product of two transfer functions A and B (cascaded stages), we get C = AB. This follows from the property log(AB) = log(A) + log(B). In words, the gain of A in decibels plus the gain of B in decibels, gives us the gain of C in decibels. 

The overall phase shift is also the sum of the phase shifts produced by each of the cascaded stages. So phase angles also add up. 

In a buck, there is a post-LC filter present. Therefore this filter stage can easily be treated as a cascaded stage following the switch. The overall transfer function is then very easy to compute as per the rules mentioned in the previous section. However, when we come to the boost and buck-boost, we don t have a post-LC filter — there is a switch/diode connected between the two reactive components that alters the dynamics. However, it can be shown, that even the boost and buck-boost can be manipulated into a canonical model in which an effective post-LC filter appears at the output — thus making them as easy to treat as a buck. The only difference is that the original inductance L (of the boost and buck-boost) gets replaced by an equivalent (or effective) inductance equal to L/(l—D)2. The C remains the same in the canonical model. 

The feedback block, on the other hand, consists of the voltage divider (if present) and the compensated error amplifier. Note that we may prefer to visualize the error amplifier block as two cascaded stages — one that just computes the error (summation node), and another that accounts for the gain (and its associated compensation network). Note that the basic principle behind the pulse width modulator stage (which determines the shape of the pulses driving the switch), is explained in the next section, and in Figure 7-11. 

As a further proof of this, note that in Figure 7-9, if we go around the cascaded stage consisting of G and H, and calculate the ratio of the input signal to the output, we get... 

The control-to-output transfer function is a product of the transfer functions of the PWM, the switch and the LC filter (since these are cascaded stages). Alternatively, the control-to-output transfer function is a product of the transfer functions of the PWM stage and the transfer function of the power stage . 

The flrst U.K. uranium isotope separation plant, built in the early 1950 s, was based on gaseous difiusion. This phenomenon depends on the observation that the rate of passage of molecules through a membrane is inversely proportional to the square root of the molecular weight. The application of this principle in a cascade stage requires a compressor, membrane, control valve, and cooler. 

Input parameters of CD code (Gokhman and Bergner 2010) are separated on two sets. The first set contains parameters that characterize the cascade stage of irradiation the direct generation rate of the single point defects, Gjp , the size dependence of the production rates of VC and dislocation loops (source term), G ,( , the ratio, q, of the number of the point defect monomers at the end of cascade stage to the total number of these defects created at the cascade stage (efficiency coefficient), and the ratio, of the number of SIAC (vacancies) that form dislocation loops (VC)... 

The rate of the number of vacancies that form VC to the total number of vacancies at the end of cascade stage in the case of ion irradiation greater than in the case of neutron irradiation... 

To determine the number of stages or flow rates and conpositions inside the cascade, stage-by-stage calculations are needed after we use the external mass balances to find concentrations. But first we use the external mass balances to find concentrations y n and y and flow rates Ej and R. Starting at stage 1 tFigure 13-201 we note that streams R and E both leave equilibrium stage 1. Therefore, these two streams are in equilibrium and the concentration of stream E can be found from an equilibrium tie line. 

Adapted from [18, 37, 38], Note that more or fewer flash cascade stages may be optimal. 

Although the number of search windows is reduced, there is still a vast amount of hypotheses to test. Thus, the proposed detector implements a Boosted Cascade [21] using Hoar [25] and Edge Oriented Histograms [26] as features to reject non-vehicle hypothesis as early as possible in the detection cascade. To further speed up the search, Activation History Features [27] is used to transfer information between the cascade stages. 

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