Critical conductivity

Each of these possibilities has a name — CCM, DCM, BCM (boundary conduction mode, also called critical conduction mode), and so on. Which of these operating modes actually occurs depends on the specific circuit (i.e. the topology) and also the application conditions (how much output power we are demanding and what the input and output voltages are). 

Note that the ratio r is defined for CCM (continuous conduction mode) operation only. Its valid range is from 0 to 2. When r is 0, AI must be 0, and the inductor equation then implies a very large (infinite) inductance. Clearly, r = 0 is not a practical value If r equals 2, the converter is operating at the boundary of continuous and discontinuous conduction modes (boundary conduction mode or BCM ). See Figure 2-5. In this so-called boundary (or critical ) conduction mode, Iac = Idc by definition. Note that readers can refer back to Chapter 1, in which CCM, DCM, and BCM were all initially introduced and explained. 

Figure 3.1. Percolation curve of a conducting composite based on nonconducting polymeric binder with conductive filler. Theoretical dependence of composite resistivity on conductive filler content. In the zone 1, the electrical resistance of the composite is similar to that of the polymer. In zone 2, the percolation fraction / represents a critical conductive filler content that permits the formation of the first conducting filament consisting of particle-to-particle contacts. In zone 3, electrical resistance of the composite is similar to that of pure conductive filler.

Janzen, J. (1975) Onthe critical conductive filler loading in antistatic composites. 

Igy is the critical conductivity at which the scaling function /3(g) vanishes], and the resistivity should be relatively temperature independent. It is reasonable to say that some local ordering takes place in samples prepared at 600°C compared with 500 C, at which they are strongly disordered. For the latter at a low scanning temperature Ip becomes and we see constancy of conductivity. For higher temperatures /p decreases, and when lp < the conductivity is not described by inelastic effects and is given by... 

Form a Faraday cage around the critical conductive patterns and components using a combination of condnctive patterns (frequently called input guarding and guard rings) and shielding enclosures. 

To apply percolation theory, Eq. (3) is simplified by noting that bonds at the critical conductance involve site energies that are high above the quasi-electrochemical potential ( d-Md > 7 ). The conductance in Eq. (3) for small applied electric fields can then be approximated in the zero-field limit as [26]... 

The critical conductance is written Gc = Goexp[-Xc]. The conductivity of the disordered system is therefore cr = Ooexp [-Xc], where Xc is the critical exponent of the critical conductance when percolation first occurs (when B = Be). 

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