Small signal theory

Transistors are always operated so that amplification is obtained for a signal whose voltage is small on the input side (relative to the bias on the emitter) and small on the output side (relative to the collector voltage). Therefore small-signal theory applies. The designer obviously wants all signals to be amplified linearly, that is, by a common factor this makes the circuit behave more reasonably. 

In small-signal theory, one considers the superposition of a small voltage vE onto the DC power-supply-generated voltage VE, and the generation of a small voltage vc on the output, thanks to the application of a large... 

By using small-signal theory, the equivalent circuit now becomes... 

Using small signal theory, we find that the fluxes and concentrations can be written in the form f = ] + J eiat, nB = hs + hseiat where Jf is the d.c. flux... 

Inserting these expressions into eqn. (604) and using small-signal theory, we... 

Steady-State Pump-Depletion Limit. In order to account for severe pump depletion associated with high conversion efficiency, the small signal theory as outlined above in Equations (11.146)-(11.149) is not adequate. Complete quantitative solutions of the coupled dynamical Equations (11.143)-( 11.145) for the e and o... 

The theory underlying their function is imperfectly understood even after almost a century... although the very nature of these units limits them to small power capabilities, the concept of small-signal behavior, in the sense of the term when applied to junction devices, is meaningless, since there is no region of operation wherein equilibrium or theoretical performance is observed. Point-contact devices may therefore be described as sharply nonlinear under all operating conditions. 

The porous electrode theory was developed by several authors for dc conditions [185-188], bnt the theory is usually applied in the ac regime [92,100,101,189-199], where mainly small signal frequency-resolved techniques are used, the best example of which are ac theory and impedance spectra representation, introdnced in the previons section. The porous theory was first described by de Levi [92], who assumed that the interfacial impedance is independent of the distance within the pores to obtain an analytical solution. Becanse the dc potential decreases as a fnnction of depth, this corresponds to the assnmption that the faradaic impedance is independent of potential or that the porons model may only be applied in the absence of dc cnrrent. In snch a context, the effect of the transport and reaction phenomena and the capacitance effects on the pores of nanostructured electrodes are equally important, i.e., the effects associated with the capacitance of the ionic donble layer at the electrode/electrolyte-solntion interface. For instance, with regard to energy storage devices, the desirable specifications for energy density and power density, etc., are related to capacitance effects. It is a known fact that energy density decreases as the power density increases. This is true for EDLC or supercapacitors as well as for secondary batteries and fnel cells, particnlarly due to the distributed nature of the pores... 

D. R. Franceschetti [1981] Small-Signal A. C. Response Theory for Systems Exhibiting Impurity Oxygen Transport, Solid State Ionics 5, 613-616. 

Small-Signal AC Response Theory for Systems Exhibiting Diffusion and Trapping of an Electroactive Species,... 

Small-Signal A-C Response Theory for Electrochromic Thin Films, J. Electrochem. Soc. 129, 1754-1756. 

J. R. Macdonald and D. R. Franceschetti [1978] Theory of Small-Signal A-C Response of Solids and Liquids with... 

Figure 2. Plots of the measured dc current density filled squares, steady state current density open circles, the current density computed from drift mobility measurements and Eq. 1 filled diamonds, the current density computed from the transient dark injection peak values. The contact under test is a carbon filled polymer coated with a transport layer (TPD/polycarbonate) that is known to support trap free hole transport. The insert shows a typical dark injection transient compared to a small signal TOF transient. Conformity of key features of the steady state and transient data with the theory of trap free space charge limited currents provides a self consistent demonstration of contact ohmicity.

The theory was very similar to that described earlier, but was simplified in view of the complexity of the problem. A number of reaction intermediates were considered explicitly, and the corresponding signals were calculated by molecular dynamics simulation. Kinetic equations governing the reaction sequence were established and were solved numerically. The main simplification of the theory is that, when calculating A5[r, r], the lower limit of the Fourier integral was shifted from 0 to a small value q. The authors wrote [59]... 

Theory tells us that the maximum gain in proton signal intensity is 50%, but normally we are dealing with changes of only a few per cent, and the magnitude of these is dependent on the distance between the irradiated proton(s) and the observed ones the effect is too small to be visible when this distance exceeds about 5 A. 

We have so far looked at the NOE only in a homonuclear manner, but of course there is also a heteronuclear NOE. Theory tells us that when we are dealing with C-H fragments in small molecules, the decoupling of the proton leads to an increase in the carbon signal intensity by up to almost 200% So signals of protonated carbons should be stronger than those of non-proton-ated carbons. 

At first blush, the increased risk of harm suit against a drug manufacturer on a negligence theory that pharmacogenomics could have been used to determine the increased risks to a portion of the population appears to be a logical extension of the doctrinal shifts in liability law signaled by Moore. The likelihood of success of this particular lawsuit is in fact small because of the nature of existing medical liability doctrine in Pennsylvania. 

Diagonalization, of General Quantum Eigenvalues or Classical Normal Mode Frequencies from a Small Number of Residues or a Short-Time Segment of a Signal. I. Theory and Application to a Quantum-Dynamics Model. 

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