Decoupled local oscillator

A separation of the through-bond interactions (Ed) into bond stretching (Eb), angle bending (Eg), out-of-plane deformation (E ), torsional angle rotation (Ef) and other terms is only possible if these terms are not coupled, and this is most likely if the force constants are very different. This is generally true and leads to largely decoupled local oscillators. In cases where this requirement is violated correction terms have to be added. This can be done by the inclusion of cross-terms which will be discussed later. 

Most of the evaluation boards of such ESR-sensitive parts are shipped out to customers with only aluminum electrolytic or tantalum capacitors at their outputs. But what really happens is that the customer happily connects the eval board (rather expectantly) into his or her system, and completely forgets there are a bunch of ceramic capacitors all over the system board (for local decoupling at different points). In effect, the switcher can lose that valuable zero in its control loop and break into oscillations (see Figure 3-5). More so if the connecting leads are short. 

Figure 2. Effect of the frequency < > of the perturbation by the core on an electron moving in a Bohr-Sommerfeld orbit of high eccentricity (low angular momentum). Plotted vs. the angle u, which varies by 2ir over one orbit. Note that the perturbation is localized near the core. In the inverse Bom-Oppenheimer limit (x 1) the perturbation oscillates many times during one orbit of the electron. (For further details and the formalism that describes the motion at high x as diffusive-like (see Refs. 3c and S.) For higher angular momentum / the effective adiabaticity parameter is x(l - e) xfl/2, where e is the eccentricity of the Bohr-Sommerfeld orbit. States of high / are thus effectively decoupled from the core.

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