Zero “sensitivity

With a thickness below quarterwave, the response decays not only with the thickness but additionally with the field amplitude approaching the node. Thus zero sensitivity is to be expected at the very surface on the metal substrate. Advantageously another ex-... 

Figure 6.17 illustrates reciprocal current injection by a small contact area PU electrode into an infinite volume of homogeneous and isotropic material with uniform current density [,(,. From the reciprocally excited PU electrode, the current spreads out in a hemispheric symmetrical geometry in accordance with Figure 6.1. The reciprocal current density near the electrode is very high, and one may be led to believe that the sensitivity is high in this zone. The voxels lying in the vertical line from the PU electrode have zero sensitivity because the reciprocal current hue is perpendicular to the horizontal current lines. Near the surface, the dot product is very high near the PU electrode.

Figure 6.23 Applying current and measuring potential difference between interleaved electrodes in a homogenous medium (a) Current density lines between electrodes 1 and 3 and reciprocal current lines between electrodes 6 and 8 (b) corresponding sensitivity field distribution — white lines showing zero sensitivity (where the current density lines are orthogonal) — positive sensitivity (light grays) between these lines and negative sensitivity (dark grays) outside the lines.

In the same manner, sensitivity component models can be obtained for the other bond graph elements. As junctions do not depend on parameters they remain junctions in a sensitivity pseudo bond graph. Sources that provide a constant become sources of value zero. Sensitivity component models of other elements differ from their element only by additional sinks. As a result, a sensitivity pseudo bond graph is of the same structure as the behavioural system bond graph. Moreover, causalities of the latter one are retained. 

Let us again refer to the problem of zero sensitivity for an important reaction. To overcome this problem often it is nessecary to take recomce to additional methods, among which is the above-mentioned analysis of reaction rates [46-49]. 

At the same time the method of sensitivity analysis seems to be more correct in the identification of the rate-limiting steps of multistep reactions. However, this method may face the problem of zero sensitivity. That is, when throughout the process a zero value of the sensitivity, relative to the change in the rate constants of the step, not always enables uniquely to characterize it as "excessive" and to exclude from the kinetic model of the reaction aimed at its reduction. To solve such a problem there is a need to attract additional tools [57,58]. 

We end this brief description of composite op-amps and amplifiers with a rule of thumb. To realize second-order filter sections with Q < 10 using /uA741 op-amps so that /o is within about 2% of the ideal value and Q is within about 5% of its ideal value with no tuning, then for /o < 2 kHz, only one op-amp or op-amp amplifier is needed for /o < 10 kHz, a first-order zero sensitivity composite op-amp or amplifier is needed and for / < 50 kHz, a second-order zero sensitivity composite op-amp or amplifier is required. With higher performance op-amps such as an LF356s, the design of active filter sections that require no tuning can readily be pushed to a value of / beyond 150 kHz. 

In the case of the potentiometric sensor this means the construction of a chain, whose cell reaction does not involve valence changes. This principle led to the CO2 sensors presented in Section 7.2 with open reference electrodes and zero sensitivity to oxygen. 

In order to resolve the ambiguity of zero sensitivity one must analyze, in addition to the sensitivities, the reaction rates. A convenient way of doing this is to define (Gardiner, 1977)... 

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