Admittance time invariance

The interpretation of dielectric measurements assumes that the sample behavior can be represented by a linear, time-invariant admittance. The meaning of each of these terms is examined in turn. 

The admittance of a linear time-invariant sample can now be defined. In the sinusoidal steady state at angular frequency oo, both v(t) and i(t) are sinusoids having some phase difference cp (see Fig. 2). 

Figure 5. Admittance data plotted as magnitude and phase angle vs. frequency as determined at the three premeasurement intervals (20, 100, and 200 ms) shown in Figure 2 and at the indicated membrane voltages. The superposition of the admittance data at each voltage indicates that the admittance is time-invariant in the interval from 20 to 200 ms after step changes in membrane voltage. Axon 87-19 internally perfused with the perfusate described in the text and externally perfused with ASW at 8 °C.

The characteristic time constant Tc in the form of tz and xyof Eqs (9.26) and (9.29) deserves some explanation. A two-component RC circuit with ideal components has a time constant t = RC. A step excitation results in an exponential response. With a CPE, the response will not be exponential. In Section 9.2.5, the time constant was introduced simply as a frequency scale factor. However, the characteristic time constant Tc may be regarded as a mean time constant because of a DRT. When transforming the Colez impedance Z to the Coley admittance Y or vice versa, it can be shown that the as of the two Cole Eqs 9.26 and 9.29 are invariant, but the characteristic time constants Tc are not. In fact ... 

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