Voltage spectral density, calculation

Ionic systems, such as water solutions of NaCl, CuS04, K2Cr04, and Ca(NOs)2 and solutions of sulfuric acid in ethyl alcohol, were among the objects of Johnson s experiments (I) that led him to conclude that there exists equilibrium electrical noise of a universal nature that manifests thermal motion of charged particles in conductors on a macroscopic level. Independently of a particular conductivity mechanism, the voltage spectral density, Sv(/), of this noise can be calculated from the real part of the system... 

Initial measurements on valinomycin-doped membranes (13, 14) showed that lipid bilayers, which provide cells with an effective permeability barrier, are equilibrium objects by this criterion. Within an accuracy of several percent, the experimentally obtained values of the spectral density of voltage noise showed agreement with those calculated from relation 1. Figure 1 illustrates this agreement for three valinomycin concentrations. For the valinomycin-K+ system chosen for these experiments and for the frequency range used in measurements, the dispersion in membrane impedance was caused only by geometrical capacitance of the bilayer the characteristic times of the transport process itself were too small to influence impedance in this range. 

Figure 11.2 (a.) Measured power spectral density of the voltage fluctuations V, and P reg a platinum disk electrode (area I0 cm ) In I M KCI solution with potassium ferri/ferrocyanide (I0 M) at the potential + 115 mV versus SCE. Curve (a) = bare platinum curve (b) = platinum covered with a gel layer (b) Calculated phase-sensitive detection ol V, Vi and P, in the same experimental conditions as in (a). Reprinted with permission from Ref. [20], Copyright 1993, AlP Publishing EEC. 

Alternatively, power spectral densities (PSD) of the noise can be calculated by means of the fast Fourier transform (FFT) or the maximum entropy method (MEM) (Schauer et al., 1998). The square root of the ratio of the voltage PSD to the current PSD also has the dimension of resistance and is a function of the frequency /. 

---