Constant phase angle

Constant phase angle — The phase angle is the angle between two phasors that rotate with the same -> angular velocity. The constant phase angle is independent of angular velocity. For a solitary -> resistor the phase angle is zero, and for a solitary -> capacitor it is ir/2. 

Closely related to the above analysis, though possibly arising from a fundamentally different physical origin, is the use by t Lam et al. of a "constant phase angle (cpa) element to replace Zsa [74,75], In fact, "Zss was represented by the circuit... 

The term constant-phase element (CPE) is applied to a general circuit element that shows a constant phase angle. Thus, the resistor, capacitor, and inductor can all be considered to be constant-phase elements. 

In the 1920s, impedance was applied to biological systems, including the resistance and capacitance of cells of vegetables and the dielectric response of blood suspensions. ° Impedance was also applied to muscle fibers, skin tissues, and other biological membranes. " The capacitance of the cell membranes was found to be a function of frequency, and Fricke observed a relationship between the frequency exponent of the impedance and the observed constant phase angle. In 1941, brothers Cole and Cole showed that the frequency-dependent complex... 

Cm is membrane capacitance, a is a number less than 1 that reflects the constant phase angle character of Cm (17), gL is the leakage conductance, and gKoo and gNa00 are the chord conductances of the respective K+ and Na+ systems. The gn term reflects the kinetic component (activation) of the potassium conductance that relaxes with time constant Tn and the gm and gh terms reflect the kinetic components (activation and inactivation, respectively) of the sodium conductance that relax with time constants tto and Th, respectively. 

Most of the literature on the dynamic properties of solid interfaces is based on the analogy between membrme and interfacial kinetics tnd the electric response of rough electrodes, for which an anomalous impedance scaling with frequency w, referred to as Constant Phase Angle behavior, Z[oj) = / 4- 0 < w <, i / has been... 

Constant phase elements (CPEs) have been used in bioimpedance models since the late 1920s. A CPE can be modeled by a resistor and capacitor, both having frequency-dependent values, in such a way that the phase angle is frequency independent. A CPE is mathematically simple, but not so simple as to realize with discrete, passive components in the real world. A particular type of CPE is the Warburg element, known from electrochemistry and solid state physics. It is diffusion controlled with a constant phase angle of 45° (Warburg 1899). 

The speeifie frequeney dependence in Eq. (36) is known as the constant phase angle (CPA) dependenee (78-80). This impedance behavior oeeurs for a wide elass of elee-trodes (75-77) and suggests the introduction of a new equivalent circuit element with impedance eharaeteristies similar to those of Eq. (36). We call this element a reeap element (derived from resistance and capacitance). The electric and fractal properties for this recap complex impedance Cy( ) are given by ... 

At long and shot wavelengths, the phase and modulation values arc constaiu, allowing assignment of 61,oil, and mj. The constant phase angles and modulations indicate that the cxciteri-statB reaction in a two-state process. 

In conclusion For a general CPE, there is no correlation between the frequency exponent m and the constant phase angle (pcPE- However, for a Fricke CPEp, cpcPEF = m7r/2 = an/2. 

See text for the particular Karplus equation type used. Fitting method applied, data source, and the number of/-couplings used in the fitting (in parenthesis) are also given. See the original publication for additional constant-phase angles. 

See the original publication for additional constant-phase angles. 

The important feature of these lines is that they produce a constant phase angle, like a Warburg impedance, but with the phase angle not restricted to ti/4. This is exactly the behavior often found at the electrode-electrolyte interface and has been termed a constant-phase element (CPE). It appears to be true that roughness is an important contributing factor to the observed frequency dispersion. Scheider s model, however, remains qualitative, and the microscopic link between the topology and the circuit is absent. 

Cl. Bohnke, O. Bohnke, and B. VuiUemin [1993] Constant Phase Angle Behavior of Sn02/W03 Thin Film Electrodes in Anhydrous LiC104-Propylene Carbonate Electrolyte, Electrochim. Acta 38, 1935-1940. 

Phase lock The control of an oscillator or signal generator so as to operate at a constant phase angle relative to a stable reference signal source. Used to ensure frequency stability in spectrum analyzers. 

Since both real and complex parts of Zw are equal, it is characterised by a constant phase angle of 7t/4 (45 ), independent of frequency. 

Sapoval B. Fractal electrodes and constant phase angle response exact examples and counter examples. Solid State Ionics 1987 23(4) 253-9. 

The frequency spectrum is plotted in Figure 8.1. For this signal, the phase spectrum is a constant phase angle of W if we recall the following ... 

Complexities associated with the simple equivalent circuit models described above include phenomena (some interrelated) associated with depressed arcs and constant phase angles [99], porous electrodes and electrodes with rough surfaces 1100-102], pseudoinduction behavior associated with electrosorbed intermediates [103], and nonidealities associated with (polymer) coatings on electrode surfaces. We now briefly explore this... 

---