Current modulation frequency response

The calculated dependence of a of the well width which results from the use of Eq. [7] in Eq. [4] is shown in Figure 2. Also shown in the same figure is the improvement in the current modulation frequency response of the laser... 

Fig. 10.5(a). Transfer function, H, relating modulated current response to modulated flow rate for tube electrode (Reference [20]), rectangular electrode embedded in a wall (Reference [12]) and modulated RDE (amplitude only). The dimensionless modulation frequency see text) is the ratio of the time scale for diffusion across the concentration boundary layer to the timescale for modulation of the hydrodynamics. 

It has to be mentioned that such equivalent circuits as circuits (Cl) or (C2) above, which can represent the kinetic behavior of electrode reactions in terms of the electrical response to a modulation or discontinuity of potential or current, do not necessarily uniquely represent this behavior that is other equivalent circuits with different arrangements and different values of the components can also represent the frequency-response behavior, especially for the cases of more complex multistep reactions, for example, as represented above in circuit (C2). In such cases, it is preferable to make a mathematical or numerical analysis of the frequency response, based on a supposed mechanism of the reaction and its kinetic equations. This was the basis of the important paper of Armstrong and Henderson (108) and later developments by Bai and Conway (113), and by McDonald (114) and MacDonald (115). In these cases, the real (Z ) and imaginary (Z") components of the overall impedance vector (Z) can be evaluated as a function of frequency and are often plotted against one another in a so-called complex-plane or Argand diagram (110). The procedures follow closely those developed earlier for the representation of dielectric relaxation and dielectric loss in dielectric materials and solutions [e.g., the Cole and Cole plots (116) ]. 

K. Tokuda, S. Bruckenstein, and B. Miller, "The Frequency Response of Limiting Currents to Sinusoidal Speed Modulation at a Rotating Disk Electrode," Journal of The Electrochemical Society, 122 (1975) 1316-1322. 

To achieve an optimal frequency response for a given device the conditions for optimised transconductance values have to be determined first. These are found at the position of the steepest slope of transfer curve (= Fgo) for a given drain-source voltage A small gate voltage modulation Vg(drain current modulation id((o). 

Fig. 3 SPEM images cf pcrhydrotripenylene inclusion crystals with a dipolar guest molecule [l-(4-nitrophenyl)piperazine], thinned in three steps. A two-dimensional mapping of the pyroelectric response in the channel direction is shown for a constant modulation frequency of the heating laser source of 415 Hz. Color code red=positive current blue=negative current Low color intensity no current.Moving from the outer to the inner part of the needle-shaped crystal shows that at all depths, there are two main domains of opposite polarization althou somehow interpenetrating. In the middle cf the needle, a cone-shaped structure cf polarity distribution is seen, which is typical for a Markov-type growth in two dimensions. Qualitative agreement with stochastic simulations is obtained. (View this art in color at www.dekker.com.)...

In general, a driving force, which may be optical or electrical is applied and the phase and amplitude of the response, which may be a current, voltage, or optical density, is measured as a function of modulation frequency. For compactness, the results are often presented in the complex plane, as the locus of the complex response as frequency is varied, although phase and amplitude data plotted against frequency may be easier to interpret. For a simple system with a single time constant, r, the response is a semicircle in the complex plane, and it is easy to show that the frequency at the point where the imaginary component of the response is a minimum, time constants in the time domain. 

Ordinary potentiostats are limited to a highest current of approximately 1 A. To study higher currents, either booster potentiostats [695] or so-caUed load banks should be used [696, 697]. In load banks, the ac current may be modulated externally and the potential drop on a load resistor (proportional to current) and potential difference at the studied object are applied to the frequency response analyzer to measure the impedance. Analysis of the impedance of fuel cells with the separation of impedances of the anode, cathode, and load were presented by Diard et al. [698, 699]. A similar correction procedure was also described in Ref. [700]. 

The impedance method consists in measuring the response of an electrode to a sinusoidal potential modulation of small amplitude (typically 5-10 mV) at different frequencies. The ac modulation is superimposed either onto an applied anodic or cathodic potential or onto the corrosion potential. Another possibility is to modulate the current and to measure the potential. Impedance measurements as a function of modulation frequency are commonly referred to in the literature as electrochemical impedance spectroscopy, abbreviated EIS. Among the different transient methods discussed in this chapter, EIS is most widely used in corrosion studies. It serves for the measurement of uniform corrosion rates, fortheelucidationofreactionmechanisms, for the characterization of surface films and for testing of coatings. 

Originally (in the technique introduced by Barker [89] in 1952) the square-wave potential was applied to the DME with constant modulation frequency (225 Hz) and slow scan rate of the voltage ramp (about 2 mV s" ). The current response was recorded at the end of each drop life in a short period of time ( 2 ms). This method could be treated by the steady-state theory in an analogous way to the derivative and differential pulse polarography. It has attained considerable attention for reversible electrode processes due to its applicability especially in trace analysis [90]. 

A typical diode laser frequency response for small amplitude modulation is shown in Fig. 9.44. As can be seen from this plot, the modulation bandwidth extends from DC to the relaxation resonance. The frequency of the relaxation resonance, /reiax> is proportional to the square root of bias current above threshold and inversely proportional to the geometric mean of the lifetimes of the carriers in the inverted population, z ,... 

The mean fluorescence lifetime may also be determined by continuous intensity measurements, if the exciting light intensity is modulated at a high frequency. Fluorescence is excited by light modulated sinusoidally at a known frequency (ajln Hz). The emission is a forced response to the excitation, and is therefore modulated at the same frequency, but with a phase shift, due to the time-lag between absorption and emission. The intensities of the two beams are monitored by photomultipliers. The difference in phase (0) between the two intensities is determined electronically. The lifetime r is given by cox = tan<. The modulation frequency must be made comparable to the decay rate, e.g., around 30 MHz for a mean lifetime of 30 ns. Such frequencies can be achieved by using a hydrogen lamp actuated by a suitably modulated current source. Commercial equipment is available. The method has been applied to quinine sulphate, fluorescein, and acridine, for example, with a precision of 1-2%. It is especially useful for very short (sub-nanosecond) lifetimes. 

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