Phase-sensitive

The amplified signal is passed to a double-balanced mixer configured as a phase-sensitive detector where the two inputs are the NMR signal (cOq) and the frequency of the synthesizer (03. gf) with the output proportional to cos(coq - co gj.)t + 0) + cos((coq + + 9). The sum frequency is much larger than the total bandwidth of the... 

Diffey W M and Beck W F 1997 Rapid-scanning interferometer for ultrafast pump-probe spectroscopy with phase-sensitive detection Rev. Sci. Instrum. 3296-300... 

Figure 9.25 (a) A Doppler-limited line, (b) The detection. V, potential psd, phase-sensitive detector... 

Circular dichroism employs standard dispersive or interferometric instmmentation, but uses a thermal source that is rapidly modulated between circular polari2ation states using a photoelastic or electro-optic modulator. Using phase-sensitive detection, a difference signal proportional to the absorption difference between left- and right-polari2ed light, AA is recorded as a function of wavenumber. Relative differential absorptions... 

The phasor difference between /( and /, i.e. results in a composite error /. The phase displacement between I2 and /, by an angle 8 is known as the phase error. The current error will be important in the accurate operation of an overcurrent relay and the phase error in the operation of a phase sensitive relay. The composite error will be significant in the operation of a differential relay. 

The detection of the AC component allows one to separate the contributions of the faradaic and charging currents. The former is phase shifted 45° relative to the applied sinusoidal potential, while the background component is 90° out of phase. The charging current is thus rejected using a phase-sensitive lock-in amplifier (able to separate the in-phase and out-of-phase current components). As a result, reversible electrode reactions yield a detection limit around 5 x 10 7m. 

As with alternating electrical currents, phase-sensitive measurements are also possible with microwave radiation. The easiest method consists of measuring phase-shifted microwave signals via a lock-in technique by modulating the electrode potential. Such a technique, which measures the phase shift between the potential and the microwave signal, will give specific (e.g., kinetic) information on the system (see later discussion). However, it should not be taken as the equivalent of impedance measurements with microwaves. As in electrochemical impedance measurements,... 

Figure 9. (a) Electrode and representative circuit for phase-sensitive electrochemical measurements (impedance measurements) compared with (b) setup for phase-sensitive microwave (impedance) measurements. 

Electrochemical impedance spectroscopy leads to information on surface states and representative circuits of electrode/electrolyte interfaces. Here, the measurement technique involves potential modulation and the detection of phase shifts with respect to the generated current. The driving force in a microwave measurement is the microwave power, which is proportional to E2 (E = electrical microwave field). Therefore, for a microwave impedance measurement, the microwave power P has to be modulated to observe a phase shift with respect to the flux, the transmitted or reflected microwave power APIP. Phase-sensitive microwave conductivity (impedance) measurements, again provided that a reliable theory is available for combining them with an electrochemical impedance measurement, should lead to information on the kinetics of surface states and defects and the polarizability of surface states, and may lead to more reliable information on real representative circuits of electrodes. We suspect that representative electrical circuits for electrode/electrolyte interfaces may become directly determinable by combining phase-sensitive electrical and microwave conductivity measurements. However, up to now, in this early stage of development of microwave electrochemistry, only comparatively simple measurements can be evaluated. 

As mentioned at the beginning of this chapter real phase-sensitive measurements of electrochemical systems have not yet been performed. Not only is the experimental technique difficult, but a reliable theory of... 

At present, the microwave electrochemical technique is still in its infancy and only exploits a portion of the experimental research possibilities that are provided by microwave technology. Much experience still has to be gained with the improvement of experimental cells for microwave studies and in the adjustment of the parameters that determine the sensitivity and reliability of microwave measurements. Many research possibilities are still unexplored, especially in the field of transient PMC measurements at semiconductor electrodes and in the application of phase-sensitive microwave conductivity measurements, which may be successfully combined with electrochemical impedance measurements for a more detailed exploration of surface states and representative electrical circuits of semiconductor liquid junctions. 

The use of phase sensitive detection with the phase fluorometer to analyze multicomponent systems was first described in 1970 by Veselova and coworkers (76). 

By using phase sensitive detection, the detector phase angle can be adjusted to be exactly out of phase with the phase-delayed emission from any single fluorophore, suppressing its contribution to the total emission signal. Phase sensitive detection, coupled with... 

Theory. If two or more fluorophores with different emission lifetimes contribute to the same broad, unresolved emission spectrum, their separate emission spectra often can be resolved by the technique of phase-resolved fluorometry. In this method the excitation light is modulated sinusoidally, usually in the radio-frequency range, and the emission is analyzed with a phase sensitive detector. The emission appears as a sinusoidally modulated signal, shifted in phase from the excitation modulation and partially demodulated by an amount dependent on the lifetime of the fluorophore excited state (5, Chapter 4). The detector phase can be adjusted to be exactly out-of-phase with the emission from any one fluorophore, so that the contribution to the total spectrum from that fluorophore is suppressed. For a sample with two fluorophores, suppressing the emission from one fluorophore leaves a spectrum caused only by the other, which then can be directly recorded. With more than two flurophores the problem is more complicated but a number of techniques for deconvoluting the complex emission curve have been developed making use of several modulation frequencies and measurement phase angles (79). 

If the signal decay is a single-exponential curve, equations 16 and 17 result in values for X that are in agreement with each other. Dissimilar values indicate multiexponential decay, which usually means that the sample contains more than one fluorophore. Multiexponential decay can be resolved by using a phase fluorometer with phase sensitive detection. A time-independent, direct-current signal is produced that is proportional to the cosine of the difference between the phase angle of the detector ( D) and the phase angle of the fluorescence ( ) ... 

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