Phase-Sensitive Detection, Lock-In Amplifiers

A lock-in amplifier uses phase-sensitive detection, in conjunction with a potentio-stat, to measure the complex impedance. The algorithm is fimdamentally different from that of the Fourier-based analyzers. These analyzers perform an assessment of the Fourier coefficients of the input and output signals, whereas the lock-in amplifier measures the amplitudes of the two signals and the phase angle of each signal with respect to some reference signal. Thus, the impedance is measured in polar, rather than Cartesian, coordinates. 

A reference square wave of unity amplitude is generated at the same frequency as the sinusoidal signal 

The product of the signals can be expanded using the trigonometric identity for the cosine of the sum of two angles and integrated over each cycle. Only the leading term of the series has a nonzero value, thus. 

The same procedure is used to analyze the second signal 

The magnitude of the impedance can be obtained from the ratio of the amplitudes, i.e., 

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Modulation techniques For reversible systems, a more suitable kind of method consists in using a potential modulation coupled with a phase-sensitive detection (lock-in amplifier) the potential may be modulated, for example, as a square wave between Vj and V2 and the signal from the detector may be sent to a lock-in amplifier. The signal from the lock-in provides a function A1((t) (change in intensity reaching the detector associated with the modulation), the average intensity 1(a) being measured either simultaneously or sequentially. The... 

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. 

Photomultipliers are generally used to convert the spectral radiation to an electrical current and often phase-sensitive lock-in amplifiers are used to amplify the resulting current. AES and AFS require similar read-out systems because both methods are measuring small signals. The difficulty associated with both these methods is the separation of the signal for the atomic transition of interest from the background radiation emitted by excited molecular species produced in the atom reservoir. AFS phase locks the amplifier detection circuit to the modulation frequency of the spectral source. Modulation of the source is also used in AAS. 

A number of different modulation techniques can be used to increase the signal-to-noise ratio (e.g., see Schiff et al., 1994a, 1994b and Brassington, 1995). For example, the laser beam can be mechanically chopped and detected using phase-sensitive detection with a lock-in amplifier. A more commonly used method for accurately measuring small absorbances is to modulate... 

One excellent way to increase the S/N ratio is to tune the detector to the exact same frequency v as the source (using a lock-in amplifier, also known as a phase-sensitive detector or as homodyne detection) and also to discriminate the phase

rc/2 or (3/2)n. This can be used to discriminate up to 60 dB. 

The signal-to-noise ratio is further improved if phase-sensitive second-harmonic detection is performed at a fixed reference frequency ct)ref is used— hence the need for a lock-in amplifier (Fig. 11.24). 

The use of magnetic field modulation together with phase-sensitive detection using a lock-in amplifier renders CW-NMRI an extremely narrow-bandwidth detection technique, and thus the penalty inherent in all other techniques of a reduced SNR with increasing gradient strength (due to the increased frequency bandwidth) is removed. 

Phase-sensitive detection is used in lock-in amplifiers, which are interfaced with potentiostats." " Only a general idea of these measurements will be presented here. In this method the measured signal, Ei, which is proportional to the ac current from the potentiostat, is... 

A programmable pulse generator produces the pulse sequences that drive the p-i-n diode switches in the microwave circuit. To resolve the microwave-induced changes in the phosphorescence intensity from the steady-state emission (usually a few percent or less) phase sensitive detection of the photomultiplier output at the microwave sequence repetition frequency (Fh is typically 150-350 Hz) is applied using a lock-in amplifier. 

The second scheme to be treated is based on a frequency modulation of the monochromatic incident wave. It was not designed specifically for laser spectroscopy, but was taken from microwave spectroscopy where it is a standard method. The laser frequency co] is modulated at the modulation frequency 2, which changes coi periodically from cul — Acol/ to cul + Acul/2. When the laser is tuned through the absorption spectrum, the difference APr = Py(col Al/2) is detected with a lock-in amplifier (phase-sensitive detector) tuned to the modulation frequency (Fig. 1.4). If the modulation sweep Acol is sufficiently small, the first term of the Taylor expansion... 

However, application of the above technique can be problematic when strong solution-phase absorption obscures weak bands of a surface species. To overcome this limitation, the phase rotation approach [263] can be used. Phase-sensitive detection such as with a lock-in amplifier (LIA) provides two signals the signal that is in phase IP) and the signal that is out of phase (the quadrature, Q) with the external perturbation [264]. These quantities can be represented at each... 

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