Frequency reference

For lock-in amplification the pump is modulated at a reference frequency w (see Fig. 7-1), which means that AT is not constant over time. Rather, its magnitude (and its phase) depends on the modulation frequency [8. In order to find the frequency-dependent A7 (cu), let us assume that the recombination dynamics are monomolecular with a single lifetime r. Then we can write for the number density of excitations N at time / ... 

Hz. Since it is only the difference between these two frequencies that concerns us, and since the use of such large frequencies would unnecessarily occupy computer memory, it is convenient first to subtract the reference frequency (300,000,000 Hz in this case) from the observed frequency, and to store the remainder (0-3600 Hz) in computer memory. 

Why it is necessary to subtract the reference frequency from the observed frequency before data storage and processing ... 

We can use the angular frequency of TMS as the reference frequency of the rotating frame. Deducting this from the Larmor frequency of the signal will leave only the differential frequency (or, in other words, the chemical shift) associated with the magnetization vector of the signal. 

If we do not subtract the reference frequency, we will have to process a very large amount of data. For example, on a 500-MHz NMR spectrometer, the frequencies to be processed would be 500,000,000— 500,003,600 Hz for protons (since protons normally resonate within 0-12 ppm, i.e., 0-3600 Hz). 

The image peaks resulting from quadrature detection can be easily distinguished from small genuine peaks since they show different phases and move with changes in the reference frequency. 

In the latter procedure, which is often called oscillometry6, one observes the frequency at which resonance occurs or one retunes the oscillator to the original frequency, e.g., with the aid of a calibrated capacitor parallel to the sample cell. Further, in oscillometry it is useful to compare in parallel with a reference frequency unit. 

We see that the multiplier output signal is made up of a term at the sum frequency and another at the difference frequency. The signal of eq. (10.5) passes through a low-pass filter of response HL(ja>) and high-frequency cut-off well below the reference frequency, in order to eliminate the sum frequency term. The output will be ... 

Since the filter is low pass, it will attenuate all the frequencies far from the reference frequency, that is, the multiplier together with the low-pass filter acts as a band-pass filter centred at the reference frequency coR. The bandwidth of such band-pass filter is the double of the bandwidth of the low-pass filter (see Fig. 10.9). This result will be used in the evaluation of the residual noise in the output signal. 

Resistance bridges sometimes contain a multiplexer to carry out measurement of several thermometers with the same bridge. However, the multiplexing procedure presents several drawbacks (e.g., the temperature readings are not taken at the same time). It is safe, when possible, to use one bridge for each thermometer. The reference frequencies of the bridges must differ for at least a few hertz and of course must not be at the frequency of the power line or motors of the turbomolecular pumps. 

Detectors with complete black body rejection capability are usually less sensitive to fires than a single frequency infrared optical detector. Because it s discrimination of fire and non-fire sources depend upon an analysis of the ratio between fire and reference frequencies, there is a variation in the amount of black body rejection achieved. A detector s degree of black body radiation rejection is in inversely proportion to its ability to sense a fire. The detectors are limited to applications that involve hydrocarbon materials. 

Here, ak is the isotropic chemical shift referenced in ppm from the carrier frequency co0, SkSA is the anisotropy and tfk SA the asymmetry of the chemical-shielding tensor, here also expressed in ppm. Note that for heteronuclear cases different reference frequencies co0 are chosen for different nuclei (doubly rotating frame of reference). The two Euler angles ak and pk describe the orientation of the chemical-shielding tensor with respect to the laboratory-fixed frame of reference. The anisotropy dkSA defines the width and the asymmetry t]kSA the shape of the powder line shape (see Fig. 11.1a). 

Chemical shift is a value derived from the resonance frequency of the nucleus as a function of the reference frequency. 

Open Path Gas Detectors (OPGDs) (Figure 7-23) produce an IR beam that is directed across the area to be monitored. The received light is analyzed at two or more frequencies, some of which is absorbed by the target gas or gases the reference frequency is not. Given the initial and final intensities, the average concentration of gas in the path is calculated and transmitted. Some instruments operate with separate trans-... 

Point Combustible Gas Detectors (IR) are used to indicate the presence of gas at a particular location (e.g., in a congested area of the planter in small ducts.) IR technology has proven to be more reliable than catalytic bead detectors. The point detector functions in the same manner as the open path detector, by comparing absorbed and reference frequencies of IR light. The main difference between these and open path type is that the path length of the point type is short (3 inches) and is kept within the confines of the instrument. 

In period measurement a second crystal oscillator is essentially used as a reference oscillator that is not coated and usually oscillates at a much higher frequency than the monitor crystal. The reference oscillator generates small precision time intervals, with which the oscillation duration of the monitor crystal is determined. This is done by means of two pulse counters the first counts a fixed number of monitor oscillations m. The second is started simultaneously with the first and counts the oscillations of the reference crystal during m oscillations of the monitor crystal. Because the reference frequency F,. is known and stable, the time for m monitor oscillations can be determined accurately to 2/F,.. The monitor oscillation period is then... 

As shown in Fig. 2.1 (b), the nuclear moments still precess with Larmor frequency v0 about the z axis in the xy plane, as does the resultant transverse magnetization (Figs. 2.1(b) and 2.2(b)). In the rotating frame (Section 1.7.3), the transverse magnetization with reference frequency v0 stands while faster or slower components with v( > v0 or v, < v0 will rotate clockwise or counterclockwise, respectively, as shown in Fig. 2.3. 

The applied B0 induces electronic currents in atoms and molecules, and these produce a further small field B aat the nucleus which is proportional to Bc. The total effective field, Beff, at the nucleus can therefore be written Befr = Bc(l-a), where a expresses the contribution of the small secondary field generated by the electrons. Using equation (2) we find that v0 = y(2ji)Bo(l-a). The magnitude of a is dependent upon the electronic environment of the nucleus, and therefore nuclei in different chemical environments give rise to signals at different frequencies. The separation of response frequencies from a reference frequency is termed the chemical shift, and expressed in terms of the dimensionless units of parts per million (ppm) [4]. 

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