Linear mode

The series-pass unit operates in the linear mode, whieh means that the unit is not designed to operate in the full on or off mode but instead operates in a degree of partially on. The negative feedbaek loop determines the degree of eonduetivity the pass unit should assume to maintain the output voltage. 

The operation of switehing power supplies ean be relatively easy to understand. Unlike linear regulators whieh operate the power transistor in the linear mode, the PWM switehing power supply operates the power transistors in both the saturated and eutoff states. In these states, the volt-ampere produet aeross the power transistor is always kept low (saturated, low-U/high-/ and eutoff, Hi-T/No-T). This El produet within the power deviee is the loss within all the power semieonduetors. 

FIGURE 16.5 Broad standard calibration (linear mode) of a semipreparative Sephacryl S-IOOO system (95 x 1.6 cm) with an aqueous mixture of Blue Dextran, Dextran T-SOO, and glucose eluent 0.005 M NaOH V, i = 75 ml. = 162 ml. 

The rf transmitter amplifies an rf pulse signal of about 1 mW up to several W or up to several kW. The amplifier should work in a linear mode (class AB) because excitation pulse shape for slice selection must be reproduced. Class AB rf transmitters such as these with blanking gates are widely available commercially. 

Figure 6.2 Whole-cell MALDI-TOF spectra of two Vibrio species taken using a modern TOF mass spectrometer. Even in the linear mode V. parahaemolyticus can be easily differentiated from V. vulnificus.

With TOF, the ions from an ion source are accelerated linearly down a chamber containing an electrical field. The flight chamber is at very low pressure that facilitates the flight of the peptide ions with minimal collisions with other molecules. The ions travel in a linear trajectory until they impact a detector at the other end of the tube. The heavier ions travel more slowly than the lower molecular weight ions and reach the detector later. Hence, TOF analyzers derive their name from the concept that the time of flight of an ion is related to its m/z ratio and velocity within a fixed distance. Linear mode TOF analyzers contain single chambers and are not favored for proteomics applications because of their lower mass accuracy. 

TOF analyzers are especially compatible with MALDI ion sources and hence are frequently coupled in aMALDI-TOF configuration. Nevertheless, many commercial mass spectrometers combine ESI with TOF with great success. For proteomics applications, the quadrupole TOF (QqTOF) hybrid instruments with their superior mass accuracy, mass range, and mass resolution are of much greater utility than simple TOF instruments.21,22 Moreover, TOF instruments feature high sensitivity because they can generate full scan data without the necessity for scanning that causes ion loss and decreased sensitivity. Linear mode TOF instruments cannot perform tandem mass spectrometry. This problem is addressed by hybrid instruments that incorporate analyzers with mass selective capability (e.g., QqTOF) in front of a TOF instrument. 

The mass accuracy is highly dependent on the mode the instrument is operating in. In the reflector mode, with time-lag focusing, the best MALDI-TOF and oa-TOF instruments are capable of achieving <5 ppm with internal standards, provided that the isotopes are resolved. In many cases it is not possible to add internal calibrants, and then the error in mass accuracy is often increased to 50-100 ppm. Operation of an instalment in a linear mode will typically decrease the mass accuracy. 

Fig.20a,b. Transient data in a extension b shear on LDPE from [81] modelled with a multi-mode version of the pom-pom constitutive equation. The linear modes (of weights and relaxation times T, ) have been decorated with the structure of pom-pom elements (adding values of and q to each mode)... 

Commonly, reflector instruments are also equipped with a detector behind the reflector allowing linear mode operation simply by switching off the reflector voltage. A complete mathematical treatment of single-stage and two-stage reflectors is found in the literature. [32,33,35] Here, we will restrict to a qualitative explanation of the reflector. 

The ability of the ReTOP to compensate for the initial energy spread of ions largely increases the resolving power of TOP instruments. While a typical continuous extraction TOP instmment in linear mode cannot resolve isotopic patterns of analytes above about m/z 500, it will do when operated in reflector mode (Pig. 4.7). At substantially higher m/z, the ReTOP still fails to resolve isotopic patterns, even though its esolution is still better than that of a linear TOP analyzer. 

Fig. 4.7. The molecular ion signal of Ceo at m/z 720 (a) and the quasimolecular ion signal of bovine insulin, m/z 5734.6, (b) as obtained on a TOF instrument in linear mode (left) and reflector mode (right). All other experimental parameters remained unchanged.

The essential independence of mean ion velocities on the molecular weight of the analyte leads to an approximate linear increase of the mean initial kinetic energies of the analyte ions with mass. High-mass ions therefore carry tens of elec-tronvolts of translational energy before ion acceleration. [33,41,50] The initial velocity of the ions is superimposed onto that obtained from ion acceleration, thereby causing considerable losses in resolution with continuous extraction TOP analyzers, in particular when operated in the linear mode. 

Fig. 10.6. Linear mode positive-ion MALDI-TOF spectra of ribonuclease B in 80 mM urea, (a) 300 fmol in CHCA, (b) 600 fmol in DHB, and (c) 300 fmol in CHCA/DHB matrix mix. Reproduced from Ref. [71] by permission. Elsevier Science, 2003.

As initial distribution corresponds to the linear mode (2.11) of the given waveguide, the deviation of T z) with respeet to unity may he eonsidered as a measure of the error in this method. The results presented in Fig.2 allow one to analyze the accuracy of the method depending on the type of finite-difference scheme (Crank-Nicholson" or Douglas" schemes have been applied) and on the method of simulation of conditions at the interface between the core and the cladding for both (2D-FT) and 2D problems. 

In terms of nonlinear dynamical systems, the second waveguide of the junction can be considered as a system that is initially more or less far from its stable point. The global dynamics of the system is directly related to the spatial transfomation of the total field behind the plane of junction. In structure A, the initial linear mode transforms into a nonlinear mode of the waveguide with the same width and refractive index. In the structure B, the initial filed distribution corresponds to a nonlinear mode of the first waveguide it differs from nonlinear mode of the second waveguide, however. The dynamics in both cases is complicated and involves nonlinear modes as well as radiation. Global dynamics of a non-integrable system usually requires numerical simulations. For the junctions, the Cauchy problem also cannot be solved analytically. 

Figure 7. Hamiltonian (3.4) calculated with A corresponding to linear mode versus the...

If a nonlinear waveguide is excited by a light beam which is not matched with nonlinear mode, the initial value of the Hamiltonian (0) is greater than. In order to estimate how far is the structure A initially from its stable state, the Hamiltonian (3.4) with a linear mode profile given by (2.11) has been calculated. In Fig.7, (0) depending on V is presented for some values of light beam power. 

An example of a linear mode transformation into the nonlinear mode in the structure A is shown in Fig.9. Unsteady-state regime " is observed that... 

The transmittance of the nonlinear step-like discontinuity in cylindrical waveguide has been evaluated under the assumption that profiles of low-intensity nonlinear modes can be approximated by profiles of linear modes. According to the results, nonlinear transmittance is less or greater than the linear one depending on waveguide parameters of the first and the second waveguides, Vi = kafafg 2= ka2(nf respectively. 

MALDl-TOF mass spectrometry (MS) has also been used to characterize PAM AM dendrimer composition with and without added Cu + [98]. linear-mode MALDI-TOF mass spectra of G2 and G3, and their complexes with Cu + ions, are shown in Fig. 9. 

Fig. 1.27 Schematic of a time of flight mass spectrometer equipped with a reflectron. The instrument can be operated in the linear mode (reflectron off) or in the reflectron mode (reflectron on).

In general the commercial TOP instruments have two detectors one for the linear mode and one for the reflectron mode. The combination of MALDI with TOP is ideal because both techniques are pulsed techniques. However, it is also possible to arrange a continuous beam as generated by electrospray ionization. Por that purpose orthogonal acceleration was developed [65]. The ion beam is introduced perpendicularly to the TOP and packets are accelerated orthogonally (oa-TOP) at similar frequencies improving the sensitivity. While a packet of ions is analyzed, a new beam is formed in the orthogonal acceleration. 

Figure 13.13 Summary of v(NC) peak assignments for CH3NC adsorbed on Pd/Al203. The peak at 2180cm is assigned to the on-top (T ) mode, the peak at 2050cm to the bridge linear mode, and the shoulder centered at 1850cm to the on-top bent (bentr ) mode [54].

The signals produced by the strain gauge can be amplified linearly or logarithmically. In the linear mode the displacement of the X-V recorder along the X or pressure axis is inversely proportional to the pore radius as given by equation (10.24)... 

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