Amplitude modulation ring

Fig. 1-11 shows five different reference patterns. Fig. 1-11 (a) is a ring pattern with phase modulation of exp[j2ncos(y/A)]. Fig. 1-11 (b) is a ring pattern with amplitude modulation of cos(y/A). Where A/2n is the period of the cosine function and is equal to 273.6pm. Fig. 1-11... 

There are two variants of amplitude modulation classic amplitude modulation (AM) and ring modulation (RM). 

SFM involves modest variations in the amplitude Vg of the RF drive potential applied to the ring electrode, such that ions move into and out of resonance with the applied single frequency tickle waveform such slight modulation of Vg changes and so as to produce a sweep of the axial secular frequency g over a narrow range of some 1-2 kHz. Thus the resonance condition for ion activation is guaranteed to be met for some fraction of the time over which the resonant excitation voltage is applied. 

Again a summation is performed, but now it is over all possible pairs of atoms in the molecule, as each interatomic distance Vij contributes to the scattering pattern. The terms ffs) and fj(s) are the scattering amplitudes of two atoms i and j. Random orientation of the molecules leads to the term sin[r(r, ,- — Kys )]/ stij, which contains the information on the interatomic distances ry. The term Kij is the anharmonicity constant, which provides small corrections to take the anharmonic nature of molecular vibrations into account by introducing modulations in the sine-wave frequency. The sine function leads to the appearance of the diffraction pattern as concentric rings with a sinusoidal intensity distribution along the radius, after multiplication by i" to remove the steep 14" descent described above. 

Lobe envelopes, however, have their own unwanted side-effects. Note that the amplitude of the whole signal now rises and falls periodically. This is a clear case of ring modulation (see Chapter 2) in which the windowing frequency acts as the modulating frequency. Enveloped windowing also may distort the analysis process, but the result is still more accurate than with windowing without envelopes. 

Hence, effectively we have a small-amplitude periodic modulation of the excitability of the medium. This modulation is resonant because its frequency coincides with the rotation frequency of the spiral wave. Now we can apply the results of our analysis of the resonance of spiral waves that was performed in Section 5. We know that under the conditions of the complete resonance a spiral wave drifts along a straight line. In the case of the scroll ring the spiral is the meridian cross-section of its surface. The drift of the spiral seen in this cross-section means that generally the scroll ring shrinks or expands while moving along the symmetry axis. 

Polarization curve of the preactivated iron disk of a HMRRD electrode in IM NaOH (dE/df = lOmV S ) with hydrogen oxidation, Fe(ll) and Fe(lll) formation at peak A1 (Epi), Fe(ll) oxidation at All (Epj), and oxide reduction at peak C. Simultaneous capacity measurements (dashed curves) (a,b) Fe(IlI) and (b,c) Fe(ll) dissolution as detected at the Pt half-ring electrodes. Frequency, W = 450min with square wave modulation amplitude, Aiv = 250min- and modulation frequency,/= 0.1 s. (From Haupt, S. and Strehblow, Langmuir, 3,873,1987)... 

It is to be noted that activation by resonance resembles axial modulation (see Chapter 4) because both require the application of a radiofrequency of type Vcostot between the endcap electrodes. There are nevertheless two important differences between the two concepts. First, the value of V is around 3 to 4 volts in axial modulation and 0.2 to 1.5 V in MS/MS where the point is not to eject the precursor ions. The second difference is the value of the radiofrequency trapping amplitude applied to the ring electrode during the application of the radiofrequency of resonance. This value is high in axial modulation and low in MS/MS where the point is to trap the daughter ions formed by collision. 

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