Frequency Modulation simple

We can divide synthesis techniques into four basic categories Additive (Linear), Subtractive, Nonlinear and Physical modeling. Synthesis algorithms depend critically on the implementation of oscillators. For example, in the implementation of Frequency Modulation (F.M.), the output of one oscillator will serve as the input to another. Since the number of real time oscillators depends on the number of simple oscillators, it is important to efficiently and speedily implement the realizations. 

The observant reader will have realized by now that the above experiment, which is a type of frequency modulation, provides no additional information beyond the simple H spectrum of acetone. Actually, that is the beauty of that experiment it has all of the elements of a 2-D correlation experiment and we can completely follow the activity of the net magnetization vector for acetone using simple vectorial models. Let us turn this prototype pulse sequence into a general format for all 2-D experiments. If we replace the first v/2 pulse with a generalized pulse that contains one or more pulses... 

The simple textbook solution of a harmonic damped oscillator becomes complex when the vibrating tip interacts with the surface of a sample, e.g., in tapping mode AFM. Although the different imaging modes and the experimental observables may vary, the underlying physics is similar. Amplitude and frequency modulated AFMs are most commonly used, labeled by AM-AFM (amplitude modulation or tapping) and FM-AFM. For a detailed review of this topic several reviews are available, e.g., [15]. 

A simple differential saturation method has been proposed (63) in which the differential saturation effects are obtained at the same overall irradiation level due to an audio-frequency modulation of the resonance frequency in the continuous-wave mode of operation. This results in the appearance of sidebands in addition to the centre band of the spectrum. By a judicious selection of the modulation index, the saturation of signals in the sidebands may be made to amount to 10 — 0-1% of those in the centre band. The lineshape of such a combination of the centre band and the two closest sidebands may be adjusted to that corresponding to the function ... 

For an illustrative purpose, we choose a simple model of the spectral diffusion, which is called a two-state jump process or a dichotomic process. We assume that the frequency modulation can be either Aco(t) = v or Aco(t) = — V, and the flipping rate between these two frequency modulations is given by R. This model will be used as a working example for which an analytical solution is obtained later in Section V. 

Appendix C. The limit T -> oo has, of course, special interest since it is used in standard line shape theories, and does not depend on an assumption of whether the frequency modulations are slow. The exact expression for Q in the limit of T oo is given in Eqs. (A.47) and (A.48). These equations are one of the main results of this chapter. It turns out that Q is not a simple function of the model parameters however, as we show below, in certain limits, simple behaviors are found. 

Frequency modulation relies on modulating the frequency of a simple periodic waveform with another simple periodic waveform. When the frequency of a sine wave of average frequency(called the carrier) is modulated by another sine wave of frequency (called the modulator), sinusoidal sidebands are created at frequencies equal to the carrier frequency plus and minus integer multiples of the modulator frequency. FM is expressed as ... 

Photoacoustic spectra can be observed with a simple microphone and optical apparatus. A diagram of a modern piece of equipment is given in Figure 42, in which there is a blackbody sample at the second input of a look-in amplifier. Corrected photoacoustic spectra can be recorded with this type of monochromator equipment. Frequency-modulated xenon lamps are used as white light sources, so that a chopper is not needed for modulation. 

Figure 2.7 illustrates a simple frequency modulation architecture. The output of the modulator is offset by a constant, represented as /c, and the result is then applied to control the frequency of the carrier. If the amplitude of the modulator is equal to zero, then there is no modulation. In this case, the output from the carrier will be a simple sinewave at frequency f - Conversely, if the amplitude of the modulator is greater than zero, then... 

Doppler width of this transition at 300 K is AwDoppier 5-71 x 10 s . If, instead of moving freely, the radiating atoms are constrained to oscillate about their mean positions with simple harmonic motion of frequency f/2ir and amplitude L, show that the emitted wave is frequency modulated. By qualitative arguments show that the line width of the radiation is given approximately by equation (17.17). Assuming a gas kinetic collision cross-section of... 

The above description refers to a Lagrangian frame of reference in which the movement of the particle is followed along its trajectory. Instead of having a steady flow, it is possible to modulate the flow, for example sinusoidally as a function of time. At sufficiently high frequency, the molecular coil deformation will be dephased from the strain rate and the flow becomes transient even with a stagnant flow geometry. Oscillatory flow birefringence has been measured in simple shear and corresponds to some kind of frequency analysis of the flow... 

In the early work of Bewick and Robinson (1975), a simple monochromator system was used. This is called a dispersive spectrometer. In the experiment the electrode potential was modulated between two potentials, one where the adsorbed species was present and the other where it was absent. Because of the thin electrolyte layer, the modulation frequency is limited to a few hertz. This technique is referred to as electrochemically modulated infrared reflectance spectroscopy (EMIRS). The main problem with this technique is that data acquisition time is long. So it is possible for changes to occur on the electrode surface. 

On the RF time scale, the transit times of electrons in long coaxial cables and the time of flight of photons in optical paths as short as a few centimeters are significant. These effects become more pronounced as the modulation frequency increases. Even simple changes made to a system will affect the resulting measurements. 

Cycled Feed. The qualitative interpretation of responses to steps and pulses is often possible, but the quantitative exploitation of the data requires the numerical integration of nonlinear differential equations incorporated into a program for the search for the best parameters. A sinusoidal variation of a feed component concentration around a steady state value can be analyzed by the well developed methods of linear analysis if the relative amplitudes of the responses are under about 0.1. The application of these ideas to a modulated molecular beam was developed by Jones et al. ( 7) in 1972. A number of simple sequences of linear steps produces frequency responses shown in Fig. 7 (7). Here e is the ratio of product to reactant amplitude, n is the sticking probability, w is the forcing frequency, and k is the desorption rate constant for the product. For the series process k- is the rate constant of the surface reaction, and for the branched process P is the fraction reacting through path 1 and desorbing with a rate constant k. This method has recently been applied to the decomposition of hydrazine on Ir(lll) by Merrill and Sawin (35). 

Prior to describing the possible applications of laser-diode fluorometry, it is important to understand the two methods now used to measure fluorescence lifetimes these being the time-domain (Tl)/4 5 24 and frequency-domain (FD) or phase-modulation methods.(25) In TD fluorometry, the sample is excited by a pulse of light followed by measurement of the time-dependent intensity. In FD fluorometry, the sample is excited with amplitude-modulated light. The lifetime can be found from the phase angle delay and demodulation of the emission relative to the modulated incident light. We do not wish to fuel the debate of TD versus FD methods, but it is clear that phase and modulation measurements can be performed with simple and low cost instrumentation, and can provide excellent accuracy with short data acquisition times. 

It will be seen that, as in the case of the LED, control of the bias voltage gives simple modulation of the laser output intensity. This is particularly useful in phase-modulation fluorometry. However, a measure of the late awareness of the advantages of IR techniques in fluorescence is that only recently has this approach been applied to the study of aromatic fluorophores. Thompson et al.(51) have combined modulated diode laser excitation at 670 and 791 nm with a commercial fluorimeter in order to measure the fluorescence lifetimes of some common carbocyanine dyes. Modulation frequencies up to 300 MHz were used in conjunction with a Hamamatsu R928 photomultipler for detecting the fluorescence. Figure 12.18 shows typical phase-modulation data taken from their work, the form of the frequency response curves is as shown in Figure 12.2 which describes the response to a monoexponential fluorescence decay. 

In the upper panel of Figure 13.6, the emission is drawn assuming a modulation frequency of 30 MHz and a lifetime of 9 nsec. Using the equations above, the phase angle is 59.5° and the demodulation factor is 0.5. (For further details, the reader is referred to Lakowicz(66)). Additionally, multifrequency phase and modulation instruments that operate over a range of frequencies have been described(67, flS) and simple instruments are possible if only one or several discrete frequencies are required (Figure 13.6, lower panel). 

---