Harmonic amplitudes

For many applications, it may be reasonable to assume that the system behaves classically, that is, the trajectories are real particle trajectories. It is then not necessary to use a quantum distribution, and the appropriate ensemble of classical thermodynamics can be taken. A typical approach is to use a rnicrocanonical ensemble to distribute energy into the internal modes of the system. The normal-mode sampling algorithm [142-144], for example, assigns a desired energy to each normal mode, as a harmonic amplitude... 

In that spirit, we now detail a quick procedure for estimating harmonic amplitudes of the square current waveform (assuming fast transitions). We will apply it to our specific lOOkHz/lA example as we go along ... 

Starting at the switching frequency, we need to invariably fix the harmonic amplitude at that point at -4dB. This follows from the basic governing equations (for more details, see the chapters on EMI in my A to Z book). Note that OdB corresponds to the full amplitude of the pedestal (1A in our example). 

The envelope of the harmonic amplitudes rolls off at -20dB/decade (assuming fast transitions). 

We know from Chapter 2 that the harmonic amplitudes depend on the rise and fall times. That is one reason why engineers often try to slow down the Mosfet (increase its transition time), usually at the expense of some efficiency, though sometimes it can even help improve the efficiency, as we will see. 

Figure 6. Relative fundamental harmonic amplitude as a function of z-oscillation amplitude. (1) Ar = 0.25 when Az = 0. (2) Ar = 0.05 when Az = 0. (Reproduced with permission from Ref. 33. Copyright 1986 Elsevier Science Publishers B.V.)...

Discussion on reasons for the deviation of the phase angle from 90° and of the exponent of the third harmonic amplitude from Figure 13.5 can be found in [4],... 

C. Perturbative Equations for the Harmonic Amplitudes in the Case of loint Diffusion... 

Figure 4.35. The second-harmonic amplitude of the orientation parameter for different values of the internal magnetic anisotropy of the particles. The set of material parameters and meanings of the thin curves are the same as those for Figure 4.34.

In this approximation, unlike the general case, the harmonic amplitudes are determined by a single self-similar argument Co/aig. Note also that for the suspensions of ferromagnetic particles, where the hysteretic remagnetization process is possible, Eq. (4.377) holds only if an additional condition... 

Fig. 3.4. Reconstructed attosecond XUV bursts for experiments where Ar and Xe were used as harmonic generation gas. The reconstruction of the XUV bursts was performed on the basis of harmonic phase differences that were determined by monitoring the yield of sideband photoelectrons as a function of XUV-IR time delay and harmonic amplitudes that were obtained from photoelectron spectra recorded in the absence of the IR dressing beam. Experiments that were performed using Kr gave results similar to the Ar results...

Fig. 4.31. Harmonic ratio of the fundamental to the second-harmonic amplitude of the measured dHvA oscillations for k-(ET)2Cu(NCS)2. The solid line represents the calculated ratio using (4.4)...

So in going from lOOkHz to IMHz, the harmonic amplitude will fall 20dB (from its value at lOOkHz). That gives us a total of 20 -i- 4 = 24dB below lA. 

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