Power attenuation

For Equation 6.7 to be valid it is assumed that all other experimental conditions are equal for the two samples. If this is not true, additional corrections may be required for differences in modulation amplitude (M), microwave power attenuation in IdBI OP), magnetic field scan width (W) (or equivalently, the step width in gauss between two subsequent digitization points), electronic gain (G), sample diameter Of), and absolute temperature (I) ... 

The NMR process, then, essentially involves placing a sample in a magnetic field, applying a radio-frequency (RF) pulse, and determining the decrease in power (attenuation) of the radiation caused by the absorbing sample. This process is shown schematically in Figure 6.79. 

Attenuate the laser power Attenuate the detector voltage Increase laser power Increase detector voltage Calibrate the instrument using standards (slight variability, -100 ppm, is normal)... 

To double the pulse power, simply increase the power by 3 dB, as log(2) = 0.3. Because pulse power is the square of pulse amplitude B, to double the amplitude we need to multiply pulse power by a factor of 4, which corresponds to increasing power by 6 dB, as log (4) = 0.6. This leads to a simple rule of thumb Every time you increase the pulse power by 6 dB, you will cut the 90° pulse (fp) in half (because B is doubled). Likewise, each 6 dB decrease in pulse power will double the 90° pulse width. This is a good rule of thumb, but as the actual power settings are not precise, you will normally have to calibrate the 90° pulse at the new power setting to be sure. To make matters worse, Bruker uses the dB scale to describe power attenuation rather than power itself, so that the higher the dB value the lower the power. This is the opposite of Varian s system. Be careful whenever you are setting power levels If you get it wrong, you can burn up the probe, the amplifiers, and your sample ... 

Fig. 8. Electron paramagnetic resonance of reduced adrenal and testis non-heme iron proteins (28). Curve A enzymatically reduced adrenodoxin curve B enzymatically reduced testis protein at 99° K, a modulation amplitude of 3.2 gauss at microwave power attenuation of 10 db...

Figure 10. The same spectra as in Figure 9 but with a sample temperature of 105 K fupper spectrum) after overnight dark storage at < 100 K, gain 5 X 10, power attenuation 20 dB flower spectrum) after illumination, gain 2.5 X 10, power attenuation 35 dB (0 dB s 20 mW).

Figure 11. The g 2 ESR signal observed for extracted lOH polymer at 4.2 K after illumiruition (gain 2.5 X Iff, power attenuation 60 dB (0 dB —= 20 mfV))...

Figure 14. Signal saturation at 105 K after sample illumination. Spectra were recorded at constant gain with power attenuations of 50 dB ( upper spectrum) 20 dB Cmiddle spectrum) arid 10 db Clower spectrum) (0 dB = 20 mW).

When the angle of incidence 6 is small enough, transmission losses for skew rays are equal in the first-order approximation to those for meridional rays with the same 6 [9]. Therefore, only meridional rays are considered in the present analysis. For the meridional ray, a power attenuation constant 2a (6) is calculated as... 

The power attenuation coefficient (2oc) for lower order leaky modes is given by [4] thus. 

Fig. 7 Power attenuation coefficient for a liquid filled capillary for various lower order modes q. Calculations are based on rii = 1.33 and = 1-46...

The effect of admitting an absorbing gaseous sample into a Fabry-Perot, or any resonant cavity, is to lower its Q by an amount proportional to the absorption coefficient a defined as the power attenuation per unit length traversed. Thus the incident power Pq is reduced to P ... 

The detection sensitivity increases with increasing spectral resolution ft)/A is stiU larger than the linewidth 8a> of the absorption line. This can be seen as follows The relative power attenuation per absorption path length Ax on the fransition with center frequency a>o is, for small absorption a Ax -cl. 

The measured relative power attenuation for an absorption pathlength Ax is therefore the product of absorption coefficient a, pathlength Ax and the ratio of absorption linewidth 8co and spectral resolution bandwidth Aco, as long as Aco > 8co. 

Cable Size (in.) Maximum Frequency (MHz) Velocity (%) Peak Power 1 MHz (kW) Average Power Attenuation ... 

Attenuation coefficient The mathematical expression for optical power attenuation, typically expressed as a change in power measured in decibels (dB), normalized to a unit length (dB/km). 

Maximum Peak Power Average Power Attenuation ... 

The bandwidth of a fiber determines the maximum transmission data rate or maximum transmission distance. Most common POF (plastic optical fiber) transmission systems adopt on-off keying by direct modulation of the optical source (laser or light-emitting diode). If an input pulse waveform can be detected without distortion at the other end of the fiber, the maximum link length is limited by the fiber attenuation. However, in addition to the optical power attenuation, the output pulse is generally broader in time than the input pulse. This pulse broadening limits the transmission capacity, namely, the bandwidth of the fiber. The bandwidth is determined by the impulse response as follows [1] Optical fibers are usually considered quasi-linear systems thus, the output pulse is described by... 

To describe attenuation, we define P z) to be the power flowing within a narrow ray tube of rays, such as those illustrated in Fig. 4-1 and discussed at the beginning of Chapter 4. We then introduce the power attenuation coefficient y(z) of a ray defined by... 

When the power absorption coefficient is uniform, i.e. aco( ) co> power attenuation coefficient of Eq. (6-6) is proportional to the real part of the profile. Ray power attenuates according to Eq. (6-8), which has the form... 

The power attenuation coefficient for cladding absorption is found either by averaging T over the ray half-period between successive reflections or... 

The ray half-period is given in Table 2-1, whence we deduce from Eqs. (6-17) and (6-26a) that the power attenuation coefficient can be expressed in the form... 

When both the core and cladding materials of a fiber are absorbing, the power attenuation coefficient y for a ray is given by the sum of the core and cladding absorption coefficients. Hence... 

Thus a fraction of T of ray power is lost at each reflection. The ray power attenuation coefficient y is found either by averaging T over a ray half-period Zp, between successive reflections, or by summing the loss at the N reflections in unit length of the fiber. Either way we have [7]... 

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