Break frequency

The frequency of maximum phase advance is to occur at the frequency that corresponds to —180° on the Bode diagram constructed in section (a). The lower break frequency XjTx is to be half this value and the upper break frequency l/r2 is to be twice this value. Evaluate T and T2 and calculate values of 0 for the frequencies specified in section (a). Construct the Bode diagram for the compensation element for the condition K = X, and read off values of modulus at the same frequencies as the calculated phase values. 

Pipe Break Frequency Estimation for Nuclear Power Plants Nuclear 19 occunences of pipe failures (breaks), supplemented by expert-opinion estimates Leaks of 1 gpm for 2 inches in diameter pipe 50 gpm tor all pipe for 81 nuclear plants 101. 

Pipe Break Frequency Estimation for Nuclear Power Plants... 

Even with MATLAB, we should still know the expected shape of the curves and its telltale features. This understanding is crucial in developing our problem solving skills. Thus doing a few simple hand constructions is very instructive. When we sketch the Bode plot, we must identify the comer (break) frequencies, slopes of the magnitude asymptotes and the contributions of phase lags at small and large frequencies. We ll pick up the details in the examples. 

The frequency at which co = l/xp is called the corner frequency (also break frequency). At this position,... 

One may question the significance of the break frequency, co = 1/x. Let s take the first order transfer function as an illustration. If the time constant is small, the break frequency is large. In other words, a fast process or system can respond to a large range of input frequencies without a diminished magnitude. On the contrary, a slow process or system has a large time constant and a low break frequency. The response magnitude is attenuated quickly as the input frequency increases. 

Chinese hamsters exposed to ozone at 0.2 ppm for 5 h had an increased number of chromosomal breaks in their circulating lymphocytes. Blood samples for study were obtained immediately after exposure and 6 and 15.5 days later. The highest break frequency was observed after the longest delay. The authors compared the effects of X irradiation and ozone singly and combined, in their system. The combined effects were less than additive this suggested some protective mechanism, perhaps analogous to that observed by Hattori et al When the authors extrapolated their data to acceptable industrial-hygiene exposures to ozone and radiation, ozone was found to be much more likely than X irradiation to produce chromosomal breaks in such exposures. 

In animal studies, mice injected with doses ranging from 0.05 to 1.0 jg U/testis as enriched uranium fluoride showed a general tendency for an increase in chromosome breaks with an increasing dose of enriched uranyl fluoride. At high-dose levels, the statistically significant difference of break frequencies between treated and control mice disappeared 60 days after treatment (Hu and Zhu 1990). 

The error/deviation from the actual curve is usually very small if we replace it with its asymptotes (for first-order filters). For example, the worst-case error for the gain of the simple RC network is only -3dB, and occurs at the break frequency. 

Since both the gain and the phase fall as frequency increases, we say we have a pole present — in our case, at the break frequency of 1/(2ttRC). It is also a single-pole, since it is associated with only a —1 slope. 

For most purposes, we can assume that the break frequency of the gain plot does not depend on the load or on the associated parasitic resistive elements of the components. So the resonant frequency of the filter-plus-load combination can be taken to be simply l/(2jr /(LC)), that is, no resistance term is included. 

The LC filter gain decreases at the rate of —2 at high frequencies. The phase also decreases providing a total phase shift of 180°. So we say we have a double-pole at the break frequency 2jt,v/(LC). 

Unlike an RC filter, the output voltage in this case can be greater than the input voltage (at around the break frequency). But for that to happen, Q must be greater than 1. 

Let us try to connect the dots now. Both the first- and second-order filters we have discussed gave us poles. That is because they both had s in the denominators of their transfer functions — if s takes on specific values, it can force the denominator to become zero, and the transfer function then becomes infinite, and we get a pole by definition. The values of 5 at which the denominator becomes zero are the resonant (or break) frequencies, that is, the locations of the poles. For example, a hypothetical transfer function 1/s will give us a pole at zero frequency (the pole-at-zero we talked about earlier). 

Note that the gain, which is the magnitude of the transfer function (calculated by putting s = jco), won t necessarily be infinite at the pole location. For example, in the case of the RC filter, we know that the gain is in fact always less than or equal to unity, despite a pole being present at the break frequency. 

But poles and zeros also add up with their own type. For example, if we have a double pole on one plot, and a single-pole on the other plot (at the same frequency), the net gain will fall with a slope of —3 after the break frequency. Phase angles also add up similarly. 

Since n = frequency of harmonic/fundamental frequency, that is, n = f x T, we get the corresponding break frequency to be... 

In other words, only for very narrow duty cycles we might get to see the first break point. Further, below the first break frequency, the envelope of the harmonics becomes flat. Theoretically, the first break point should be calculated and the envelope should be made flat below this frequency. But other than that, we can use the following equations to describe all the cn (note that in these equations, the cn are no longer the actual coefficients of the Fourier expansion, rather they represent the envelope) ... 

This is 98 - 66 = 32 dB higher than allowed. And that means that we need to use a filter to attenuate the noise. We need to pick a low-pass LC filter which provides an attenuation of 32 dB at 150 kHz. Knowing this, we can calculate its break frequency. For example if we are using an LC low-pass filter, it has an attenuation characteristic of about 40 dB/decade above its break frequency (i.e. 1/2tt /(LC)). So from Figure 14-9 we can see that its equation is... 

This equation is therefore flat untill the break frequency, after which it rolls off at 20 dB/decade. The flat part (the pedestal ) can be found using the approximation sin x/x = 1. It is... 

Fig. 7. Raman spectra of homologous compounds of the aliphatic chlorinated hydrocarbon series (frequencies in cm ). One observes that comparing spectra of 2a to 10a the lines belonging to the valence frequencies are fixed in the same place, while the break frequency lines (around 400) are shifted.

DNA single-strand break frequency was measured by alkaline elution [16] and sister chromatid exchanges (SCEs) were assayed by the method described by Wolff [32]. Hypoxanthine-guanine phosphoribosyl transferase (HPRT 6-thioguanine) and Na/K ATPase (ouabain) resistant mutants of CHO were determined by the methods described by Cleaver [7]. Repair replication after MMS treatment was measured in isopycnic gradients [8]. 

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