Corner frequency

A good starting point is to assume the need for 24 dB of attenuation at 50 kHz. That make the corner frequency of the common-mode filter... 

Assume that a damping factor of 0.707 or greater is good and provides a -3dB attenuation at the corner frequency and does not produce noise due to ringing. Also assume that the input line impedance is 50 ohms since the regulatory agencies use an TISN test which make the line impedance equal this value. Calculate the values needed in the common-mode inductor and Y capacitors ... 

Real world values do not allow a capacitor of this large a value. The largest value capacitor that will pass the ac leakage current test is 0.05 pF. This is 50 percent of the calculated capacitor value, so the inductor must be increased 200 percent in order to maintain the same corner frequency. The inductance then becomes 900 pH and the resultant damping factor is 2.5 which is acceptable. The resulting schematic is shown in Figure 3-77. 

The first major pole is contributed by the output L-C filter. It represents a second order pole which exhibits a Q phenomenon, which is typically ignored, and a -40dB/decade rolloff above its corner frequency. The phase plot will quickly begin to lag starting at a frequency of 1/lOth the corner frequency, and will reach the full 180 degrees of lag at 10 times the corner frequency. The location of this double pole is found from... 

The more complicated methods of compensation, such as this, allow the designer much more control over the final closed-loop bode response of the system. The poles and zeros can be located independently of one another. Once their frequencies are chosen, the corresponding component values can be easily determined by the step-by-step procedure below. The zero and pole pairs can be kept together in pairs, or can be separated. The high-frequency pole pair appear to yield better results if they are separated and placed as below. The zero pair are usually kept together, but can be separated and placed either side of the output filter pole s corner frequency to help minimize the gain effects of the Q of the T-C filter (refer to Figure B-23). 

A reasonable beginning is that one needs about 24 dB of attenuation at the switehing frequency of the switching power supply. This, of course, should be modified in response to the actual conducted noise spectral shape. One determines the corner frequency of the filter by... 

For this example, the switching frequency is assumed to be 50 kHz. The corner frequency to produce -24 dB of attenuation at this point is... 

The minimum damping factor (Q should be no less than 0.707. Less than that would allow ringing to occur and produce less than 3dB of attenuation at the corner frequency. 

Sometimes the high-frequency attenuation is insufficient to meet the specifications and a third pole needs to be added to the EMI filter. This filter is typically a differential-mode filter and will share the Y capacitors from the common-mode filter. Its corner frequency is typically the same as the commonmode filter. This filter is made up of a separate choke on each power line, and is placed between the input rectifiers and the common-mode filter. 

Place ujm at the modulus crossover frequency of 2 rad/s and position the compensator corner frequencies an octave below, and an octave above this frequency. Set the compensator gain to unity. Flence... 

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

Therefore the flicker noise is expected to grow with 7 as the device size is scaled down. In deep submicron MOSFETs the corner frequency at which thermal noise equals flicker noise may be as large as 100 MHz, indicating that, at low frequency, 1/f noise is the most severe noise source which affects sensor performance. 

The frequency at which (V, comp)max occurs is located at the mid-point between the frequencies cocl = 1/r, and mc2 - /t2 (i.e. the two corner frequencies in the corresponding Bode diagram—see Section 7.10.4). The determination of the appropriate values of r, and r2 to provide a given stability specification requires a trial and error procedure as shown in Example 7.10. 

The reported unfolding force of type 1 pilus by Miller et al. [50] of 60 pN was performed for an elongation speed of l-3 xm/s. Since this is significantly higher than the corner frequency, L, their value is assumed to be an assessment of the unfolding force under dynamic conditions. 

The dashed line represents the common situation of infrequent, off-line optimization. Performance is good and the profit losses are small for disturbances that occur at a much lower frequency (longer period) than the off-line analysis. The off-line analysis is not effective for disturbances occurring faster than the off-line analysis frequency, and as discussed, the disturbance effects decrease for a frequency beyond process corner frequency. Note that the off-line analysis performance requires the technology and software tools described here for RTO if off-line analysis is performed using simplified technology, profit losses are likely to occur even at very low disturbance frequencies. 

Note that if we increased the amplifier input impedance by a factor of 100, we would lower the low-corner frequency to 0.40 Hz. 

Output voltage is linearly related to the plate separation x (equation (2.25)). A high-frequency source (e.g. 50 kHz) V,(icu) is used. The circuit produces an amplitude-modulated output voltage yo(i< ). The mean value of Vo(icu), proportional to j , is determined by demodulation and low-pass filtering (10 kHz corner frequency). In order to provide bias current for the amplifier (which should be an FET op amp), a discharge resistor R must be connected in parallel with Cx- The value of the feedback resistance should be high with respect to the reactance of C. ... 

We can use frequency response techniques (see Chapter 17) to identify experimentally a poorly known process. Do you have any ideas on how you could do it To help you in your thoughts, consider the Bode diagrams of various systems that were examined in Chapter 17. Notice the information provided by characteristics such as the corner frequency (determines the unknown time constant), the level of low-frequency asymptotes (determines the value of static process gains), the slope of high-frequency asymptotes (determines the order of a system), and the behavior of phase lag (keeps increasing for systems with dead time). Note For further details, consult Ref. 11.)... 

As to - oo, then zpa> - oo and from eq. (17.30) log AR -log zp(o. This is the high-frequency asymptote shown also by a dashed line in Figure 17.3a. It is a line with a slope of -1 passing through the point AR = 1 for zpco = 1. The frequency co = l/zp is known as the corner frequency. At the corner frequency, as can be seen from Figure 17.3a, the deviation of the true value of AR from the asymptotes is maximum. 

Any spectral components (including noise) lying outside either limits will be folded back into the spectrum. In order to prevent this, a low pass filter with corner frequency near the high frequency edge of the range of interest can be used. 

In order to construct a magnitude and phase vs. frequency plot of the transfer function, the nondimensional time will be converted back to real time for use on the frequency axis. For the conversion to real time the following physical variables will be used po = 1350 kg/m, b = 15 p.m, and /Hf = 0.85 mPa/sec. The general frequency response is shown in Figure 64.4. The flat response from DC up to the first corner frequency establishes this system as an accelerometer. This is the range of motion frequencies encountered in normal motion environments where this transducer is expected to function. 

The phase shift is At fo cp = 45°, at lOfo cp = 5.7°, and at lOOfo cp = 0.57°. The phase shift in a filter is thus substantial even far away from die comer frequency in the passband, and the frequency must be much higher than the corner frequency to ensure negligible phase shift. 

The same precaution holds for the phase shift to ensure low phase shift, the frequency must be much lower than the corner frequency. These low-pass filtering effects are an important source of error when reading signals through such high-impedance systems as microelectrodes because of inevitable stray capacitance between the inner conductor and the surrounding tissue. 

Variation of S-W0V Corner Frequency with angle Irom Sli ) Vector or Plane 1 Ewe ml 041013000... 

Variation or S-wav Corner Frequency with angle from Slip Victor of Plane 2 Event 1041013000... 

In order to test the merit of this numerical module, we carried out a comparison test with low-pass Butterworth filter. Fig. 5 shows the signal filtered by digital Butterworth filter with corner frequency 200 Hz. 

The constants are explained in table 1. The first two factors in this equation are also present in the regular Warburg impedance, further discussed in (Barsoukov and Macdonald 2005). The last factor is a coth function with the ratio of layer thickness 8 and penetration depth as parameters. As this ratio approaches 1 the imaginary part of the Impedance starts to decrease. This corner-frequency-like effect is usable for parameter extraction even though the... 

The ECG amplifier can readily be designed using the instrumentation amplifier as the principal building block. Active filters with a lower-comer frequency of 0.05 Hz and an upper-corner frequency of 100 Hz are also typically added [8]. 

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