Lower 3 dB frequency

The goal functions can also be used to find the lower 3 dB frequency. Select Trace and then Eval Goal Function. Evaluate the expression lowar3dB (V (VOOT)) ... 

Run the PSpice simulation Select PSpice and then Run from the Capture menu bar. When the simulation is complete, the Probe window will open. Add the trace DB(V(VO) ) to plot the gain in decibels. Use the cursors to label the mid-band gain, and upper and lower -3 dB frequencies. Your cursor values may be slightly different than those shown here. 

When we design a circuit with tolerance, we may sometimes want to find the worst case upper or lower 3 dB frequency with component tolerances. Unfortunately, calculating a 3 dB frequency requires that we find the mid-band gain and then find the frequency where the gain is 3 dB less than the mid-band. This type of calculation cannot be specified in the Monte Carlo/Worst Case dialog box. However, we can run a Monte Carlo analysis and then determine the 3 dB frequency using the Performance Analysis capabilities available in Probe. In this example, we will illustrate finding the maximum lower 3 dB frequency (FL), minimum upper 3 dB frequency (FH), and maximum and minimum bandwidth (FH - FL) for a common-emitter amplifier. Wire the circuit below ... 

Next, we would like to display a histogram of the lower 3 dB frequency. We will first delete the displayed trace. Click the LEFT mouse button on the text V(VO) to select the trace. When the trace is selected, the text ViVO) will be highlighted in red. Press the DELETE key to delete the trace. (Your trace may be labeled differently than Vfl/O).) A blank Probe screen will result. 

This function finds the lower 3 dB frequency and marks the coordinates of the point xl and yl. It then finds the upper 3 dB frequency and marks the coordinates of the point x2 and y2. The function returns the bandwidth, x2 - x1. 

We will first plot a histogram of the lower 3 dB frequency. Enter the trace lower3dB (V (VO)) s... 

We see that the maximum lower 3 dB frequency is at 80.2421 Hz. In the screen capture above, the number of histogram divisions has been set to 100. See page 519 for instructions on how to change this setting. To view the upper 3 dB frequencies, add the trace upper3dB(V(VO)) ... 

Bandwidth The range of frequencies over which a system instantaneously operates, i.e., passes a signal, usually taken as the difference between the upper —3 dB point in the response and the lower —3 dB... 

In general, it is desired to make the pilot sequence as short as possible, however, very short pilot sequences lead to an inaccurate PDF estimation, and thus to incorrect estimations of Ar and r0nS(H. Fig. 19 shows the estimation performance for Lpii0t = 250,500,1000, and 2000. Fig. 19.(a) depicts 5at which describes the relative estimation error of Ar. For Lpoot = 2000, 8at decreases monotonically with increasing WNR, and is lower than 1% for WNR > —3 dB. Shorter pilot sequences lead to an increased relative estimation error. However, for some WNR, robust estimation is no longer possible at all. Lowering the WNR further introduces so much noise into the PDF estimation that the largest component of the computed DFT spectrum appears at any random frequency index 0 < l < Ldft — 1. 

If an adjustable-gain high-pass filter has been used to eliminate the low-frequency contamination, the resulting spectrum would look like a band-pass filter spectrum. But, such a filter introduces a limit in the low range of the meter, and a nonlinearity at the lower end of the meter range. The comer frequencies or 3-dB points of such a filter will yield a frequency at the high end that can be related to the lowest possible measurable flow. 

Seismometers can be further categorized by the lower comer frequency (—3 dB point) of the amplitude frequency response of the instmment. Geophones have lower comer frequencies from 1 to 40 Hz. Short-period seismometers have lower comer frequencies from 1 to 4 Hz, and broadband seismometers have lower comer frequencies from 0,027 to 1 Hz. Broadband seismometers typically have lower noise floors over wider bandwidths than short-period seismometers, and short-period seismometers are typically quieter than geophones. Accelerometers are approaching the performance levels of some geophones and short-period seismometers and can be considered for downhole applications too. 

A-weighted SPL is a better representative of how we hear than linear SPL. We do not hear low and high frequencies well, so weighting networks are often used to better rqrresent the linear SPL that is measured to the SPL that humans actually hear. Differences of 2 -3 dB are perceptible by most people. Lower is better. 

Vibration can be perceived from a frequency of approximately 3 Hz. The lower frequencies appear to cause the most discomfort. At high levels (above 120 dB) vibration can be physically damaging to people, and resonance of the human body occur at the following frequencies ... 

Table 5.8 shows a summary of the results of the sound of explosions measured at the mock storage shed. Data is shown at the impulse level, and data from the fast level is usually 3.5-5.5dB lower than the impulse level data. Impulse levels were used for the dB values. The frequencies used for a linear response were l-90Hz for the special linear characteristic and 10-20Hz for the special flat characteristic. In many cases the explosive sound was measured over 100Hz to include the main components. One must pay close attention to methodology when comparing and analyzing measured values of sounds. 

FIGURE 633 Comparison of 3-D model calculations with experimental results of Zhou and coworkers [1994] for amplitude at the place x = 19 mm as a function of frequency. The scales are logarithmic (20 dB is a factor of 10 in amplitude). Case 1 shows a direct comparison with the physical parameters of the experiment, with isotropic BM and viscosity 28 times that of water. Case 2 is computed for the viscosity reduced to that of water. Case 3 is computed for the BM made of transverse fibers. Case 4 shows the effect of active OHC feed forward, with the pressure gain a = 0.21 and feed-forward distance )a25 fim. Thus lower viscosity, BM orthotropy, and active feed forward all contribute to higher amplitude and increased localization of the response. 

The sensitivity of the human ear is biased toward the lower end of the audible frequency spectrum, around 3 kHz. At 50 Hz, the bottom end of the spectrum, and 17 kHz, at the top end, the sensitivity of the ear is down by approximately 50 dB relative to that at 3 kHz (see Fig. 12.89). Additionally, there are very few audio signals, music or speech based, that carry fundamental frequencies above 4 kHz. Taking advantage of these characteristics of the ear, the structure of audible sounds and the redundancy content of the PCM signal is the basis used by the designers of the ADPCM or predictive range of compression algorithms. 

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