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# set terminal svg enhanced size 875 1250 fname "Times" fsize 25 set terminal postscript enhanced portrait dashed lw 1 "Helvetica" 14 set output "bode.ps" # ugly part of something G(w,n) = 0 * w * n + 100000 # 1 / (sqrt(1 + w**(2*n))) dB(x) = 0 + x + 100000 # 20 * log10(abs(x)) P(w) = w * 0 + 200 # -atan(w)*180/pi # Gridlines set grid # Set x axis to logarithmic scale set logscale x 10 set ...
It is usually a combination of a Bode magnitude plot, expressing the magnitude (usually in decibels) of the frequency response, and a Bode phase plot, expressing the phase shift. As originally conceived by Hendrik Wade Bode in the 1930s, the plot is an asymptotic approximation of the frequency response, using straight line segments .
A frequency ratio expressed in octaves is the base-2 logarithm (binary logarithm) of the ratio: = An amplifier or filter may be stated to have a frequency response of ±6 dB per octave over a particular frequency range, which signifies that the power gain changes by ±6 decibels (a factor of 4 in power), when the frequency changes by a factor of 2.
Bode plot illustrating phase margin. In electronic amplifiers, the phase margin (PM) is the difference between the phase lag φ (< 0) and -180°, for an amplifier's output signal (relative to its input) at zero dB gain - i.e. unity gain, or that the output signal has the same amplitude as the input.
A Nichols plot. The Nichols plot is a plot used in signal processing and control design, named after American engineer Nathaniel B. Nichols. [1] [2] [3] It plots the phase response versus the response magnitude of a transfer function for any given frequency, and as such is useful in characterizing a system's frequency response.
[6] [failed verification] Similar arguments apply to vibrating air columns in wind instruments (for example, "the French horn was originally a valveless instrument that could play only the notes of the harmonic series" [7]), although these are complicated by having the possibility of anti-nodes (that is, the air column is closed at one end and ...
In this type the derivative (slope) of the wave's amplitude (in sound waves the pressure, in electromagnetic waves, the current) is forced to zero at the boundary. So there is an amplitude maximum (antinode) at the boundary, the first node occurs a quarter wavelength from the end, and the other nodes are at half wavelength intervals from there:
As a voltage ratio this is a fall to / of the passband voltage. [1] Other ratios besides the 3 dB point may also be relevant, for example see § Chebyshev filters below. Far from the cutoff frequency in the transition band, the rate of increase of attenuation ( roll-off ) with logarithm of frequency is asymptotic to a constant.