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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 .
# 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 ...
G (w,n) = 1 / (sqrt (1 + w ** (2 * n))) dB (x) = 20 * log10 (abs (x)) # Phase is for first order P (w) =-atan (w) * 180 / pi # Gridlines set grid # Set x axis to logarithmic scale set logscale x 10 # No need for a key set no key #0.1,-25 # Frequency response's line plotting style set style line 1 lt 1 lw 2 # Asymptote lines and slope lines are ...
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.
Magnitude response of a low pass filter with 6 dB per octave or 20 dB per decade roll-off. Measuring the frequency response typically involves exciting the system with an input signal and measuring the resulting output signal, calculating the frequency spectra of the two signals (for example, using the fast Fourier transform for discrete signals), and comparing the spectra to isolate the ...
Using the Smith chart, the normalised impedance may be obtained with appreciable accuracy by plotting the point representing the reflection coefficient treating the Smith chart as a polar diagram and then reading its value directly using the characteristic Smith chart scaling. This technique is a graphical alternative to substituting the values ...
Bode magnitude plot for the voltages across the elements of an RLC series circuit. Natural frequency ω 0 = 1 rad/s, damping ratio ζ = 0.4. Sinusoidal steady state is represented by letting s = jω, where j is the imaginary unit. Taking the magnitude of the above equation with this substitution:
Sometimes other ratios are more convenient than the 3 dB point. For instance, in the case of the Chebyshev filter it is usual to define the cutoff frequency as the point after the last peak in the frequency response at which the level has fallen to the design value of the passband ripple. The amount of ripple in this class of filter can be set ...