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In electrical engineering and control theory, a Bode plot is a graph of the frequency response of a system. 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.
# 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 ...
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 ...
Roll-off of a first-order low-pass filter is 20 dB/decade (≈6 dB/octave) A simple first-order network such as a RC circuit will have a roll-off of 20 dB/decade. This is a little over 6 dB/octave and is the more usual description given for this roll-off.
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 ...
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:
This can be apportioned to two first order lattices in cascade, using the Type IV circuits from Bode’s chart [6]: 252 to give the circuit shown. Bode equalizer (lattice) Bode equalizer (bridged-T) This can be easily converted to a cascade of standard constant resistance bridged-T sections of the form described earlier, as shown on the right.