The Bode plot for a first-order Butterworth filter

A Bode plot, named for Hendrik Wade Bode, is usually a combination of a Bode magnitude plot and Bode phase plot: Image File history File links Download high resolution version (1250x875, 110 KB) File links The following pages link to this file: Bode plot Butterworth filter ... Image File history File links Download high resolution version (1250x875, 110 KB) File links The following pages link to this file: Bode plot Butterworth filter ... The Bode plot of a first-order Butterworth low-pass filter The Butterworth filter is one type of electronic filter designs. ...

A Bode magnitude plot is a graph of log magnitude against log frequency often used in signal processing to show the transfer function or frequency response of an LTI system. It makes multiplication of magnitudes a simple matter of adding distances on the graph, since Logarithms to various bases: red is to base e, green is to base 10, and purple is to base 1. ... Sine waves of various frequencies; the lower waves have higher frequencies than those above. ... Signal processing is the processing, amplification and interpretation of signals. ... A transfer function is a mathematical representation of the relation between the input and output of a linear time-invariant system. ... Frequency response is the measure of any systems response to frequency, but is usually used in connection with electronic amplifiers and similar systems, particularly in relation to audio signals. ... LTI can refer to: A book by Victor Klemperer, LTI - Lingua Tertii Imperii A linear, time-invariant system. ...

The Bode plot describes the output response of a frequency-dependent system for a normalised input. The magnitude axis of the Bode plot is often converted directly to decibels. The decibel (dB) is a measure of the ratio between two quantities, and is used in a wide variety of measurements in acoustics and electronics. ...

A Bode phase plot is a graph of phase against log frequency, usually used in conjunction with the magnitude plot, to evaluate how much a frequency will be phase-shifted. For example a signal described by: Asin(ωt) may be attenuated but also phase-shifted. If the system attenuates it by a factor x and phase shifts it by −Φ the signal out of the system will be (A/x) sin(ωt − Φ). The phase shift Φ is generally a function of frequency. Waves with the same phase Waves with different phases The phase of a wave relates the position of a feature, typically a peak or a trough of the waveform, to that same feature in another part of the waveform (or, which amounts to the same, on a second waveform). ...

The magnitude and phase Bode plots can seldom be changed independently of each other — if you change the amplitude response of the system you will most likely change the phase characteristics as well and vice versa.

A typical application of a Bode plot is to show the frequency response of a filter. It is especially useful in this case because the complex curves that appear in a linear magnitude-frequency plot can often be approximated by straight lines in a Bode plot. Electronic filters are electronic circuits which perform signal processing functions. ...

These asymptotic approximations are useful because they can be drawn by hand following a few simple rules. Simple plots can even be predicted without drawing them. A lowpass RC filter, for instance, requires only one calculation. It has an asymptote at 0 dB and an asymptote with a slope of −20 dB per decade, which meet at the cutoff frequency point f_c (in hertz): A low-pass filter passes low frequencies fairly well, but attenuates high frequencies. ... A resistor-capacitor circuit (RC circuit), or RC filter or RC network, is one of the simplest analogue infinite impulse response electronic filters. ... The Butterworth filters frequency response, with cutoff frequency labeled. ... The hertz (symbol Hz) is the SI unit of frequency. ...

See also

• Nyquist plot
• Frequency response
• Transfer function

A Nyquist plot is a graph used in signal processing in which the magnitude and phase of a frequency response are plotted on orthogonal axes. ... Frequency response is the measure of any systems response to frequency, but is usually used in connection with electronic amplifiers and similar systems, particularly in relation to audio signals. ... A transfer function is a mathematical representation of the relation between the input and output of a linear time-invariant system. ...

External links

• [1] [2] - Examples of Bode plots
• Explanation of Bode plots with movies and examples
• How to draw piecewise asymptotic Bode plots
• Summarized drawing rules (PDF)
• Bode plot applet - Accepts transfer function coefficients as input, and calculates magnitude and phase response
• Biography of Bode
• Blode Plotting on the HP49