# Bode Plot

The Bode plot describes the output response of a frequency-dependent system for a sine wave input. It is a combination of a Bode magnitude plot and a Bode phase plot.

A Bode magnitude plot is a graph of log magnitude against log frequency. It makes the multiplication of magnitudes a simple matter of adding distances on the graph since log (a*b)= log a + log b. The magnitude axis of the Bode plot is often converted directly to decibels.

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.

The accompanying image shows an example of a Bode plot of an RC filter (Low-Pass Filter).

A low-pass filter is a filter that passes low frequencies well but attenuates (or reduces) frequencies higher than the cutoff frequency. The actual amount of attenuation for each frequency varies from filter to filter.

Transfer function:

V_{OUT} /V_{IN} =1/[1+j(f/f_{c} )]

The cutoff frequency point fc (in Hertz) is at the frequency f_{c} =1/(2πfRC), which is frequently referred to as the −3 dB point.

Magnitude plot referred:

It consists of two lines, for frequencies below f_{c}, it is a horizontal line at 0 dB and for frequencies above f_{c}, it is a line with a slope of −20 dB per decade.

Phase plot referred:

Responding to 0.1f_{c}, f_{c}, 10f_{c}, the phase shift is -5.7°, -45°, -90°, respectively.