Bode Plots

Bode plots are graphical tools that use logarithmic scales for frequency on the x-axis and gain in decibels on the y-axis. This logarithmic method allows a wide range of frequencies to be compactly displayed, enabling the analysis of component effects on circuit behavior across a broad frequency spectrum.

A network function represents the ratio of a system's output to its input, with the magnitude and phase angle derived from the complex network function. The decibel logarithmic gain is determined by multiplying the base-ten logarithm of the network function's magnitude by 20.  The gain in a Bode plot is expressed logarithmically. The unit of logarithmic gain is the decibel, also known as gain in dB. Decibels (dB) quantify gain, where 1 dB is one-tenth of a bel, which honors Alexander Graham Bell.

Bode plots, which are semilogarithmic graphs, show the logarithmic gain in decibels and the phase angle in degrees over a range of frequencies. These plots facilitate the understanding of a system's frequency response.

At lower frequencies, both the logarithmic gain and the phase angle approaches zero, forming horizontal lines on the Bode plot known as low-frequency asymptotes. These lines indicate minimal filter impact on signals at these frequencies. As frequency increases, the gain and phase angle calculations reflect their frequency dependence. On the Bode plot, these dependencies appear as straight lines with negative slopes, called high-frequency asymptotes. These lines demonstrate how the filter attenuates higher-frequency signals. The low- and high-frequency asymptotes intersect at the corner frequency. Here, the asymptotic magnitude deviates by about -3 decibels from the exact value, marking a significant change in the filter's response. Additionally, the phase angle at the corner frequency is approximately -45 degrees.

Asymptotic Bode plots provide reasonable approximations of actual Bode plots, allowing for simplified analysis while maintaining reasonable accuracy.