# Bode Plots

The frequency range required in frequency response is often so wide that it is inconvenient to use a linear scale for the frequency axis. Also, there is a more systematic way of locating the important features of the magnitude and phase plots of the transfer function. For these reasons, it has become standard practice to use a logarithmic scale for the frequency axis and a linear scale in each of the separate plots of magnitude and phase. Such semilogarithmic plots of the transfer function—known as Bode plots—have become the industry standard.
Bode plots are semilog plots of the magnitude (in decibels) and phase (in degrees) of a transfer function versus frequency.
Bode plots contain the same information as the nonlogarithmic plots discussed in the previous section, but they are much easier to construct, as we shall see shortly. The transfer function can be written as
$$H = H \angle φ = H e^{jφ}$$
Taking the natural logarithm of both sides,
$$ln H = ln H + ln e^{jφ} = ln H + jφ$$
Thus, the real part of $ln H$ is a function of the magnitude while the imaginary part is the phase. In a Bode magnitude plot, the gain
$$H_{dB} = 20 log_{10} H$$
is plotted in decibels (dB) versus frequency. Table 1 provides a few values of H with the corresponding values in decibels. In a Bode phase plot, φ is plotted in degrees versus frequency. Both magnitude and phase plots are made on semilog graph paper.
Table 1: Specific gains and their decibel values.