Logarithm

Like the decibel, the neper is a unit in a logarithmic scale. While the bel uses the decadic (base-10) logarithm to compute ratios, the neper uses the natural logarithm.

The Bode plot can be constructed by plotting each factors of transfer function \(\mathbf{H}(\omega)\) separately and adding them graphically. The factors can be considered one at a time and then combined additively because of the logarithms involved.

The frequency range required in frequency response is often so wide that it is inconvenient to use a linear scale for the frequency axis. For these reason, it has become standard practice to plot the transfer function on a pair of semilogarithmic plots: The magnitude in decibels is plotted against the logarithm of the frequency; on a separate plot, the phase in degrees is plotted against the logarithm of the frequency.