# Graphing with Decibels

(This help is also available inside Numerari.)

To show power gain in decibels for engineering and scientific applications, Numerari offers two scales: 20log dB for functions representing intensity or amplitude and 10log dB for functions representing power. These can be used for the y axis on rectangular grids and for the r axis on polar grids.

To determine the dB range shown and the positioning of the graph, Numerari first finds the maximum function value over the specified x (or θ) range. If your function takes on larger values outside of the specified x (or θ) range, these larger values will not be considered when determining the maximum function value.

Numerari then positions the graph so that the maximum function value is placed at a specific dB reference level. By default, that reference level is 0 dB. However, if you specify the y (or r) max limit, Numerari uses that limit as the reference level. If you do not set the y (or r) max limit but you do set the y (or r) min limit, then the reference level will be set to 40 dB above the min limit.

Below is a graph of the absolute value (modulus or magnitude) of a complex network function using the 20log dB scale for the y axis. In this case, x represents a frequency so the x axis uses a regular logarithmic scale as is common for a frequency axis. The y max limit sets the decibel reference level at 20 dB for the maximum function value instead of the default 0 dB.

Note that you usually graph the absolute value of a function when using decibel scales since taking the logarithm of a negative or complex number does not result in a real number.

Even though the graph below of the complex argument (or phase) of the same network function does not use a decibel scale, it is included for completeness. It is very common to show both the absolute value and phase of a network function as frequency varies.

Below is a polar graph of an antenna radiation pattern using the 20log dB scale for r. The reference level for the maximum function value was left at the 0 dB default, but it could have been changed by setting the r max limit. Note that for the decibel scales, negative values may be shown on the polar axis. By default, a 40 dB range will be shown below the reference dB level. However, you can show a different range by setting the r min limit to the dB level you want the center of the graph to represent. (Note that for a function like that below, the calculator needs to be in radian mode so an one of the outer sine functions does not interpret the result of an inner sine as degrees.)