# 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.)