Linear gain in a chain of cascaded components is by far the easiest parameter to calculate. Because its value is a first-order entity with no dependence on any other parameter of a particular component (assuming no signal feedback or leakage), combining gain two successive stages is the simple addition of each stage's gain if expressed in units of dB, or multiplication if expressed as a unitless ratio.
Click here to view an example of a cascaded system.
For example, if a 1st and 2nd stage in a cascade have power (as opposed to voltage) gains of 3.01 dB (multiplication factor of 2) and 10.0 dB (multiplication factor of 10), respectively, then the total gain is:
3.01 + 10.0 = 13.01 dB,
or a multiplication factor of:
2 x 10 = 20 [check: 10 * log10 (20) = 13.01 dB].
It's that simple!
A Typical Chain of Cascaded Components
Combining 2 Stages at a Time for Calculations