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.
Cascading Gain Values in a Chain of Components
Click here to view an example of a cascaded system.
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!