# Signal Composition: in-phase and not-in phase

## Main Question or Discussion Point

I will state here what I understand in this topic which I am a little confused:

If I have 2 sinusoidal signals perfectly in phase, with distinct power levels, say -13dBm and -10dBm, the composition ("sum") of both signals is -8.23dBm. Or, for -10dBm and -10dBm signals, the sum is -7dBm.

Now, if one signal which lags around 180 degrees in relation to the other signal, the composition of both signals is almost 0 (a very low value in dBm, say -300dBm) because there is a cancellation of signals.

But, for different values of this delay-angle (difference between signal phases), it is expected a huge variation of the signal composition.

In the mentioned example, the variation is from -8.23 dBm to -infinite dBm (no signal).

I would like to:
(1) confirm if I am correct with my explained reasoning. If not, please, express your argument with numbers of this example.

(2) get a hint about where I can find theoretical material with the formula for such signal composition (assume sinusoidal signal with different amplitudes) or the formula itself. However, I need to maintain the notation in dBm (assume fixed load impedance). Using cos function, we can measure the phase delay with values from -1 to 1. Now, how to plug this in the original problem?

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