The relationship between Mono Mixdown and Pan Law

[pdtakeitslow]

Hi there,
I'm writng because I don't understand what I'm testing about the relationship Mono Mixdown and Pan Law.

DAW : Cubase 7
Test Source : -6dB Sine wave (Mono, Panned to Center)

Test 1) Project Pan Law : 0dB

With this pan law. mono sine wave that is panned center is not attenuated at all.
So, both channels (L,R) on the mono track have -6dB sine wave respectively.
After all, what I got through Mono Mixdown was 0dB Sine wave (Mono).

-6dB Sine wave (Mono) -> -6dB(L) + -6dB(R) -> (Mono Mixdown) -> 0dB Sine wave (Mono)

Test 2) Project Pan Law : -6dB

Contrary to the above, -6dB pan law attenuates the mono channel by 6dB when it’s panned to center.
So, both channels (L.R) on the mono track have -12dB sine wave respectively.
Then I had to get -6dB Sine wave, but I got -12 dB Sine wave.

I expected :

-6dB Sine wave (Mono) -> -12dB(L) + -12dB(R) -> (Mono Mixdown) -> -6dB Sine wave (Mono)

Actual results are :

-6dB Sine wave (Mono) -> -12dB(L) + -12dB(R) -> (Mono Mixdown) -> -12dB Sine wave (Mono)

The result of the Test 2 is not understood.
Isn't the principle of Mono Mixdown summing L+R?

[Romantique Tp]

nvm

[HanafiH]

Actual results are :

-6dB Sine wave (Mono) -> -12dB(L) + -12dB(R) -> (Mono Mixdown) -> -12dB Sine wave (Mono)

That's the bit I don't believe. The electrical summation of two identical signals causes an increase in amplitude of 6dB. Adding -12dB to an identical -12dB results in -6dB in any physical electrical system.

[HanafiH]

Thinking on, a -12dB mono signal panned through to stereo under -6 pan law would have an amplitude of -18dB and two such signals would sum, in the center of the stereo field, to -12dB.