The dB and phase angle summation?

[Ethan]

This is bugging me...
If a sine wave of "4dB" is electronically combined with an identical wave 90degrees apart, what is the total resulting dB?

How would calculate this?

 

[PRR]

Define "electronically combined".

For many reasonable interpretations of the question, the answer is: 3dB higher than one sine, and shifted 45 degrees.

 

[moamps]

[quote author="Ethan"]
If a sine wave of "4dB"[/quote]
V1=Ao*sinx

is electronically combined

summed

with an identical wave 90degrees apart

V2=Ao*sin(x+90)

what is the total resulting dB? How would calculate this?

sin(x+y)=sinx*cosy+siny*cosx,
for y=90, sin90=1, cos90=0,
then
sin(x+90)=cosx
V2=Ao*cosx

V=V1+V2=Ao(sinx+cosx)
=Ao*1.41*(0.707*sinx+0.707*cosx), 1..41*0.707=1!!
for sin45=0.707 and cos45=0.707
then
V=1.41*Ao*(cos45*sinx+sin45*cosx)
and

V=1.41*Ao*sin(x+45)

20*log (1.41)=3dB

Regards,
Milan

 

[TedF]

PRR (as usual) asked the right question and gave the right answer; but the other question is why would you need to know? :shock:

If you draw graphical representations of the two waves and imagine that one is added simply and arithmetically to the other, it's easy to see the 3dB gain, and 45 degree phase shift.

 

[Ethan]

Thanks guys. Makes sense. Just a strange (somewhat undefined) question that popped up in some sort of "audio test" I found. I think it's for broadcast engineers or summmin' :roll: