What's the equation for summing 2 ac waveforms?

[Jim85IROC]

I'm creating a little "project" in excel to model the response of various filters on imported CLIO responses. Although I realize that similar tools already exist, I'm doing this strictly as a learning tool.

Right now I've got graphs for the individual driver responses in a 2-way design, but I want to also generate a summing signal. I can't remember all the useful equations I was taught in college, and I'm having a tough time finding them on the internet, so hopefully somebody here has them handy.


One more area that I could use guidance in...
Right now my design is rather crude with a constant 6/12/18/24/whatever dB/octave rolloff beyond a specific point. I want to change my equations to incorporate a more accurate rolloff slope. I'd also like to be able to incorporate an equation with a variable "Q" for the crossover. I've seen crossover equations with a variable "Q" to determine capacitor and inductor values, but does anybody have an equation to determine SPL at frequency "X" , given a desired crossover frequency "Y", and crossover "Q" value?

Thanks. I made great progress on this spreadsheet yesterday morning to the point where it's actually been quite useful. If I can now make it just a tad more accurate, it'll be that much better!

[SY]

Summing has to account for phase. Normally, you convert magnitude and phase of each waveform into a real and imaginary part, sum the real parts, sum the imaginary parts, and you now have the summed signal. Then this can be expressed as a magnitude and phase.

For a signal with magnitude R and phase theta, real part = R cos theta, imaginary part = R sin theta. Working backwards, for a signal expressed as A + jB, magnitude = A² + B² , phase = arctan (B/A).

[Jim85IROC]

ahh... some of it is starting to come back to me now.

Thanks.

[phase_accurate]

magnitude = A2 + B2

Haven't you forgot a tiny little thing ???

magnitude = sqrt (A^2 + B^2)

Regards

Charles

[Jim85IROC]

It was close enough that I knew what he meant. Even that isn't giving me what I'm looking for though, but I walked around the office and found some friends that had their college textbooks here. I'm getting closer.

[Ron E]

Do you know complex math and transfer functions?....Probably not or you wouldn't ask the question.

You can do it with phasors, but IMO that is a PITA.

[SY]

Originally posted by phase_accurate


Haven't you forgot a tiny little thing ???

magnitude = sqrt (A^2 + B^2)

Regards

Charles

Wups!

I was so proud of myself for getting the sup tags right, I forgot the most important part.

[jneutron]

Originally posted by SY


Wups!

I was so proud of myself for getting the sup tags right, I forgot the most important part.

magnitude=√(A² + B²)

Sigh...am I gonna have to teach youze agains??

Cheers, John

[5th element]

Summation of two electrical signals that are coherent.

Vtotal^2 = V1^2+V2^2 - 2V1V2cos(180-angle)

summation of incoherent

Vtotal^2 = V1^2 + V2^2

Sound pressures for incoherent sounds

Ptotal^2 = P1^2+P2^2+..Pnth^2

Sound pressures for coherent

Ptotal^2 = P1^2+P2^2 + 2P1P2cos(angle)

[Jim85IROC]

Originally posted by Ron E
Do you know complex math and transfer functions?....Probably not or you wouldn't ask the question.

You can do it with phasors, but IMO that is a PITA.

I'm familiar with them, but I can't spout them off at will. I learned all of this in college, but crammed it into my brain very tightly next to a million other things, and usually it exploded shortly after the final exam, never to be seen again.

Right now I'm working in the filter slopes with known capacitor and inductor values, but what I'm trying to make is a simpler filtering system where you get to change the filter frequency and slope instead of changing component values. It's a little bit different approach that I haven't seen anywhere else. I've screwed around with it for a day with my crude approximations and it really seems to make crossover selection a little bit more fun to screw with. Now I'm trying to make it more accurate, and if I can get it to spit out some suggested component values at the end, that'll be ok too.