Sinewave question

[WTP Pepper]

I used to be able to do this but I have forgot and all my reference books are in the loft.
Not a homework question but something I need to consider in a design.
I need the maths and not an algorithm as I can do that.
OK.
1 master fixed frequency sine wave ~ 1 Hz split into three (assume splitter has no loss). Each of the 3 outputs of the splitter come with a different known phase shift from this master, but will have a same fixed frequency and amplitude into a summing circuit .
I need to work out (given their known phases to the master reference signal before they where phase split) where the peak occurs with reference to this master signal in time. i.e. its phase. Then (and I can do this) work out the max output signal at this point.
I need the simplest of methods.
Thanks in advance.
WTP.

 

[MrAl]

Hi,

So you want to use a 1Hz reference sine, then feed that into a circuit that outputs three different sine waves each at a different phase?

Do you require any specific phase shift, such as 10 degrees, 20 degrees, 45 degrees, etc.?

And they all should be the same amplitude right, but does that amplitude have to be defined as say 1v peak each or can the amplitude be anything as along as they are all the same?

 

[JimB]

If I understand correctly, you are just looking for a mathematical method.

If you have a spreadsheet like MS Excel, just set up the equation and graph the signal for a couple of cycles.

JimB

 

[MrAl]

Hi,

Oh you just want the math? That is just too easy so i assumed you wanted something that you could actually build, but also include the math.

The math is too easy sin(wt+ph) for each phase where ph is the phase angle for each phase. Generating this with a circuit is just a tiny bit more involved because various implementations take various complex or simple circuits. If the actual absolute amplitudes only have to be the same and not at some set level this works out to a passive circuit for example. The math for this would be a tiny bit more too that would include statements for amplitude and phase shift.
For example, using an RC phase shift network we get:
Amplitude=1/sqrt((w*R*C)^2+1)
PhaseShift=-atan(w*R*C)

and we could easily use this information to create any phase shift and with a tiny bit more work we could get equal amplitudes with an all passive circuit.

 

[Ratchit]

WTP Pepper,

No matter how many sinusoids at whatever phase you add together, the result will be another sinusoid at the same frequency with a different phase. I understand you have three sinusoids, each at the same amplitude and frequency, but differing only in phase. The attachment shows how to calculate the phase where the max of the resultant will occur, and its max value.

Ratch

 

[misterT]

No matter how many sinusoids at whatever phase you add together, the result will be another sinusoid at the same frequency with a different phase.

If you add two sinusoids with 180 degree phase difference the result is a flat line (zero).

 

[JimB]

Similarly if you add three sinewaves with a 120 degree shift you also get zero.
And probably 4 with 90, 5 with 360/5 etc as well.

JimB

 

[NorthGuy]

If you add two sinusoids with 180 degree phase difference the result is a flat line (zero).

Which is also a sinusoid, but with zero amplitude.

 

[Ratchit]

To all,

Yes, anything that adds up to zero on the denominator of the arctan above will result in a zero magnitude.

Ratch

 

[crutschow]

Which is also a sinusoid, but with zero amplitude.

You sure it's not a square-wave with zero amplitude?

 

[Ratchit]

crutschow,
I can't speak for NorthGuy, but I am sure. Joe Fourier tells me that it takes several waves of different frequencies and different amplitudes, and all the same phase to make a square wave.

Ratch

 

[NorthGuy]

crutschow,
I can't speak for NorthGuy, but I am sure. Joe Fourier tells me that it takes several waves of different frequencies and different amplitudes, and all the same phase to make a square wave.

Ratch

With zero amplitude, it only takes zero waves. LOL!

 

[crutschow]

crutschow,
I can't speak for NorthGuy, but I am sure. Joe Fourier tells me that it takes several waves of different frequencies and different amplitudes, and all the same phase to make a square wave.

It was intended to be a tongue-in-cheek reply, zero is zero.

 

[WTP Pepper]

Thanks Ratchit. Your explanation was just what I wanted.