# Combining/adding more that two sines/waves.

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#### Henrik Jensen

##### New Member
I'm trying to make a sheet that shows how the signals add up together with the ability to extract exact numbers if needed.

I've read about how to combine two waves amplitude and phase to get the resulting amplitude, the formula is: =KVROD(A1^2+B1^2+2*A1*B1*COS(B1)). It's a trig function I believe?

But do you know how to combine 3 or more waves with different phase differences and get the resulting amplitude?

I hope you can help me.

Best Regards
Henrik

#### Henrik Jensen

##### New Member
Hi Somendra Misra,

Thank you very much!
it's a very good sheet that shows how to add two sines.
The initial question was about adding more than two sines, do you also know how to add more than two sines?

I've tried cascading the formula but it shows wrong values for other phase differences than 180. I've also tried summing several formulas but that gives different errors as well.

Best Regards

#### Somendra Misra

##### Excel Ninja
Give me some time, to work on the maths parts of it.

Regards,

#### Henrik Jensen

##### New Member
Thanks Hui!
I will look into that.

Thanks SM

#### Hui

##### Excel Ninja
Staff member
For those who don't know Dutch, including me, Kvrod() is same as Sqrt()

#### Hui

##### Excel Ninja
Staff member
Henrik
The formula you posted: =KVROD(A1^2+B1^2+2*A1*B1*COS(B1))
Looks remarkably like the Law of Cosines?

If that is what it is I don't know why you would be using that to add 2 Cosine waves together?

#### Henrik Jensen

##### New Member
Hui, exactly that is danish for square root, sorry!

I'm not an expert, the formula is the same as used in SM's sheet, to get the resulting amplitude from two signals at same frequency with a phase difference. It works fine for doing that and the result is the same as I get from other filter software. I've picked it up here: http://2000clicks.com/mathhelp/GeometryTrigEquivPhaseShift.aspx

How would you do it?

#### Hui

##### Excel Ninja
Staff member
You have copied the formulas slightly incorrectly

They are
r = sqrt(a2 + b2 + 2ab cos(A-B))
θ = atan2(a cos A + b cos B, a sin A + b sin B),

Do you have the original equations or parameters available for the various waves?

#### Henrik Jensen

##### New Member
Thanks Hui, will get back soon with the data used.

#### KenU

##### Active Member
@Henrik Jensen,

I have attached a workbook in which I have plotted the amplitude resulting from combining sine waves. Currently, it has three waves specified, but that list can be expanded simply by continuing the Height and Period inputs.

The input and plot are on the sheet named "1" and a "Description" sheet shows the formulas defined in the name manager. You can extract the results of the named formulas to a worksheet by array entering the name (i.e, CTRL + SHIFT +ENTER).

Hope that helps.
Ken

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#### Hui

##### Excel Ninja
Staff member
KenU,
Nice piece of work
Hui...

@Henrik Jensen,

I have attached a workbook in which I have plotted the amplitude resulting from combining sine waves. Currently, it has three waves specified, but that list can be expanded simply by continuing the Height and Period inputs.

The input and plot are on the sheet named "1" and a "Description" sheet shows the formulas defined in the name manager. You can extract the results of the named formulas to a worksheet by array entering the name (i.e, CTRL + SHIFT +ENTER).

Hope that helps.
Ken

#### Henrik Jensen

##### New Member
Hi Hui,

Here's the data with a cascaded formula.
It's wrong but at least this shows the idea of what I would like to show, it's the sum of several signals amplitude and phase delay.

I hope that it gives you an idea of the issue.

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#### Henrik Jensen

##### New Member
Thanks Ken, nice work, I will check it out.

#### Somendra Misra

##### Excel Ninja
Hi Henrick,

Are you intending to plot Bode plot in excel?

Regards,

#### Henrik Jensen

##### New Member
Hi SM,

Yes, either with radians or frequencies

Thanks

#### Somendra Misra

##### Excel Ninja
Than I would ask you What is the transfer function and why you are doing summation like sine?

Regards,

#### Henrik Jensen

##### New Member
Hi SM,

I had an idea that I would like to sum amplitude and phase of more than 3 signals in excel the simplest way possible and then compare it to different software to see if it is accurate. It's seems that summation of two signals is easy but not 3 or more.

The idea came because summation or addition of several signals really puzzles me and would like to get a better idea of what's going on if not for a real purpose then just for the fun of it. I'm interested in music, speakers and electronic instruments.

The signals in the sheet are not derived from functions, they are just 1 original(no phase delay) and several others with a phase delay. It's similar to connecting 5 sweep generators to a signal mixer and then measuring the output to see the effects at different frequencies.

#### Somendra Misra

##### Excel Ninja
See if this video is of any help.

Regards,

#### Henrik Jensen

##### New Member
Thanks, I've seen it a few days ago.
I'm not sure if I have got all the details right, but since he is generating all his sines and displaying them as step response/time response, he is just adding the sines and not summing them together using their amplitude and phase, am I correct? An engineer has told me that I need to use vector summing, so I will try that and see if it works.

#### Somendra Misra

##### Excel Ninja
Yes correct you need to do vector summing and than may have to do a Fourier transform to get the result.

Regards,

#### KenU

##### Active Member
After revisiting the post, I realized that the workbook I posted did not allow the user to input a phase shift. I have updated it to include phase shift and to plot the first four wave components separately in order to see the individual contributions to the resultant plot (more than four gets kind of busy).

Essentially, the resulting amplitude is simply the summation of the amplitudes of all components for the corresponding time within the series (horizontal axis is time in seconds).

Hope that helps.

Regards,
Ken

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#### Henrik Jensen

##### New Member
Hi Ken,

Thank you very much, I will check it out.

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