# Sum of sines in phasor form

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Ygor Marca on 21 Sep 2023
Answered: Peter O on 21 Sep 2023
How to perform the sum in the following equation in phasor form? I mean analytical using matlab.
Equation:
Ax1*Ax2*sin(2*pi*50*t + Theta_a1 + Theta_a2) + Ax1*Ax3*sin(2*pi*50*t + Theta_a3 + Theta_a2)

Peter O on 21 Sep 2023

You can treat them as the sum of 2 phasors. Assuming they always have equal frequencies then it's a vector sum of the real and imaginary components.

`    Sum = Ax1*Ax2*exp(1j*(theta1+theta2-pi/2) +Ax1*Ax3*exp(1j*(theta3+theta2-pi/2)`

Notice I shifted the waveforms to cosine to make the real and imaginary components work.

The magnitude and angle of the resulting wave are M=abs(sum) ThetaS = angle(sum) Y = M*cos(2*pi*50*t + ThetaS)

(Typing on mobile so please excuse if there's a typo or sign error)

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