How to determine the lag angle between two snine wave

% I need to calculate the angle of the rotational vector B=Bmx+i*Bmy

% wheree Bmx and Bmy are 90 degree outof phase

% here is the code

clc

clear

close all

f=50;w=2*pi*f;Tperiod=1/f;Tmax=4*Tperiod;Dt=Tperiod/(6*f);N=(Tmax/Dt)+1;

t0=0.00001;

t=zeros(N,1); Bmx=zeros(N,1); Bmy=zeros(N,1);

thetaB=90;Bmax=1.6;

for k=1:N+1

t(k)=t0+Dt*(k-1);

Bmx(k)=Bmax*sin(w*t(k));

Bmy(k)=Bmax*sin(w*t(k)-(thetaB)*pi/180);

end

%when I use this command the lag angle between Bmx ,,and Bmy is not 90

phase_difB= acos( dot(Bmx,Bmy) / (norm(Bmx)*norm(Bmy)) )*180/pi;

% the result is 94 and the lag angle between is is thetaB=90;

% and if there is another vector H=Hx+i*Hy

%how can I determine the angle between B and H

%Regards

[David Goodmanson]

Hi Hassan, I ran your code and got 90.0026

Answer 1

[the cyclist]

I believe you will only get exactly 90 if you could sample at infinitesimal resolution and/or a signal that extends for infinite time.

Due to the finite resolution and extent, you will only get an approximation.

[Hassan Abdelazeem]

Ok, thank you indeed for your reply

Answer 2

[David Goodmanson]

Hi Hassan

Consider the complex wave

exp(i*(w*t+theta)) = cos(w*t+theta) + i*sin(w*t+theta)    

While it's true that the cos and sin terms are 90 degrees out of phase, I think there are better ways to look at things than concentrating on that particular phase shift. It's better to take that phase shift for granted an look at the complex wave as a single entity:

exp(i*(w*t+theta)) = exp(i*w*t)*exp(i*theta)

In a system with several components oscillating at a single frequency, the exp(i*w*t) factor is common to all of them and the exp(i*theta) factor (the phasor) determines the relative phase of the components. For example,

t = (0:.001:1)';   % column vector
f = 10
w = 2*pi*f;
A1 = 5;
A2 = 2;
th1 = 30*(pi/180);
th2 = 175*(pi/180);
sig1 = A1*exp(i*(w*t +th1));
sig2 = A2*exp(i*(w*t +th2));   % the two systems have relative phase of 145 degrees.

% determine the relative angle by similar method to that in the question
relative_angle = angled((sig1'*sig2)/sqrt((sig1'*sig1)*(sig2'*sig2)))

   relative_angle = 145.0000

Here angled was used since it converts to degrees

[Hassan Abdelazeem]

Dear David

Thank you for your reply, it is quite useful for me

Regards