lab no.08

Designed by : Dawar [email protected]

CECOS College of Engineering and IT March – July 2012

Lab No.08

Complex exponentials and phasors


Complex number , z = (3,4) = 3+4i

‘z’ can be defined in MatLab as , z=3+4i;

Now, try the following commands.

real(z) Real part of zimag(z) imaginary part of zabs(z) magnitude or modulus of zangle(z) phase or angle of zconj(z) conjugate of z

Complex numbers


1. for z = 1+2i+3 , find the real and imaginary parts of z.

2. for z = 2+3i = Aejθ , find A and θ.

3. for z1 = 1+2i and z2 = 2+3i and z3 = z1.z2 = BejФ , find B

and Ф.

Task


A complex exponential signal is defined as

x(t)=Aej(wt+Ф)

where

A= amplitude

w= frequency in rad/sec

Ф= phase

Complex exponential signals

According to Euler’s formula

Aej(wt+Ф) = Acos(wt+Ф) + jAsin(wt+Ф)


For the complex exponential signal x(t), verify the

Euler’s relation ship by plotting the real and imaginary

parts of x(t), for x(t)= 2ej(4πt)

Task

Plot the real and imaginary parts of the conjugate of x(t)

In MATLAB x(t)=Aej(wt+Ф) is defined as

x=A*exp(i*(wt+Ф))


Sinusoids having same frequency can be added using

their phasors

Phasor representation of x(t)=Acos(2πft + ф), is X=Aejф

Example :

x1(t)=1.7cos(2π10t+70π/180) ------- X1=1.7ej 70 π/180

x2(t)=1.9cos(2π10t+200π/180) ------- X2=1.9ej 200 π/180

To find x3(t)=x1(t)+x2(t) , we first add their phasors

Phasor addition


X3= X1 + X2

X3= 1.7ej 70 π/180 + 1.9ej 200 π/180

Convert them to rectangular form, add them, and then

convert back to polar form (Task)

X3 = 1.532ej 141.79 π/180

x3(t) =1.532cos(2π10t + 141.79π/180)

Phasor addition


Verify the phasor addition graphically, by showing that

1.7cos(2π10t+70π/180) + 1.9cos(2π10t+200π/180)= 1.532cos(2π10t + 141.79π/180)

Task

lab no.08

Documents