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# Lab no.08

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### Lab no.08

1. 1. Lab No.08 Complex exponentials and phasors Designed by : Dawar Awan dawar@cecos.edu.pk CECOS College of Engineering and IT March – July 2012
2. 2. Complex numbers  Complex number , z = (3,4) = 3+4i  ‘z’ can be defined in MatLab as , z=3+4i;  Now, try the following commands. real(z) imag(z) abs(z) angle(z) conj(z) CECOS College of Engineering and IT Real part of z imaginary part of z magnitude or modulus of z phase or angle of z conjugate of z March – July 2012
3. 3. Task 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. CECOS College of Engineering and IT March – July 2012
4. 4. Complex exponential signals  A complex exponential signal is defined as x(t)=Aej(wt+Ф)  where A= amplitude w= frequency in rad/sec Ф= phase  According to Euler’s formula Aej(wt+Ф) = Acos(wt+Ф) + jAsin(wt+Ф) CECOS College of Engineering and IT March – July 2012
5. 5. Task  In MATLAB x(t)=Aej(wt+Ф) is defined as x=A*exp(i*(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)  Plot the real and imaginary parts of the conjugate of x(t) CECOS College of Engineering and IT March – July 2012
6. 6. Phasor addition  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 CECOS College of Engineering and IT March – July 2012
7. 7. 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) CECOS College of Engineering and IT March – July 2012
8. 8. Task  Verify the phasor addition graphically, by showing that 1.7cos(2π10t+70π/180) + 1.9cos(2π10t+200π/180) = 1.532cos(2π10t + 141.79π/180) CECOS College of Engineering and IT March – July 2012