Page 102 - Numerical Analysis Using MATLAB and Excel

Exponential and Polar Forms of Phasors

The polar form is essentially the same as the exponential form but the notation is different, that is,

∠
Ce jθ = C θ (3.82)
where the left side of (3.82) is the exponential form, and the right side is the polar form.

We must remember that the phase angle is always measured with respect to the positive real axis,
θ
and rotates in the counterclockwise direction.
In Examples 3.8 and 3.9 below, we will verify the results with the following MATLAB co-ordi-
nate transformation functions:

[theta,r] = cart2pol(x,y) − transforms from Cartesian to polar co−ordinates.
[x,y] = pol2cart(theta,r) − transforms from polar to Cartesian co−ordinates

Example 3.8
Convert the following phasors to exponential and polar forms:

a. 3 + j4 b. 1 + j2 c. 2 – j d. 4 – j3
–
–
Solution:
a. The real and imaginary components of this phasor are shown in Figure 3.8.

Im
4
5

53.1° Re
3
Figure 3.8. The components of 3 + j4
Then,
– ⁄ ) j53.1°
2
2
∠
3 + j4 = 3 + 4 ⋅ e j (tan 4 3 = 5e = 553.1°
Check with MATLAB:

x=3+j*4; magx=abs(x); thetax=angle(x)*180/pi; disp(magx); disp(thetax)
5

53.1301
or

Numerical Analysis Using MATLAB® and Excel®, Third Edition 3−15
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