PRACTICAL MATLAB® FOR ENGINEERS PRACTICAL MATLAB

386 Practical MATLAB® Applications for Engineers

Example 4.3

Let the FS expansion for a periodic sawtooth wave be given by

ft()

 11

1

6

 n nw t^0

n

∑ sin ( )

(same as in Example 4.2)

with period T = 2 s, and fundamental frequency given by w 0 = 2 π/T = π.

Let f(t) represent the voltage drop across a resistor R = 5 Ω. Create the script fi le

Fourier_ applic that returns the following:

1. The fi rst 10 FS coeffi cients


2. Its RMS value


3. The percentage of the total harmonic distortion


4. The average power dissipated by R = 5 Ω


5. The power concentrated in the fi rst 10 harmonics


6. The plot of the percentage of total power (dissipated) versus its harmonic
   frequencies


7. Check the % of total power dissipated in the fi rst 10 harmonics.
   MATLAB Solution
   % Script file: Fourier _ applic
   % Calculations of the Fourier coefficient
   for n = 1:10;
   c(n) = -1/(n*pi);
   p(n) = c(n).^2;
   end
   C = c;
   % RMS calculations

FIGURE 4.37
Plots of part e of Example 4.2.

error1(t) = sawtooth wave-harmonics 1

error3(t) = sawtooth wave-harmonics 1,2,3

error5(t) = sawtooth wave-harmonics 1,2,3,4,5

error2(t) = sawtooth wave-harmonics 1,2

error4(t) = sawtooth wave-harmonics 1,2,3,4

error6(t) = sawtooth wave-harmonics 1,2,3,4,5,6

0.5

0.5

−0.5

−0.5

0

0

0.5

−0.5

0

0.5

−0.5

0

0.5

−0.5

0

0.5

−0.5

0

Amplitude

Amplitude

Amplitude

Amplitude

Amplitude

Amplitude

01 2 3 4

01 23 4

01 23 4

time (in sec) time (in sec)

0123 4

0123 4

0123 4