Problem # 3
_ The equation for the current passing through a single-phase half-bridge
inverter with RL load is given by:
$\infty$
$i_o = \frac{V_o}{Z} = \frac{V_o}{R + j\omega L} = \sum_{n=1,3,5,\dots}^{\infty} \frac{2V_s}{n\pi \sqrt{R^2 + (n\omega L)^2}}\sin(n\omega t - \theta_n)$
$\theta_n = \tan^{-1}(\frac{n\omega L}{R})$
+\\
$V_s$
$V_s$
$V_s/2$
$V_s/2$
$C_1$
$L$
$R$
$i_o$
$a$
$C_2$
$D_1$
$D_2$
$T_1$
$i_1$
$i_2$
$T_2$
Write a code to calculate the magnitude of the output current, magnitude of the impedance, and
power dissipated in the load due to the current for the fundamental component (n=1) and
harmonics (n > 1). You result should have four properly organized columns to calculate:
(i) n (only odd values as you can see in the summation)
(ii) $Z_n = \sqrt{R^2 + (n\omega L)^2}$
(iii) $i_o(n) = \frac{2V_s}{n\pi \sqrt{R^2 + (n\omega L)^2}}$
(iv) Power dissipated in the load: $P_o = i_o(n)_{rms}^2 \ast R = \frac{\sqrt{2}V_s^2}{n^2 \pi^2 [R^2 + (n\omega L)^2]} \ast R$
Ask user to enter five items as a list:
(i) Number of harmonics, n
(ii) Resistor
(iii) Inductor
(iv) Supply voltage, $V_s$
(v) Cyclic frequency in Hertz (Remember, $\omega = 2\pi f$)
