(Solved): Consider the three-phase inverter circuit of Fig.1 with R-L load and Y-connected source with R=2.0 ...

Consider the three-phase inverter circuit of Fig.1 with R-L load and Y-connected source with $R=2.0?,L=10\mathrm{mH}$, inverter frequency of $f_0=47.619\mathrm{Hz}$, dc input voltage of $V_{\mathrm{S}}=$ $313.97\mathrm{V},v_{\mathrm{TH},\mathrm{A}}(t)=105.73\sin \left({?}_{0}t?12.36^{?}\right),v_{\mathrm{TH},\mathrm{B}}(t)=105.73\sin \left({?}_{0}t?132.36^{?}\right)$, and $v_{\mathrm{TH},\mathrm{C}}(t)=105.73\sin \left({?}_{0}t?252.36^{?}\right)$. The inverter uses 180 -degree conduction control (see Fig. 6.6 of course textbook pp. 297). Any transistor may be used in place of the MOSFETs; all six must be identical. 1. Theoretical Background (a) (i) Determine $v_{\text{An1 }}$ by means of Fourier analysis of the $v_{\text{An }}$ waveform. (ii) Using the results of 1(a)(i), obtain the ripple component $v_{\text{ripple }}$ waveform in the output voltage. (iii) Obtain $i_{\mathrm{A}1}$ by means of Fourier analysis of the $i_{\mathrm{A}}$ waveform. (iv) Using the results of 1(a)(iii), obtain the ripple component $i_{\text{ripple }}$ waveform in the output voltage.