Q$1.$ For a sinusoidal PWM having a modulation index of $1$ and a frequency ratio of $7,$ calculate and compare the modulation control indices for unipolar and bipolar PWM$.$

$(5$ Marks$).$

Q$2.$ It is required to generate a space vector of amplitude $0\mathrm{.}5$ at an angle of $150$ degree $($anti$-$clockwise$)$ from the a$-$axis. How much time should the inverter system spend in the bounding states to generate this equivalent space vector in a period of $50$ us$?$ What are the bounding states? $(5$ Marks$).$

Q$3.$ It is required to generate a space vector at an angle of $30$ degrees $($anti$-$clockwise$)$ from the a$-$axis such that the vector tip just touches the hexagonal boundary. How much time should the inverter system spend in the bounding states to generate this equivalent space vector in a period of $50$ us$?$ What are the bounding states? $(5$ Marks$).$

Q$4.$ Discuss the sequencing of the inverter states such that the inverter switching frequency is half the space$-$vector carrier frequency. $(5$ Marks$).$

Q$5.$ In space$-$vector PWM$,$ if the time spent in the zero state is split into two halves and appended on either side of the active bounding sector state times, then what is the effect on the harmonics of the modulating signal? What is the shape of the modulating signal? Discuss. $(5$ Marks$).$ Q$6.$ Determine the number of notches and the notch angles of a multiple$-$notch harmonic elimination PWM pattern such that the $5$th$,7$th and $11$th harmonics are eliminated.