Time Domain Analysis
Time Domain analysis:
Fig: Normalized load voltage and load current for L/R =0.1T Fig: Normalized load voltage and load current for L/R = 0.5T
Fig: Normalized load voltage and load current for L/R = 2T Fig: Normalized fundamental and 3rd harmonic components of load current for L/R = 2T
Under steady state the load current waveform in a particular output cycle will repeat in successive cycles and hence only one square wave period has been considered. Let t=0 be the instant when the positive half cycle of the square wave starts and let I0 be the load current at this instant. The negative half cycle of square wave starts at t=0.5T and extends up to T. The circuit equation valid during the positive half cycle of voltage can be written as below:
Similarly the equation for the negative half cycle can be written as
where T (=1/f) is the time period of the square wave.
The instantaneous current ‘i’ during the first half of square wave may be obtained by solving Eqn.(34.2) and putting the initial value of current as I0.
where τ= L/R is the time constant of the R-L load.
The current at the end of the positive half cycle becomes the starting current for the negative half cycle. Thus the next half cycle starts with an initial current is
The circuit equation for the next half cycle may now be written as