Answer :
Final answer:
The Total Harmonic Distortion (T.H.D.) for a device can be calculated mathematically, and the output voltage for both boost and buck-boost DC to DC converters can be expressed as a function of the input voltage and the duty cycle.
Explanation:
The Total Harmonic Distortion (T.H.D.) for any device, including a boost and buck-boost DC to DC converter, can be expressed as the square root of the sum of the squares of all harmonic voltages (except the fundamental), divided by the fundamental voltage itself.
Mathematically, it can be written as
THD = sqrt(V2^2 + V3^2 + … + Vn^2) / V1.
Each V represents the RMS voltage at each harmonic frequency, with V1 being the fundamental frequency.
The output voltage of a boost converter is typically greater than the input voltage and can be expressed as Vo = Vi / (1 - D),
where D is the duty cycle (expressed as a fractional number), and Vi is the input voltage.
For a buck-boost converter, the output voltage is inverted and can be either greater or less than the input voltage.
The output voltage can be expressed as Vo = -DVi / (1 - D).
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