Question

1. Consider the triangular voltage wave form applied to an electrical circuit shown below. /a I Derive the Fourier series for the above waveform Write down the amplitude of the fundamental, first harmonic and second harmonic componen ts Calculate the THD value for the above waveform

Answer 1

Given Triangular wave form general fourier series expression for any wave form [f (t) = a_0 + Sigma^Infinity_n = 1 (a_n cos nt + b_n sin n t)] here a_0 is De exponent in given wave form a_n b_n are coefficient of cosine since terms give triangular wave defined by f (t) = [t + v_2 - 1/2 lessthanorequalto t 0 -t + 1/2 0 lessthanorequalto t lessthanorequalto 1/2] total time period is- 1/2 to 1/2 [t . 1] \r\n for value of a_0 [a_0 - 1/ T Integral^1/2_- 1/2 f (t) dt] = 1 /[Integral^0_-2 (t -1/2) dt + Integral^1/2_0 (- t + 1/2) dt = 1 [[t^2/ 2 + t/2]^0_-1/2 + [- t^2/2 + t/2]^1/2_0] [Because integral dt = t^2/ 2 integral k dt k t] on substituting limits we get [a_0 = 1/ 4] for value of a_n a_n = 2/ T Integral^-1 /2_1/2 t (t) dt 2 [Integral^0_-1 /2 (t- 1/2) dt + Integral^1/2 (- t + 1/2) dt]