Question

2. Suppose we want to design a de power supply by filtering the output, Vree(t), of a full-wave rectifier through the following low-pass filter Choke-Input Filter Pulsating DC From Rectifier Filtered DC Output To Load Assume that the trigonometric Fourier series expansion of Vree t) is given by: Vree(t)-Vpsin(2T50t) n(1-4n2) a) From known properties of linear systems, write down an expression for the steady state output of the filter b) What are the amplitudes of the de component and the dominant (largest) ac component of the filter output? c) Assuming RL = 15 Ω, L = 5 mH, choose a value of C such that the amplitude of the dominant ac component of the filter output is (1/25) times the de component of the filter output Hint: First find the transfer function, H(s), of the filter and then find its steady state response due to Vre(t).]

Answer 1

V_rec(t) = 2V_P/pi + sigma^infinity_n = 1 4 V_P/pi(1 - 9n^2) cos(200 n pi t) here d.e part 2V_P/pi will not effected by L & can't pass through d so, we get 2V_P/pi volt d.e output across R_L for a.e terms i.e cos 2w t cos 4w t.. term 1/n w d < < R_L so, A.C component of current through L & d due to time varying part is i = sigma^infinity_n = 1 4 V_P/pi(1 - 4n^2) cos(200n pi t) middot e^plusminus i pi/2 1/w_if - 1/w_n e (a) so, steady state output is V_out = 2V_P/pi + sigma^infinity_n = 1 4 V_P/pi(1 - 4n^2) e^plusminus i pi/2 (-J^dot/w_n e)/w_n L - 1/w_n e cos (200 n pu t) implies V_out = 2V_P/pi + sigma^infinity_n = 1 4V_P/pi(1 - 4n^2) 1/w_n^2 - LC - 1 cos(200n pi t) e^plusminus i pi/2 - pi/2 here w_n = 200n pi(2n) (b) so, amplitude of d.e component is V_d.e = 2V_P/pi dominated a.e component is amplitude is V_a.e = Vertical-bar 4V_P/pi(1 - 4) 1/(400 pi)^2 LC - 1 Vertical-bar (we take mod value)