22. R-L circuit (a) Sketch a series R, shunt L circuit with an input voltage, v(t) → V(s) and the output being the volta
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- 22 R L Circuit A Sketch A Series R Shunt L Circuit With An Input Voltage V T V S And The Output Being The Volta 1 (13.68 KiB) Viewed 45 times
Please solve from (e) to (m), (a) to (d) have been solvedat https://www.answers.com/homework-help/que ... q100060506.
22. R-L circuit (a) Sketch a series R, shunt L circuit with an input voltage, v(t) → V(s) and the output being the voltage across the inductor, v₁(t) » Vz(s).
(b) (c) (d) From the circuit, find the s-domain V output(s); inpur(s) here denoted H(s) · = V₁ voltage-out-over-voltage-in transfer function, i.e., H(s) Vz(s) V.(s) Sketch the s-domain transfer function H(s) (L.e., the poles and zeros) Find the output voltage across the inductor, for a delta input voltage, denoted V(s). Is it the same expression and same units as the transfer function?
(e) (f) From your sketch of(s), sketch the magnitude of the TWO-SIDED Fourier spectrum of the output voltage, V(0)|. 1. 2. Recall, the Fourier spectrum is a line representing a cut through the s-plane for positive and negative frequencies at o=0. Your labeling should include the values at dc (@=0), and → +∞. Apply (i) the initial value theorem and (ii) the final value theorem to (s), to find the limiting values of the time function, which we can denote v (t) V (s).
60 (h) (i) (j) Calculate (t) from your (s). VI Find the limiting values: v(t+0¹), v(t→∞); directly from your time domain expression. Calculate the output voltage for a unit step input voltage, using the s-domain system concept, i.e., Voutput(S) = H(S) Vinput(S); i.e., for this question, V" (s) = H(s) V"(s). (i) Sketch V (s) on the s-plane; and from this, (ii) sketch the magnitude of the ONE-SIDED Fourier spectrum, V(0)|, labeling its dc value and its value for (1)→∞⁰.
(k) (1) (m) Use (i) the initial value theorem and (ii) the final value theorem to calculate the limit values of v"(t). Calculate (t) from your V)(s), for t> 0 (but remember to put in the u(t) VL anyway!) and sketch it. Use your v"(t) to find its limit values (ie., at t=0*, ∞). Check your result by applying the time-domain conversion from your v(t), to v(t). Show all your working.