Figure is at sinusoidal steady state.The sources are given as: v1(t) = A1 cos(ω1t) v2(t) = A2 sin(ω2t) (a) Determine the Thevenin’s Equivalent as seen from the terminals of ZL (i.e. b-b’ terminals) in terms of A1, A2, ω1, ω2, R, L, C, N1 and N2. Remainder: ω1 not equal to ω2, and A1 not equal to A2 in general! (b) Assuming that ω1 = ω2 = ω = constant, determine the impedance ZL = RL + jXL in terms of ω, R, L, C, N1 and N2, for maximum average power transfer to ZL. (c) Are RL and XL depend on the frequency of the sources in part (b)? Justify your answer. (d) If ω1 not equal to ω2, can you determine ZL for maximum power transfer? Explain. (e) Let ω1 = ω2 = ω = constant. Assume that ZL is purely resistive (i.e. ZL = RL). Find value of RL for maximum power transfer in this case. (f) Let again ω1 = ω2 = ω = constant, but ZL = jXL, with XL > 0 (i.e. the load impedance is purely inductive). Determine the value of XL for maximum average power transfer to ZL. (g) Now assume that ω1 = ω2 = ω, but you can change ω freely. The value of ZL is fixed as ZL = Ro. At which frequency or frequencies ω maximum power is transferred to Ro? (h) Let R = 50Ω, L = 1mH, C = 10nF, and N1 = 100, N2 = 1000, ω1 = ω2 = ω = 100π rad/s. ZL = RL, where RL is chosen as in part (e). Determine vbb'0(t) and i2(t), if A1 = A2 = 10√2V. (i) How much of the total average power generated by the sources v1(t) and v2(t) is transferred to Ro in part (h)? What is the efficiency η = |PRo| / |Ptotal| × 100?
Figure is at sinusoidal steady state.The sources are given as:
v1(t) = A1 cos(ω1t)
v2(t) = A2 sin(ω2t)
(a) Determine the Thevenin’s Equivalent as seen from the terminals of ZL (i.e. b-b’ terminals) in terms of A1, A2, ω1, ω2, R, L, C, N1 and N2. Remainder: ω1 not equal to ω2, and A1 not equal to A2 in general!
(b) Assuming that ω1 = ω2 = ω = constant, determine the impedance ZL = RL + jXL in terms of ω, R, L, C, N1 and N2, for maximum average power transfer to ZL.
(c) Are RL and XL depend on the frequency of the sources in part (b)? Justify your answer.
(d) If ω1 not equal to ω2, can you determine ZL for maximum power transfer? Explain.
(e) Let ω1 = ω2 = ω = constant. Assume that ZL is purely resistive (i.e. ZL = RL). Find value of RL for maximum power transfer in this case.
(f) Let again ω1 = ω2 = ω = constant, but ZL = jXL, with XL > 0 (i.e. the load impedance is purely inductive). Determine the value of XL for maximum average power transfer to ZL.
(g) Now assume that ω1 = ω2 = ω, but you can change ω freely. The value of ZL is fixed as ZL = Ro. At which frequency or frequencies ω maximum power is transferred to Ro?
(h) Let R = 50Ω, L = 1mH, C = 10nF, and N1 = 100, N2 = 1000, ω1 = ω2 = ω = 100π rad/s. ZL = RL, where RL is chosen as in part (e). Determine vbb'0(t) and i2(t), if A1 = A2 = 10√2V.
(i) How much of the total average power generated by the sources v1(t) and v2(t) is transferred to Ro in part (h)? What is the efficiency η =
|PRo| / |Ptotal| × 100?
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