ECE201_Lecture40

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1 ECE201 Linear Circuit Analysis I Lecture 40 Topic: Maximum Power Transfer in Sinusoidal Steady State 1. Review Problem: Effective value for multiple sources at different frequencies. Assumption: ω 1 ≠ ω 2 Then: P ave,R = I 1 2 2 + I 2 2 2 = I 1, eff 2 + I 2, eff 2 I eff = I 1,eff 2 + I 2,eff 2 Key steps in derivation: i R (t) = i 1 + i 2 = I 1 cos ω 1 t + φ 1 ( ) + I 2 cos ω 2 t + φ 2 ( ) i R 2 (t) = I 1 2 cos 2 ω 1 t + φ 1 ( ) + 2I 1 I 2 cos ω 1 t + φ 1 ( ) cos ω 2 t + φ 2 ( ) + I 2 2 cos 2 ω 2 t + φ 2 ( ) = I 1 2 2 + I 2 2 2 + Sum of Sinusoidal Functions 2 I 2 I (t)dt i T 1 P 2 2 2 1 T 0 2 R R ave, + = =

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2 2. Maximum Power Transfer Theorem The average power delivered to the load is maximum when Z load = Z th * , or equivalently. R load = R th and X load = –X th . Furthermore, if ˜ V oc = V oc,rms φ , then P ave,load,max = V oc,rms 2 4R th 3. Maximum Power Transfer for Resistive Load Assuming X load is fixed and R

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• Spring '08
• ALL
• Electrical network, Electrical impedance, Thévenin's theorem, maximum power transfer, Maximum power theorem, xload

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