ECE201_Lecture40 - load is adjustable, then the condition...

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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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Unformatted text preview: load is adjustable, then the condition of maximum power transfer is R load = R th 2 + X th + X load ( ) 2 +-V ~ oc V ~ load Z th = R th + jX th + Z load = R load + jX load load I ~ 3 4. Example Let f = 500 Hz. Find Z L (j2500) for maximum power transfer. Step 1. Find impedance values for circuit elements. Z R = Z L = Z C = Step 2. Find the Thevenin equivalent circuit seen by the load, i.e., find V oc,eff and Z th . 4 Step 3. Apply maximum power transfer theorem to find Z L . Step 4. Compute P ave,load . Step 5. Find an appropriate circuit for Z L ....
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This note was uploaded on 04/19/2011 for the course ECE 201 taught by Professor All during the Spring '08 term at Purdue University-West Lafayette.

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ECE201_Lecture40 - load is adjustable, then the condition...

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