5 DC Circuit II

5 DC Circuit II - ELEC101 DCcircuits36 2010/11Spring I...

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ELEC 101 DC circuits 36 2010/11 Spring load R L source voltage V S Power Transfer I source resistance R S V S for maximum current flow into load, R L = 0 , I L = V S /R S for maximum voltage across load, R L = , V L = V S I L = V S /R S V L = V S + R S R L = R L = 0 I L + V L V S R S V S V L I L S S R V 0 R L = 0 R L = Vary R L to maximize P L Load line KVL : V s = I L R s + V L (load line) P = V L x I L Question: Given a fixed voltage source with a fixed output impedance, what is the load impedance that will maximize power extraction? Example: voltage source can be the output of a sensor, and load can be the input to an amplifier. This is an impedance matching problem.
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ELEC 101 DC circuits 37 2010/11 Spring Maximum power extraction from a voltage source derivation •V a r y R L to maximize P L Differentiate P L to get max •R e s u l t : 1:1 voltage divider 0 dR dP L load R L source voltage V S source resistance R S I L + V L  2 s R V P 4 Short circuit Open circuit 0 0.05 0.1 0.15 0.2 0.25 0.3 024681 0 1 2 Load resistance Power M aximum power delivered to load when R L = R S
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ELEC 101 DC circuits 38 2010/11 Spring Example •V o l t a g e source of 10V. Output impedance = 100 •W h a t is the power delivered to a load of 10 ? •I load = V/R = 10V / 110 = 91 mA •P load = I 2 R = 83 mW h a t is the power delivered to a load of 50 ? load = 10V / 150 = 66.6 mA load = 222 mW h a t is the power delivered to a load of 100 ? load = 10V / 200 = 50 mA load = 250 mW (This is the maximum) h a t is the power delivered to a load of 1000 ? load = 10V / 1100 = 9.1 mA load = 83 mW load R L source voltage V S source resistance R S I L + V L PRS
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ELEC 101 DC circuits 39 2010/11 Spring Maximum power extracted from a current source Current source has output shunt impedance Differentiate P L wrt R L and set to zero •M a x i m u m power transfer occurs when R s = R L a x i m u m power (1:1 current divider):  2 L s R I P V R s R L I s 4 1
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ELEC 101 DC circuits 40 2010/11 Spring DC circuit analysis •G i v e n values of all circuit elements, all the voltage and current sources, find the currents for each branch and voltages of all nodes • Approaches: use KCL and KVL to generate a set of linear equations. Usually there will be N independent equations for N unknowns. Need to solve simultaneous linear equations •N o d a l analysis–Use KCL at each node to generate the equations, useful for circuits with current sources • Mesh analysis–Use KVL for each loop to generate the equations, useful for circuits with voltage sources •S o m e t i m e s get redundant equations. E.g. N nodes = N equations. But there are only N 1 independent voltages. So one of the N equations is redundant 3k 1k 12V 6k 3k 3V 2k
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ELEC 101 DC circuits 41 2010/11 Spring Nodal Analysis A circuit can be very complicated, and one needs a systematic way to analyze it use nodal analysis .
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5 DC Circuit II - ELEC101 DCcircuits36 2010/11Spring I...

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