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Circuit Analysis I

by: Tyree Funk

Circuit Analysis I EGR 214

Tyree Funk
GPA 3.68


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This 3 page Class Notes was uploaded by Tyree Funk on Saturday September 26, 2015. The Class Notes belongs to EGR 214 at Grand Valley State University taught by Staff in Fall. Since its upload, it has received 40 views. For similar materials see /class/214380/egr-214-grand-valley-state-university in Engineering and Tech at Grand Valley State University.

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Date Created: 09/26/15
TMY W01 GRAND VALLEY STATE UNIVERSITY Padnos School of Engineering EGR 214 Note 1 The General Thevenin39s Equivalent Circuit The 39 Power Transfer Theorem LOAD RL FIG 1 Ideal Thevenin s Equivalent Circuit Figure 1 illustrates a loaded ideal Thevenin39s equivalent circuit When loaded the power to the load is Z P VTH R RLV39fH O RTHRL L RmRL2 The power output Po to the load as a function of RL has a unique maximum since Po 0 for RL 0 and RL 00 The maximum power output to the load is found by 3110 v RTH RL 2 2RijHRm RL 3 0 RW RL 2RL Rm RL L Maximum power is delivered to the load when the load RL is made equal to RTH This is the quotmatched loadquot condition a very bad design criterion For this design criterion the efficiency of the system is only 50 very low for today39s energy conscience environment To illustrate the relationship between power output and efficiency both the power output function and the efficiency function are expressed in terms of the variable RTHRL and the power output function is normalized with respect to the maximum power output 11ng V3 P0max 4RiH 4RTH 2 Let FLm550m Pamp PO max v1 Rm RL2 4R TH EGR 214 The General Thevenin39s Equivalent Circuit W01 The load resistance RL can vary from 0 S RL S 00 quotNo loadquot is represented by RL 00 and quotfull loadquot is represented by RL RTH Values of the load resistance less than RTH offer no bene t in operation and the system is then said to be quotoverloadedquot Therefore values of the load resistance RL less than RTH are in a quotnonoperatingquot region The quotnorma quot operating range for the load is RTH S RL S 00 This is numerically an impossible range to plot However the normal operating range can be expressed between 0 and 1 by de ning a new variable R as R RTHRL 4111 R PltRgt L 4R R 1 R m 1 RL Ffficiencv for the Ideal Thevenin39s F 39 Circuit Efficiency of a system is defined as the ratio of power output to power input Power output and power input can never be equal since this system represents a perpetual motion machine Power is always lost somewhere in the system For the Ideal Thevenin39s Equivalent Circuit power is lost in RTH Since this power loss is proportional to the load this power is referred to as the quotvariable lossquot Power input to the system is V V2 13N m Vm m RTH RL RTH RL RLVfH P R R 2 R 11 O L and mterms ofR 11R PIN VTH RTH RL 1 R Rm R 1 Ideal Thevenin39s Equivalent Circuit PR TIR EGR 214 The General Thevenin39s Equivalent Circuit W01 Observe from the plots of power output and ef ciency that the power indeed peaks at full load RL RTH or the quotmatched circuitquot condition and that over the normal operating range there is no peak in ef ciency The ef ciency is 100 at no load a trivial result since this is not practical or obtainable In order to represent a practical system the ef ciency must be zero at zero power output ie at R 0 The General Thevenin s Equivalent Circuit The Ideal Thevenin s Equivalent Circuit can be made realistic by adding just a single resistor across the Thevenin39s voltage source This resistor accounts for a quot xed lossquot without altering the Thevenin39s Equivalent Circuit This implies that all the power output relations are the same as with the Ideal Thevenin39s Equivalent Circuit However the power input is altered to account for the fact that every practical system must in addition to losses proportional to power output have power input when there is no power going out Every system electrical or mechanical behaves this way LOAD RL FIG 2 The General Thevenin39s Equivalent Circuit With RF added the power input in now RLVfH v2 v2 R R 2 R R PIN TH TH and the ef crency 1s 11 2 TH 2 F L RF RTHRL vm vm RmRL RFRmRL n RFRL RFRL R 2RLRm RjH RFRm R H R RF 2RTHRL RFRm RjH In representing the ef ciency RF is not easy to use However if the xed loss is expressed as a percentage of the maximum power output then RF can be represented in a useful form V1211 R 4R 4R Let FL 2F TH or RF m Now th1s 1s 1n a more useful form for expressrng RF vm RF FL 4RTH


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