![]() ![]() Other three do not present an example in which dependent sources are Three of these present an exampleĬircuit containing a dependent source which is never deactivated. Specifically refer to the sources as being independent in stating (unaltered) during the superposition process. Source is present, it is never deactivated and must remain active Fourteen explicitly state that if a dependent ![]() The author has investigated the presentation of superposition inĬircuits texts by surveying twenty introductory books on circuitĪnalysis. Superposition of dependent sources isn't prohibited: Superposition of Dependent Sources is Valid in Circuit Analysis. So my question is: What is going on? Why is it "prohibited" to treat dependent sources this way when the results are the same? $$Vx = -3.2(6 + 4 - Vx / 8) + 9.6 + 6.4$$Īnd this is the simulation I made on Multisim: Using the above equation to eliminate Ix from Vx: I can find Ix by Kirchhoff's Current Law, the currents in the top node of the circuit are: Using the same procedure as above, by current divider I find Vx3:įinally, the total voltage Vx is the sum of each individual voltage Vx (Vx1, Vx2, Vx3): Using the current divider formula and multiplying by 8 I get Vx2įinally, I turn off all sources but the 4A current source: Now I shut down all sources (including the dependent voltage source like if it were an independent source) and leave the 6A source on: However, if I treat the dependent current source as an independent current source, I get the same results, Here's the procedure I followed: Normally I would leave the dependent source on, turn off the 4A current source and find Vx1, then I would turn off the 6A current source and find Vx2, add them up and find Vx. Simulate this circuit – Schematic created using CircuitLab "Find Vx using the superposition principle" Take the following problem from Alexander/Sadiku's Book as an example, which states: Ive simulated this, compared to the end-of-chapter problem solutions and it all turns out the same. However recently I've noticed that I can get the same results if I treat the dependent source as a regular independent source. "Dependent sources should never turn off when using the superposition principle analysis, they should be left intact since they are controlled by variables somewhere in the circuit". However, regarding dependent sources, every electric circuits book I've read says the same thing: Since I began studying, I was taught that when analysing a circuit using multiple sources, independent sources could be turned off, meaning that I could transform a voltage source into a short, and a current source into an open circuit and analyze the circuit by how each individual source acts on it. ![]()
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