EC-1.2 Network Theorems
You can replace any linear network seen from two terminals with a source and one impedance, and say when superposition, reciprocity and maximum power transfer apply and when they do not.
These theorems all say the same useful thing in different words: a linear network is far simpler than it looks from outside. Reducing everything but the part you care about to one source and one impedance turns a page of algebra into a line of it, and it is the move a practising engineer makes automatically. Each theorem has a condition attached, and remembering the condition matters more than remembering the statement, because every one of them fails on a nonlinear element.
Work through these
Superposition: one source at a time, and what killing a source means
A linear network's response to several sources is the sum of its responses to each alone, with voltage sources shorted and current sources opened while the others act. It is the theorem that fails first when any element is nonlinear.
NPTEL: Circuit Theory · CourseThevenin's theorem: the open-circuit voltage and the resistance seen looking back
Everything on one side of two terminals collapses to one source in series with one impedance. Finding the impedance means suppressing the independent sources and looking back into the terminals, which is a different calculation from finding the voltage.
MIT OpenCourseWare 6.002: Circuits and Electronics · CourseNorton's theorem, and converting between the two forms
The same network is equally a current source with an impedance beside it, and the two forms convert by one division. Choosing the form that matches what the rest of the circuit needs saves most of the work.
Networks with dependent sources: find the impedance by exciting the terminals
A dependent source cannot be suppressed, so the resistance seen from the terminals is found by applying a test source and taking the ratio of voltage to current. This is the version examinations reach for.
Maximum power transfer, and why it is a poor design rule for a power supply
The load draws the most power when it matches the source impedance, and at that point half the power is burnt inside the source. That is the right answer in a signal chain and the wrong one where efficiency matters.
NPTEL: Circuit Theory · CourseReciprocity: swap the source and the meter, and read the same number
In a linear network with no dependent sources, exciting one pair of terminals and measuring at another gives the same result as exchanging the two. It is a strong check on an answer you are unsure of.
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