ECE201_Lecture12

# ECE201_Lecture12 - “dead” = definition of R th ⇒ v =...

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1 ECE201 Linear Circuit Analysis I Lecture 12 Topics: Thevenin’s and Norton’s Theorems 1. Motivation 2. Thévenin’s theorem (1) R th : “Thévenin equivalent resistance,” computed by (i) shorting all voltage sources and open all current sources, and (ii) computing the equivalent resistance seen from terminal (A,B). (**) Note the difference between R eq and R th . v oc : “open-circuit voltage,” computed by (i) disconnecting the load from (A,B), and (ii) calculating the voltage across (A,B). v oc

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2 (2) Proof The concept of equivalence: same v-i relationship at (A,B) without the load. Apply an indep. current source i to terminal (A,B): According to the general linear relationship: v = (sum of responses due to all internal indep. sources) + β i = v’ + v” v’ = voltage at terminal (A,B) when is open circuit = v oc v” = voltage at terminal (A,B) when all internal voltage sources are short circuit and all internal current sources are open circuit β = equivalent resistance of the network seen at terminal (A,B) when all internal sources are

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Unformatted text preview: “dead” = definition of R th ⇒ v = v oc + R th ⋅ i Hence the equivalence at terminal (A,B). 3 3. Norton’s theorem (1) Norton’s theorem = Thévenin’s theorem + source transformation (2) Parameters R th : same as before i sc : according to source transformation i sc = v oc R th sc: “short-circuit” Note that if we shorted AB, then i sc is the current flowing through the AB branch – hence the name “short-circuit” current. Useful relationship: v = v oc + i ⋅ R th i = v R th − i sc i sc R th 4 4. Examples (1) Find Thévenin and Norton equivalent circuits Step 1. Find R th first. Step 2. Find v oc . 5 Step 3. Thevenin equivalent is Step 4. Norton equivalent (using source transformation) 6 (2) Find Thévenin and Norton equivalent circuits for the circuit below. Step 1. Find v oc . Step 2. Find R th . 7 Step 3. Thevenin Equivalent Circuit Step 4. Norton Equivalent Circuit...
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ECE201_Lecture12 - “dead” = definition of R th ⇒ v =...

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