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Lecture 341 Source Transformation

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Lecture 342 Equivalent Sources An ideal current source has the voltage necessary to provide its rated current. An ideal voltage source supplies the current necessary to provide its rated voltage. A real voltage source cannot supply arbitrarily large amounts of current. A real current source cannot have an arbitrarily large terminal voltage.

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Lecture 343 A More Realistic Source Model vs(t)vs(t) RsRs + - The Circuit The Source i(t)i(t) + - v(t)v(t)

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Lecture 344 I-V Relationship The I-V relationship for this source model is v(t) = v s (t) - R s i(t) v(t)v(t) i(t)i(t)

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Lecture 345 What are the points where the I-V characteristics intersect the axes?

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Lecture 346 What do these intersection points represent physically?

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Lecture 347 Open Circuit Voltage If the current flowing from a source is zero, then it is connected to an open circuit. The voltage at the source terminals with i(t) equal to zero is called the open circuit voltage: v oc (t)

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Lecture 348 Short Circuit Current If the voltage across the source terminals is zero, then the source is connected to a short circuit. The current that flows when v(t) is zero is called the short circuit current: i sc (t)

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Lecture 349 v oc (t) and i sc (t) v(t)v(t) i(t)i(t) v oc (t) i sc (t)

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Lecture 3410 v oc (t) and i sc (t) Since the open circuit voltage and the short circuit current determine where the I-V line crosses both axes, they completely define the line. Any circuit that has the same I-V characteristics is an equivalent circuit.

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Lecture 3411 Equivalent Current Source is(t)is(t)RsRs The Circuit i(t)i(t) + - v(t)v(t)

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Lecture 3412 Voltage and Current Sources VsVs + - RsRs IsIs RsRs

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Lecture 3413 Source Transformation Equivalent sources can be used to simplify the analysis of some circuits. A voltage source in series with a resistor is transformed into a current source in parallel with a resistor. A current source in parallel with a resistor is transformed into a voltage source in series with a resistor.

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Lecture 3414 Averaging Circuit How can source transformation make analysis of this circuit easier? + - V out 1k V1V1 + - V2V2 + -

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Lecture 3415 Source Transformations + - V out 1k V1V1 + - V2V2 + -

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Lecture 3416 Source Transformations + - V out 1k V 1 /1k 1k V 2 /1k

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Lecture 3417 A Single Node-Pair Circuit!

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