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Lecture 7. Realistic Sources & Source Transformation • Ideal sources vs. realistic sources • Open circuit voltage, Voc • Short circuit current, Isc • I - V relationship • Source transformation 1 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. 2 A More Realistic Source Model i(t) + vs(t) Rs + v(t) - The Circuit A Realistic Source: Modeled by an ideal source in series with a resistor 3 I-V Relationship The I-V relationship for this source model is v(t) = vs(t) - Rs i(t) v(t) i(t) 4 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: voc(t) 5 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: isc(t) 6 voc(t) and isc(t) v(t) voc(t) isc(t) i(t) 7 voc(t) and isc(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. 8 Equivalent Current Source i(t) + is(t) Rs v(t) The Circuit - v s (t ) is (t ) Rs 9 Voltage and Current Sources Rs Vs + Is - Vs Rs I s Rs Vs Is Rs 10 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. 11 Example: Averaging Circuit 1kW V1 + - 1kW + Vout + 1kW - V2 How can source transformation make analysis of this circuit easier? 12 Source Transformations 1kW V1 + - 1kW + Vout + 1kW - V2 - 13 Source Transformations 1kW V1 /1kW + 1kW 1kW V2 /1kW Vout - 14 A Single Node-Pair Circuit! 1 1 Req kW 1 1 1 3 1kW 1kW 1kW I eq V1 V2 1kW 1kW V0 Req I eq 1 V1 V2 3 15 Class Examples • Drill Problems P3-3 and P3-4 16