Lect6EEE 2021 Resistor Combinations; Source Transformation Dr. Holbert February 4, 2008.

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Lect6EEE 2021 Resistor Combinations; Source Transformation Dr. Holbert February 4, 2008

Lect6EEE 2022 Introduction For analysis, series resistors/impedances can be replaced by an equivalent resistor/ impedance Parallel resistors/impedances can be replaced by an equivalent resistor/ impedance Complicated networks of resistors/ impedances can be replaced by a single equivalent resistor/impedance

Lect6EEE 2023 Equivalent Resistance R eq is equivalent to the resistor network on the left in the sense that they have the same i-v characteristics The rest of the circuit cannot tell whether the resistor network or the equivalent resistor is connected to it i(t)i(t) + – v(t)v(t) i(t)i(t) + – v(t)v(t) R eq

Lect6EEE 2024 Series Resistance R1R1 R3R3 R2R2 R eq R eq = R 1 + R 2 + R 3

Lect6EEE 2025 Parallel Resistance R3R3 R2R2 R1R1 R eq

Lect6EEE 2026 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

Lect6EEE 2027 A More Realistic Source Model vs(t)vs(t) RsRs The Circuit The Source i(t)i(t) + – v(t)v(t) +–+–

Lect6EEE 2028 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)

Lect6EEE 2029 Open Circuit Voltage If the current flowing from a source is zero, then the source 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)

Lect6EEE 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) equals zero is called the short circuit current: i sc (t)

Lect6EEE 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 v(t)v(t) i(t)i(t) v oc (t) i sc (t)

Lect6EEE Equivalent Current Source is(t)is(t)RsRs The Circuit i(t)i(t) + – v(t)v(t)

Lect6EEE Source Transformation VsVs RsRs IsIs RsRs +–+–

Lect6EEE 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 of the same value A current source in parallel with a resistor is transformed into a voltage source in series with a resistor of the same value

Lect6EEE Averaging Circuit How can source transformation make analysis of this circuit easier? + – V out 1k  V1V1 V2V2 +–+– +–+–

Lect6EEE Source Transformations + – V out 1k  V1V1 V2V2 +–+– +–+–

Lect6EEE Source Transformations + – V out 1k  V 1 /1k  1k  V 2 /1k  Which is a single node-pair circuit that we can use current division on!

Lect6EEE Class Examples Drill Problems P3-1, P3-2, P3-3