Resistor Combinations Source Transformation Dr Holbert February 4
Resistor Combinations; Source Transformation Dr. Holbert February 4, 2008 Lect 6 EEE 202 1
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 Lect 6 EEE 202 2
Equivalent Resistance • Req is equivalent to the resistor network on the left in the sense that they have the same i-v characteristics i(t) + + v(t) Req – – • The rest of the circuit cannot tell whether the resistor network or the equivalent resistor is connected to it Lect 6 EEE 202 3
Series Resistance R 1 R 2 Req R 3 Req = R 1 + R 2 + R 3 Lect 6 EEE 202 4
Parallel Resistance R 1 Lect 6 R 2 R 3 EEE 202 Req 5
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 Lect 6 EEE 202 6
A More Realistic Source Model i(t) vs(t) + – Rs + v(t) The Circuit – The Source Lect 6 EEE 202 7
I-V Relationship The I-V relationship for this source model is v(t) = vs(t) – Rs i(t) v(t) i(t) Lect 6 EEE 202 8
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: voc(t) Lect 6 EEE 202 9
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: isc(t) Lect 6 EEE 202 10
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 Lect 6 EEE 202 v(t) voc(t) isc(t) i(t) 11
Equivalent Current Source i(t) + is(t) Rs v(t) The Circuit – Lect 6 EEE 202 12
Source Transformation Rs Vs Lect 6 + – Is EEE 202 Rs 13
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 Lect 6 EEE 202 14
Averaging Circuit 1 k. W + V 1 + – Vout 1 k. W + – V 2 – How can source transformation make analysis of this circuit easier? Lect 6 EEE 202 15
Source Transformations 1 k. W + V 1 + – Vout 1 k. W + – V 2 – Lect 6 EEE 202 16
Source Transformations V 1 /1 k. W + 1 k. W V 2 /1 k. W Vout – Which is a single node-pair circuit that we can use current division on! Lect 6 EEE 202 17
Class Examples • Drill Problems P 3 -1, P 3 -2, P 3 -3 Lect 6 EEE 202 18
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