Ch. 4 – Circuit Theoremstomrebold.com/engr12/CUR/Lecture4-annot.pdf · Ch. 4 – Circuit...
Transcript of Ch. 4 – Circuit Theoremstomrebold.com/engr12/CUR/Lecture4-annot.pdf · Ch. 4 – Circuit...
Linearity- Linear relationship between cause and effect
Linear Circuit- output is linearly related (proportional to) the input.
Ex. = Ri
A. Homogeneity (scaling)
B. Additivity
Ch. 4 – Circuit Theorems
Find the current in resistor R2.
The response of a circuit due to multiple sources can be taken as the sum of the effects of each source acting alone (all others off)
Superposition
Turning Off Sources:a) Vs replace with short circuitb) Is replace with open circuit
Note: Only independent sources can be turned off. Dependent sources should be left on.
Example 1. Apply superposition to find the current in the 3- resistor. Ans: 5/6 A
Example 2. Find the terminal voltage Vab using superposition.Ans: 6 V
Source Transformation
- Should be equivalent for any load attached to a-b.Extreme cases:
For an arbitrary RL:
For Independent Sources:
For Dependent Sources:
Example 3. Find the current in RL=8 using source transformation.
Example 4. Find vx using source transformation.
Find the v-i characteristic of the circuit as seen by RL.a) Remove RL (replace by open terminals a-b)
Given the circuit.
b) Determine (“measure”) the open-circuit voltage vab.
c) Connect a voltage source Vnew equal to vab at b.
Vnew = 16 VVab = 16 VVaa’ = 0 V
d. Reconnect RL.
What is the current through RL?Vaa’ = 0 VIRL = 0 A
e. Use superposition:
IRL = Iorig + IVnew only = 0Iorig = -IVnew only = I(-Vnew)
Current in the original circuit = current produced by Voc = -Vnew
Thevenin’s Theorem
A linear two-terminal circuit can be replaced by an equivalent circuit consisting of a voltage source VTh in series with a resistor RTh, where:
VTh = Voc = open-circuit voltage at the terminalsRTh = equivalent resistance at the terminals with all the independent sources turned off.
Example 5. Find the Thevenin equivalent circuit with respect to terminals a-b. Find the current through RL = 6, 16, and 36 .
Ans: 30V, 4
Thevenin Equiv. Circuit: with dependent sources
VTh = Voc = open-circuit voltage at the terminalsRTh = equivalent resistance at the terminals with all the independent sources turned off.
Finding RTh:a) Turn off all independent sources.b) Apply either:
• A test voltage source Vo Find Io.• A test current source Io Find Vo.
c) RTh = Vo/Io
Note: Easier to use test voltage or test current of value ONE.
Example 6. Find the Thevenin equivalent circuit.
Norton’s Theorem
- A corollary of to Thevenin’s Theorem
RN = RTh, and IN = VTh/Rth
Finding Norton Current:
Norton Equivalent Circuit
A linear two-terminal circuit can be replaced by an equivalent circuit consisting of a current source IN in parallel with a resistor RN, where:
IN = Isc = short-circuit current through the terminalsRN = equivalent resistance at the terminals with all the independent sources turned off.
Example 7. Find the Norton equivalent circuit.Answer: 1A, 4 ohms
Maximum Power Transfer
Find the value of the load resistor that will receive maximum power from the circuit.