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ELEC130 Electrical Engineering 1
Week 3Module 2 DC Circuit Tools
5 March, 1999 Lecture 3 2
Administration Items Tutorials - Will be held in ES 210 this week.
Answers tutorial 1 will be revised Introduction to Electronic Workbench - Revised document Faculty PC’s Rm. ES210 - Go to Diomedes
Login: cstudentnumber Password: access keys on students card + daymonth (ddmm) of birth
Use Drive u: to save your work
Laboratory - THIS WEEK in EE 103(a)
Allocation of Laboratory and Tutorial Times NO more changes after Friday 12 March 1999 4 pm If you cannot make your time, please ask for alternative
Quiz 1 - THIS WEEK
5 March, 1999 Lecture 3 3
Survey Results
Subject Home Page: - through Dept. Pages http://www.ee.newcastle.edu.au/
Then to Undergraduate studies Then to Course Information/Syllabus Then to Subject Web Pages
From the web site you have the option to save the file in power point
You are expected to read the specified text references to build the background information to the topic areas we are covering. You should think of the lecture as an opportunity to reflect on your reading and clarify difficult concepts.
5 March, 1999 Lecture 3 4
Survey Results (cont.)
Current Sources DC power supply, transistors
Conductance - Parallel Resistance's
Voltage and Current Division
Why - Delta - tutorial 1 Question 19 part 4 Floyd pg. 309 Example 8-19 pg. 312
Superposition
5 March, 1999 Lecture 3 5
Conductance
Sometimes easier to use inverse of resistance called conductance G = R-1
Symbol: G Units:Siemens S (mhos)
NB: Useful when resistors are connected in parallelGeq = G1 + G2 +... +Gn
1/Req = 1/R1 + 1/R2 +... +1/Rn
Case of two parallel resistance's: Req = R1R2 /(R1 + R2)
Vs R1
I1
+
-R2
I2
5 March, 1999 Lecture 3 6
Week 2 Summary cont.
Voltage Division Current Division
vR
R RVs1
1
1 2
iR
R RIs1
2
1 2
R2R1
I1 I2
Is
+
-
I R1
R2
V1
+
_
V2
+
_
Vs
5 March, 1999 Lecture 3 7
Survey (cont.)
Current Sources DC power supply, transistors
Conductance - Parallel Resistance's
Voltage and Current Division
Why - Delta - tutorial 1 Question 19 part 4 Floyd pg. 309 Example 8-19 pg. 312
Superposition
5 March, 1999 Lecture 3 8
Wye Delta Transformations
Need to find equivalent resistance to determine current. HOW?(They are not in series, not in parallel)
Use Y to transformation
5 March, 1999 Lecture 3 9
Survey
Current Sources DC power supply, transistors
Conductance - Parallel Resistance's
Voltage and Current Division
Why - Delta - tutorial 1 Question 19 part 4 Floyd pg. 309 Example 8-19 pg. 312
Superposition
5 March, 1999 Lecture 3 10
Week 2 Summary (cont.)
Superposition:
If a linear circuit is excited by more that one independent source, then the total response is simply the sum of the responses of the individual sources.
Voltage sources - short circuit
Current source - open circuit
5 March, 1999 Lecture 3 11
Power Calculations
Power is not linear! Superposition will not work
directly! With 2 A source opened P’1 = 25
W With 10 V Source shorted P’’1 = 1
W Total P = P’ + P’’ = 26 W
(incorrect)
Must calculate current by superposition and then work out power I’ = 5 A & I’’ = -1 A Total I = I’ + I’’ = 4 A Power P = 42 R = 16 W
5 March, 1999 Lecture 3 12
Example Week 3
Find I ?
Determine VBC ?
What power is delivered by 4V source ?
I
VBC
C
5 March, 1999 Lecture 3 13
Week 3
How does the current in the load change if RL is (say) doubled?
5 March, 1999 Lecture 3 14
Thevenin’s Theorem
Any linear network with a pair of terminals can be replaced by a circuit comprised of a voltage source in series with a resistor.
The observed voltages and currents in the load will be the same using the “Thevenin equivalent” circuit as would be seen using the original circuit.
5 March, 1999 Lecture 3 15
Thevenin’s Components
VTh Thevenin Voltage
‘open circuit’ voltage
VTh is the voltage which would appear across the terminals of the original and equivalent circuit if those terminals are open circuited.
RTh Thevenin Resistance
Independent sources inactivated
RTh is the total resistance seen when looking into the original circuit with sources inactivated
Can also be obtained by observing the short circuit current. RTh = VTh / Isc.
5 March, 1999 Lecture 3 16
Steps to finding the Thevenin Equivalent
Step 1 Determine the two points from which the Thevenin is to be found. NB:Polarity
–
Step 2 Find open circuit voltage across these two points by removing the Load (resistance)
VTh = Vo/c
Step 3 Find RTh by looking from the two points into the circuit after replacing all independent
sources
Step 4 Draw the Thevenin Equivalent– Voltage source in series with a resistor
5 March, 1999 Lecture 3 17
Example Week 3
Find I ?
Determine VBC ?
What power is delivered by 4V source ?
What is the Thevenin Equivalent circuit between A & B ?
I
VBC
C
5 March, 1999 Lecture 3 18
Norton’s Theorem
Any linear network with a pair of terminals can be replaced by a circuit comprised of a current source in parallel with a resistor.
The observed voltages and currents in the load will be the same using the “Norton equivalent” circuit as would be seen using the original circuit.
5 March, 1999 Lecture 3 19
Norton’s Components
IN Norton Current
‘short circuit’ current
IN is the current which would appear through the terminals of the original and equivalent circuit if those terminals are short circuited.
RN Norton Resistance
independent sources inactivated
RN is the total resistance seen when looking into the original circuit with sources inactivated
Can also be obtained by observing the open circuit voltage. RN = Voc / IN .
5 March, 1999 Lecture 3 20
Steps to finding the Norton Equivalent
Step 1 Determine the two points from which the Norton is to be found. NB:Polarity
–
Step 2 Find the short circuit current through these two points by putting a short across them IN = Is/c
Step 3 Find RN by looking from the two points into the circuit after replacing all independent sources
Step 4 Draw the Norton Equivalent– Current source in parallel with a resistor
5 March, 1999 Lecture 3 21
Example Week 3 Find I ?
Determine VBC ?
What power is delivered by 4V source ?
What is the Thevenin Equivalent circuit between A & B ?
What is the Norton Equivalent circuit between A & B ?
I
VBC
C
5 March, 1999 Lecture 3 22
Relationship between Thevenin & Norton
A particular circuit can be represented by Thevenin or Norton equivalent. Therefore Thevenin and Norton equivalent circuits must be the same.
Hence Req = Rth = RN
RTh = VTh / Isc = VTh / IN VTh = RN IN
RN = Voc / IN = VTh / IN IN = VTh / RTh