ESE 271 / Spring 2013 / Lecture 3
Last time we learned
Resistor and Ohm’s
Ohm s law:
Series connection of resistors:
1
ESE 271 / Spring 2013 / Lecture 3
Last time we learned
Voltage divider:
2
ESE 271 / Spring 2013 / Lecture 3
Last time we learned
Parallel connection of resistors:
3
ESE 271 / Spring 2013 / Lecture 3
Last time we learned
Current divider:
4
ESE 271 / Spring 2013 / Lecture 3
Last time we learned
Serious connection of ideal voltage sources:
Parallel connection of ideal current sources:
5
ESE 271 / Spring 2013 / Lecture 3
Equivalent subcircuits
This is equivalent two‐terminal subcircuit.
Thi
i
i l
i l b i i
Equivalent means it has the same terminal voltage and current.
6
ESE 271 / Spring 2013 / Lecture 3
Thevenin and Norton equivalent subcircuits
Thevenin equivalent
Some
Some Kind of Circuit
(SKC)
Norton equivalent
q
Any circuit can be replaced by its either Thevenin or Norton equivalent.
How can we find VEQ, IEQ and REQ?
7
ESE 271 / Spring 2013 / Lecture 3
Thevenin and Norton equivalent subcircuits
Any circuit can be replaced by its either Thevenin or Norton equivalent.
How can we find VEQ, IEQ and REQ?
Open-circuit voltage:
Short-circuit current:
8
ESE 271 / Spring 2013 / Lecture 3
Example 1
Find Thevenin equivalent
9
ESE 271 / Spring 2013 / Lecture 3
Example 2
Find Thevenin and Norton
equivalents
10
ESE 271 / Spring 2013 / Lecture 3
Another way of looking at Thevenin and Norton equivalents Sources and Resistors
The circuit has the following terminal law:
Let’s plot this equation.
1. Find VOC or ISC;
2. Find REQ by finding equivalent yf
g q
resistance with all independent sources “killed”, i.e. voltage sources replaced with short‐circuits and current sources replaced with open‐circuits.
l d ith
i it
11
ESE 271 / Spring 2013 / Lecture 3
Example
Find V1
12
ESE 271 / Spring 2013 / Lecture 3
Example ‐ cont.
13
ESE 271 / Spring 2013 / Lecture 3
Practical sources
Ideal voltage source
loaded with short-circuit
fixed
Impossible
p
in
real world
Thevenin model of practical source (practical voltage source)
14
ESE 271 / Spring 2013 / Lecture 3
Power delivery and dissipation
Ideal source
Practical source
Power delivered to load:
Power dissipated in source:
Total power generated:
when
when
15
ESE 271 / Spring 2013 / Lecture 3
Maximum Power delivery
useful
useless
16
ESE 271 / Spring 2013 / Lecture 3
Norton model of practical source (practical current source) When loaded with short-circuit:
When loaded with open-circuit:
open circuit:
Ideal source
when
17
ESE 271 / Spring 2013 / Lecture 3
Example
Find power generated by 16V and 3A sources
18
ESE 271 / Spring 2013 / Lecture 3
Example – cont.
Find power generated by 16V and 3A sources
19
ESE 271 / Spring 2013 / Lecture 3
Example – cont.
Find power generated by 16V and 3A sources
Generated negative 16W, i.e. absorbs 16W
Generated p
positive 72W.
Power dissipated in resistors:
20
ESE 271 / Spring 2013 / Lecture 3
Dependent Voltage and Current sources
will be used to model transistor-based circuits
21
ESE 271 / Spring 2013 / Lecture 3
Example 1
Find β to yield V = 8V.
Slightly rearrange circuit
22
ESE 271 / Spring 2013 / Lecture 3
Example 2
Find REQ as seen by current source
assume β = 2
23