Circuits Lecture 3: Thevenin and Norton Theorem
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Transcript Circuits Lecture 3: Thevenin and Norton Theorem
Circuits
Lecture 8: Thevenin and
Norton Theorem (1)
李宏毅 Hung-yi Lee
Textbook
• Chapter 2.5
Network
• A two-terminal network is a function represented
by i-v characteristics
• Given a network, computing its i-v characteristics,
and then label it with simpler equivalent network
i
v
Computing i-v characteristics
i
i
v
v
Add a voltage source v
• v is a unknown variable
Find i
• Represented by v
Obtain the relation of
i and v
Add a current source i
• i is a unknown variable
Find v
• Represented by i
Obtain the relation of
i and v
Computing i-v characteristics
i
Voltage
source v
v
Independent
Sources
x1, x2, x3 ……
i is the weighted sum of the voltage (or current) of the
sources.
i av an xn
n
constant
i av b
The relation of i and v
is linear!
Computing i-v characteristics
• The v-i characteristics is linear!
i
i=mv
Case 1: current source
Case 2: voltage source
Case 3: resistor
v
i
v
R
Resistor
with resistance 1/m Ω
m>0, normal resistor
m<0, ?
Negative resistor
Computing i-v characteristics
Case 4: resistor
+voltage source
Rt
i
voc
voc
Rt
voc
v
v voc Rt i
v voc
i
Rt Rt
Computing i-v characteristics
• The v-i characteristics is linear!
Case 1: current source
Case 2: voltage source
Case 3: resistor
Case 4: resistor +voltage source
i
v
Thevenin Theorem
Two
Terminal
Network
Two terminal network consists entirely of
independent source, resistor and controlled
sources.
If controlled sources are present, then the
control variables is within the same network.
Find voc and Rt directly without drawing i-v characteristics?
Thevenin Theorem - voc
Two
Terminal
Network
voc
voc
Keep two terminals open
Thevenin Theorem - Rt
• Textbook P72 - 73
i
i
v
Suppress the independent sources:
Voltage Source
Short
Open
Current Source
(As we have done in Superposition)
v
v
Rt
i
Why?????
Thevenin Theorem - Rt (Example)
Suppress the
independent sources
• Refer to lecture 7
3
3
2
4V
2
Thevenin Theorem - Rt
i
i
v
v
v voc iRt
voc
1
i v
Rt
Rt
Superposition:
Voltage source v
Independent Sources in
network: x1, x2, x3 ……
i av an xn
n
0
v
Rt
i
0
Norton Theorem
Thevenin
Theorem
Two
Terminal
Network
voc
i sc
Rt
Rt
Norton
Theorem
Norton Theorem - isc
Two
Terminal
Network
i sc
i sc
Rt
Let two terminals short
After we find isc,
If we already know voc, Rt=voc/isc
If we already know Rt, voc=iscRt
i sc
Thevenin Parameters
• Voc, Rt and isc are Thevenin parameters
• voc: keep the two terminals open
• Rt: suppress the independent sources
• isc: let the two terminals short
Know any of two can find the last one
Example 2.14
i sc
Rt
Example 2.14
Open circuit
Find voc
Short Circuit
Find isc
Set to Zero
Find Rt
Example 2.14
i sc
3mA
Rt
• Short Circuit
3mA
v x 5v x
vx 0
ix 0
Then “open circuit” or “source set to zero”?
i sc
3mA
Example 2.14
• Source set to zero
i
v x 5v x vt
Rt
10k
vt
Rt
it
Find
equivalent
resistance Rt
vt 4v x
v x 4v x v x
vx
4v x
it ix i
it
2k 40k
2k 10k 10k
vt 4v x
Rt
10k
4v x
it
10k
Example 2.14
10k
i sc
3mA
Rt
10k
voc isc Rt
3mA 10k 30V
Example 2.14
• Check: Open circuit
10k
voc 30V
v x 5v x v
v 4v x
v x 4v x v x
vx
4v x
3mA
2k 40k
2k 10k 10k
30
v 4v x 4 30
4
30
vx
4
Example
• Find the current and voltage on RL
Circuit Analysis
Three-terminal networks?
Obliterate RL
Thevenin Theorem
Example
• Find the current and voltage on RL
𝑅𝐿
i
+
-
Find Thevenin Parameters
Example
• Find the current and voltage on RL
Open circuit
Short Circuit
Set to Zero
Find voc
Find isc
Find Rt
Example
• Find the current and voltage on RL
𝑣𝑜𝑐 = 𝑣𝑎 − 𝑣𝑏
𝑅3
𝑅4
= 𝑉𝑠
− 𝑉𝑠
𝑅1 + 𝑅3
𝑅2 + 𝑅4
So easy!
Open circuit
Find voc
Example
• Find the current and voltage on RL
R1, R2, R3, R4:
𝑖𝑉𝑠
𝑉𝑠
=
𝑅𝑒𝑞
𝑖𝑅1
𝑉𝑠
𝑅2
=
𝑅𝑒𝑞 𝑅1 + 𝑅2
𝑖𝑠𝑐 = 𝑖𝑅1 − 𝑖𝑅3 =
Short Circuit
Find isc
𝑅𝑒𝑞 =
𝑣𝑜𝑐 = 𝑉𝑠
𝑅1 𝑅2
𝑅3 𝑅4
+
𝑅1 + R 2 𝑅3 + R 4
𝑖𝑅3
𝑉𝑠
𝑅4
=
𝑅𝑒𝑞 𝑅3 + 𝑅4
𝑉𝑠
𝑅2
𝑅4
−
𝑅𝑒𝑞 𝑅1 + 𝑅2 𝑅3 + 𝑅4
𝑅3
𝑅4
− 𝑉𝑠
𝑅1 + 𝑅3
𝑅2 + 𝑅4
(last page)
𝑅𝑡 =
𝑣𝑜𝑐
=⋯
𝑖𝑠𝑐
Example
• Find the current and voltage on RL
Simple (but hard to figure out)
𝑅1 𝑅3
𝑅2 𝑅4
𝑅𝑡 =
+
𝑅1 + R 3 𝑅2 + R 4
Set to Zero
Find Rt
𝑅𝑡 =
𝑣𝑜𝑐
?
𝑖𝑠𝑐
Check by yourself
Example
• Find the current and voltage on RL
𝑅𝐿
i
+
𝑅3
𝑅4
− 𝑉𝑠
𝑅1 + 𝑅3
𝑅2 + 𝑅4
𝑅1 𝑅3
𝑅2 𝑅4
𝑅𝑡 =
+
𝑅1 + R 3 𝑅2 + R 4
𝑣𝑜𝑐 = 𝑉𝑠
Homework
• 2.62, 2.64
Homework
Homework
Thank you!
Answer
• 2.62
• Rt=5k, isc=vs/8k, voc=5vs/8
• 2.64
• Rt=-60, isc=is, voc=-60is
Homework
Rt=100k,isc=-20m
Homework
Rt=-1k/60, voc=2
Acknowledgement
• 感謝 徐瑞陽(b02)
• 糾正錯誤的作業答案
• 感謝 林楷恩(b02)
• 糾正錯誤的作業答案