Chapter 2: Properties of Resistive...
Transcript of Chapter 2: Properties of Resistive...
![Page 1: Chapter 2: Properties of Resistive Circuitscc.ee.ntu.edu.tw/~ultrasound/classnotes/ckt1/chapter2WEB.pdfChapter 2: Properties of Resistive Circuits. Chapter 2: Outline *Self-reading:](https://reader030.fdocuments.net/reader030/viewer/2022040212/5e863fb0da64ff7cb064c6bd/html5/thumbnails/1.jpg)
Chapter 2: Properties of Resistive Circuits
![Page 2: Chapter 2: Properties of Resistive Circuitscc.ee.ntu.edu.tw/~ultrasound/classnotes/ckt1/chapter2WEB.pdfChapter 2: Properties of Resistive Circuits. Chapter 2: Outline *Self-reading:](https://reader030.fdocuments.net/reader030/viewer/2022040212/5e863fb0da64ff7cb064c6bd/html5/thumbnails/2.jpg)
Chapter 2: Outline*Self-reading: 2.1 and 2.2.
![Page 3: Chapter 2: Properties of Resistive Circuitscc.ee.ntu.edu.tw/~ultrasound/classnotes/ckt1/chapter2WEB.pdfChapter 2: Properties of Resistive Circuits. Chapter 2: Outline *Self-reading:](https://reader030.fdocuments.net/reader030/viewer/2022040212/5e863fb0da64ff7cb064c6bd/html5/thumbnails/3.jpg)
Circuits with Controlled Sources
![Page 4: Chapter 2: Properties of Resistive Circuitscc.ee.ntu.edu.tw/~ultrasound/classnotes/ckt1/chapter2WEB.pdfChapter 2: Properties of Resistive Circuits. Chapter 2: Outline *Self-reading:](https://reader030.fdocuments.net/reader030/viewer/2022040212/5e863fb0da64ff7cb064c6bd/html5/thumbnails/4.jpg)
Independent vs. Dependent Sources
l Independent sources:the source voltage or current does not depend on any other voltage or current.
l Dependent (or controlled) sources: the source voltage or current depends on other voltage or current.
![Page 5: Chapter 2: Properties of Resistive Circuitscc.ee.ntu.edu.tw/~ultrasound/classnotes/ckt1/chapter2WEB.pdfChapter 2: Properties of Resistive Circuits. Chapter 2: Outline *Self-reading:](https://reader030.fdocuments.net/reader030/viewer/2022040212/5e863fb0da64ff7cb064c6bd/html5/thumbnails/5.jpg)
Types of Controlled Sources
Control variable
Voltage gain
Transconductance
Current gain
Transresistance
![Page 6: Chapter 2: Properties of Resistive Circuitscc.ee.ntu.edu.tw/~ultrasound/classnotes/ckt1/chapter2WEB.pdfChapter 2: Properties of Resistive Circuits. Chapter 2: Outline *Self-reading:](https://reader030.fdocuments.net/reader030/viewer/2022040212/5e863fb0da64ff7cb064c6bd/html5/thumbnails/6.jpg)
Example 2.6: Amplifier with a Field-Effect Transistor
outout iv ⋅= 6
ing vv65
=gm=5 mSFind vout in terms of vin.Note: Consistency of units.(kΩ, V, mA, mS)
gmout vgi ⋅−=
inout vv ⋅−= 25
Inverting amplifier
![Page 7: Chapter 2: Properties of Resistive Circuitscc.ee.ntu.edu.tw/~ultrasound/classnotes/ckt1/chapter2WEB.pdfChapter 2: Properties of Resistive Circuits. Chapter 2: Outline *Self-reading:](https://reader030.fdocuments.net/reader030/viewer/2022040212/5e863fb0da64ff7cb064c6bd/html5/thumbnails/7.jpg)
Example 2.7
(1). KVL: v2=3i1
(2). KCL: i=1.5i1
(3). KVL: i1=vs/9
All variables are zero if vs=0.
![Page 8: Chapter 2: Properties of Resistive Circuitscc.ee.ntu.edu.tw/~ultrasound/classnotes/ckt1/chapter2WEB.pdfChapter 2: Properties of Resistive Circuits. Chapter 2: Outline *Self-reading:](https://reader030.fdocuments.net/reader030/viewer/2022040212/5e863fb0da64ff7cb064c6bd/html5/thumbnails/8.jpg)
Load Networkl Load network: any two-terminal network that contains
no independent sources. If controlled sources are included, the control variables must be within the same network.
l Equivalent resistance theorem: when a load network consists entirely of resistances or resistances and controlled sources, the terminal voltage and current are related by:
constanta is where, eqRieqRv =
![Page 9: Chapter 2: Properties of Resistive Circuitscc.ee.ntu.edu.tw/~ultrasound/classnotes/ckt1/chapter2WEB.pdfChapter 2: Properties of Resistive Circuits. Chapter 2: Outline *Self-reading:](https://reader030.fdocuments.net/reader030/viewer/2022040212/5e863fb0da64ff7cb064c6bd/html5/thumbnails/9.jpg)
Load Network
constanta is where, eqRieqRv =
A combination of i-v curves.
![Page 10: Chapter 2: Properties of Resistive Circuitscc.ee.ntu.edu.tw/~ultrasound/classnotes/ckt1/chapter2WEB.pdfChapter 2: Properties of Resistive Circuits. Chapter 2: Outline *Self-reading:](https://reader030.fdocuments.net/reader030/viewer/2022040212/5e863fb0da64ff7cb064c6bd/html5/thumbnails/10.jpg)
Example 2.8: Equivalent Resistance
KCL
RgR
iv
R
vgR
vgRv
i
meq
mm
−==
−=−=
1
)1
(
Depending on gmReq can be positive, infinite (open circuit),negative (provide energy)
![Page 11: Chapter 2: Properties of Resistive Circuitscc.ee.ntu.edu.tw/~ultrasound/classnotes/ckt1/chapter2WEB.pdfChapter 2: Properties of Resistive Circuits. Chapter 2: Outline *Self-reading:](https://reader030.fdocuments.net/reader030/viewer/2022040212/5e863fb0da64ff7cb064c6bd/html5/thumbnails/11.jpg)
Linearity and Superposition
![Page 12: Chapter 2: Properties of Resistive Circuitscc.ee.ntu.edu.tw/~ultrasound/classnotes/ckt1/chapter2WEB.pdfChapter 2: Properties of Resistive Circuits. Chapter 2: Outline *Self-reading:](https://reader030.fdocuments.net/reader030/viewer/2022040212/5e863fb0da64ff7cb064c6bd/html5/thumbnails/12.jpg)
Linearity and Proportionality
l A circuit is linear if it consists entirely of linear elements (e.g. , controlled sources, linear resistors) and independent sources.
l For a linear function , where x is the input and y is the response, both the proportionality and the superposition properties need to be satisfied.
l Proportionality property:
KyxKfKxf == )()(
![Page 13: Chapter 2: Properties of Resistive Circuitscc.ee.ntu.edu.tw/~ultrasound/classnotes/ckt1/chapter2WEB.pdfChapter 2: Properties of Resistive Circuits. Chapter 2: Outline *Self-reading:](https://reader030.fdocuments.net/reader030/viewer/2022040212/5e863fb0da64ff7cb064c6bd/html5/thumbnails/13.jpg)
Example 2.9: Circuit Analysis Using Proportionality
ables.other vari thefind ,72ˆ Vvs =In example 2.7, we found: i1=vs/9
Set i1=1
v2=3, i2=1/2
i=3/2, vs=9
Ω===
==⇒=
6ˆˆ
88ˆ8ˆ
11
iv
iv
R
iivv
sseq
s
s
Equivalent resistance
![Page 14: Chapter 2: Properties of Resistive Circuitscc.ee.ntu.edu.tw/~ultrasound/classnotes/ckt1/chapter2WEB.pdfChapter 2: Properties of Resistive Circuits. Chapter 2: Outline *Self-reading:](https://reader030.fdocuments.net/reader030/viewer/2022040212/5e863fb0da64ff7cb064c6bd/html5/thumbnails/14.jpg)
Superposition
l For a linear circuit containing two or more independent sources, the value of any branch variable is the algebraic sum of the individual contributions from each source with all other independent sources set to zero.
l Suppressed sources: Zero independent voltage source is short circuit, zero independent current source is open circuit. Controlled sources are not suppressed.
byaybxfaxfbxaxf +=+=+ )()()(
![Page 15: Chapter 2: Properties of Resistive Circuitscc.ee.ntu.edu.tw/~ultrasound/classnotes/ckt1/chapter2WEB.pdfChapter 2: Properties of Resistive Circuits. Chapter 2: Outline *Self-reading:](https://reader030.fdocuments.net/reader030/viewer/2022040212/5e863fb0da64ff7cb064c6bd/html5/thumbnails/15.jpg)
Example 2.10: Superposition
Find i1.
Aiiii
i
i
i
5.0
428
1124
3
5.21230
3121111
31
21
11
−=++=
−=−=
=×=
==
−−−
−
−
−
![Page 16: Chapter 2: Properties of Resistive Circuitscc.ee.ntu.edu.tw/~ultrasound/classnotes/ckt1/chapter2WEB.pdfChapter 2: Properties of Resistive Circuits. Chapter 2: Outline *Self-reading:](https://reader030.fdocuments.net/reader030/viewer/2022040212/5e863fb0da64ff7cb064c6bd/html5/thumbnails/16.jpg)
Example 2.11: Superposition with a Controlled Source
i1-1=0.5
i1-2=0.2
i1=0.5+0.2=0.7A
![Page 17: Chapter 2: Properties of Resistive Circuitscc.ee.ntu.edu.tw/~ultrasound/classnotes/ckt1/chapter2WEB.pdfChapter 2: Properties of Resistive Circuits. Chapter 2: Outline *Self-reading:](https://reader030.fdocuments.net/reader030/viewer/2022040212/5e863fb0da64ff7cb064c6bd/html5/thumbnails/17.jpg)
Linear Circuits:Proportionality and Superposition
∑ ∑= =
⋅+⋅=α β
1 1
)(or i j
sjjsii iKvHiv
bybKayaKbxfbKaxfaKbxbKaxaKf +=+=+ )()()(
Power dissipation (p=vi=Ri2) by a linear resistor is not linear.
22
21
221 )( RiRiiiR +≠+
![Page 18: Chapter 2: Properties of Resistive Circuitscc.ee.ntu.edu.tw/~ultrasound/classnotes/ckt1/chapter2WEB.pdfChapter 2: Properties of Resistive Circuits. Chapter 2: Outline *Self-reading:](https://reader030.fdocuments.net/reader030/viewer/2022040212/5e863fb0da64ff7cb064c6bd/html5/thumbnails/18.jpg)
Thévenin and Norton Networks
![Page 19: Chapter 2: Properties of Resistive Circuitscc.ee.ntu.edu.tw/~ultrasound/classnotes/ckt1/chapter2WEB.pdfChapter 2: Properties of Resistive Circuits. Chapter 2: Outline *Self-reading:](https://reader030.fdocuments.net/reader030/viewer/2022040212/5e863fb0da64ff7cb064c6bd/html5/thumbnails/19.jpg)
Source Networkl A source network is any two-terminal network that consists
entirely of linear elements and at least one independent source. The control variables of all controlled sources (if any) must bewithin the same network.
![Page 20: Chapter 2: Properties of Resistive Circuitscc.ee.ntu.edu.tw/~ultrasound/classnotes/ckt1/chapter2WEB.pdfChapter 2: Properties of Resistive Circuits. Chapter 2: Outline *Self-reading:](https://reader030.fdocuments.net/reader030/viewer/2022040212/5e863fb0da64ff7cb064c6bd/html5/thumbnails/20.jpg)
Thévenin Parameters
l Open-circuit voltage:l Short-circuit current:l Thévenin resistance:
0=≡ ivocv
0=≡ visci
sciocvtR /≡
![Page 21: Chapter 2: Properties of Resistive Circuitscc.ee.ntu.edu.tw/~ultrasound/classnotes/ckt1/chapter2WEB.pdfChapter 2: Properties of Resistive Circuits. Chapter 2: Outline *Self-reading:](https://reader030.fdocuments.net/reader030/viewer/2022040212/5e863fb0da64ff7cb064c6bd/html5/thumbnails/21.jpg)
Thévenin’s and Norton’s Theoreml Thévenin's theorem: Any linear resistive source network
acts at its terminals like an ideal voltage source of value vocin series with a resistor of Rt, i.e., v= voc- Rti.
l Norton's theorem: Any linear resistive source network acts at its terminals like an ideal current source of value isc in parallel with a resistor of Rt, i.e., i= isc- v/Rt.
voc, isc and Rt areThévenin parameters.
![Page 22: Chapter 2: Properties of Resistive Circuitscc.ee.ntu.edu.tw/~ultrasound/classnotes/ckt1/chapter2WEB.pdfChapter 2: Properties of Resistive Circuits. Chapter 2: Outline *Self-reading:](https://reader030.fdocuments.net/reader030/viewer/2022040212/5e863fb0da64ff7cb064c6bd/html5/thumbnails/22.jpg)
Thévenin’s and Norton’s Theoreml Duality between Thévenin and Norton.l Proof of Thévenin’s theorem by superposition:
α voltage sourcesβ current sources
Source Network
∑ ∑= =
⋅+⋅=
=α β
1 1oc
0 (1).
i jsjjsii
OUT
iKvHv
I
(2). All inside sources = 0
Source network à Load network
Reduces to a single resistor
(3). Superposition
i
vvoc
Rtisc
IOUT
iv
![Page 23: Chapter 2: Properties of Resistive Circuitscc.ee.ntu.edu.tw/~ultrasound/classnotes/ckt1/chapter2WEB.pdfChapter 2: Properties of Resistive Circuits. Chapter 2: Outline *Self-reading:](https://reader030.fdocuments.net/reader030/viewer/2022040212/5e863fb0da64ff7cb064c6bd/html5/thumbnails/23.jpg)
Example 2.12: Thévenin Parameters from a v-i Curve
Use PSpice simulations
Find v= voc- Rti at two different RL’s.
![Page 24: Chapter 2: Properties of Resistive Circuitscc.ee.ntu.edu.tw/~ultrasound/classnotes/ckt1/chapter2WEB.pdfChapter 2: Properties of Resistive Circuits. Chapter 2: Outline *Self-reading:](https://reader030.fdocuments.net/reader030/viewer/2022040212/5e863fb0da64ff7cb064c6bd/html5/thumbnails/24.jpg)
Example 2.13: Equivalent Source Network
Find RL such that v=24V or i=8A.
AiVv
R
SC
OC
t
1040
420||5
==
Ω==
RL=6 Ω
or
RL=1 Ω
![Page 25: Chapter 2: Properties of Resistive Circuitscc.ee.ntu.edu.tw/~ultrasound/classnotes/ckt1/chapter2WEB.pdfChapter 2: Properties of Resistive Circuits. Chapter 2: Outline *Self-reading:](https://reader030.fdocuments.net/reader030/viewer/2022040212/5e863fb0da64ff7cb064c6bd/html5/thumbnails/25.jpg)
Thévenin Parameters
l Thévenin resistance: the equivalent resistance of a source network when all independent sources have been suppressed (i.e., turned off).
scitRocv = tRocvsci /=
![Page 26: Chapter 2: Properties of Resistive Circuitscc.ee.ntu.edu.tw/~ultrasound/classnotes/ckt1/chapter2WEB.pdfChapter 2: Properties of Resistive Circuits. Chapter 2: Outline *Self-reading:](https://reader030.fdocuments.net/reader030/viewer/2022040212/5e863fb0da64ff7cb064c6bd/html5/thumbnails/26.jpg)
Example 2.14: Calculating Thévenin Parameters
mAisc 3=
ViRv sctoc 30−=⋅=
KVLKCL
Ω−= kRt 10
![Page 27: Chapter 2: Properties of Resistive Circuitscc.ee.ntu.edu.tw/~ultrasound/classnotes/ckt1/chapter2WEB.pdfChapter 2: Properties of Resistive Circuits. Chapter 2: Outline *Self-reading:](https://reader030.fdocuments.net/reader030/viewer/2022040212/5e863fb0da64ff7cb064c6bd/html5/thumbnails/27.jpg)
Source Conversions
![Page 28: Chapter 2: Properties of Resistive Circuitscc.ee.ntu.edu.tw/~ultrasound/classnotes/ckt1/chapter2WEB.pdfChapter 2: Properties of Resistive Circuits. Chapter 2: Outline *Self-reading:](https://reader030.fdocuments.net/reader030/viewer/2022040212/5e863fb0da64ff7cb064c6bd/html5/thumbnails/28.jpg)
Example 2.15:Circuit Reduction by Source Conversion
KCL18=v2/2+v2/4v2=24V
![Page 29: Chapter 2: Properties of Resistive Circuitscc.ee.ntu.edu.tw/~ultrasound/classnotes/ckt1/chapter2WEB.pdfChapter 2: Properties of Resistive Circuits. Chapter 2: Outline *Self-reading:](https://reader030.fdocuments.net/reader030/viewer/2022040212/5e863fb0da64ff7cb064c6bd/html5/thumbnails/29.jpg)
Example 2.16:Thévenin Network via Source Conversions
![Page 30: Chapter 2: Properties of Resistive Circuitscc.ee.ntu.edu.tw/~ultrasound/classnotes/ckt1/chapter2WEB.pdfChapter 2: Properties of Resistive Circuits. Chapter 2: Outline *Self-reading:](https://reader030.fdocuments.net/reader030/viewer/2022040212/5e863fb0da64ff7cb064c6bd/html5/thumbnails/30.jpg)
Chapter 2: Problem Set
l 23, 29, 35, 36, 40, 46, 55, 57, 61, 67, 71, 77