회로이론
Millimeter-wave Integrated Systems Lab. (MISL)
Ch. 2
Resistive Circuits
Dept. Electrical and Electronics Engineering
1
Prof. Yang, Jong-Ryul
Prof. Yang, Jong-Ryul
Lecture’s Goals: Ohm’s Law
§ Use Ohm’s Law to Calculate the Voltages and Currents in Electric Circuits
§ Understand the Physical Meaning of Ohm’s Law
§ The Resistor : The Simplest Passive Element
Electrical Circuit
1
Prof. Yang, Jong-Ryul
2
Ohm’s Law
§ Ohm’s Law: Voltage-Current Relationship for Resistance> 고유특성
ü It is named by the German physicist Geog Simon Ohm.
ü Definition: The voltage across a resistance [Ω, ohm] is directly proportional to
the current flowing through it.
! " =$% " ,
'ℎ)*) $ ≥ 0
ü Resistor: A circuit element whose electrical characteristic is primarily resistive is
called a resistor.
Electrical Circuit
1Ω = 1 //1
Prof. Yang, Jong-Ryul
3
Various Resistors
§ There are a lot kinds of Resistors for Power-handling Capabilities,
Precision Values, Operating Frequencies, and so on.
가변저항,
δ
Electrical Circuit
Prof. Yang, Jong-Ryul
4
Assumption in Resistors
§ Assumption: Resistors are linear and are thus described by a straightline characteristic that passes through the origin.
à But it exhibit a nonlinear resistance! à Operating Conditions is presented!
O
U LR
=
ㆁ
Electrical Circuit
_
↑
큰 전류 o 아
큰 저항의 걸릴 때
,
Prof. Yang, Jong-Ryul
5
“Power” supplied to the terminals
K- 2단위주로사용
(단위 잘 읽기
.
M 106
§ Resistor: Power-consumed Device!
=
hM
:903
ü The energy absorbed is dissipated by the resistor in the form ofσ
heat when the
thoisethernal
current passes through the resistor.
1열 잡음 ]
.
ü The rate of energy dissipation (the instantaneous power)
! " = $ " %(")
: nonlinear function of either current or voltage
: always a positive quantity
Electrical Circuit
$! "
! " =(% " =
(
!
P II
=
'
Prof. Yang, Jong-Ryul
6
Conductance (G)
§ Definition: the reciprocal of Resistance [S, siemens]
2=
1
$
% " = 2 !(")
ü Another expression of Ohm’s law
Electrical Circuit
1 3 = 1 1//
%! "
6 " =
= 2 ! ! (")
2
Prof. Yang, Jong-Ryul
7
Two special values of Resistance
§ Short-Circuit
§ Open-Circuit (개방회)
$ = 0, 2 = ∞
$ = ∞, 2 = 0
sriitch
suitch
off
ON
.
ㆀ
! " =$% " =0
The current can exist.
Electrical Circuit
% " =
! "
=0
$
The voltage can exist.
Prof. Yang, Jong-Ryul
8
Example 2.1
§ Determine I and P.
/ 12
8= =
= 6 <1
$ 2:
= = /8 = 12 × 6×10"# = 0.072 A = 72 <A
Electrical Circuit
Prof. Yang, Jong-Ryul
9
Example 2.2
§ Determine V and I.
/$!
= = → /$! = = C $ = 3.6×10
$
→ /$ = 6 /
"#
3.6×10
8!$ = = → 8! =
10:
→ 8 = 0.6 <1
Electrical Circuit
Prof. Yang, Jong-Ryul
10
Example 2.3
§ Find VS and PR.
8 0.5×10"#
/$ = =
= 10 /
"%
2 50×10
^
정천압원
-
Electrical Circuit
8!
0.5×10"# !
== =
= 5 <A
2
50×10"%
Prof. Yang, Jong-Ryul
11
Example 2.4
§ Find VS and R.
=
80×10"#
$= !=
= 5:Ω
8
4×10"# !
^
정전류원
,
Electrical Circuit
/$ = 8$ = 4×5 = 20 /
Prof. Yang, Jong-Ryul
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Advanced Example
§ Find P when the charge q(t) is applied at A to the resistance of HI.
J " = 10 cos(") [<O]
A
&'
B
Electrical Circuit
QJ(")
% " =
= −10 sin "
Q"
<1
! " = $% " = −20 sin "
</
= = $% ! " = 200 sin! (") UA = 0.2 sin! " [<A]
Prof. Yang, Jong-Ryul
13
Summary: Ohm’s Law
§ The Ohm’s Law
! " =$% " ,
< 10
전압천류 S
)
:
A
0
'ℎ)*) $ ≥ 0
J) 이 구간 제외하고는 따져보야됨
,
§ Linear Approximation, but let’s consider nonlinear characteristics in Resistor
§ Resistance ↔ Conductance
§ Physical Meaning of Resistance and Ohm’s Law
L 성얼마나전류의흐름을방해하는지 "전압과전류의
Electrical Circuit
비
Break Point
Prof. Yang, Jong-Ryul
Lecture’s Goals: Kirchhoff’s Law
§ Apply Kirchhoff’s current and voltage laws (KCL, KVL) to determine the
voltages and currents in an electric circuit.
§ Understand the Physical Meaning of Kirchhoff’s Law
§ Resistors are only considered in this chapter.
ü However, the calculation methodology is valid in the calculation using other
passive components.
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Prof. Yang, Jong-Ryul
Terminologies
§ NODE: A point where two, or more, elements are joined
ü A node connects several components, but it does not hold any
charge.
ü The total current flowing into the node must equal the total
out of the node.
ü Wires are all the perfect conductors (0 I).
§ LOOP: A closed path that never goes twice over a node
§ BRANCH: Component connected between two nodes
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Prof. Yang, Jong-Ryul
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Kirchhoff Current Law (KCL)
§ The algebraic sum of the currents entering any node is zero.
%
) %" (") = 0
"#$
%! " − %& " + %' " − %( " = 0
%! " + %' " = %& " + %( "
!!
!
" !!
4%2)33A!&%(*"+,!-%%,!&"%.%!"#A
,1%A0),/.*A!& %&"%&'A%!A-.&,/A
(*"+,!-%")&%"( %&'A%!"#A
“Conservation of Energy”
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Prof. Yang, Jong-Ryul
17
Example 2.6
§ Determine I4.
Node 4:
%( " = 20 <1 + 30 <1
Node 3:
%) " + 40 <1 = 60 <1 + %( "
%) " = 70 <1
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Prof. Yang, Jong-Ryul
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Example 2.7
§ Determine the relationship of the currents.
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Node 1:
%$ " + %! " = %' (")
Node 2:
%) " = %! " + 50%! " = 51%! (")
Node 3:
%$ " = %& " + 50%! (")
Node 4:
%' " = %) " + %& (")
Prof. Yang, Jong-Ryul
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Kirchhoff’s Voltage Law (KVL)
§ The algebraic sum of the voltages around any loop is zero.
ü A Conservation of Energy Principle
%
) $" (") = 0
"#$
−/* + /+$ + /+! + /+) = 0
/* = /+$ + /+! + /+)
/+$ − 5 + /+! − 15 + /+) − 30 = 0
/+$ + /+! + /+) = 50
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Prof. Yang, Jong-Ryul
20
Example 2.11
§ Find Vae and Vec.
1
2
Loop 1: *!" + 10 − 24 = 0
Loop 2: 4 + 6 − *"# = 0
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Prof. Yang, Jong-Ryul
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Single-Loop Circuits
§ Voltage Division
KVL: 7 8 = 7$! + 7$"
Ohm% s Law: 7$! 8 = ?& @ A(8)
7$" 8 = ?' @ A(8)
A 8 =
7$! 8 =
?&
@7 8 ,
?& + ?'
−7 8 +
Electrical Circuit
7 8
?& + ?'
7$" 8 =
?'
@ 7(8)
?& + ?'
?&
?'
@7 8 +
@7 8 =0
?& + ?'
?& + ?'
Prof. Yang, Jong-Ryul
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Example 2.14
§ Determine Pload and Pline.
*()!* =
183.5
× 400K = 367 K*
183.5 + 16.5
M+, = 400K* × 2KN = 800 OP
≡
M()!* = Q ' ?()!* = 2KN ' @ 183.5 = 734 OP
M(-." = M+, − M()!* = 800 − 734 = 66 OP = Q ' ?(-."
Electrical Circuit
Prof. Yang, Jong-Ryul
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Single-Loop Circuits
§ Multiple-Source/Resistor Networks
7$! + 7' 8 − 7/ 8 + 7$" + 70 8 + 71 8 − 7& 8 = 0
?& + ?' A 8 = 7& 8 − 7' 8 + 7/ 8 − 70 8 − 71 8
= 7(8)
→ 7 8 = 7& 8 + 7/ 8 − 7' 8 + 70 8 + 71 8
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Prof. Yang, Jong-Ryul
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Single-Loop Circuits
§ Multiple-Source/Resistor Networks (cont’d)
7 8 = 7$! + 7$" + ⋯ + 7$# = ?& A 8 + ?' A 8 + ⋯ + ?, A(8)
→ 7 8 = ?2 A 8 ,
?2 = ?& + ?' + ⋯ + ?,
A 8 =
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7 8
?2
Prof. Yang, Jong-Ryul
Example 2.16
§ Find VS and Pline.
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Prof. Yang, Jong-Ryul
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Single-Node-Pair Circuits
§ Current Division
A 8 = A& 8 + A' 8
A& 8 =
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A 8 =
7 8
7 8
1
1
7 8
+
=
+
7 8 =
?&
?'
?& ?'
?3
7 8
?'
=
A 8
?&
?& + ?'
A' 8 =
7 8
?&
=
A 8
?'
?& + ?'
?3 =
?& ?'
?& + ?'
Prof. Yang, Jong-Ryul
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Example 2.17
§ Find I1, I2, and Vo.
*) = 80K @ Q' = 24*
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Single-Node-Pair Circuits
§ Multiple-Source/Resistor Networks
≡
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Prof. Yang, Jong-Ryul
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Single-Node-Pair Circuits
§ Multiple-Source/Resistor Networks (cont’d)
≡
Current Division:
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Example 2.19
§ Find IL.
1
1
1
1
=
+
+
→ ?4 = 4 KΩ
?4 18K 9K 12K
Q5 = −
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4K
4K + 12K
1×106/ = −0.25 VN
Prof. Yang, Jong-Ryul
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Summary: Kirchhoff’s Laws
§ Kirchhoff’s Current & Voltage Laws
%
) %" (") = 0
%
@ NODE
"#$
) $" (") = 0
@ LOOP
"#$
§ Voltage Division
§ Current Division
§ Physical Meaning of KCL & KVL
Electrical Circuit
Break Point
Prof. Yang, Jong-Ryul
Lecture’s Goals: Series & Parallel Resistors Comb.
§ Determine the equivalent resistance of a resistor network where the
resistors are in series and parallel.
§ Calculate the voltages and currents in a simple electric circuit using
voltage and current division.
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Prof. Yang, Jong-Ryul
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Series and Parallel Resistor Combinations
§ The equivalent resistance of N resistors in series
"! = "" + "# + ⋯ + "$
§ The equivalent resistance of N resistors in parallel
1
1
1
1
=
+
+ ⋯+
"% "" "#
"$
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Prof. Yang, Jong-Ryul
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Example 2.20
§ Determine the resistance at terminals A-B.
≡
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Prof. Yang, Jong-Ryul
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Resistor Specifications
Typical tolerances:
1%, 5%, 10%
Typical power ratings:
¼ W, ½ W, 1 W, 2 W
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Prof. Yang, Jong-Ryul
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Example 2.23
a) Find R
/W + 5 = 24 → /W = 19 /
5
19
8=
= 1.282 <1 → $ =
= 14.82 :Ω
3.9:
1.282<
b) ±10% ∶ 14.82×0.9 = 13.34 KΩ,
14.82×1.1 = 16.3 KΩ
⟹ 15 :Ω
c) /#.[\]
24
8=
= 1.27 <1 → / = 1.27< × 3.9: = 4.95 /
3.9: + 15:
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Prof. Yang, Jong-Ryul
37
Example 2.23
d) % error in V1
4.952 − 5
= −0.96%
5
e) =W = 8 ! $ = 1.27 mA ! 15k = 24.2 mW
¼ W resistor can be used in this application.
Electrical Circuit
Prof. Yang, Jong-Ryul
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Example 2.24
§ Find all the I and V.
Q& 9K + 3K = 12 → Q& = 1VN
*! = Q& 3K = 3*
Q' = Q/ = 0.5Q& = 0.5VN
*! − *7 = 3K Q/ → *7 = 1.5 *
= 4KQ0 → Q0 =
1.5 3
= VN
4K 8
Q/ = Q0 + Q1 → Q1 =
*# = Q1 3K =
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1
VN
8
3
*
8
Prof. Yang, Jong-Ryul
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Example 2.25
§ Find Vo when I4=0.5 mA.
1& = 0.5 34 → 1) = 1 34 → 1! = 1) + 1&
= 1.5 34
/, = 27 ×1.53 = 3 /,
1' =
/- = 37 ×13 = 3/
3/ + 3/
= 1.5 34 → 1$ = 1! + 1' = 3 34
37 + 17
−/. + 67 1$ + /, + /- + 47 ×1$ = 0
Loop 2: 4 + 6 − V89 = 0
/. = 18 + 3 + 3 + 12 = 36 /
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Prof. Yang, Jong-Ryul
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Example 2.26
§ Find VS and VAD.
*) = Q: ×2 → Q: = 2 N → Q; = −3 + 2 = −1 N
Q/ = 3 N,
*<= = 12 * → Q> =
12
=4N
3
Q0 + Q> + Q: = 0 → Q0 = −6 N
*<? = *<= + *=? = 12 + 6 = 18 *
Q1 =
18
= −3 N → Q' + Q1 = Q> + Q; → Q' = 6 N
6
*@< = 12 *,
Q& = Q' + Q/ = 9 N
−*A + *@< + *<? = 0 → *A = 12 + 18 = 30 *
*@< = *@B + *B< = 12 → *@B = 12 + 8 = 20 *
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Prof. Yang, Jong-Ryul
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Summary: Series & Parallel Resistor Comb.
§ Resistance Combinations
"! = "" + "# + ⋯ + "$
1
1
1
1
=
+
+ ⋯+
"% "" "#
"$
§ Analysis Direction
1) From Load to Source
2) Simple node or loop, first
§ Matrix calculation can help the analysis à Engineering Math or Numerical Analysis!
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Break Point
Prof. Yang, Jong-Ryul
Lecture’s Goals: ∆-Y Transformations
§ Transform the basic Y (wye) resistor network to a ∆ (delta) resistor
network, and visa versa.
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Prof. Yang, Jong-Ryul
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∆-Y Resistance Network
A
ü If there is no current in R3, what can it simplify?
IR3 is dominant in the network characteristics.
C
B
From a to c,
Electrical Circuit
(,/ = ($ ∥ (! + ()
(,/ = (, + (/
Prof. Yang, Jong-Ryul
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∆-Y Resistance Network (cont’d)
(,- = (, + (- = (! ∥ ($ + () =
=
($ (! + (! ()
∑ (0
(-/ = (- + (/ = () ∥ ($ + (! =
=
(! () + () ($
∑ (0
(,/ = (, + (/ = ($ ∥ (! + () =
=
Electrical Circuit
($ (! + () ($
∑ (0
(! ($ + ()
($ + (! + ()
() ($ + (!
($ + (! + ()
($ (! + ()
($ + (! + ()
Prof. Yang, Jong-Ryul
45
∆-Y Resistance Network (cont’d)
(, =
(- =
($ (!
,
($ + (! + ()
(! ()
,
($ + (! + ()
(/ =
() ($
($ + (! + ()
(, (- + (- (/ + (/ (,
($ =
(Q^ ?! = ?7 = ?# → ?& = ?' = ?/
?C =
Electrical Circuit
1
? (? = 3?C )
3 ∆ ∆
(! =
(, (- + (- (/ + (/ (,
(/
(! =
(, (- + (- (/ + (/ (,
(,
Prof. Yang, Jong-Ryul
46
Example 2.27
∆ `a8bcdK
18 k
12 k
6k
(, =
($ (!
= 127 ×187/367 = 67
($ + (! + ()
(! ()
1
(- =
= 187×67
= 37,
($ + (! + ()
367
Electrical Circuit
12
QA =
= 1.2 VN
6K + 4K
(/ =
() ($
1
= 67 ×127
= 27
($ + (! + ()
367
Prof. Yang, Jong-Ryul
47
Example 2.28 Wheatstone Bridge
ü Equivalent Potential between nodes in the
galvanometer (Balanced Condition)
$e $!
$!
=
→ $f =
$#
$# $f
$e
The strain gauge has a resistance of 120 Ω under
no-load conditions and change value under load
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Prof. Yang, Jong-Ryul
48
Example 2.28 Wheatstone Bridge (cont’d)
@ `a bacQ
$e $!
100 110
=
→
=
→ $# = 109.0909 Ω
$# $f
$#
120
@ d`Q)* bacQ
$e $!
100
110
=
→
=
→ $# = 109.3091 Ω
$# $f
$#
120.24
Δ$# = 109.3091 − 109.0909 = 0.2182 Ω
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Prof. Yang, Jong-Ryul
Resistor Technologies for Manufacturing
§ SMT Resistors
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Prof. Yang, Jong-Ryul
50
Resistor Technologies for Manufacturing (cont’d)
§ Thick-film Resistors vs. Thin-film Resistors
TaN or NiCr
RuO2
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Prof. Yang, Jong-Ryul
Resistor Technologies for Manufacturing (cont’d)
§ Resistors in IC Designs
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Prof. Yang, Jong-Ryul
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Summary: ∆-Y Transformations
§ Wye-Delta Transformation
(, =
($ (!
,
($ + (! + ()
(- =
(! ()
,
($ + (! + ()
(/ =
() ($
($ + (! + ()
(,/ = ($ ∥ (! + ()
(,/ = (, + (/
§ Kinds of Resistors
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Break Point
Prof. Yang, Jong-Ryul
Lecture’s Goals: Circuits with Dependent Sources
§ Analyze electric circuits to determine the voltages and currents in
electric circuits that contain dependent sources.
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Prof. Yang, Jong-Ryul
Problem-Solving Strategy
1. When writing the KVL and/or KCL equations for the network, treat the
dependent source as though it were an independent source.
2. Write the equation that specifies the relationship of the dependent
source to the controlling parameter.
3. Solve the equations for the unknowns. Be sure that the number of
linearly independent equations matches the number of unknowns.
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Prof. Yang, Jong-Ryul
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Example 2.29
§ Determine the Vo.
Applying KVL,
−12 + 371$ − /1 + 571$ = 0
→ −12 + 871$ − 271$ = 0 → 1$ = 2 34
/. = 571$ = 10 /
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Prof. Yang, Jong-Ryul
56
Example 2.30
§ Find the Vo.
Applying KCL,
A
10×102) +
/*
/*
+
− 41. = 0,
27 + 47 37
→ 10 +
/* /* 4
+ − /* = 0 → /* = 12 /
6
3 3
/. =
Electrical Circuit
1. =
47
×12 = 8 /
27 + 47
/*
37
Prof. Yang, Jong-Ryul
57
Example 2.31
§ Find the Vo.
Applying KVL,
−12 + 371 + 2/. + /. = 0,
/. = 17 @ 1
→ −12 + 371 + 371 = 0 → 1 = 2 34
∴ /. = 17 1 = 2 /
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Prof. Yang, Jong-Ryul
58
Example 2.32. An Equivalent Circuit for IC Amp.
§ Determine the voltage gain((&(*)/(' (*)) of the amplifier.
!h " = −fi !j " ×$g
$!
!j " =
! "
$e + $! k
1
1
1
1
=
+
+
$g $# $) $(
Electrical Circuit
!h "
fi $g $!
→ 1l =
=−
!k "
$e + $!
Prof. Yang, Jong-Ryul
59
Example 2.33 Application Example 1
1. Positions A, B, C, and D à high / medium / low / off
?& < ?'
[sol.] A: off à open connection
Constant voltage source means that
low resistance à high heating condition
B: R2. C: R1 à ($ < (! à B – low, C – med
D: ($ ||(! à D – high
2. Medium/high power consumption 1.2 kW / 2.0 kW
Resistive
Nichrome
strips
Electrical Circuit
/*!
230!
= 1.27 → ($ =
= 44.1 Ω
($
1.27
230!
E3456 = E+! + E+" → E+" = 800 =
,
(!
(! = 66.1 Ω
Prof. Yang, Jong-Ryul
60
Example 2.34 Application Example 2
§ Modeling
ü While the starter kicked the engine, you probably saw the headlights dim then
return to normal brightness once the engine was running on its own.
25 mΩ
1A
100 A
*5 = *7!EE − QF5 ?7!EE
Electrical Circuit
*5 = *7!EE − (QF5 + Q2E!GE )?7!EE
Prof. Yang, Jong-Ryul
61
Example 2.35 Design Example 1
§ To add a back-lit display panel to the stereo amplifier
ü
7 light bulbs – two operate at 12 V/15 mA, five at 9 V/5 mA
ü
12 V dc supply, no 9 V supply : V2 = 9 V. the variation in V2 be no more than ±G%
ü
Determine R1 and R2.
I$ & I! are not considered to determine /! .
The variation is related to the switch operation.
Max. voltage = 9 (1+0.05) = 9.45 V
Min. voltage = 9 (1-0.05) = 8.55 V
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Prof. Yang, Jong-Ryul
62
Example 2.35 Design Example 1 (cont’d)
ü The condition to have the max. voltage:
à All switched off (no additional current path)
*' = 9.45 = 12
?'
?& + ?'
→ 12
K
,
1+K
K=
?'
?&
9.45
K
?'
=
→K=
= 0.27
12
1+K
?&
ü The condition to have the min. voltage:
à All switched on (no additional current path)
1.8K ∥ 1.8K = 0.9K,
Electrical Circuit
0.9K ∥ 0.9K = 450,
450 ∥ 1.8K = 360,
*' = 8.55 = 12
360?&
+ 360 + ?&
12
?'
=
= 1.4 → ?& = 360 1.4 − 1 − 0.27 = 48.1Ω,
360
8.55
?' ∥ 360
?& + ?' ∥ 360
?' = 178.3Ω
Prof. Yang, Jong-Ryul
63
Example 2.36 Design Example 2
§ Design a circuit to produce a 5-V output from a 12-V supply.
ü Power consumption: 240 mW
/h = /ko
$!
$e + $!
5
$!
→
=
→ $e + $! = 2.4$!
12 $e + $!
12!
144
==
≤ 0.24 → $! ≥
= 250 Ω
$e + $!
0.24×2.4
$e = 1.4$! → $e ≥ 350 Ω
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Prof. Yang, Jong-Ryul
64
Example 2.36 Design Example 2 (cont’d)
ü Let’s consider the percent error when we use the resistor we can select.
∆= 0.037 → 2% or less tolerances
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Prof. Yang, Jong-Ryul
65
Example 2.37 Design Example 3
§ Design a current-to-voltage converter to produce a 5-V output when the
current is 20 mA.
5
(=
= 250 Ω
0.02
1* =
/*
/*
+
,
(* (7489 + 250
1:450,; =
Electrical Circuit
/*
(7489 + 250
Q2-H.!(
1
=
?
+ 250
QA
1 + I-G"
?A
Prof. Yang, Jong-Ryul
66
Example 2.38 Design Example
§ Design the amplifier by choosing the transistor to produce the most
accurate gain.
*) = −wJ * ?) ∥ ?5
?-.
*=
*
?A + ?-. 2
Electrical Circuit
*)
?-.
NK =
= −wJ
*A
?-. + ?A
NK& = −277.78
?) ∥ ?5
NK' = −211.77
NK/ = −167.32
Prof. Yang, Jong-Ryul
67
Summary of Chapter 2
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Break Point
Prof. Yang, Jong-Ryul
Problems #2.1.6
§ Series Connection vs. Shunt Connection
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Prof. Yang, Jong-Ryul
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Problems #2.2.7
1$ + 21< = 43,
1< = 43 + 23
à 1$ = 43 − 2 63 = −8 34
A
Electrical Circuit
Prof. Yang, Jong-Ryul
70
Problems #2.2.15
/$ = −3 + −3/< = −3 + /! + 6 = 6 + /) − 15
/< = 15 − 3 = 12 /
/$ = −39 / → /! = −42 / → /) = −30 /
Electrical Circuit
Prof. Yang, Jong-Ryul
71
Problems #2.3.8
/, = −271,
/- = 471
/, + 4/- + 12 = /- − 2/,
3 /, + /- + 12 = 671 + 12 = 0
→ 1 = −2 34
E$!= = −23 ×12 = −24 3L
Electrical Circuit
Prof. Yang, Jong-Ryul
72
Problems #2.4.2
67×127
($ =
= 47
67 + 127
Electrical Circuit
1. =
47
× −1234 = −3 34
47 + 127
Prof. Yang, Jong-Ryul
73
Problems #2.5.5
No current flow
4K ∥ 4K = 2K
Electrical Circuit
Prof. Yang, Jong-Ryul
74
Problems #2.6.23
*L + 12 − 24
24
+2=
→ *L = 20 *
2
4
*L
A
Q&
QA =
20
32 − 24 32 − 16
+2+
+
5
2
4
= 6 + 4 + 4 = 14 N
Electrical Circuit
Prof. Yang, Jong-Ryul
75
Problems #2.7.11
x y'
z y'
{ y'
{ y'
| y'
Electrical Circuit
Prof. Yang, Jong-Ryul
Problems #2.7.11 (cont’d)
Electrical Circuit
76
Prof. Yang, Jong-Ryul
77
Problems #2.8.9
1* =
/. =
/*
11
57
1
=
4 → 1- = 1* ∗
=
4
100 + 57 ∥ 500 24,400
57 + 500 2440
300
120000
/.
11.44
−4×10' 1- = −
= −11.44 / → 4= = = −
= −45.75
47 + 300
43 ∗ 244
/:
0.25
Electrical Circuit
Prof. Yang, Jong-Ryul
78
Problems #2.8.17
3 KΩ
/< =
37
/.
∗ /. =
37 + 37
2
/.
/<
/.
/.
/.!
5!
−53 +
+
+
+
= 0 → /. = 5 / → E> =
=
= 2.083 3L
27 2000 37 + 37 127
127 127
Electrical Circuit
Prof. Yang, Jong-Ryul
79
Appendix. Circuit Simulation using LTSpice
§ Simulation Process
§ LTSpice
ü Freeware supported by Linear Technology
http://www.linear.com/designtools/software/
Electrical Circuit
Prof. Yang, Jong-Ryul
80
How to Simulate the Circuit using LTSpice
Start with a New Schematic
Loop 2: 4 + 6 − V89 = 0
Electrical Circuit
Prof. Yang, Jong-Ryul
81
Example using LTSpice
A
B
Loop 1
Loop 2
1) Verify Ohm’s law using VR1 and IR1.
2) Verify KVL from Loop 1 or Loop 2.
Electrical Circuit
3) Verify KCL from Node A or Node B.