電子回路論第3回 electric circuits for physicists #3...電子回路論第3回 electric...
TRANSCRIPT
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電子回路論第3回
Electric Circuits for Physicists #3
東京大学理学部・理学系研究科
物性研究所
勝本信吾
Shingo Katsumoto
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電源の雑知識 (続き)
Miscellaneous knowledge
on power supplies (continued)
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DC Stabilized Power Supply 直流安定化電源 Series (Dropper) regulation
From TDK web page
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Series regulator power supply
Uni-polar Dual tracking
High precision Bi-polar current source
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Switching regulation
From TDK
web page
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Switching regulator power supply
Molecular beam epitaxy
Control panel
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Bin 電源ビン
Complicated power lines Bin
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Outline 2.5 Theorems for paired terminal circuits
Superposition, Ho-Thevenin, Reciprocity
2.6 Duality
2.7 Passive devices (elements) and active devices
Ch.3 Transfer function and transient response
3.1 Transfer function of single-pair terminal circuits
Resonance circuit
Bode plot
General properties
Appendix B Bridges and balance circuits
Appendix C General properties of resonance circuits
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Concept of terminal pair
Electric circuit: a viewpoint
Two-terminal elements : linear response: Impedance
: power (energy) source (electromotive force)
Lumped constant circuit
Local electromagnetic field
One can pull out
a 2-terminal
element
terminal pair
with current
conservation
J
J
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Two terminal-pair circuit
terminal pair index: k Jk
current : Jk
Jk
voltage : Vk
Vk Terminal pair parameters
Linear relations between terminal-pair parameters: terminal-pair matrices
F-matrix (cascade matrix)
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Impedance matrix, Admittance matrix
Impedance matrix
Admittance matrix
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Cascade connection of 4-terminal circuits
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Series connections of 4-terminal circuits
Series connection of
2-terminal elements
𝑉1
𝑉2
Stack along voltage direction
𝑍1
𝑍2
𝑍1
𝑍2
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Parallel connections of 4-terminal circuits
𝑌1
𝑌2
Parallel connection of
2-terminal elements
Current participation
with a common voltage
𝑌1
𝑌2
𝑉𝑖𝑛
𝐽𝑖𝑛
𝑉𝑜𝑢𝑡
𝐽𝑜𝑢𝑡
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Theorems for terminal-pair circuits
Superposition theorem:
+
- P1
P2 J
+
- P1
JP1 P2 JP2
J JP1 JP2 + =
Jpi: The current caused on the output by i-th power source.
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Ho-Thevenin’s theorem
+
-
J
Z
1
2
3
+
- Vo Zi
Consider a circuit with an open terminal pair (No.3). Obtain current J when the
open pair is connected with impedance Z.
1. Measure the open terminal voltage 𝑉0.
2. Turn off all the power sources (voltage sources: short, current
sources: open). Measure the open circuit impedance 𝑍𝑖.
Then
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Ho-Thevenin’s theorem
Because:
+
- +
- 𝑉0
𝑍 𝐽𝑡 = 0
+
- 𝑉0
𝑍 𝐽0 = −𝑉0
𝑍 + 𝑍𝑖
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Norton’s theorem
+
- Y +
- Yi
V JS
Dual theorem to Ho-Thevenin
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Review: Tellegen’s theorem
𝑖 = 1,⋯ ,𝑚: index of branches
Power of i-th branch
1. Power conservation law
2. Holds for any kind of circuit (irrespective of linear, or non-linear)
3. Holds for two independent circuit conditions (as long as D is the same)
Comments
D: incidence matrix
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Reciprocity theorem
An 𝑛-terminal pair linear circuit
At one state 𝑉1, 𝐽1 , 𝑉2, 𝐽2 , ⋯ , (𝑉𝑛, 𝐽𝑛),
at another state 𝑉′1, 𝐽′1 , 𝑉′2, 𝐽′2 , ⋯ , (𝑉′𝑛, 𝐽′𝑛)
Proof: Consider a two terminal-pair circuit with 𝑚 branches.
𝑉1
𝐽1
𝑉2
𝐽2
𝑉𝑘 = 𝑍𝑘𝐽𝑘 𝑉′1
𝐽′1
𝑉′2
𝐽′2
𝑉′𝑘 = 𝑍𝑘𝐽′𝑘
Tellegen’s theorem But
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Duality 双対性
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Duality
Series Parallel
Open Short
Voltage Current
Impedance Admittance
Capacitance Inductance
Electric field Magnetic field
Resistance Conductance
Ho-Thevenin Norton
Kirchhoff’s 2nd law Kirchhoff’s 1st law
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2.7 Definition: Passive elements and active elements
Two terminal: current J, voltage V
𝐽𝑉 ≥ 0: passive element
𝐽𝑉 < 0: active element
Locally active
two-terminal element
More than three-terminal: treat as a terminal pair circuit
𝑃 ≥ 0: passive element
𝑃 < 0: active element
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Ch.3 Transfer function and
transient response
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3.1 General Properties of Resonance and Resonance Circuits
3.1.1 Resonance Phenomena
Harmonic oscillator:
Kirchhoff's law
Resonant (angular) frequency
R
C
L
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Transfer function, resonance and phase shift
Re Z
Im Z
0
R
1
w =0
w 0
w 0
w 0 w
2 w
1
w 2
Re Y
Im Y
0
w
w w
) ( w i Z
(a) (b) (c)
Resonance: Reactance =0 Total Phase Shift Change: p
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The Bode diagram (plot)
10-2
100
102
104
0.001 0.01 0.1 1 10 100-1.5
-1
-0.5
0
0.5
1
1.5
𝑍/𝑅
ar
g (
Z)
Q=10 5
2
1
Q=20
10 5
2 1
Plot of absolute value and argument
of an impedance as a function of
frequency.
Absolute value: log-log mode
Argument: semi-log mode
L R
C Example:
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Transient response of resonant circuit
R C L
V
V 𝑉0
t
Damped oscillation with time constant 𝛾−1, frequency 𝜔𝑠
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Transient response of resonance circuit (transfer function)
Synthesized impedance, admittance
Zero (pole) of 𝑍tot(𝑠) (𝑌tot(𝑠))
Laplace transformation of voltage: 𝑉(𝑠)
Natural current
Time constant: Re(𝑠0) Frequency: Im(𝑠0)
𝑠𝑖: poles of 𝑌(𝑠)
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Quartz crystal filter
F r e q u e n c y ( H z )
R e s
p o n s e
( d B
)
4 4 3 3 . 2 5 4 4 3 3 . 5 4 4 3 3 . 7 5 4 4 3 4 4 4 3 4 . 2 5 - 6 0
- 4 0
- 2 0
0
(a)
(b) (c)
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Kondo Resonance and Phase shift
Jun Kondo
1
2𝑠↑ 𝑑 ↓ − |𝑠 ↓ |𝑑 ↑
𝐸F
E
Many body resonance.
But still has the phase shift of p/2 !
Co atoms on Ag (111) surface Co (magnetic) Defect (non-magnetic)
Schneider et al., Phys. Rev. B65, 121406 (2002).
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Resistance bridge 抵抗ブリッジ
Wheatstone bridge
AVS-47 Resistance bridge
Not a “bridge” circuit!
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Schering Bridge
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Hartshorn bridge
Magnetic moment measurement
Resistance measurement
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Capacitance bridge キャパシタンス ブリッジ
General Radio
3-terminal
Capacitance bridge
Agilent E4981A
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What is Spice?
SPICE: Simulation Program with Integrated Circuit Emphasis
A language which describes electronic circuits (corresponding to circuit diagrams).
ex) a CR circuit and a dc power source * 0---R1---1---C1---2---V1---0
R1 0 1 10
C1 1 2 20
V1 2 0 5
.END
Graphical user interface: Circuit diagram
Linear Technology
web site
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Circuit Simulator
Download LTSpice from
the web site of Linear
Technology
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Operation example
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Theorems for paired terminal circuits
Superposition, Ho-Tevenin, Reciprocity
Duality
Passive devices (elements) and active devices
Transfer function and transient response
Transfer function of single-pair terminal circuits
Resonance circuit
Bode plot
General properties
Summary