2009/4/21 1 impedance analyzer rlc meter 簡世森 東海大學物理系 [email protected]...
TRANSCRIPT
2009/4/21 2
Contents
A. AC wave & Complex number polar form (1)B. Impedance
1. Capacitance/resistance (1)2. Impedance and admittance (2)3. Inductance (1)4. Series & parallel (1)
C. RLC circuits1. Impedance spectrum (2)2. Phase, quality factor, dissipation factor (0.5)3. Resonance (2)
D. RLC meters 1. Bridge method, resonant method, I-V method, auto-balanced
bridge method (3)2. Connection configuration (1)
E. Applications (2)1. MOS devices, LEDs, solar cells
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AC waves
V cos @ real V- coordinate
= t
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Musical pitch notes and octave
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Complex munber
V cos @ real V- coordinate
exp( )V i@ complex polar coordinate
虛部是人為加入的，不存在 !
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Addition
z = |z| (cos + i sin ) w = |w| (cos + i sin )Z + W = |Z|cos + |W|cos + i (|Z|sin + |W|sin )
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Multiplication
z = |z| (cos + i sin ) w = |w| (cos + i sin )zw = |zw| (cos ( + ) + i sin ( + )) = |zw| exp( i ( + ))
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AC resistorVoltage, current & power
E = I RE = E0 exp (it)I = I0 exp (it) = E0 exp (it)/R
E & I are in phase
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Capacitance
0
, exp( )
exp( )
exp( ( ))2
,
1,
o
o
C C
Q CE
dQ dEI C E E i t
dt dtI i CE i t
CE i t
I iBE B C
E iX I XC
B: susceptance 電納XC: capacitive reactance 容抗
reactance 電抗
i 的效果 : Current leads voltage by 90°
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Capacitance & reactance
, for resistance
, for capacitance
1, capacitive reactance
C
C
E RI
E iX I
XC
• 將 R 、 XC 放在複數平面中討論• i 的意義是使電壓落後 90°，不表示 reactance是虛構的
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Complex Impedance Coordinate
, for resistance
, for capacitance
( )
R
C C
T R C C C
C
E RI
E iX I
E E E RI iX I R iX I
Z R iX
E ZI
Z: impedance
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Example: RC series
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Impedance vs Admittance
E = ZII = E/Z = YE,Y = 1/Z, Y: admittance 導納
E = RI, for resistanceI = E/R = GEG = 1/R, conductance 電導
I = iBCE, for capacitance
BC = C 電納
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Complex Admittance Coordinate
/
( )
R
C C
T R C
C
C
C
I E R GE
I i CE iB E
I I I
GE iB E
G iB E
YE
Y G iB
此時 Z R - i XC ?
G
BY
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Example: RC parallel
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Series & Parallel
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Physicist vs. EngineerEngineer
0
1exp( ), ,C CE E i t X B C
C
XC
Impedanceplane
Admittanceplane
Physicist
0
1exp( ), ,C CE E i t X B C
C
XC
BC
BC
Z = R - i XC Z = R + i XC
Y = G + i BC Y = G - i BC
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Inductance
1,
,
L L
L
dIE L
dtE i
I Ei L L
I iB E BL
E i LI X L
BL: susceptance 電納XL: inductive reactance 感抗
reactance 電抗
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Example: RL series
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Example: RL parallel
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Complex CoordinateEngineer 1
,
1,
C C
L L
X B CC
X L BL
XC
Impedanceplane
Admittanceplane
XL
BC
BL
0 exp( )E E i t
Z = R + i (XL - XC)
Y = G + i (BC - BL)
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Example: RLC series
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Example: RLC parallel
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Example: RLC series-parallel
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Impedance Spectrum: RC series
RC & CR are different!
10-1 101 103 105 10710-4
10-2
100
102
104
XC
0.0 2.5 5.0 7.5 10.0
10-3
10-1
101
103
105
XC
R (
10-1 101 103 105
10-6
10-4
10-2
100
G
0.000.020.040.060.08
B
w R Xc Z G B
1 51.00E+0
45-10000i 5.00E-08 1.00E-04
10 51.00E+0
35-1000i 5.00E-06 1.00E-03
100 51.00E+0
25-100i 4.99E-04 9.98E-03
1000 51.00E+0
15-10i 4.00E-02 8.00E-02
10000 51.00E+0
05-i 1.92E-01 3.85E-02
100000 5 1.00E-01 5-0.1i 2.00E-01 4.00E-031000000 5 1.00E-02 5-0.01i 2.00E-01 4.00E-04
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RC parallel
w G B Y R Xc
1 0.21.00E-04
0.2+0.0001i
5.00E+00 -2.50E-03
2 0.22.00E-04
0.2+0.0002i
5.00E+00 -5.00E-03
5 0.25.00E-04
0.2+0.0005i
5.00E+00 -1.25E-02
10 0.21.00E-03
0.2+0.001i
5.00E+00 -2.50E-02
20 0.22.00E-03
0.2+0.002i
5.00E+00 -5.00E-02
50 0.25.00E-03
0.2+0.005i
5.00E+00 -1.25E-01
100 0.21.00E-02
0.2+0.01i
4.99E+00 -2.49E-01
200 0.22.00E-02
0.2+0.02i
4.95E+00 -4.95E-01
500 0.25.00E-02
0.2+0.05i
4.71E+00-
1.18E+00
1000 0.21.00E-01
0.2+0.1i 4.00E+00-
2.00E+00
2000 0.22.00E-01
0.2+0.2i 2.50E+00-
2.50E+00
5000 0.25.00E-01
0.2+0.5i 6.90E-01-
1.72E+00
10000 0.21.00E+
000.2+i 1.92E-01 -9.62E-01
20000 0.22.00E+
000.2+2i 4.95E-02 -4.95E-01
50000 0.25.00E+
000.2+5i 7.99E-03 -2.00E-01
100000
0.21.00E+
010.2+10i 2.00E-03 -1.00E-01
200000
0.22.00E+
010.2+20i 5.00E-04 -5.00E-02
500000
0.25.00E+
010.2+50i 8.00E-05 -2.00E-02
1000000
0.21.00E+
020.2+100i 2.00E-05 -1.00E-02
0 200000 400000 600000 800000 1000000
0
2
G
X Axis Title
0
20
40
60
80
100
B
0 1 2 3 4 5
-3
-2
-1
0
XC
R
Cole-Cole plot
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Quality Factor & Dissipation
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Q & D
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Q factor
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Resonance
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LC series
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CL parallel
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RLC series & Q factor
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Resistor frequency response
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Capacitor frequency response
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Bridge method
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Resonance method
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I-V method
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Auto balancing bridge method
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Comparison among RLC meters
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Auto balancing bridge
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Schematic
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Block diagram
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Vector ratio detector
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Two-terminal configuration
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Five-terminal configuration
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Four-terminal pair configuration
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Residuals and open/short compensation
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Open measurement
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Short measurement
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Precision LCR meter: Agilent 4284A
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Display
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Functions
CP-DCP-QCP-GCP-RP
CS-DCS-QCS-RS
LP-DLP-QLP-GLP-RP
LS-DLS-QLS-RS
R-XZ-
G-BY-
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data
2009/4/21 55
RC parallel-0V
12
0527
R:100 kohm
C:10 nF10mvac
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P-N junction
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Depletion layer capacitance (reverse bias)
''
R
dQC
dV
'd n a pdQ eN dx eN dx
1/ 2
2 ( ) 1s bi R an
d a d
V V Nx
e N N N
'
' nd
R R
dxdQC eN
dV dV
1/ 2
'
2( )( )s a d
bi R a d
e N NC
V V N N
2009/4/21 58
PN-100hz
+ -
n p
10mvac
14
0527
X10
-1.0 -0.5 0.0 0.5 1.00.0
500.0E
1.0e21
1.5e21
2.0e21
C^(
-2)
Reverse Voltage(v)
2009/4/21 59
MOS
o
o
C CjC
C Cj
2/F cm
2
2
1
21
o ox
A s
C
C V
qN d
oxoC d
The oxide capacitance per unit area
sjC W
The semiconductor depletion-layer capacitance
The surface potential
o sV V
The potential across the oxide
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MOS-CV
min ( / )ox
ox s m
Cd W
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MOS-1MHz
100mvac
0525
2-GD
X10
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MOS-25Hz
100mvac
0525
3-GD
X10
2009/4/21 63
References
• www.allaboutcircuits.com• 大學物理學 ( 三 ) 23 章 交流電路• Impedance Measurement Handbook, Agilent 2006.