Transcript Non-linear EIS

Novocontrol Alpha Analyzers
Fundamentals
Dirk Wilmer
Novocontrol Technologies
Novocontrol Technologies GmbH & Co. KG
Top-class impedance
analyzers with test
interfaces for various
applications
Reliable sample
environment for various
temperature ranges and
pressure variation
Turnkey Dielectric
and Impedance
Spectrometers
Software for instrument
control, automation, and
data analysis
Sample cells for a
large variety of
applications
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Principle of measurement
Voltage u (t )  U 0 cos(t )
Generator Sample Capacitor Sample
u(t)
Current harmonic base wave
Fourier transform over n periods
i(t)
U0
Phase Sensitive
Voltage, Current
Analyzer
u(t)
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I ( ) 
nT
*
I0, 
i (t ) exp( jt ) dt
I ''
I'
*
I
Permittivity  * ( )  ( ) 1
U 0 jC0
t
T=2/
0
I 0  I '2  I ' '2 , tan(  ) 
U0
i(t)

nT
A
C0   0
empty cell capacity
d
I0
Conductivity
t
t
t 
I * ( ) d
 ( )  j 0[ ( )   ' ()] 
U0 A
*
*
d electrode spacing, A electrode area
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Impedance Measurement Requirements
for Dielectric Measurements
• Broad frequency range
• Wide impedance range
• Small loss factors tan(d) = ’’ / ’ = Zs’ / Zs’’
Sample is in first order approximation a capacitor
Capacitive impedance Z = j / (C)
Relaxation usually adds small changes in Z
DC conductivity adds parallel resistance
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Parallel Representations: Same Voltage in Re, Im
Admittance
Parallel Imp.
Zp'
*
I
Yp* 
 j *C0
U0
1
1
1
1
*
Z p : '  j ''  ''  j '
Yp
Yp  C0
 C0
1
 'C 0
''
 C0
Zp'
Serial Imp.
Z s* 
U0
1
  j


I * j *C0 C0 ( '2   ''2 )
Zp''
1
1
 ''C0  'C0
Serial Representations: Same Current in Re, Im
''
Cp'
'
Zs'
Zs''
 ''
C0 ( '2   ''2 )
'
C0 ( '2   ''2 )
Zp
Z s'
 ''
tan( d )  '   ''   '

Zs
Zp
''
Loss Factor
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Impedance
Range
Z p''  
Z p'  
1
 ' C0
Z p''
tan( d )
Typical
dielectric
sample
’ C0 = 100 pF
tan(d) =
10-4..1
1015
I'
I''
U
Zp
'=
1012
Impedance Zp', Zp'' []
Requirement
10 9
Zp
'':
10
0
Zp
pF
,t
an
':
10
0
(d
)=
1
Zp'' =
pF
,t
an
(d
)=
10 4
10 6
Di
U
I''
Zp' =
Zp' DC
Conductivity
Contribution
el
e
Conductivity Range
10 3
R
C
ct
ric
Ra
U
I'
0
dc C0
10
fF
ng
e
1p
F
10 0
10
0p
F
1
F
10-3
-6
10
-3
10
0
3
10
10
Frequency [1/s]
6
10
10
nF
9
10
11
10
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Alpha-A modular measurement system
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Impedance analyzer system highlights
• Broad frequency range 3 µHz .. 40 MHz (> 13 decades)
• Ultra wide impedance range 10-4 .. 1014 Ω (18 decades) covers range
from conductors to best isolators in a single instrument set-up
• Ultra wide capacity range 10-15 .. 1 F allows broadband measurement
of smallest capacities down to 1 fF.
• High phase accuracy (2.10-3 °) and loss factor tan(δ) absolute
accuracy (3.10-5) for low loss dielectric materials and isolators
broadband characterization.
• Supports non-linear Dielectric, Conductivity and Impedance
Spectroscopy or gain phase measurements in combination with all
test interfaces.
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Short terminals
Polyethylene
100 GOhm resistor
Open terminals
100 Ohm resistor
15
10 
10
10
106
102
-2
10
-3
10 
-6
10
Impedance [Ohms]
14
10
Alpha total
impedance
range
Typical results
covering 18
orders of
magnitude
dynamics
0.1 Ohm resistor
15 kOhm resistor
1 TOhm resistor
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Measurement
examples
10-3 10-2
10-1
100
101
102
103
104
105
106
107
108
Frequency [Hz]
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Impedance analyzer system highlights
• High speed measurements for online monitoring of time-dependent
processes in the 5 ms range (with Option F)
• Automatic self calibration and diagnosis by user compensates long
term internal drift and verifies functionality.
• Precision digital frequency response analyzer up to 40 MHz for two
channel gain phase measurements with 0.001° phase - and 10-5 in
amplitude resolution included. Operates like a broadband lockin
amplifier with two channels, extended accuracy and frequency range.
• Optional control WinDETA software for turnkey calibration, operation,
data evaluation, 2- and 3- dimensional graphical representation
including non linear spectroscopy.
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Alpha-A: impedance measurements up to 40 MHz
Alpha-AT+ZG4
RC network standard
test sample
New Alpha-A signal
generator
Improved calibration
procedures
40 MHz also available
for ZG2 and ZGS
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Higher harmonics
u(t)
U0
u (t )  U 0 cos(t )
2
I ( ) 
NT
*
k
t
Sample Capacitor
i(t)
t

NT
0
i (t ) exp( k jt ) dt
U0
Z ( )  *
I k ( )
*
k
k = 1: first harmonic
(or base wave)
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HVB 4000: new high voltage test interface for
the Alpha-A modular measurement system
Dielectrics, semiconductors or electronic components at high AC
and/or DC voltages for
• non-linear dielectric / impedance spectroscopy;
• characterization of materials or components under stress;
• extremely high impedance samples exceeding 1014 Ω.
Materials measurements: Novocontrol High Voltage Sample Cell
Earlier products:
- HVB 300 (3 µHz to 1 MHz, 300 Vpp AC and/or DC)
- HVB 1000 (3 µHz to 10 kHz, 1000 Vpp AC and/or DC)
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HVB 4000: new high voltage test interface for
the Alpha-A modular measurement system
• Frequency:
3 µHz ... 10 kHz (9.5 decades)
• Impedance:
1kΩ .. 2·1015 Ω (12 decades)
• Capacitance:
1 fF ... 0.01 F (13 decades)
• Loss factor tan(δ):
10-5 .. 104
• AC signal out:
30 mV .. 2000 Vp, 2.7 mA max
• DC bias out:
-2000 VDC .. +2000 VDC,
2.7 mA max
• Output impedance:
750 kΩ
• Voltage in:
max. ± 2000 Vp dc coupled
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Electrochemical Impedance Measurements (EIS)
• Defined DC Voltage / Current referred to a third (differential) reference
electrode
• Potentiostat/Galvanostat function for defined cell DC polarization
• DC measurement
• Superimposed AC voltage / current for impedance measurement
• Classical applications
Interface polarization
Intrinsic electrolyte conductivity
RC Layer structures
• Phase accuracy, impedance range not as critical as for dielectric
measurements?
• Additional applications:
Ion conductivity, relaxation, sensors, fuel cells
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POT/GAL: electrochemical test interfaces for the
Alpha-A modular measurement system
• Reliable impedance measurements up to 1 MHz
• Very wide impedance range: 10-4  up to 1013 
• Variable output resistance
• Sample protection:high-power counter electrode signal
output supports fast voltage and current limiters
independent of the main control loop. Both voltage and
current limits continuously adjustable and operate
simultaneously in both potentiostat and galvanostat mode.
• Two models: 30 V/2 A and 15 V/10 A
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POT/GAL: electrochemical test interfaces for the
Alpha-A modular measurement system
• 4 channel 24 bit digitizer for simultaneous dc signal
measurements of the counter-, two reference- and the
working electrodes.
• High accuracy working electrode current input converter
with reference technique for accurate measurement of
both strong conductors and insulators.
• Non-linear EIS by higher harmonic measurements both
on instrument and WinDETA application software level.
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POT/GAL: electrochemical test interfaces for the
Alpha-A modular measurement system
• Automatic dc level shifters at the working and
reference electrodes inputs compensate dc voltage and
current offsets in order to accurately measure the small
superimposed ac signals for EIS.
• Supports real-time measurements by up to 150
impedance data points / second (option) and 1.500
voltage current data points / second in time domain
mode.
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An important competitor: specification
• No high-impedance
measurements
• Limited phase and tan(d)
resolution
• Limited usability
at f>10 kHz
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POT/GAL: electrochemical test interfaces for the
Alpha-A modular measurement system
4-wire impedance
mode accuracy
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