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Prof. Sam Ben-Yaakov 1
Ferroelectric ceramic capacitors:
There is more than meets the eye
Presented at:
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Prof. Sam Ben-Yaakov 2
Resources
This lecture is recorded and be available at the YouTube channel:
https://www.youtube.com/user/sambenyaakov/videos
LinkedIn Group ” Where analog and power electronics meet knowledge “
https://www.linkedin.com/groups/13606756
Papers and university lectures
http://www.ee.bgu.ac.il/~pel/
Thanks to Mr. Evgeny Rozanov assisting in the preparation of this presentation
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Prof. Sam Ben-Yaakov 3
Background
Ceramic capacitors are one of the most popular electronic
devices. They are used for filtering, decoupling and
bypass. And yet, not all the features of these devices are
understood or even known.
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Prof. Sam Ben-Yaakov 4
Objective
To present unfamiliar characteristics of ceramic
capacitors (especially ferroelectric type) relevant to power
electronics.
• For ceramic capacitor types and classification see
https://en.wikipedia.org/wiki/Ceramic_capacitor
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Prof. Sam Ben-Yaakov 5
Outline
1. General specifications of commercial ceramic capacitors
2. ESR as a function of bias voltage
3. Piezoelectricity
4. Nonlinear capacitor modeling
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Prof. Sam Ben-Yaakov 6
General specifications of commercial ceramic capacitors
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Prof. Sam Ben-Yaakov 7
Wikipedia
Structure of ceramic capacitors
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Prof. Sam Ben-Yaakov 8
Commercial Ceramic capacitors
• Practical ceramic capacitors are build around paraelectric (Class I)
and ferroelectric (Class II,III) dielectric materials
• Predominant Class I material is C0G (NPO) – low dielectric constant
• Class II, III includes different dielectric materials e.g. X7R, Y5V ……
High dielectric constant, Class III the highest, small capacitors
• Single, or multilayer (MLCC)
Ferroelectric – dependence on electric field
Similar to ferromagnetic – dependence on magnetic field
Has nothing to do with ferro (iron)!
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Prof. Sam Ben-Yaakov 9
Paraelectric - COG (NPO)
Small 𝜀𝑟 , smaller ESR
Ferroelectric
Large 𝜀𝑟, larger ESR
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Prof. Sam Ben-Yaakov 10
Feroelectricity - Electric polarization
Polarization: a measure of
electric dipole moment, ability to
bound charge
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Prof. Sam Ben-Yaakov 11
Electric polarization of dielectric materials
Paraelectricity, ferroelectricity
Ferroelectric material
∝Q
∝V
Constant dielectric
Paraelectric
Ferroelectric 𝜀𝑟 of ferroelectric material is very large up to 7000
Small capacitors
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Prof. Sam Ben-Yaakov 12
Ferroelectric hysteresis and capacitance
Charge [Q]
Voltage [V]
𝐶𝑑 =𝑑𝑄
𝑑𝑉
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Prof. Sam Ben-Yaakov 13
Commercial paraelectric
ceramic capacitors (C0G)
are limited to about 0.1μF
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Prof. Sam Ben-Yaakov 14
EIA - Electronic Industries Alliance JIS - Japanese Industrial Standards
GOC
(NPO)
Temperature dependence
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Prof. Sam Ben-Yaakov 15
𝜔0 =1
𝐿𝐶𝑓0 =
1
2𝜋 𝐿𝐶
At resonance:
CESR ESL
ESRCESR ESL
𝑓 < 𝑓0 : 𝑍 =1
𝜔𝐶
𝑓 > 𝑓0 : 𝑍 = 𝜔𝐸𝑆𝐿
𝑓0
𝜔𝐸𝐶𝐿
𝐸𝑆
𝜔𝐸𝑆𝐿
Typical ceramic capacitor data sheet parameters
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Prof. Sam Ben-Yaakov 16
𝑃 = 𝑖𝑟𝑚𝑠2 ∙ 𝐸𝑆
∆𝑇 = 𝑃 ∙ 𝑡𝑒𝑟𝑚𝑎𝑙
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Prof. Sam Ben-Yaakov 17
1 1
1 1
𝑓0 1𝑓10
𝑍
Why 0.1uF in parallel to a larger capacitor?
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Prof. Sam Ben-Yaakov 18
1 1
1 1
𝑓0 1𝑓10
𝑍
𝜔𝐿 =1
𝜔𝐶
𝜔 =1
𝐿𝐶
Resonant
frequency
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Prof. Sam Ben-Yaakov 19
Local, Small signal, Cd Large signal Cac
1kHz
Capacitance definition (?)
Why the peak?CVAC
0.5Vrms
C
VBIAS
1VAC
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Prof. Sam Ben-Yaakov 20
The effect of size on C=f(Vbias)(No endorsement/affiliation implied)
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Prof. Sam Ben-Yaakov 21
The effect of size
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Prof. Sam Ben-Yaakov 22
The effect of size and WDCV
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Prof. Sam Ben-Yaakov 23
ESR as a function of bias voltage
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Prof. Sam Ben-Yaakov 24
C, ESR C1, ESR1 C2, ESR2
CE
SR
ES
L
C1, C2 < C
ESR1, ESR2 >ESR
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Prof. Sam Ben-Yaakov 25
Large capacitance
Smaller ESR?
Small capacitance
Larger ESR?
?
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Prof. Sam Ben-Yaakov 26
Significant question because ceramic capacitors losses are:
𝑃 = 𝐸𝑆 ∙ 𝑖𝑟𝑚𝑠2
CINCO
S
D
L
RL
IC
VC
VDC
VAC
t
t
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Prof. Sam Ben-Yaakov 27
With DC bias Without DC bias
Z5U
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Prof. Sam Ben-Yaakov 28
Measurements
by Mr. Hermann Haag of Omicron LAB,
and Vorarlberg University of Applied Sciences,
Austria
using Omicron’s Bode 100 Network Analyzer
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Prof. Sam Ben-Yaakov 30
ESR
400V bias0V bias
According to Bode 100 measurements ESR is increasing with bias
(consistent with paper)
C1812W334KCRACTU (same as K-SIM data)
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Prof. Sam Ben-Yaakov 33
80V bias increases
ripple current loss by
more then 10 fold!
???
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Prof. Sam Ben-Yaakov 34
X7R
0.33uF
500V
1812
Same as the one
tested by Bode 100
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Prof. Sam Ben-Yaakov 35
K-SIM KEMET
Z
ESR
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Prof. Sam Ben-Yaakov 36
According to K-SIM ESR is decreasing with bias
(not consistent with papers and Bode100 results)
456mΩ & 10kHz68mΩ & 10kHz
400V bias
0V bias
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Prof. Sam Ben-Yaakov 37
?
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Prof. Sam Ben-Yaakov 38
Voltage bias effect on the ESR of ferroelectric ceramic capacitors
Hermann Haag1, Florian Hämmerle1, and Shmuel (Sam) Ben-Yaakov2
1 Omicron Lab, Austria2 Ben-Gurion University, Israel
Submitted to PCIM- 2020
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Prof. Sam Ben-Yaakov 39
X7R, 15nF, 1000V capacitor
(KEMET, C1206W153KDRACTU), X7R, 15nF, 50V capacitor
(Wurth, 885012208082).
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Prof. Sam Ben-Yaakov 40
Material Capacitance Voltage ESR
change
ESR
K-SIM
X5R 3.3µF 25V +25.1% -68.0%
X5R 10µF 25V +30.5%
X5R 47µF 16V +1.2%
X7R 330nF 50V +20.4% -20.0%
X7R 2.2µF 50V +64.8%
X7R 15nF 50V +13.7%
X7R 15nF 1000V +76.3%
X7R 68nF 1000V +71.1%
Table I. A summary of measured ESR and comparison to K-SIM simulation
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Prof. Sam Ben-Yaakov 41
Piezoelectricity
1. Ferroelectric dielectric is piezoelectric
2. Reciprocal relation between electrical field and mechanical stress
3. When electrically driven by AC ceramic capacitors emit acoustic waves
4. Multiple resonant frequencies
5. Can cinduce“ singing capacitors” phenomenon
5. Can be used to detect defects
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ESRESR
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Measurements
by Mr. Hermann Haag of Omicron LAB,
and Vorarlberg University of Applied Sciences,
using Omicron’s Bode 100 Network Analyzer
ESR
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Prof. Sam Ben-Yaakov 47
Experiment Setup for Film Capacitor
Film Film Film
Measurements
by Mr. Stanislav Tishechkin, Department of ECE, Ben-Gurion University,
using Omicron’s Bode 100 Network Analyzer
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Prof. Sam Ben-Yaakov 48
Results for Film Capacitor
ESR
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Prof. Sam Ben-Yaakov 49
Experiment Setup and results for X7R Capacitor
Film
4.7uF
X7R Film
4.7uF
ESR
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Submitted to PCIM - 2020
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ESR and piezoelectricity of ceramic capacitors:
more research is required
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Nonlinear capacitors modeling
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Local, Small signal, Cd Large signal Cac
1kHz
Capacitance definition
Why the peak?CVAC
0.5Vrms
C
VBIAS
1VAC
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Prof. Sam Ben-Yaakov 57
( )dt
vCdv
dt
dvvCi
)()( +=
𝑖 =𝑑{𝐶 𝑣 ∙ 𝑣}
𝑑𝑡
𝑖 = 𝐶(𝑣)𝑑𝑣
𝑑𝑡
Which model is correct?
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Prof. Sam Ben-Yaakov 58
Q
V
Q
The fundamental property of a charge storing device - Q=f(V)
𝛼
𝑖 =𝑑{𝑄}
𝑑𝑡
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Prof. Sam Ben-Yaakov 59
Redefining ‘capacitance’
v
vQvCt
)()( =
dv
vdQvCd
)()( =
𝐶𝑎𝑐(𝑣, 𝐴) =∆𝑄
∆𝑉
Total Capacitance
Local Capacitance
Small signal
Large signal Capacitance
Cac =∆Q
∆V
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Redefining ‘capacitance’
Cac =∆Q
∆V
0.5Vrms
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Prof. Sam Ben-Yaakov 61
dv
vdQvCd
)()( =
dvvCvQ d )()( =
𝑖 = 𝐶𝑑(𝑣)𝑑𝑣
𝑑𝑡
v
vQvCt
)()( =
v
dvvCvC
v
d
t
= 0
)()(
𝑄(𝑣) = 𝑣𝐶𝑡(𝑣)
( )dt
vCdv
dt
dvvCi t
t
)()( +=
Cac =∆Q
∆V
Total Capacitance Local Capacitance
Small signal
𝑖 =𝑑{𝑣𝐶𝑡(𝑣)}
𝑑𝑡dt
dvvC
dt
vdQd )(
)(=
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𝑖 = 𝐶𝑑(𝑣)𝑑𝑣
𝑑𝑡
v
dvvCvC
v
d
t
= 0
)()(
( )dt
vCdv
dt
dvvCi t
t
)()( +=
Conclusion: Both models are correct
Provided that the ‘capacitances’ are defined properly
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So why the peak?
Cac
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Prof. Sam Ben-Yaakov 64
Thank you for your attention!