THERMAL NOISE MODEL OF CAPACITIVE
ACTIVE ELECTRODE FOR INDIRECT-CONTACT ECG
Yong Gyu Lim
Department of Oriental Biomedical Engineering, Sangji University, Wonju, Republic of Korea
Keywords: Indirect-contact ECG, Active electrode, Electrode impedance, Background noise of ECG, Cloth impedance.
Abstract: The indirect-contact ECG (IDC-ECG) shows large background noise in comparison with conventional ECG
measurement. To improve the signal quality, close study of the background noise is necessary. This study
was carried out to investigate how much the thermal noise influences the background noise in IDC-ECG. To
do so, the thermal noise model was built for the active electrode. And then, the parameters which determine
the thermal noise were estimated by measuring the gain of the active electrode. Finally, the level of thermal
noise was estimated and compared with actual background noise. The results show that the thermal noise is
the dominant component of background noise and the intrinsic noise of the preamp’s active devices is
negligible.
1 INTRODUCTION
The need for physiological signal measurement at
home is increasing due to the interest in the early
disease detection and the continuous or frequent
prognosis monitoring. In addition, the need for
health monitoring in daily life is increasing for the
sake of improving life quality. For the above stated
uses, we introduced an ECG measurement method
adequate for daily long-term measurement (Lim,
2006). Using the introduced method, ECG was
measured through usual clothes without direct
contact between the skin and instrument.
In comparison with conventional ECG, the
background noise of IDC-ECG is large, and its
characteristics vary widely according to the
measurement conditions. To improve the signal
quality, an analysis of the background noise is
necessary.
In this study, we carried out an experiment to
determine the gain of IDC-ECG measurement for
some sample cloth, cotton. And based on the
measured gain, the thermal noise level was
estimated. By the comparison between the estimated
thermal noise and the actual background noise of
IDC-ECG, we investigated how much the thermal
noise influences the background noise.
2 METHODOLOGY
2.1 Indirect-contact ECG
Measurement
Indirect-contact ECG (IDC-ECG) is a method that
enables ECG measures without direct contact
between the electrodes and bare skin. The method is
composed of two components. One is a high-input-
impedance capacitive and active electrode that
enables ECG measurement through the high
impedance of the clothes. The other component is
the indirect-contact grounding through the clothes.
Figure 1: Diagram of the IDC-ECG measurement system
showing the electrode impedance (Z
CLTH
), input
impedance of the preamp (Z
B
), and impedance between the
body and ground (Z
G
).
Figure 1 shows the diagram of the whole
measurement system. The ECG generated in the
subject’s body is sensed by the two active electrodes
through cloth impedance Z
E
. The difference between
the outputs of the two electrodes is acquired by an
110
Lim Y..
THERMAL NOISE MODEL OF CAPACITIVE ACTIVE ELECTRODE FOR INDIRECT-CONTACT ECG.
DOI: 10.5220/0003720901100113
In Proceedings of the International Conference on Biomedical Electronics and Devices (BIODEVICES-2012), pages 110-113
ISBN: 978-989-8425-91-1
Copyright
c
 2012 SCITEPRESS (Science and Technology Publications, Lda.)

instrumentation amplifier, and it is filtered and
amplified by circuitry behind the instrumentation
amplifier. The final bandwidth is 0.5-35 Hz and the
total gain is 5000.
2.1.1 Frequency Response of the Active
Electrode
Figure 2 shows a model of the presented active
electrode. The preamp in the active electrode is
simply composed of one op-amp and one discrete
resistor (R
B
), which is a path for the bias current of
the op-amp’s input terminal. C
B
is the parasitic
capacitance between the input and the ground. The
parallel connection of R
A
and C
A
represents the input
impedance of the op-amp. Z
E
is the electrode
impedance, which is present between the electrode
face and the skin. The electrode impedance is
represented as a parallel connection of R
CLTH
and
C
CLTH
.
Figure 2: Model of active electrode with signal source.
The ECG source signal (the potential variation at
skin surface) is represented as a voltage source E
S
.
Therefore, the gain for the input E
S
is
//
()
//
BA
S
E
BA
ZZ
Gs
Z
ZZ
=
+
(1)
In the electrode designed in this study, the input
impedance Z
A
of the op-amp is so large in
comparison with Z
B
that it can be disregarded.
Therefore, the gain leads to
()
()()
B CLTH B CLTH
S
B CLTH B CLTH B CLTH
RC RR s
Gs
R
RCCRRs
+
=
+++
(2)
2.1.2 Model of the Thermal Noise in the
Electrode
Figure 3 shows various noise sources to be
considered for the evaluation of the electrode output
noise. E
V
and I
A
denote the voltage noise source and
the current noise source, respectively, of the intrinsic
op-amp noise (Ott, 1988). We can obtain detailed
information about the op-amp noise from the data
sheet provided by the manufacture (TI, 1998). E
CLTH
and E
B
are thermal noises (also called as Johnson
noises) produced at the resistances R
CLTH
and R
B
,
respectively. The thermal noise amplitude is
described by the root-mean-square (rms) voltage as
follows:
4
rms
VkTBR=
(3)
where k: Boltzmann’s constant (1.38 x 10
-23
joules/
◦
K)
T: absolute temperature (
◦
K)
B: bandwidth of noise (Hz)
R: resistance (Ω).
The thermal and op-amp noises are generated at the
active electrode components, and can be called
internal noises
Figure 3: Model of active electrode including noises.
The effects of noises on the op-amp output can be
compared with each other by conversion to the
voltages observed at the op-amp input. The total
voltage V
IN
at the op-amp input is expressed as
() () () ()
IN S S N
Vf GfEfVf=+
(4)
where G
S
is the ECG signal gain as defined in eqs.
(1) and (2), and V
N
is the total noise shown at the op-
amp input.
It seems reasonable to suppose that the noises are
random and uncorrelated with each other (Ott,
1988). On this assumption, the total noise voltage
can be decomposed as
()
1/2
2222 2
() () () () () ()
NVABEEXT
Vf Vf Vf Vf Vf V f=++++
(5)
where the total noise V
N
(f) and all of its components,
such as V
B
(f), are RMS voltages per square root of
bandwidth and their unit is
VHz
.
The voltage components at the op-amp input are
acquired as shown below.
() ()
VA
Vf Ef=
(6)
() ()
CLTH B
AA
RR
Vf If
D
=
(7)
() ()
CLTH
BB
R
Vf Ef
D
=
(8)
() ()
B
ECLTH
R
Vf E f
D
=
(9)
THERMAL NOISE MODEL OF CAPACITIVE ACTIVE ELECTRODE FOR INDIRECT-CONTACT ECG
111

2
() ()
EXT CLTH B
EXT EXT
fC R R
Vf Ef
D
π
=
(10)
where
2( )
CLTH B CLTH B CLTH B EXT
DR R j fR RC CC π =++ ++
Since the input impedance of the op-amp was much
greater than Z
B
in the case of our electrode design,
we disregard it for the induction of equations (6) to
(10).
3 RESULTS
Equation (2) shows that the cloth impedance (Z
E
)
can be estimated if we know the gain and input
impedance of the preamp (Z
B
). The Z
B
is already
known because it is determined by the design (R
B
=
3 GΩ, C
B
= 17 pF). The gain was measured by the
experimental setup shown in fig. 4. The electrode
was laid on a sample cotton cloth and sinusoidal
signal was provided by a copper plate put under the
cloth.
Sinusoidal Signal
from Function
Generator
Figure 4: Gain measurement setup.
1 10 100
10
6
10
7
10
8
10
9
Fre
q
uenc
y
(
Hz
)
Impedance (Ohm)
10
1
10
2
10
3
Capacitance(pF)
Impedance
Resistance
Capacitance
Figure 5: Estimated electrode impedance (Z
E
), and its
parallel component R
CLTH
and C
CLTH
.
Figure 5 shows the estimated electrode impedance
which was obtained by applying (2) to the gain
measurement.
We can calculate the internal noise components
by applying eqs. (6) - (10) to the estimated Z
E
shown
in Fig. 5. Figure 6 shows the estimated internal noise
components for the sample cloth. The figure shows
that the noise spectral density decreases at high
frequency range that is expected by (6)-(10). In the
graph, we can also see that the noise components (V
V
and V
A
), originating from the intrinsic op-amp noise,
are negligible in comparison with the other two
thermal noise components (V
B
and V
E
).
Figure 6: Noise spectral densities were estimated
theoretically for the cotton sample cloth. Each noise
component is defined in (6) – (10).
It is desirable to compare the spectral density of
background noise in actual ECG with that of
theoretical thermal noise. However, we cannot get
the spectral density of background noise alone
because the signal ECG cannot be removed. Instead
of the quantitative comparison, a comparison
between waveforms by eye was performed. For that
comparison, pseudo-noise waveform was generated.
Its spectral density was
2
times the spectral density
shown in Fig. 6, because the ECG was measured
through two electrodes.
0 1 2 3
-0.1
0
0.1
0.2
ECG through Cotton
Time (s)
Voltage (mV)
Figure 7: ECG waveforms acquired by IDC-ECG with
Ag-AgCl grounding (upper trace) and pseudo-noises
synthesized artificially for cotton (lower trace). The
frequency band was from 1 to 35 Hz.
BIODEVICES 2012 - International Conference on Biomedical Electronics and Devices
112

Figure 7 shows the ECG and its corresponding
synthesized pseudo-noise for the sample cloth. The
figure shows that the background noise of actual
ECG and pseudo-noise look similar to each other in
amplitude and morphology. This result shows that
the thermal noise is the dominant component of
IDC-ECG.
4 CONCLUSIONS
A thermal noise model for the active electrode was
built, regarding the impedance between the electrode
and body through clothes as parallel connection of a
resistance and a capacitance. The results show that
the thermal noise generated in the resistances of the
clothes and the electrode is the dominant component
of the background noise in the IDC-ECG. And
furthermore, the intrinsic noise of the preamp’s
active devices is negligible in comparison with the
thermal noise generated by the passive components.
This study explains why the IDC-ECG makes so
large background noise in comparison with
conventional ECG measurements and shows what to
do in order to reduce the background level.
ACKNOWLEDGEMENTS
This research was supported by the Happy tech.
program through the National Research Foundation
of Korea (NRF) funded by the Ministry of
Education, Science and Technology (No. 2010-
0020809)
REFERENCES
Lim Y G, Kim K K, Park K S, 2006. ECG measurement
on a chair without conductive contact. IEEE Trans
Biomed Eng 53: 956-959
Ott H W, 1988. Noise Reduction Techniques in Electronic
Systems, John Wiley & Sons, New York
TI, 1998. Data sheet of OPA124.
THERMAL NOISE MODEL OF CAPACITIVE ACTIVE ELECTRODE FOR INDIRECT-CONTACT ECG
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