The rigid surface of the conventional PCB-based capacitive electrode produces an undefined distance between the skin and the electrode surface. Therefore, the capacitance introduced by them is uncertain and can vary from electrode to electrode due to their different positions on the scalp. However, textile electrodes which use conductive fabric as electrode surfaces, are bendable over the scalp. Therefore, it provides a certain value of the capacitance which is predictable and calculable accurately if the effective distance to the scalp surface can be determined. In this paper noise characteristics of textile electrodes with different fabric sizes as electrode’s surface and capacity calculations related to each size are presented to determine the effective distances for each electrode size.

Keywords:
EEG;
Capacitive electrode

Capacitive electrodes for the evaluation of human body bioelectric potentials are a very attractive alternative to conventional galvanically coupled electrodes for long term diagnostic applications especially when the signals have to be measured through insulating materials like cloth. These electrodes are always constructed in a similar way based on ideas which have been proposed already in the middle of the last century [1, 5]. In the last years many research groups have developed new applications based on these electrodes [2, 3, 6]. We concentrated in our work on the application in a multichannel helmet for electroencephalography (EEG) application e.g. in a brain-computer interface [4]. The common geometric arrangement of the first stage of a capacitive electrode is depicted in Fig. 1.

A capacitive electrode for bioelectric potential measurements consists of a piece of conductive material which forms a capacitor together with some part of the body surface. The electric charges on the body surface caused by the electric body potentials interact with corresponding charges in the conductive electrode which is placed above the body surface separated by some insulating material. As insulator either air or any other dielectric can be employed. Therefore, we will have a capacity *C _{e}* of

(1)
C
e
=
є
0
є
r
A
e
d
.

Here *є* = *є _{r}є*

Together with the input resistance *R _{in}* of the impedance converter stage the capacitance is part of an electronic high-pass filter. Normally, the cut-off frequency of the high-pass filter

(2)
f
c
=
1
2
π
·
R
i
n
·
C
e

is chosen at about 0.1 Hz in agreement with the bandpass filters used commonly in electrocardiography or electroencephalography.

Here *R _{in}* is the bias resistor in parallel with the input resistor of the amplifier which is almost equal to the bias resistor because the input impedance of the amplifier is larger than the bias resistor.

We used stretchable conductive fabric which is made from interwoven copper wires. The fabric is not solderable, therefore, we used conductive glue to paste it to the main electronic circuit. For these measurements a PCB plate is used as second side of the input capacitor which is connected to the input and lays underneath the fabric, thus forming the input capacitance *C _{e}*.

According to equation (2) to have a lower cut-off frequency, the input resistance *R _{in}* and input capacity

In this paper we measured the transfer function and noise spectra of electrodes with areas of the fabric electrodes of 64 cm^{2}, 32 cm^{2}, and 16 cm^{2}.

In figure 2, the transfer function of the circuit with different areas of the fabric is depicted, the input resistor *R _{in}* is 1

From figure 2 we obtain a 3dB cut-off frequency of 0.23 Hz for an area of 64 cm^{2}, 0.52 Hz for an area of 32 cm^{2}, and 0.90 Hz for an area of 16*cm*^{2}. The corresponding capacitance values for each of the areas can be determined from equation (2). We find *C _{e}*(64 cm

Figure 3 shows the dependence of the cut-off frequency and the electrode capacity on the area of the electrode surface. According to equation (1) and (2), *C _{e}* should be proportional to the fabric area while the cut-off frequency should be inversely proportional to the area.

Taking these capacity values and assuming air as dielectric between the surfaces of the capacitors, the distances d were calculated by equation (1) to be about 0.1 mm for all cases. However, looking at figure 3 one sees that the data points for the capacitance vs. area do not lie on a straight line as expected for a constant distance d. To estimate the uncertainty in the distance d, we repeated measurements of the transfer function after assembling and disassembling the capacitors. For the fabric electrode with 16 cm^{2}, we determined the standard deviation of the cutoff frequency as 0.25 Hz. With

(3)
δ
C
=
−
1
2
π
R
f
¯
3
dB
2
δ
f
3
dB

one can calculate the uncertainty*C* to 0.034 nF with
*δA* and the contribution from the uncertainty *δC*. It is found that the contribution to the uncertainty in distance d of *δC* by far exceeds that of *δA*. Thus, the uncertainty in the distance can be calculated by

(4)
δ
d
=
є
r
є
0
A
C
¯
2
δ
c

resulting in an uncertainty value*d* = 0.015 mm.

The voltage noise spectra of the electrodes with different areas of fabric are depicted in Fig. 5. The simplified noise model of the electrode is shown in fig. 4. The effect of the noise of the resistor at the output can be calculated by

(5)
S
v
,
R
t
o
o
t
a
l
=
1
1
+
j
ω
R
C
4
k
R
T
δ
f

in which k is Boltzmann constant, T is temperature, R is the input resistor, C is input capacitor and δ*f* is the bandwidth. The total noise of the electrode is

(6)
S
v
,
T
o
o
t
a
l
=
S
v
,
R
t
o
o
t
a
l
2
+
S
v
,
o
p
2

The white noise of the spectra is the noise of the amplifier *S _{v}*,

The cut-off frequency of the high-pass filter of the capacitive electrodes is determined by the input capacity which is received from the electrode surface parallel to the skin surface and the input resistance. In order to have a lower cut-off frequency, the value of input resistor or capacitor should increase. In rigid surface electrodes, an increase in the capacity by increasing the surface of the electrode is not possible because the area of the electrode surface which has a small distance to the scalp is rather small and unpredictable. However, by using conductive fabric as an electrode surface it is possible to increase the area quite considerably while still maintaining the same distance between layers over the whole surface which consequently results in a definite capacity in the input. Therefore, it is possible to shift the cut-off frequency to lower frequencies by increasing the size of fabric in textile electrodes. Simultaneously the voltage noise at lower frequencies is reduced. The distance measured in this work (d = 0.1 mm) is in rough agreement with what we measured for the thickness of the fabric. However, it is clear that more measurement with different fabric should be done to predict what distance should be expected for new unknown fabric.

The author S.N. gratefully acknowledges the financial support by the Braunschweig International Graduate School of Metrology (B-IGSM)(PhD Scholarship,S.N.).

**Conflict of interest**: Authors state no conflict of interest. Material and Methods: Informed consent: Informed consent has been obtained from all individuals included in this study. Ethical approval: The research related to human use has been complied with all the relevant national regulations, institutional policies and in accordance the tenets of the Helsinki Declaration, and has been approved by the authors’ institutional review board or equivalent committee.

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