2.1. Two-Wired Active Electrode Design
Active electrodes require an active power supply. At least three wired connections are needed, instead of a single wire, for both the power supply and signal transmission. Compared to conventional passive electrodes that do not require a power supply, the additional wires make it difficult to handle rigid wires and increase the design complexity of the biopotential acquisition system. To reduce the number of wires for the active electrodes, a bootstrap technique [
33] was employed for the proposed active dry electrodes. This technique reduces the number of electrode wires by replacing the conventional voltage-based power supply with a current source-based power supply. The power supply rails and signal transmission lines can be shared over a single wire, resulting in an active electrode design that requires only two wire connections.
Figure 1 shows the simplified schematic of the bootstrap technique-based active electrode system using an operational amplifier buffer. The half-power supply bootstrap scheme is implemented by connecting the amplifier’s positive power supply rail with its signal output node to a current source. At this point, the current source
feeds current to the positive power rail of the amplifier, while the signal output node of the amplifier consumes the surplus current. The signal output voltage is therefore determined as follows:
where
,
, and
are the amplifier’s open-loop gain, output impedance, and quiescent current on the positive power supply rail, respectively.
Generally, the open-loop gain of an amplifier is very large, so the current biasing effects on the output node are neglected. Therefore, the output node voltage will be followed to the input node voltage, and the bootstrapped wire connected with output node can then be used as a signal output link for the active electrode system. However, this circuit design lowers the voltage delivered to the amplifier’s positive power supply rail unintentionally, making it difficult to meet the minimum operating voltage for normal amplifier operation in some special cases. To avoid this cases, the operating voltage range of the amplifier needs to be checked. This requirement is discussed further in
Section 2.3.2.
The unity-gain buffer configuration allows transformation from the low impedance of the biopotential source to the possible highest impedance [
34]. Because the input impedance of the buffer circuit is determined as the differential input impedance multiplied by the open-loop gain, this configuration enables maximizing the electrode impedance. The extremely high input impedance of the dry electrode enables virtually perfected isolation between the source and load, and thus eliminates the loading effects. This property helps to provide a robust signal, which is hardly affected by motion artifacts and power line interferences.
2.2. Electrical Model Analysis and Design Considerations
To investigate the electrical characteristics such as source-to-output gain and input-referred noise of the active circuits, we analyzed the electrical coupling model of the skin–electrode interface for the proposed active circuit. A general electrical model of the active electrode circuit was analytically studied by Chi [
13].
Figure 2 shows an equivalent electrical model of the proposed active dry electrode reinterpreted from the general active electrode model. In this circuit model,
and
denote the biopotential source generated from the human brain and output node of the active circuit, respectively.
and
represent the resistive and capacitive properties of the scalp-electrode interface established by dry contact of the spring-loaded probes, respectively.
and
indicate the input resistance and capacitance of the amplifier, respectively.
denotes the parasitic capacitance [
35] originating from the voltage difference between the signal input and output through active shielding.
is the gain of the circuit and is set to unity because the proposed active circuit is designed to operate under a buffer configuration. In order to easily calculate the gain and input-referred noise of the circuit model, the resistances and capacitances have been substituted in parallel at the interface layer (
) and input node of the amplifier (
) for impedance
and
, respectively. Using nodal analysis, the formulation for source-to-output gain of the equivalent circuit model can be derived as:
With a low-frequency biopotential source, the contributions of the resistive components are relatively high because of the reduction of the factor. In the extreme DC case, where is equal to zero, this gain formula simply changes to . As the value of increases, becomes negligible, which means that the input impedance specification of the amplifier directly affects the gain attenuation of the low-frequency biopotential source.
Conversely, with a high-frequency biopotential source, the contribution of the capacitive components increases. Hence,
needs to be maximized, while
and
need to be minimized in order to avoid gain attenuation of the high-frequency biopotential source.
can be minimized by suppressing the leakage current between the input and output nodes. This can be achieved by shielding the input node with the output node of the same potential as the input node.
is the amplifier’s internal parasitic capacitance that originates from between the input node and both of the power supply rails [
36]. Thus, this parasitic capacitance can be considered as a combination of the capacitance built up between the input node and the positive rail (
) and between the input node and negative rail (
). Applying the bootstrap topology to the proposed active circuit, the voltage difference between the signal output node, which has the same potential as the signal input node, and the positive voltage supply rail of the amplifier can be minimized. Therefore,
can be effectively eliminated, and the total capacitance of
can also be minimized.
is involved in the electrode contact efficiency with the scalp surface. When using non-flexible rigid probes, it is difficult to achieve tight contact with the scalp, resulting in an air gap between the probes and scalp surface. This air gap is equivalent to another extra capacitor, which is connected with
in series. Consequently, the total capacitance of
will be reduced because of the series connection of two individual capacitors. The flexible spring-loaded probes, on the other hand, can easily adjust their contact intensities in accordance with the curvature of the scalp surface, thus preventing to the building of air gaps. Therefore, the maximization of
can be achieved by employing spring-loaded probes.
To quantitatively analyze the noise performance of the active circuit, the noise voltage with respect to the biopotential source input can be expressed as:
and the power density, which is equal to the root-mean-squared (RMS) power of the input-referred noise voltage, can also be derived as:
where
and
denote the RMS-squared power of the voltage and current noise sources
and
, respectively. These noise sources are derived from the noise model of the amplifier [
37], and these parameters depend on the electrical characteristics specified in the amplifier datasheet. Therefore, amplifier selection is a key optimization factor for low-noise biopotential acquisition, and it will be discussed in
Section 2.3.2.
For low input-referred noise performance, it is obvious that the operand terms multiplied with the voltage and current noise sources need to be minimized. To lower the voltage noise , firstly needs to be maximized. The bootstrapping topology provides low input capacitance characteristics by reducing the parasitic capacitance of the amplifier, resulting in high input impedance of the amplifiers. should also be minimized for further reduction of the voltage noise term, which can be achieved by preventing leakage current with robust shielding of the input node. The current noise is typically dominated by the scalp–electrode coupling impedance , which is inversely proportional to the electrode contact efficiency. To lower the current noise , high contact efficiency is required, meaning that low coupling impedance with low resistance and high capacitance must be achieved. These requirements can be achieved by equipping multiple spring-loaded probes in the design of the proposed electrode. Installation of the twelve parallelly connected probes lowers the resistive impedance, which in turn prevents poor electrical coupling caused by loose installation of the electrode unit. In addition, the probe’s shrinkable structure fills the air gaps caused by microcontact failures at the scalp–electrode interface, thereby continuously keeping high capacitance characteristics.