2E7 Engineering Science: Electrical Engineering

4B15 Introduction to Bioengineering

Electrodes and Transducers

Lecture 2: Steady-State Response of Electrodes 2.1IntroductionIn measuring electrical bio-signals, electrodes act as the interface between the surface of the skin and the input of the recording amplifier. They essentially perform the task of converting the ionic current associated with electrical activity in the body into electronic current which is fed into the input of a recording amplifier. This is facilitated through the medium of an electrolyte in the form of the coupling gel. As the signal of interest is electrical in nature and the amplifier and its associated circuitry is electrical, it is essential to know how the electrode will influence the electrical behaviour and performance of the measurement set-up. This means that it is important to establish an electrical equivalent model for the electrode so that the electrical behaviour of the measurement set-up can be examined. Only in this way can the performance requirements of the recording amplifier be established to ensure that the signal presented at the output of the amplifier is an accurate and reliable representation of the electrical activity in the body which it is intended to observe.The typical ECG electrodes shown below are pre-jelled with an electrolyte so that this electrolyte makes contact with the skin when the electrode is placed and adheres to it.

Fig. 1 Adhesive, Pre-jelled ECG Electrodes

2.2 Electrode Electrical ModelA simplified model of the electrode skin interface is shown in Fig. 2. When the electrolyte gel comes into contact with the skin, the ionic chemical interaction establishes a polarisation potential which is represented by the dc voltage source, VPOL, shown. The resistor RS represents the series contact and lead resistance, which is usually very small compared to the impedances of the other components. The capacitor CP represents the capacitance formed by the contact area of the electrode on the one side and the skin on the other. The resistor RP represents the conductance of the coupling gel as a poor dielectric but also the electrical interaction with the surface of the skin. These latter two elements therefore appear in parallel.CP

RS

RP

VPOL

Fig. 2. A Simple Electrode Model

2.3 Frequency ResponseIt is imperative to investigate the effect of the equivalent circuit impedances on the frequency response of the overall recording system. The front-end of this system can be treated as a signal source feeding two electrodes, one on either leg of the inputs to a differential amplifier as shown in Fig 3. CP1

RS1

RP1

CP2RS2RP2

RinVinVSAmplifieriin

Fig. 3. A Model of the Front End of the Recoding SystemFor the present the input impedance of the amplifier is taken as purely resistive. The polarisation potential is dc and so can be ignored from the point of view of the ac analysis.

For steady state conditions let s = j then the transfer function is given as:

Then the transfer function is given as:

If RS1 = RS2 = RS , RP1 = RP2 = RP and CP1 = CP2 = CP then this becomes:

If Rin >> 2RS then this can be taken as:

The term on the left hand side can be taken as the dc attenuation factor:

This means that the frequency response is of the form:

where:

Expressing the response in the form of magnitude and phase gives:

This is a universal form of transfer function for such a pole-zero combination.In this case with we have:

When 0 we have:

When we have:

Consider also a frequency of the geometric mean of the pole and zero locations at which gives:

But again with this gives:

which finally becomes:

The asymptotic values and the value at the geometric mean of the response allow a Bode sketch of the gain and phase to be plotted.

mag

1

1

2

3

0

PZP1P2P3 (log scale)

/2

phase

3

2

1

0

P1 Z (log scale)

P3 Z

P2 Z

Fig. 4 A Bode Diagram of the Frequency Response of the Electrode Model

2.4Amplifier Input Impedance RequirementsIt can be seen that the high frequency magnitude is unity while the low frequency asymtote depends on the attenuation factor, . The phase response is asymtotic to zero at high and low frequencies, but has a peak phase which also depends on the attenuation factor which is given as:

Note also that the location of the zero frequency depends only on the properties of the electrode, while that of the pole depends in addition on the attenuation factor since:

The attenuation factor itself depends of the input resistance of the amplifier, Rin.Typical values for the electrode components for modern disposable adhesive electrodes are RS = 50, RP = 200k and CP = 0.5F. These values give the frequency of the zero as:

It should be noted that this frequency is well within the spectrum of the ECG signal at low heart rates. The fundamental component in the spectrum of the ECG at a heart rate of 40 bpm is 0.67 Hz, which is used in some regulation standards as the lower end of the spectrum. The frequency of the zero given above is more than twice this. The frequency of the pole depends on the degree of attenuation present, i.e. on the value of . For a range of values of the frequency of the pole can be evaluated as in Table I below. The value of the maximum phase actually occurs at the frequency of the geometric mean of the pole and the zero and also depends on the value of and is shown in Table I also.

Table I Pole Frequency and Phase for Different Values of 0.10.250.50.75.9

fP15.96.363.182.121.77Hz

54.936.919.58.23.0degrees

Older performance specifications for electrocardiographs issued by bodies such as the American Heart Association (AHA) suggest that the magnitude response within the bandwidth of the ECG should be flat to within a variation of 0.5dB which corresponds to 6% and should not have a phase shift exceeding that introduced by a single-pole, high-pass filter with a pole frequency of 0.05Hz. Such a filter has a phase shift of 5.6O at a frequency of 0.5Hz. In order to keep the attenuation less than 6%, the value of needs to be higher than 0.94. This gives:

which means:

or

so that:

For the values of these components given above as RS = 50, RP = 200k this means:

This is easily attained with an amplifier input resistance of 10M. It can be seen from Table I above that an attenuation factor of 0.96 is associated with a maximum phase shift of less than 3O which will therefore also satisfy the phase requirement of the performance standards. However, it must be noted that electrodes having values of the model components which may give much higher impedances than those above will require an amplifier having a much higher input resistance than 10M. Dry electrodes which do not require a coupling gel and which are the subject of current research fall into this category.

Of course the universal solution is to make the amplifier input impedance as high as possible so that:

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