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4 Measurement of Biosignals and Analog Signal Processing

R1

10k

R2

10k

R3

10k

C1

22n

Ue

5V

-5V

Ua

5V

-5V

Fig. 4.25: Active low-pass filter of 1st order with cutoff frequency 723 Hz and gain by a factor of 2.

with the load from the actual RC filter element. Figure 4.25 shows the equivalent cir-

cuit of an RC low-pass filter with operational amplifier. The first operational amplifier

acts as an impedance converter (also called a voltage follower) on the signal source.

The second one is connected as a non-inverting amplifier and provides signal ampli-

fication, in addition to the impedance conversion¹¹. Magnitude and phase frequency

response of the circuit from Figure 4.25 are shown in Figure 4.26. Filter circuits with

active components such as operational amplifiers or transistors are called active fil-

ters. When used in filter circuits, the relatively low bandwidth of operational ampli-

fiers must be taken into account.¹² With regard to high-frequency interference above

the bandwidth of the operational amplifiers used, active filters lose their filtering ef-

fect. Furthermore, for applications with a very small biosignal amplitude, it should be

taken into account that semiconductor components generate more noise (shot noise,

1/f noise) than passive components.

With the circuit from Figure 4.25 higher order filters can be realized by series con-

nection. However, the circuit complexity increases rapidly. A more efficient possibility

results from the introduction of a positive feedback branch. In Figure 4.27, a 2nd-order

low-pass filter with only one operational amplifier is shown¹³. The output voltage is fed

back to the positive input by the capacitor C2.

In practice the resistors R1 = R2 = R and the capacitors C1 = C2 = C are often

chosen equal. For this case, the transfer behavior, i.e. the ratio of output voltage (Ua)

to input voltage (Ue) as a function of frequency, is now to be calculated. To do this, we

make use of the auxiliary voltages U1 (voltage between resistors R1 and R2) and U2

(voltage at the positive input of the right OPV), both referenced to ground respectively.

11 The operational amplifier forms a non-inverting amplifier with the resistors R2 and R3. The gain is

1 + R2/R3.

12 The bandwidth of many operational amplifiers is limited to a range from 10 kHz to 100 kHz. Above

this bandwidth, operational amplifiers lose their amplifying effect.

13 Filters of this type are also called Sallen-Key filters.