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4 Measurement of Biosignals and Analog Signal Processing

According to Table 4.5, in order to realise the desired low-pass filter with a cut-off fre-

quency fD of 200 Hz from the normalised low-pass filter, the normalised angular fre-

quency Ω= 2πF must be replaced by a suitable frequency transformation. In this case

this would be F = ^f

fD ^resp.

Ω= ^ω

ωD

,

mit ωD = 2π ⋅200 Hz .

(4.33)

For the desired low-pass we then obtain the complex transfer function

ATP(jω) = AnTP (P = jΩ= j ^ω

ωD

) =

1

jω

2π⋅200 Hz ^{+ 1}

.

(4.34)

A 1st order RC low pass can be realised by a simple voltage divider. The transfer func-

tions of the calculated power low-pass and the RC element must be identical, i.e.

ATP(jω) =

1

jω

2π⋅200 Hz ^{+ 1}

= ARC(jω) =

1

1 + jωRC ^.

(4.35)

From this follows the condition

RC = ¹

ωD

=

1

2π ⋅200 Hz ^{= 795.8 μS .}

(4.36)

For example, if one chooses for C = 1 nF, one obtains for R = 800 kΩ. The RC circuit

diagram with the frequency response calculated with LTspice and the corresponding

frequency response is shown Figure 4.40.

Bandstop 2nd order

For the suppression of a mains hum interference signal during the measurement of an

ECG, a passive Butterworth-bandstop 2nd order with a centre frequency f0 of 50 Hz at

V1

C1

1n

R1

800k

magnitude / dB

phase / °

magnitude

phase

Fig. 4.40: Circuit for a 1st order RC power filter (left) and associated frequency response by mag-

nitude and phase (right).