138

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4 Measurement of Biosignals and Analog Signal Processing

Fig. 4.44: Circuit of a 2nd order RLC Chebyshev-filter with a cut-off frequency of 200 Hz (left) and an

associated frequency response by magnitude and phase (right).

From this we obtain the following conditions:

RC = 0.9101795/ωD ,

LC = 1.4142137/ω²

D ^.

(4.65)

Choosing R = 100 Ω, we get ωD = 2π ⋅200 Hz for the inductance L = 123.6454 mH

and for the capacitance C = 7.2 μF. The RLC circuit diagram with the frequency re-

sponse calculated with LTspice and the corresponding frequency response is shown

in Figure 4.44.

Of course, this filter can also be realised actively with the help of an operational

amplifier, whereby the constant factor A0 can be realised exactly. In addition, this filter

synthesis can also be done without coils, which makes it cheaper to produce. If one

chooses an active filter according to the „Sallen Key“-structure [76], then it follows for

its transfer function ^̃ATP(jω):

̃ATP(jω) =

1

1 + jω(R1 + R2)C1 + (jω)²R1R2C1C2

.

(4.66)

A comparison with Equation 4.64 gives:

(R1 + R2) ⋅C1 = 0.9101795/ωD

and

R1R2C1C2 = 1.4142137/ω²

D ^.

For example, choosing C1 = 47 μF and C2 = 0.33 μF gives ωD = 2π ⋅200 Hz.

R1 = 6.34 kΩ

und

R2 = 9.09 kΩ.

(4.67)

The circuit with associated transfer function is shown in Figure 4.45.