4.5 Design of Analogue Filters

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139

Fig. 4.45: Circuit of an active RC-Chebyscheff-filter of 2nd order with a structure according to „Sallen

Key“(left) and associated frequency response according to magnitude and phase (right).

Fig. 4.46: Magnitude frequency response of inverse Chebyshev filters with a normalised cut-off

frequency of ΩS = 2 and ϵ = 3.18.

4.5.1.4 Inverse Chebyshev Filter

With an inverse Chebyshev filter, the tolerance range is not approximated in the pass-

band, but in the stopband. For this purpose, a Chebyshev polynomial is again taken

for the characteristic function, but this time with a different argument:

K(Ω) = ϵ ⋅

1

Tn ( ^ΩS

Ω⁾

,

with

ΩS : blocking cut-off frequency .

(4.68)

However, according to Equation 4.68, the magnitude square of the normalised transfer

function |AnTP(jΩ)|² = 1/(1 + K(Ω)²) does not have the value 1/(1 + ϵ) at the norm-

alised passband frequency Ω= 1 as before. This value is only reached at the normal-

ised blocking frequency ΩS. At this frequency , however, a much smaller value of the

magnitude of the transfer function should normally be achieved. Therefore ϵ must be

chosen correspondingly larger. For example, if the magnitude of the transfer function

at the normalised blocking frequency ΩS is to have the magnitude of 0.3, ϵ = 3.18