4.5 Design of Analogue Filters

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127

normalized low pass

frequency-

transformation

low pass

high pass

band pass

band stop

Fig. 4.36: Conversion of normalised low-pass to other standard filters (non-normalised low-, high-,

band-pass and band-stop).

A(p) = A0

1 + b1p + b2p² + ⋅⋅⋅+ bmp^m

1 + c1p + c2p² + ⋅⋅⋅+ cnpⁿ

(4.16)

For example, if the impedance of a coil with jΩL is replaced with Ω:= 2πF by the

impedance ωB/jωC, the transfer function A(jω) to Equation 4.16 remains fractionra-

tional in p. This transformation can be achieved by replacing Ωwith ωB/ω and the

inductance L with the capacitance C = −1/L. However, there is the difference that

now, because of the 1/ω function, the frequency axis is now subdivided differently,

i.e. a low frequency is mapped to a high frequency and a high frequency to a low fre-

quency. So a low pass becomes a high pass.

A summary of the frequency transformations from a normalised low-pass to a non-

normalised low-pass (nTP ⇒TP), a normalised low-pass to a high-pass (nTP ⇒HP),

a normalised low-pass into a band-pass (nTP ⇒BP), and a normalised low-pass into a

bandstop (nTP ⇒BS) is shown in Table 4.5. Explanatory examples of this are covered

in the following sections on power and Chebyshev-filters.

The design of a selective filter can therefore be limited to the design of a normal-

ised low-pass filter. For this, however, only the conditions for the magnitude frequency