Filter synthesis
Alan Keith Walton · Cambridge University Press eBooks · 1987
Introduction An ideal filter would perfectly transmit signals at all desired frequencies and completely reject them at all other frequencies. In the particular case of an ideal low-pass filter, for example, the modulus of the transfer function, | J |, would behave as shown in figure 12.1( a ). Up to a certain critical pulsatance ω c , | J | would be unity but above this pulsatance, | J | would be zero. Any practical filter can only approximate to such an ideal, of course. In section 8.2 it was pointed out how | J | 2 for a simple single-section L–R or C–R filter comprising just one reactive component only reaches a maximum rate of fall-off outside the pass band of 20 dB per decade of frequency compared with an infinite rate of fall-off for an ideal filter. Remember that the significance of | J | 2 is that it indicates the power in the load for a fixed amplitude of input signal. Increasing the number of reactive components in the filter stage to two, as in the simple low-pass L–C filter of figure 8.7( a ), causes | J | 2 to reach a maximum rate of fall-off outside the pass band of 40 dB per decade of frequency. With n reactive components in the filter stage, the maximum rate of fall-off of | J | 2 outside the pass band becomes 20 n dB per decade of frequency and the filter is accordingly said to be of nth order .