ABSTRACT

With the realization of second-order filters discussed in the previous chapters of this section, we will now treat methods for practical filter implementations of order higher than two. Specifically, we will investigate how to realize efficiently, with low sensitivities to component tolerances, the input-to-output voltage transfer function

H(s) ¼ Vout Vin

¼ N(s) D(s)

¼ ams m þ am1sm1 þ þ a1sþ a0

sn þ bn1sn1 þ þ b1sþ b0 (15:1)

where nm and n> 2. The sensitivity behavior of high-order filter realizations shows that, in general, it is not advisable to realize the transfer function H(s) in the so-called direct form [5, Chapter 3] (see also Chapter 5). By direct form we mean an implementation of Equation 15.1 that uses only one or maybe two active devices, such as operational amplifiers (op-amps) or operational transconductance amplifiers (OTAs), embedded in a high-order passive RC network. Although it is possible in principle to realize Equation 15.1 in direct form, the resulting circuits are normally so sensitive to component tolerances as to be impractical. Since the direct form for the realization of high-order functions is ruled out, in this section we present those methods that result in designs of practical manufacturable active filters with acceptably low sensitivity, the cascade approach, the multiple-loop feedback topology, and ladder simulations. Both cascade and multiple-loop feedback techniques are modular, with active biquads used as the fundamental building blocks. The ladder simulation method seeks active realizations that inherit the low passband sensitivity properties of passive doubly terminated LC ladder filters (see Chapter 9).