APPLICATION NOTE
1
Introduction
Filters are often described in terms of a number of parameters including type, order, and response. There are four
filter types:
Lowpass
Highpass
Bandpass
Bandreject
The order of the filter usually determines the amount of attenuation the filter provides–the higher the order, the
more the attenuation. There are a number of filtering responses available. The most commonly used are
Butterworth, Chebyshev, and Bessel. Each response has its advantages and disadvantages.
Lowpass Filter Behavioral Models
A block diagram of a general lowpass filter is shown in Figure 1. The diagram consists of one first-order and a
number of second-order sections, allowing different filter orders to be simulated. For example, connecting one first
and two second-order sections yields a fifth-order filter. The overall voltage transfer function of the circuit is
obtained by multiplying the transfer functions (TF) of the individual sections:
(Vout/Vin)=(1st-orderTF)*(2nd-orderTF)N
Figure 1: Square Roots Sub-circuit
The first- and second-order section transfer functions, H(s), are
H(s)=x/(s+x) ; x=2piαFc
H(s)=x
2
/(s
2
+(x/Q)s+x
2
); x=2piωFc
where s is the Laplace variable, and Fc is the filter cutoff frequency or bandwidth. The parameters α, ω, and Q
define the pole positions of the various filtering responses.
Following is the behavioral Butterworth lowpass filter model text:
