Introduction

Generally an active filter consists of a network of active integrators. As active components usually suffer far more from non-linearities than passive components, usually the maximal signal level at the output of the filter is determined by the maximal signal level at the inputs or outputs of the integrators. As the outputs of the (extrinsic) integrators are directly connected to the inputs of other integrators, it does not matter whether the signal level is actually limited at the inputs or the outputs of the integrators; the results are the same. It is also assumed that the maximal signal level is the same for all the integrators.

The minimal signal levels in the filter are determined by the noise generation of the filter. In Section 10.2 it is shown that the noise of the filter can be linked to the capacitor values. So at least three things must be known to determine the dynamic range:

• the maximum signal levels at the outputs of the integrators,

• the total capacitance available to realize the filter,

• the noise factor of the active parts of the filter.

Consider the following example.

butterworth(3);
ctot = 30e-12;
umax = 1;
noisefactor = 1;
output: dr;

This specifies a third-order Butterworth filter with 30pF capacitance, 1V maximum root-mean-square signal level, and unity noise factor (which means that the active parts are assumed noiseless, the noise only stems from the passive components, that is, the resistors or the transadmittances). The FA output is then

Output noise level: 3.715373e-05 V.
Scaling is L-infinity.
Maximum output level: 6.314818e-01 V.
Dynamic range: 1.699646e+04 (84.61 dB).

The following section will discuss the definition of the dynamic range. After this, we will see how we can optimize the dynamic range.